FISHING TOOLS INSTRUCTIONAL APPROACH AND STUDENTS’ ACHIEVEMENT, RETENTION AND INTEREST IN SENIOR SECONDARY SCHOOL GEOMETRY

BY

OJOKO, SUNDAY ERIC PG/Ph.D/10/57032

DEPARTMENT OF SCIENCE EDUCATION FACULTY OF EDUCATION UNIVERSITY OF NIGERIA, NSUKKA

OCTOBER, 2015.

i

1

TITLE PAGE

FISHING TOOLS INSTRUCTIONAL APPROACH AND STUDENTS’ ACHIEVEMENT, RETENTION AND INTEREST IN SENIOR SECONDARY SCHOOL GEOMETRY

BY

OJOKO, SUNDAY ERIC PG/Ph.D/10/57032

THESIS SUBMITTED TO THE DEPARTMENT OF SCIENCE EDUCATION UNIVERSITY OF NIGERIA, NSUKKA, IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE AWARD OF DOCTOR OF PHILOSOPHY (Ph.D) IN SCIENCE EDUCATION (MATHEMATICS)

SUPERVISOR: PROF. U.N.V AGWAGAH

OCTOBER, 2015.

i 2

CERTIFICATION OJOKO, SUNDAY ERIC, a postgraduate student in the Department of Science Education with the Registration Number PG/Ph.D/10/57032, has satisfactorily completed the requirements for the Degree of Doctor of Philosophy in Science Education (Mathematics). The work embodied in this thesis is original and has not been submitted in part or full for any other diploma or degree of this or any other university.

______Ojoko, Sunday E Prof. U.N.V. Agwagah Student Supervisor

ii 3

APPROVAL PAGE This thesis has been read and approved for the Department of Science Education, University of Nigeria, Nsukka.

By

______Prof. U. N. V Agwagah Dr. J. J. Agah Supervisor Internal Examiner

______Prof. I. O. Enukaoha Prof. Z. C. Njoku External Examiner Head of Department

______Prof. Uju. Umo Dean, Faculty of Education

iii 4

DEDICATION This work is dedicated to my Excellent Lord and Saviour Jesus Christ, for lavishing His infinite love, goodness and favour upon me, my family and humanity.

iv

5

ACKNOWLEDGEMENTS With deep sense of joy and humility, the researcher wishes to express his profound appreciation and gratitude to his supervisor, Prof. (Lady) U.N.V. Agwagah for her warm encouragement, guidance, patience, suggestions, pieces of advice, attention and untiring effort in making this work a huge success. The researcher is also thankful to Prof. A. Ali (of blessed memory), Prof. K. O. Usman, Dr B. C. Madu, Dr J. J. Agah and Chf (Dr) W. J. Ubulom (KSC) for validating the instruments used for the study. Also duly recognized and appreciated for reading the work are: Dr B. C. Madu, Dr E. K. N. Nwagu, Dr J. J. Agah, Dr J. J. Ezeugwu, Dr F. M. Onu, Dr (Mrs) J. A. Ukonze and Barr. S. O. Ojoko (Jnr). The researcher is highly indebted to Prof. Z. C. Njoku (HOD, Science Education) and Prof. E. C. Osinem for chairing the proposal and seminar sessions of the study respectively. Also, his sincere gratitude goes to: Prof. N. E. Dienye, Prof. M. J. Ahiakwo and Prof. (Mrs) J. I. Alamina for their inspiration, motivation, mentorship and encouragement. Special appreciation and commendation go to his dearly beloved wife, Mrs. Ngokimun S. Ojoko and his blessed children: Dr. A. S. Ojoko, Christianah, Esther, Ifukikaloawaji, Mbeekiji, Nnwonisi and Irotnte for their delightful concern, encouragement, understanding, financial support and prayers. The researcher is also grateful to his parents, Mr. Eric Ojoko Ijente and Mrs. Christianah E. Ojoko (both of blessed memory) for their investment and financial support. The researcher also appreciates King Andrew Ojoko Ijente Efuya X, Late Chief Micah L. Ojoko Ijente and Chief E. D. Mbikan Uduyok-Ugane for their mentorship and encouragement. His younger brother, Pastor Egbert E. Ojoko is also commended for support and encouragement. To all his well-wishers in this strenuous task, may God bless and reward them all abundantly in Jesus Precious Name, Amen. Finally and most importantly, the researcher is deeply grateful to God Almighty for giving him life and enablement to complete the programme successfully. May His name alone be highly exalted and glorified in Jesus Mighty Name, Amen.

Ojoko, Sunday E. Department of Science Education, University of Nigeria, Nsukka. October, 2015.

v 6

TABLE OF CONTENTS

Title page i Approval page ii Certification iii Dedication iv Acknowledgements v Table of Contents vi List of Tables ix List of Figures x Abstract xi CHAPTER ONE: INTRODUCTION Background of the Study 1 Statement of the Problem 13 Purpose of the Study 14 Significance of the Study 15 Scope of the Study 18 Research Questions 19 Research Hypotheses 19 CHAPTER TWO: LITERATURE REVIEW Conceptual Framework 21 Current status of teaching and learning Mathematics/ Geometry 22 Concept of instructional materials, types and uses 32 Fishing tools as mathematics teaching resources 39 Concept and perspective of fishing tools 39 Meaning and types of fishing tools 43 Construction of some fishing tools 47 Uses of fishing tools in teaching and learning of some geometrical concepts 49

Retention and achievement in mathematics/geometry 51 Interest and achievement in mathematics/geometry 57 Gender and mathematics achievement 59

vi

7

Theoretical Framework 64 Piaget’s theory of cognitive development 64 Bruner’s theory on mathematics Instruction 68 Empirical Studies 69 Studies on achievements in mathematics 69 Studies on instructional materials and achievements in mathematics 75 Retention as a factor in mathematics achievements 77 Interest as a factor in mathematics achievements 80 Gender as a factor in students’ achievements in Mathematics 82 Summary of Literature Review 87 CHAPTER THREE: RESEARCH METHOD Design of the Study 90 Area of the Study 91 Population of the Study 91 Sample and Sampling Technique 92 Instruments for Data Collection 92 Development of Geometry and Retention Tests 92 Validation of the Instruments 94 Reliability of the Instruments 95 Experimental (Treatment) Procedures 96 Control of Extraneous Variables 97 Method of Data Collection/Scoring 99 Method of Data Analysis 99 CHAPTER FOUR: RESULTS Results of Research Questions 100 Results of Research Hypotheses 103 Summary of Finding 110 CHAPTER FIVE: DISCUSSION, CONCLUSION AND SUMMARY Discussion of Findings 113 Students’ Achievement in Geometry 113 Students’ Retention in Geometry 115 Students’ Interest in Geometry 116 Influence of Gender on Students’ Achievement in Geometry 116

vii 8

Gender Influence on Students’ Retention and Interest in Geometry 118

Interaction Effects of Method and Gender on Achievement, Retention and Interest in Geometry 119

Conclusion 120 Educational Implications of the Study 121 Recommendations 122 Limitations of the Study 123 Suggestions for Further Study 123 Summary of the Study 123 REFERENCES 126 APPENDICES 144 A: Geometry Achievement test (GAT) 144 B: Geometry Retention Test (GRT) 151 C: Geometry Achievement Test (GAT) marking scheme 158 D: Delayed Geometry Achievement Test marking scheme 159 E: Pre-Geometry Interest Scale (PREGIS) 160 F: Post- Geometry Interest Scale (POSTGIS) 161 G: Lesson plans using Fishing Tools Instructional Approach 162

H: Lesson Plans using Conventional Method 193

I: Computation of the Reliability of Geometry Achievement Test (GAT) 211

J: Analysis of WAEC from 2000-2004 adapted from Kurumeh (2006) 218 K: Table of Specification or Test Blue Print on Geometry Achievement Test (GAT) 219

L: Some Fishing Tools 220

M: Types of Fishes with Pictures 224

N: Senior Secondary I Students’ Population of Schools as at 2014/2015 academic session in Andoni Local Government Area 228

O: ANCOVA for GAT Output 229

viii 9

LIST OF TABLES Table Page

1: Mean and Standard deviation of pretest and post test scores of students taught geometry of two and three-dimensional objects using the fishing tools instructional approach and those taught with conventional (lecture) method. 100

2: Mean and Standard deviation of retention scores of the students taught geometry of two and three-dimensional objects using the fishing tools instructional approach and those taught with conventional (lecture) method. 101

3: Mean and Standard deviation of interest scores of students taught geometry of two- and three-dimensional objects using the fishing tools instructional approach and those taught with conventional (lecture) method 102

4: Mean and Standard deviation of mean achievement scores of male and female students

taught geometry of two-and three-dimensional objects using fishing tools instructional approach. 102

5: Mean and Standard deviation of retention scores of male and female students taught geometry of two-and three-dimensional objects using fishing tools instructional approach 103 6: Mean and Standard deviation of interest scores of male and female students taught geometry of two-and three-dimensional objects using fishing tools instructional approach 104

7: Analysis of Covariance (ANCOVA) of the mean achievement scores of students taught geometry of two-and three-dimensional objects using the fishing tools instructional approach and those taught with conventional (lecture) method 105 8: Analysis of Covariance (ANCOVA) of the mean retention scores of students taught geometry of two-and three-dimensional objects using the fishing tools instructional approach and those taught with conventional (lecture) method 106 9: Analysis of Covariance (ANCOVA) of the mean interest scores of students taught geometry of two-and three-dimensional objects using the fishing tools instructional approach and those taught with conventional (lecture) method 107

ix

10

LIST OF FIGURES Figure 1: A schematic representation of the essential variables in the study. 63

x 11

Abstract This study was designed to determine the efficacy of fishing tools instructional approach and students’ achievement, retention and interest in Senior Secondary One (SS I) geometry. Six research questions and nine hypotheses were formulated to guide the study. The study employed a quasi-experimental-non-equivalent control group design and was restricted to Andoni Local Government Area of Rivers State, Nigeria. Four public and co-educational secondary schools were drawn for the study using purposive sampling technique. Out of the four selected schools, two were randomly assigned to Fishing Tools Instructional Approach (FTIA) – the experimental group, while the other two to the control group (CG). A sample of 200 SS I students was involved (104 male and 96 female students) for the study. The instruments for data collection were geometry achievement test (GAT) and geometry interest scale (GIS). Data collected were analyzed using mean, standard deviation and analysis of covariance (ANCOVA). The result of the study revealed that the use of Fishing Tools Instructional Approach in teaching geometry of two-and three-dimensional objects to senior secondary one (SS I) students enhanced their achievements, retention and interest in geometry. The study also revealed that the use of fishing tools instructional approach had no statistically significant difference on male and female students’ achievement, retention and interest. Furthermore, there was significant interaction between gender and fishing tools instructional approach and students’ achievements, retention and interest. Based on the findings, the researcher recommended that the Fishing Tools Instructional Approach should be adopted in the teaching of geometry (mathematics) in primary and secondary school levels of education system. It was also recommended that seminars, workshops, and conferences should be mounted by professional bodies, federal and state ministries of education on the use of Fishing Tools Instructional Approach for mathematics teachers, students and others. This will enable the mathematics educators, serving teachers, students and all to benefit from such an approach.

xi

1

CHAPTER ONE

INTRODUCTION

Background of the Study

The two broad goals of senior secondary education according to the Federal Republic of

Nigeria (FRN, 2013) are to prepare the individual for useful living within the society and higher education. The secondary education, in specific terms, shall among others, provide trained manpower in the applied science, technology and commerce at sub-professional grades and inspire students with a desire for self-improvement and achievement of excellence. The above goals can never be achieved without proper knowledge of the subject Mathematics. It is in line with the above goals/objectives that today’s Mathematics Curriculum tries to prepare students for their future roles in the society. It aims at equipping them with essential mathematical knowledge, skills, abilities and attitudes of reasoning, problem solving, communication, innovation, and most importantly, sustaining the motivation to learn continually on their own.

Against this background, the major objectives of school Mathematics are to afford the learner the opportunity of: developing originality, creativity and curiosity; acquiring manipulative skills; discovering and appreciating the beauty and elegance of Mathematics; demonstrating the applicability of Mathematics in various fields. These objectives, as cited in Obioma (1991), are supposed to satisfy three major aspirations, namely: personal aspirations to help learners solve everyday problems of adult life, vocational aspirations to give foundation upon which a range of specialized skills can be built and humanistic aspirations to show Mathematics as part of the learner’s cultural heritage.

According to Sidhu (2006), Mathematics has played very important roles in building up modern civilizations by perfecting all sciences. Every teacher of Mathematics needs to be informed and convinced about the educational values of this subject. The knowledge of its values and aims will stimulate and guide the teacher to adopt effective methods, devices, and illustrative materials.

1 2

“Shut out mathematics from daily life and all civilization comes to a standstill’’ (Sidhu, 2006). So,

Mathematics can be described as the mirror of civilization. In this world of today, nobody can live without Mathematics for a single day (Sidhu, 2006:12). Mathematics is intimately involved in every moment of everyone’s life. Right from human existence on this earth, it has been a faithful companion. Every Mathematics teacher recognizes, for example, that Mathematics is omnipresent in today’s world-notably in the technological items all around us and in exchange and communication processes-but it is generally not in evidence (UNESCO, 2012:10).

According to Maduabum and Odili (2006), Mathematics as a science of quantity and space occupies a key position in Nigeria’s educational system and reflects accurately the vital roles the subject plays in contemporary society. For a nation like Nigeria aspiring for scientific and technological breakthrough, the need to pay due attention to students’ academic achievement in

Mathematics especially in geometry, cannot be over emphasized.

Mathematics is a human invention, borne out of human resolve to solve human problems

(Kolawole and Oluwatayo, 2005). For instance, in Nigeria, Mathematics is made one of the core subjects in both primary and secondary school curricula (FRN, 2004). That is, it is compulsory for all students at school certificate level. This is because apart from the fact that success in the subject enhances the quality of certificate, the trend has shown that in order to secure admission into most lucrative prestigious courses at higher levels of education, a credit pass in Mathematics is an advantage (Usman, 2002).

In spite of the aims and importance accorded Mathematics in the educational system, the

Nigerian secondary school students’ poor achievements in ordinary level Mathematics examinations over a decade now cast doubt on the country’s hope of higher attainment in science and technology (Kurumeh, 2006). A study conducted by Maduabum and Odili (2006), on students’ performances in general Mathematics at the Senior School Certificate level in Nigeria over a twelve year period (1991-2002), has confirmed students’ poor achievement in Mathematics. Also

3 the report of the West African Examinations Council (WAEC) on examinations results (2000-

2004), shows that students’ achievements at credit pass has never reached 50% (Kurumeh, 2006).

(Appendix J1 on page 216) and WASSCE results May/June 2005-2013 (Appendix J2 on page

217).

Students’ achievements in Mathematics in internal and external examinations are consistently reported to be low as over fifty percent (50%) of candidates that registered for

Mathematics in West African Senior School Certificate Examinations failed to obtain a credit pass

(Olunloye, 2010). Olunloye described this mass failure as a national disaster as this limits learners’ choices of careers.

The WAEC (2007-2011) reports further showed that the worst attempted questions in the public Mathematics examinations were in geometry. Geometry, though, an important part of school

Mathematics that has everyday application in the life of the students especially in construction, technology and spatial relationships is least understood by students thereby contributing to the students’ low achievement in the subject (Abakpa and Igwue, 2013). Specifically, research reports

(Olunloye, 2010; Abakpa and Igwue, 2013) revealed that most students haphazardly attempted geometry questions or avoided them completely especially those of the essay test items and problem solving types.

These situations call for some investigations in order to address the problems of mathematics education in Nigeria. Ale (2002) cited in Aburime (2003), has observed that the standard of mathematics teaching in Nigeria is low and identified teaching problems as one of the root causes of poor achievement in mathematics. This situation according to Usman (2003), could be as a result of shortage of human resources in science and mathematics education. This has resulted in the co-opting of unprofessional mathematics teachers to teach mathematics, making it difficult to have effective implementation of mathematics curriculum.

4

Also contributing, Amoo (2002), had advanced some reasons for students’ poor achievement and lack of motivation in mathematics to include: non-chalant attitudes towards mathematics, poor study habits, and over–engagement in non-academic activities. Teacher-related problems according to Amoo (2002) include: inadequate preparation, failure to use instructional materials, lack of consideration given to textbooks and calculating devices, inadequate knowledge of subject matter and inadequate equipment meant to teach practical aspects of mathematics.

Similarly, Harbor-Peters (2002) and Akinsola (2004), stressed that lack of commitment by the teachers and teaching methodology are the major problems associated with under achievement in mathematics. Also, Obodo (2004), stated that poor sequencing method and negative attitude in certain concepts are some other reasons. According to Akinsola (2004), part of the problems of under achievement in mathematics is that most teachers still believe that the most effective means of communicating knowledge is via the conventional (lecture) ‘talk and chalk’ strategy. For

Agwagah (2008) and Adebayo (2001), the most striking part of under achievement is the lack of appropriate approach in teaching some topics. The conventional (lecture) ‘talk and chalk’ strategy as used in this context, is the traditional way of imparting knowledge whereby the students are passive during teaching/learning process. It is a teacher-centered method of teaching/learning.

(Agwagah, 2008).

In June, 1999, the National Mathematics Centre sampled some twenty states of the

Federation to find out the problems of teaching and learning of mathematics. Among the problems highlighted from the states were:

Poor attitudes of both teachers and students to mathematics; poor teaching methods; teachers not being able to teach some aspects of the mathematics content; and mathematics phobia especially among female students (Azuka, 2001).

On the other hand, students’ poor achievements in mathematics is traceable to limited funds, unstable government policies and inadequate research on the teaching and learning of the

5 subject with regards to Nigerian situation (Betiku & Ochepa, 2004). Irregular seminars/workshops for mathematics teachers also constitute part of the problems in the teaching and learning of mathematics.

Also, in an attempt to enhance pedagogy and help the society produce more people who can think creatively in quantitative and qualitative terms, the search for more appropriate approaches to the teaching and learning of mathematics in general, and geometry of two-and three-dimensional shapes in particular, becomes necessary. This is because from the researcher’s experiences as a teacher, students find it difficult to understand the conventional approaches (lecture and expository) involved in solving geometry of two-and three-dimensional problems.

Geometry, as the science of space and extent, (Sidhu, 2006), deals with the position, shape and size of bodies. It is merely pictured Algebra (Sidhu, 2006). Geometry is defined as the study of space and its subsets (Lassa, 2012).Geometry derived its name from the Greek words; geo

(meaning land or earth) and metric (meaning measure).It is one of the oldest branches of mathematics (Harbor-Peters, 2002). It is a special branch of mathematics and it follows that if teachers of mathematics do not possess adequate knowledge of geometry, the teaching and learning of mathematics is likely to be seriously deficient. Researching on geometry of two and three dimensional shapes as concepts in mathematics (Kurumeh (2004) and Fiase (2009), supported the assertion that mathematics is indispensible to man as it is being used on a daily basis. According to these researchers, geometry of two- and three- dimensional shapes as concepts in mathematics are used in many areas of mathematics, science, engineering, and other areas of study. On the other hand, some teachers also experience difficulties in achieving effective teaching in the school system (Harbor-Peters, 2002). One of such areas teachers and students have problems is geometry.

The poor performance was attributed to weak working order (steps), poor geometrical constructions and drawings among other reasons (Abakpa & Igwue (2013). This could be as a result of most mathematics teachers not being able to present the topics in such a way that students

6 can comprehend (Obodo & Onoh,2001). Hence exposing the students to solve mathematics problems anyhow and the notion that some areas are very difficult to handle. This makes the students develop dislike for some aspects of mathematics.

In the same vein, the former Director, National Mathematical Centre Abuja, Professor Alex

Animalu, attributed the sorry state of mathematics in the nation primary and secondary school levels to acute shortage of teachers of the subject in the country. (The Punch, Tuesday April 11,

2000: 29). The Director also blamed the problem of mathematics in schools on inadequate training.

Contributing, Lassa (2012), stated that the teaching and learning of mathematics has been problematic in schools. Failures in GCE, SSCE, and NECO have been high and have become worrisome to all stakeholders, since mathematics is crucial to further education and everyday activity of the individual. In another dimension, students dislike certain topics because they feel the topics are difficult and cannot be understood easily (Eraikhuemen, 2003). It has also been revealed that some teachers lack techniques and materials in teaching some topics to the extent that if they had a choice they will not teach such topics. Also the teachers believe that these topics are difficult and not easy to teach. For these reasons, many students in secondary schools experience difficulties in the learning of some aspects of the mathematics curriculum.

The difficulties encountered by students in the study of geometry include: deficiencies in verbal and visual skills and lack of an intuitive basis of geometric concepts either defined or undefined (Odogwu, 2002). According to Harbor-Peters (2002), the causes of the wide spread of low performance in mathematics especially in Geometry in secondary schools could be largely ascribed to uninteresting teaching and unorganized teaching methods.

It was added that the artistry of teaching involves motivating and sustaining the interest of students in mathematics and challenging the reluctant learners. Also, Harbor-Peters (2002) and

Galadima (2002), suggested teaching that promotes students’ involvement and activity. Through motivation, teachers can achieve generating and sustaining students’ interest in mathematics

7

(Obodo, 2000, 2004). Students can be motivated through teaching that involves the use of teaching resources available in their local environment, such as fishing tools.

Students’ poor achievement in mathematics could also be attributed to their interest in mathematics. Interest, according to Agbo (2002), increases students’ success in the learning tasks.

According to Adedeji (2007), interest in activities tends to increase the likelihood that an individual can formulate goals relating to that activity and invest more time and efforts to achieve the goals. It has been stated that the teaching approach adopted by the teacher can make the learners to develop negative or positive attitude towards the learning tasks. Therefore, the need to explore appropriate teaching approach that will enhance students’ retention and interest in geometry has continued to be a critical issue to mathematics educators. Thus mathematics teachers focus on pedagogy that will improve students’ achievement, retention and interest in geometry.

According to Wikipedia (2009), fishing tackle (tools) is a general term that refers to the equipment used by fishermen in fishing. Tackle that is attached to the end of a fishing line is called terminal tackle (Wikipedia, 2009). Fishing tackle can be contrasted with fishing techniques.

Fishing tackle refers to the physical equipment that is used when fishing, whereas fishing techniques refers to ways (methods) the tackle is used when fishing. Some examples of fishing tools are hooks, lines, sinkers (like lead, anchor), floats (like cork, pyramidal (terminal) fishing floats), rods, reels, baits, lures, spears, nets, gaffs, traps, waders, leaders, swivels, split rings, wire, snaps, beads, spoons, blades, spinners, clevishes to attach spinner blades to fishing lures, and tackle boxes (Wikipedia, 2009).

However, fishing is done in ocean, sea, river, creek, lake, and fish pond with different fishing vessels such as trawlers, speed boats, dugout boats, canoes and so on. In addition, fish farming, as the principal form of aquaculture, involves raising fish commercially in tanks or enclosures, usually for food. Fishing techniques include; hand gathering, spear fishing, netting, angling and trapping. Moreover, fishing with various kinds of nets and other associated fishing

8 tools like net, lead, floats, conical fishing trap among others mentioned earlier are considered in the research.

Fishing tools are geometrical in shape. While a bundle of thread, twine or rope could be cylindrical, a float (buoy) could either be cylindrical or pyramidal; racket, lead and net are two- dimensional. Similarly, a solid is anything that occupies space and has three dimensions, namely, length, breadth (width) and thickness (depth); examples: block, brick, book, box, cube, cuboid, cone, cylinder, pyramid, sphere (Sidhu, 2006). But a two-dimensional object has length and breadth (width) like square, rectangle, rhombus, parallelogram, kite, trapezium and so on. Again, while net meshes, racket and lead (sinkers) are two-dimensional; a bundle of thread, twine, rope, and a float (buoy) are solids. Fishing as the activity of trying to catch fish, has cultural impact among others. For fishing settlements/communities, fisheries where fishes are caught in commercial quantities, provide not only a source of food and work but also a community and cultural identity (Wikipedia, 2009).

For the purpose of this study, Ethnomathematics is defined as the culturally influenced mathematical approach, which makes the learning of mathematics very meaningful (Kurumeh,

2004). Ethnomathematics is practical, learner – oriented, active and applicable to the local environment. Ethnomathematics is the mathematics of the environment or the mathematics of the community. It is the mathematics among the indigenous people. Ethnomathematics is the mathematics used by a defined, peculiar or specified cultural group in the course of dealing with environmental problems and activities (Kurumeh, 2004). Such activities include classifying, ordering, counting, constructing and measuring, different from those of other groups. It is that mathematics used in daily life practices quite different from the mathematics taught in schools.

Ethnomathematics approach then is an approach to mathematics, which is closer to dealing with real problems such as those posed by modern society. This method builds on the initiative, understanding and practiced methods the students (learners) brought with them to schools.

9

Ethnomathematics is seeking or using the mathematics observed in the cultural activities of the people. For the mathematical instructions to improve the achievement, retention and interest of the learners, there is a need for mathematics teaching that has the learner’s cultural background, such as fishing tools instructional approach.

Ethnomathematics is defined as the mathematics practiced among cultural groups such as national-tribal societies, labour groups, children of a certain age bracket, professional classes and so on (D’ Ambrosio, 2001). Rather than looking at the mathematics of different cultures, this area focuses on the mathematics of different social groups based on activities, occupation, age, gender and so on. This is another area in which examining the connections between gender and mathematics arises. Ethnomathematics and mathematics education address first, how cultural values can affect teaching, learning and curriculum and second, how science and mathematics education can then affect the political and social dynamics of a culture (D’ Ambrosio, 2001, 2007).

One of the stances taken by many educators is that it is crucial to acknowledge the cultural context of mathematics students by teaching culturally based mathematics that students can relate with.

Can teaching mathematics through cultural relevance and personal experiences help the learners know more about reality, culture, society and themselves?.

Ethnomathematics has become common practice all over the world. The meaning of

“ethno” concept has been extended throughout its evolution. It has been viewed as an ethnical group, a national group, a racial group, a professional group, a group with philosophical or ideological basis, a socio-cultural group and a group that is based on gender identity (Powell,

2002:19). Ethnomathematics as dealing with learner’s everyday mathematical practices has equality of all learners as its main objective. (D’Ambrosio, 2007a). The teaching process tries to reach and involve all learners in the learning of mathematics, irrespective of their cultural diversities. The expansion of ethnomathematics as a way of teaching mathematics which takes the diversities of the learners’ mathematical practices into account can be justified (D’ Ambrosio,

10

2007a). The extended notion of ethnomathematics as dealing with learners’ cultural diversities and their everyday mathematical practices brings mathematics closer to the social environment of the learner. Ethnomathematics is an implicitly value-driven program and practice on mathematics and mathematics education (D’ Ambrosio, 2007b).

Every classroom nowadays is characterized by (ethnical, linguistic, gender, social, cultural…) diversities. Mathematics teachers in particular, have to deal with the existing cultural diversity since mathematics is defined as human and cultural knowledge (Powell, 2002).

Mathematics teachers are therefore challenged to handle people’s cultural diversities occurring within every classroom setting.

Another approach suggested by Ethnomathematicians like D’Ambrosio (2001, 2007a, b) and Powell (2002), is exposing students to the mathematics of a variety of different cultural contexts often referred to as multicultural mathematics. This can be used both to increase the social awareness of students and offer alternative methods of teaching mathematics instead of the conventional approach. One of such ways that may make the students to have interest, retention in geometry of two- and three-dimensional shapes and get higher achievement could be by using fishing tools instructional approach. Harbor Peters (2002), stated that for learning mathematics to be more meaningful and interesting so as to improve student’s performance, especially in geometry, there is the need to find alternative methods and techniques. Thus, the fishing tools instructional approach is a strategy that uses relevant and concrete instructional materials in teaching and learning geometry of two-and three-dimensional objects and could enhance students’ interest, retention and achievement in mathematics.

Achievement is the measurement of the effects of specific programme of instruction or training (Sidhu, 2007). It can also be defined as something that somebody has succeeded in doing, especially after a lot of efforts. It is an art of finishing something successfully. Achievements could also be regarded as something very good and difficult, which was carried out successfully.

11

Anekwe (2006), described it as something which has been accomplished successfully, especially by means of exertion, skills, practice or perseverance. Anekwe (2006), saw achievement as a test for the measurement and comparison of skills in various fields of academic study. Ifeakor (2005), regarded achievement as a change in behaviour exhibited at the end of a given period of time or within a given time range. Achievement in this context refers to accomplishment, remarkable feat or outstanding performance realized after exerting much effort. Nwagu (1992), defined achievement testing as “systematic and purposeful quantification of learning outcomes”.

Achievement tests are the most common tests given to pupils. These are meant to measure how much a pupil has learned in specific content area such as reading, recognition or de-coding, reading comprehension, language usage, computation, science, social studies, mathematics and logical reasoning. An achievement test therefore, is a test measuring how much pupils have learned in a given content (Woolfolk, Hughes and Walkup, 2008).

Retention is the continued possession of something or the continued existence of something

(Hornby, 2010). Retention in other words, is the continued existence of what has been. Anih

(2000), and Anyor and Iji (2014), defined retention as the “remaining impressions of experience or learning” Retention therefore involves the amount of a learning experience that is correctly remembered at a later time. Students’ ability to retain what they learnt for a long period of time aids their overall performance in a subject. Most often, terminal examinations are administered to students and their achievements in this case depends on how much of what was done in the class lessons they were able to remember. Retention is also the ability to reproduce the learnt concept when the need arises (Demirel, 2004). Retention is the ability to recall correctly what had been learnt when the need arises.

Oriaifo (2003), posited that retention is higher when the degree of original learning is high.

In other words, any strategy that will lead to mastery learning will lead to higher retention.

Students’ ability to remember what was taught for a long period can be a measure of how well the

12 teacher taught. Like interest, retention is an important variable in the teaching and learning process.

Would the use of fishing tools instructional approach enhance students’ retention in the subject?

Interest is an important variable in learning because when one becomes interested in an activity, one is likely to be more deeply involved in that activity (Imoko and Agwagah, 2006).

According to Harbor-Peters (2001), interest is a subjective feeling of concentration or curiosity over something. It is the preference for particular types of activities. It is the tendency to seek out and participate in certain activities. It can be expressed through simple statements made by individuals of likes and dislikes. One is likely to do well in a discipline of interest.

The issue of gender differences in male and female students’ achievements in geometry has been a source of worry to mathematics educators and researchers. Anekwe (2006), found some items which account for gender disparity. These include among others, unfair behaviour of teachers which retard female students’ interest and participation, unequal access for male/female students to participate in classroom discussion, higher achievement level set for boys than girls and female students being assisted often in practical, projects and other assignments even by some of their teachers. These could also affect students’ achievement. Ezeugo and Agwagah cited in Etukudo

(2002), revealed that male gender achieve significantly better than their female counterparts in mathematics reading. Etukudo and Utin (2006), discovered that there was no significant gender difference in mathematics achievements.

These inconsistent results in mathematics achievements bother the researcher. Based on this type of variance in different studies, this study also seeks to investigate the achievement, retention and interest of male and female students in geometry of two-and three-dimensional shapes when taught using fishing tools instructional approach. The instructional challenges to teachers is to go beyond the conventional teaching method and introduce teaching that articulates goals, motivates and promotes strategies for solving problems and provide students with guided practice (Harbor-

Peters, 2002). Thus, there is the need to find methods and techniques to make learning of

13 mathematics more meaningful and interesting so as to improve student’s performance, especially in geometry of two-and three-dimensional shapes. Therefore this study intends to find if the use of fishing tools could enhance achievement, retention and interest in learning geometry of two-and three dimensional shapes among senior secondary school students. From the researches conducted into the teaching of mathematics generally, there appears to be no study known to this researcher yet on the fishing tools instructional approach on students’ achievement, retention and interest in senior secondary school geometry in Nigeria. The non existence of such study motivated this researcher to carry out this present study.

Statement of the Problem

It is a well-known fact that the subject of mathematics affects all aspects of human life and that the social, economic, scientific and technological aspects of man are centred on numbers. Being the basic skill that underlies all scientific and technological skills, mathematics is generally seen as the language of most branches of science and technology. It is closely related to other school subjects like physics, computer science, chemistry, economics, geography, among others, that deal with numeration, variation, graphs, fractions, logarithms and indices, algebraic processes, solution of equation, as well as areas and volume computations. Expectedly, a sound background in basic mathematical principles has become a pre-condition for progression to tertiary education and thus one of the key requirements for a gainful professional employment. For instance, in 2013, when teachers were recruited in

Rivers State, a sound background in basic mathematical knowledge was an advantage for gainful employment (Ministry of Education, Port Harcourt, 2014). Among other branches of mathematics, mensuration, which comprises geometrical and trigonometrical concepts of the

Senior Secondary School (SSS) Mathematics Curriculum, represents the most difficult area

(Chief Examiner’s Report, 2005; Kurumeh, 2007; Olunloye, 2010; Abakpa & Igwue, 2013).

Even though various instructional techniques have been adopted by teachers to improve

14 students’ achievement in mathematics, very few of these appear to have focused on the teaching of geometry. Traditional teaching aids for mathematics include: chalkboards, - coins; and logos, while visual aids and drawing of pictures have been used in teaching of geometry. Helpful as these measures may be, they have not proved to be effective for the improvement of students’ performance in mathematics. There is therefore need to explore the effectiveness of other alternative teaching strategies, such as fishing tools instructional approach, that is based on the learner’s cultural background, in the improvement of students’ achievement, retention and interest in geometry. Therefore, the problem of the study put in question form is, Would the use of fishing tools instructional approach enhance students’ achievement, retention and interest in geometry?

Purpose of the Study

The main purpose of this study was to investigate the effect of fishing tools instructional approach on students’ achievement, retention and interest in senior secondary school geometry.

Specifically, the study sought to:

1. Determine the students’ mean achievement scores in geometry of two-and three-

dimensional objects when taught with fishing tools instructional approach and conventional

(lecture) method.

2. Determine the students’ mean retention scores in geometry of two-and three-dimensional

objects when taught with fishing tools instructional approach and conventional method.

3. Determine the students’ mean interest scores in geometry of two-and three-dimensional

objects when taught with fishing tools instructional approach and conventional method.

4. Determine the mean achievement scores of male and female students taught geometry of

two-and three-dimensional objects with fishing tools instructional approach.

5. Determine the mean retention scores of male and female students taught geometry of two-

and three-dimensional objects with fishing tools instructional approach.

15

6. Determine the mean interest scores of male and female students taught geometry of two-

and three-dimensional objects using fishing tools instructional approach.

7. Ascertain the interaction effect of fishing tools instructional approach and gender on mean

achievement of students in geometry of two- and three-dimensional objects.

8. Ascertain the interaction effect of fishing tools instructional approach and gender on mean

retention of students in geometry of two-and three-dimensional objects.

9. Ascertain the interaction effect of fishing tools instructional approach and gender on mean

interest of students in geometry of two- and three-dimensional objects.

Significance of the Study

The theoretical significance hinges on Piaget’s and Bruner’s theories of cognitive development of learning. Piaget (1964), propounded the theories of cognitive development of learning which stipulates that learning takes place through three processes namely:

i. Formation of mental concepts (structure)

ii. Adaptation of concepts as a result of experience

iii. Relating concepts to form a network.

Piaget exposed that these learning processes can be carried out in four (4) stages of cognitive development. These are:

i. Sensori-motor stage : (Ages of 0-2 years)

ii. Pre-operational stage: (Ages of 2+ -7 years)

iii. Concrete operational stage: (Ages of 7+ -12 years)

iv. Formal operational stage : (Ages of 12+ and above)

The formal operational stage of Piaget’s cognitive development coincides with the upper

(senior) secondary school level. Students at this stage are capable of reflective and abstract thinking and are able to isolate variables from such expression like 2xy = 10. The students can now understand more complex conceptual relationships, solve complex problems such as total surface

16 areas and volumes of three dimensional objects, control all variables while testing one and are capable of using sound logical procedures in problem solving.

Piaget’s theory stresses the importance of activities in the learning process. The psychologist is of the view that mathematics teaching should involve activities and students should be made to interact with one another. More so, the teacher should make the classroom situations to be in such a way that there would be interplay between the teacher and students where they could be active participants, not passive listeners. Mathematics teachers should create more involvement for students, hopefully, leading them to a mathematics practical situation in which, there could be maximum learning through participation and sharing of ideas, where instructions become

“learners’ centred”.

Like Piaget, Bruner presented a system of cognitive development that resembles that of

Piaget and proposed that children’s thinking abilities develop in three stages which Adekanye

(2008), described as: enactive (events represented through motor responses), iconic (events represented through mental images of the perceptual fields) and symbolic (events represented through design features that represent remoteness and arbitrariness).

Jerome Bruner’s (1966) theory also projected the idea that every discipline has structure and the learner should be helped to see to the structure with the aim of meaningfully relating the contents and their various parts to previous learning. Bruner (1966), developed the discovery teaching model which strongly endorses aiding the learner to discover what is intended to be learnt through research, questioning, interaction with the environment, investigation and so on. This implies that meaningful learning can occur if the teacher uses appropriate teaching approach and materials that can motivate the students to learn. This is because students are always excited and full of certainty anytime the students are faced with instructional materials. The teacher guides the students on how to use the materials. The students store up the discovered fact and use it to see its relationship or connection with the new concepts in geometry.

17

Bruner’s theory is relevant to the present study, since it emphasizes discovery, intuition and analytic language. It also promotes the use of appropriate instructional materials and innovative approach which in turn, helps to promote creativity, cooperation between students and teachers.

These activities also serve as a good evaluation technique.

For the practical significance, the findings of the study will be of benefit to: Teachers, curriculum planners, students, mathematics textbook writers, supervisors, inspectors of education and teacher training institutions. Secondary school teachers would acquire new instructional approach to teaching geometry. This will make the teaching of mathematics more interesting and thus improve teachers’ effectiveness. The study will also make available, relevant and concrete instructional materials for teaching geometry in particular and mathematics which hitherto was not and posed a serious problem in teaching and solving problems involving geometry of two-and three- dimensional shapes.

The findings of the study could sensitize curriculum planners on the use of fishing tools for teaching geometry of two- and three- dimensional objects based on environment and cultural background. This would be done through conferences, seminars and workshops. The curriculum planners could therefore, incorporate the fishing tools instructional approach and its relevant and concrete instructional resources into the new secondary school mathematics curriculum thereby enriching the curriculum for the teaching and learning of mathematics and geometry in particular.

The findings from this study would make students have a better understanding of geometry of two-and three-dimensional objects. Students’ involvement in using relevant and concrete fishing tools like net, racket, lead, float, conical fishing trap, among others might generate interest and hence facilitate better achievement.

The use of fishing tools instructional approach would furnish the mathematics text book writers with additional information and variety in the manner of presenting mathematical materials and instructions that will work in Nigerian school setting.

18

Supervisors and inspectors of education will also benefit from such conference at the state and federal levels. This, it is hoped will ensure improvement in mathematics methodology in the schools to enhance achievement, sustain retention and to generate students’ interest in the subject.

The findings would furnish the teacher training institutions such as institutes of Education,

Faculties of Education, and Colleges of Education with useful methods, learning strategies and materials that are useable in secondary schools which can be incorporated in the special mathematics methods classes.

Scope of the Study

The study was limited to senior secondary one (SS1) students in Andoni Local Government

Area of Rivers State of Nigeria.

The choice of SS1 students was because the students were in the foundation stage of the senior secondary school contact with the topics in geometry. Like the foundation of a house that is well laid, if the students’ interest in mathematics is sustained, it is likely that the students’ achievement and retention will be enhanced or improved. The topics covered the following contents.

a) Identification and properties of a rectangle, a rhombus and other plane shapes.

b) Some word problems involving rectangles, rhombuses and other plane shapes using

relevant fishing tools instructional approach.

c) Identification and properties of a cylinder, a pyramid and other solid shapes using relevant

fishing tools instructional approach.

d) Some word problems involving cylinders, pyramids and other solid shapes using relevant

fishing tools instructional approach.

19

Research Questions

The research questions formulated to guide this study are as follows:

1. What are the mean achievement scores of the students taught geometry of two-and three-

dimensional objects using the fishing tools instructional approach and those taught with

conventional (lecture) method?

2. What are the mean retention scores of the students taught geometry of two-and three-

dimensional objects using the fishing tools instructional approach and those taught with

conventional (lecture) method?

3. What are the mean interest scores of the students taught geometry of two-and three-

dimensional objects using the fishing tools instructional approach and those taught with

conventional (lecture) method?

4. What are the mean achievement scores of male and female students taught geometry of

two-and three-dimensional objects using fishing tools instructional approach?

5. What are the mean retention scores of male and female students taught geometry of two-

and three-dimensional objects using fishing tools instructional approach?

6. What are the mean interest scores of male and female students taught geometry of two-and

three-dimensional objects using fishing tools instructional approach?

Research Hypotheses

The following null hypotheses were posed to be tested at 0.05 level of significance:

1. There is no significant difference in the mean achievement scores of students taught

geometry of two-and three-dimensional objects using the fishing tools instructional

approach and those taught with conventional (lecture) method.

2. There is no significant difference in the mean retention scores of students taught geometry

of two-and three-dimensional objects using the fishing tools instructional approach and

those taught with conventional (lecture) method.

20

3. There is no significant difference in the mean interest scores of students taught geometry of

two-and three-dimensional objects using the fishing tools instructional approach and those

taught with conventional (lecture) method.

4. There is no significant difference in the mean achievement scores of male and female

students taught geometry of two-and three-dimensional objects using fishing tools

instructional approach.

5. There is no significant difference in the mean retention scores of male and female students

taught geometry of two-and three-dimensional objects using fishing tools instructional

approach.

6. There is no significant difference in the mean interest scores of male and female students

taught geometry of two-and three-dimensional objects using fishing tools instructional

approach.

7. There is no significant interaction effect between fishing tools instructional approach and

gender on students’ achievement in geometry of two-and three-dimensional objects.

8. There is no significant interaction effect between fishing tools instructional approach and

gender on students’ retention in geometry of two-and three-dimensional objects.

9. There is no significant interaction effect between fishing tools instructional approach and

gender on students’ interest in geometry of two-and three-dimensional objects.

21

CHAPTER TWO

LITERATURE REVIEW

The literature review of this study was done under the following subheadings.

Conceptual Framework v Current status of teaching and learning Mathematics/Geometry v Concept of instructional materials, types and uses v Fishing tools as Mathematics teaching resources § Concept and perspective of fishing tools § Meaning and types of fishing tools § Construction of some fishing tools § Uses of fishing tools in teaching and learning of some geometrical concepts v Retention and achievement in mathematics/geometry v Interest and achievement in mathematics/geometry v Gender and mathematics achievement Theoretical Framework v Piaget’s theory of cognitive development v Bruner’s theory on mathematics Instruction Empirical Studies v Studies on achievement in mathematics v Studies on instructional materials and achievement in mathematics v Retention as a factor in mathematics achievement v Interest as a factor in mathematics achievement v Gender as a factor in students’ achievement in mathematics Summary of Literature Review

21

22

Conceptual Framework

Current status of Teaching and Learning of Mathematics/Geometry

Mathematics occupies a central place in school curricula. Hence, the International

Association of Evaluation of Educational Achievement estimates that for most school systems in the world, at least one fifth of the learners’ time is devoted to the study of mathematics at the pre- tertiary level (Walberg, 2000). Mathematics apart from being a science of quantity and space is the corner stone in every field of education (Ezeamenyi & Alio, 2004). It is one of the core subjects for both the junior and senior secondary school stages (Federal Republic of Nigeria (FRN, 2004). This implies that every student must offer mathematics. This is indicative of the importance attached to mathematics in nation-building, technological and industrial development (Abdullahi cited in Tsue

& Anyor, 2006). According to Amoo (2002), the position mathematics occupies in the National

Policy on Education and its role towards technological and industrial development put mathematics in a special place in primary, secondary and tertiary levels of education. It also implies that mathematics is seen as the backbone of all the sciences and a vital part of the necessities of life.

Suffice it to say that mathematical method has strongly penetrated many fields of knowledge and its application has extended to all human developments. Put in another way, Abdullahi cited in

Anih (2000) said that mathematics like an octopus has its numerous tentacles in all branches of knowledge and its continual application makes life more enjoyable. This importance notwithstanding, mathematics continues to present special problems to students at all levels.

Recent survey reveals that students’ achievement in the subject continues to decline and almost getting to a dangerous peak (Maduabum & Odili, 2006). This mass failure and consistent poor achievement in mathematics which students have shown over a decade now cast serious doubt on the country’s high attainment in science and technology. The problems facing mathematics in

Nigeria are mainly in its teaching and learning and these cannot be dismissed by a wave of the hand. These problems start right from the primary school up to the tertiary level. As one finds

23 pupils shying away from mathematics in the lower levels so are many students who are admitted for courses related to mathematics not left out. According to Anih (2000), some students developed their indifference and dislike for mathematics at the early stage(s) of their education. Such indifference, together with several other factors, contributes to the very low achievement observable in many students. These factors, as problems to mathematics achievement level, can be seen to be results of the attitudes of not only the students but also the teachers, parents and government, to mention but a few.

Most of the problems leading to the low achievement of students in mathematics/geometry result from attitudes. Such attitudes constitute problems to the students’ grasping mathematical knowledge; students’ inability to take learning as their responsibility, poor study habits (Amoo,

2002) and assumption that mathematics is just a read-and-understand subject like the liberal art

(Anih, 2000), are among the major problems of a mathematical student. Commonly, students shun practicing of mathematics not knowing that a true understanding of mathematics systems depends largely on the amount of time devoted to practicing it. Unfortunately, the students do not realize the fact that mathematics/geometry is more than memorizing a set of rules and being able to apply them to appropriate situations. The students are fond of memorizing solutions and formulae without any attempt to understand or query their derivation or relevance. Little wonder, the students are often in a fix when required to solve problems which are new to them. This method of learning by rote memorization of mathematical facts gives little or no room for a mental development and creativity (Kurumeh, 2006). Students’ not being able to have confidence in their ability to follow mathematical reasoning (Anih, 2000), constitutes another problem. Consequently, the students fail to discover that the basic principles of mathematics are surprisingly simple and interesting. Ogunshilire cited in Anih (2000), commented on the achievement of students who attempted to pick mathematical problems and practice, sometimes only skip or cross over some exercises which to them appear to be too simple without knowing that little mastery of one theorem

24 can be invalid in such exercise which they might discover themselves. Students’ inattentiveness when mathematics lesson is going on (Amoo, 2000), also constitutes a problem. Many students prefer reading another subject when mathematics lesson is on. Some even prefer to be absent from mathematics lesson or have irregular attendance, among others too numerous to list. According to

Sanni and Ochepa (2002), some students often state that mathematics is difficult, abstract, a magic, like a game, not useful to them and so on. Mathematics is self-creating. It is completely man-made

(Kolawole and Oluwatayo, 2005). In the teaching and learning of certain concepts which the students regard as being abstract, past knowledge prevents students from grasping the new ones; the students find it difficult to acquaint themselves with new methods particularly when the students are used to the old ones which might have proven to be difficult. It is true that past knowledge, may assist in many good ways in grasping the new concepts, but it should not make students evaluate new situations with prejudice. According to Kolawole and Oluwatayo (2005), behind every successful mathematics lesson, there is a good teacher. Effective teaching implies productive result-oriented, purposeful, qualitative, meaningful and realistic teaching. For this reason, the mathematics teachers are said to be responsible for the general education of their students mathematically. This is because it takes a good teacher to apply correct strategy in his presentation to arouse the interest and enhance retention of his students and to make the best use of available structures to achieve higher goal. Anih (2000), noted that in the recent time, an average mathematics teacher seems to be able to exhibit any of these traits because the teacher only understands mathematics as a set of manipulative tricks he has to pass on to his students and not a dynamic conceptual structure, interesting, essential and vital to today’s developmental scheme. The teachers in many cases, do not understand the concepts because of their inadequate knowledge of the subject matter and low self-concept in mathematics (Amoo, 2002). According to Akinsola

(2004), many teachers in schools used strategies that are known to them, even if it is not relevant to the concept under discussion. Students are left at the mercy of the syllabus which cannot teach but

25 can only guide the teacher. Teachers especially in our secondary schools, take the greatest share of the blame that comes from lack of students’ interest, poor retention and achievement in mathematics because of the lack of the knowledge of geometrical concepts in particular, and mathematical concepts in general. Teachers can be blamed for their non-chalant attitude to the teaching of mathematics to achieve goals, as well as expanding, through carelessness, the already wrong ideas students have about mathematics as discipline instead of correcting it. Osefehinti cited in Akinsola (2004), is in support of the above assertion. The researcher stressed that lack of commitment by the teachers and the teaching methodology are the major problems associated with under-achievement in mathematics. The fact that most students think that knowledge of mathematics requires any special talent or that there exists a magic wand which confers little mastery of mathematical secrets, is not totally unconnected with the teachers’ method and attitudes towards teaching of mathematics. It will not be funny to hear a student who does not feel shy to say that he can never understand mathematics when a teacher works problems for the class as if by magic, without trying to explain the intricacies of the diagram and formula used in the problem.

Mathematics is looked upon by most students as an abstruse subject, lying beyond the students’ knowledge, because of misguided teachings.

According to Anih (2000), most teachers do not bear in mind that mathematics is a brainwork and requires a sort of logic and fun to transmit it to the students. It requires arousing the students’ interest, enhancing their retention and captivating their emotional responses and mental alertness. The way some teachers even present their lessons does a lot to disturb the brain of the students and brings fear instead of love in the students’ minds. For example, the total surface area of a cylinder is given by the formula 2πr(r + h) square unit. Some teachers do not take time to explain carefully and logically how the formula came about and what makes up the terms in the formula and indeed how the terms can be applied in solving total surface area of every cylinder.

Worse still, no concrete cylinder or diagram is displayed to the students. Instead, the teachers

26 simply write down the formula and apply in the particular problem. The situation is the same when solving problems with other solids and two-dimensional objects.

The above mentioned assertion is supported by personal experiences which the researcher of this study had during the course of this research. The researcher once trekked with some secondary school students on uniform from Government Secondary School, Ngo, Andoni of Rivers

State on the 21st March, 2014. The researcher overheard the conversation on the formulae used in solving geometry of two-and-three dimensional objects especially those of cylinders and pyramids and became curious and asked them whether they knew how the formulae were derived and what each variable (that is, term) in the formulae represents, or whether the students knew how to use the formulae well. The students answered no, that the mathematics teacher was wicked and liked only those that were intelligent and also liked teaching only the science class students. This type of attitude seems to accrue from teachers’ superiority complex. For the fact that such teachers have successfully studied and passed through the higher institutions in mathematics, such teachers consider themselves demi-gods and go into the classroom to show superiority by performing

‘magic’, more so when teaching more abstract topics especially in geometry. Thus, the teachers feel slighted in making students understand that Mathematics is simple. Most teachers do not even know that constructive and sympathetic response to students can lead to success in mathematics lessons especially in geometry that requires relevant and concrete diagrams or shapes. This fact is supported by Kolawole and Oluwatayo (2005), when they said that the notion by some secondary school students that mathematics is a difficult subject and taught by a wicked teacher should no longer be tenable in this new millennium, if Nigeria is to develop scientifically, economically, politically, technologically, and so on.

It was revealed that some of the problems facing the teaching and learning of mathematics are inadequate preparation to teach mathematics, poor tutorship in terms of devotion, and dedication to duty (Amoo, 2002). Agwagah (2001), also revealed that some of the problems facing

27 the teaching and learning of mathematics are the poor methods of teaching applied by the teachers, and teachers’ non-use of instructional materials in the teaching of mathematics concepts. Obodo

(2004), also supported this fact by stating that many of the professional teachers do not use appropriate methods and teaching aids in the classroom. Some use sterile and uninspiring methods.

Instruction is usually didactic and most often pitched at abstract level. Some teachers cannot improvise instructional materials for use in mathematics/geometry lessons. The teachers give little or no consideration to the psychology of the learner who may require concrete realities especially in geometrical shapes.

Cognitive competence of the mathematics teacher with respect to the teacher’s style of teaching influences students’ achievement in mathematics (Obodo, 1990). Obodo opined that: “an effective and efficient teacher of mathematics is one who knows the mathematics to teach and approaches to teaching such concepts creatively, employing a variety of teaching procedures, materials and aids”.

Emenalor (1986), indicated some of the teachers’ characteristics that will make students not to participate effectively in mathematics class as follows:

1. The teacher who continually tells students that mathematics is the most difficult subject is

wrong and instills fear into many beginners, for a student who has the feeling of not

passing the subject ever before the starting of the course is inhibited from trying to

succeed.

2. The teacher who marks only correct answers even though the method of solution is

wrong, is considered not a good mathematics teacher.

3. The teacher who presents or encourages students to make use of already – made

mathematical formulae in solving mathematics/geometry problems is also not a good

mathematics teacher even though most examination papers carry the warning that

answers without proper statements of work will lead to considerable loss of marks.

28

Much attention thus needs to be given to the development of students who have a good intuitive feeling for mathematics/geometry. Teachers should now start to use active participation activity strategies during teaching and learning as listed in the background of this study. Akinsola

(2004), is in support of the above mentioned assertion when he advised that the students should be allowed to be actively involved in the teaching process, such as constructing and drawing geometrical shapes, learning to be independent learners, linking new information to prior knowledge and thinking about what the learners already know, anticipating in what the students are to learn, assimilating and consolidating new knowledge. It is noted that when students are exposed in an environmental and culturally friendly manner by engaging the students actively in practical work during teaching and learning activity, the student will tend to have the zeal to participate fully and learn more. Students’ interest and curiosity will be aroused, thereby giving rise to achievement, retention and positive attitude to life and values and reducing the problems facing the teaching and learning of mathematics/geometry.

It was therefore necessary to investigate if the fishing tools instructional approach would reduce the problems facing the teaching and learning of geometry in particular, and improve students’ achievement, retention and interest in mathematics/geometry.

In reviewing the current status of teaching and learning Mathematics/Geometry in Nigeria, what first comes to one’s mind is dearth’. There is dearth of qualified teachers, dearth of encouragements and infrastructure needed for use in the schools to improve the teaching and learning process. The governments – both federal and state – have not made available workable rules in many schools. Thus, mathematics is taught in total abstraction, creating the impression that the subject is difficult. According to Anih (2000), there are textbooks but many of them are not indigenous. If most of the textbooks available are foreign, one wonders how the teachers will bring students nearer to their environments, and with examples and illustrations, may feel more relaxed and confident, learning through students’ daily experiences and seeing mathematics/geometry in

29 almost all their activities. The above fact is supported by Amoo (2002), when the researcher revealed that inadequate facilities is one of the problems facing the teaching and learning of mathematics/geometry in Nigeria.

Apart from lack of facilities, there has not been enough encouragement from the government to both the students and the teachers of mathematics. Since financial and material awards have been neglected from the beginning, only a few students go into the higher institutions to study mathematics and when some students do, their only urge is the ‘love of mathematics’. In fact, there is no incentive.

More so, available statistics have shown that ratio of mathematics teachers to students in most government owned secondary schools is 1:130; 1:115; and 1:118 in some education zones

(Adamu, 2007). This number of teachers includes those with HND in engineering drafted to teach mathematics. This ratio, with the introduction of Universal Basic Education (UBE) programme has been widened. For the same reason, that it takes a brave student to study mathematics, one would suppose that the government gives sufficient encouragement to those who study mathematics. Ilori

(1986), noted another aspect of this when the researcher said that most of the good materials or personnel prefer to go into the professions such as medicine, engineering and management studies because these other professions are the best rewarding.

As a result of the fact that teachers are not honoured both by the government and the society, and since mathematicians and mathematics educators are believed to have no other place in the society than the four walls of the classroom, that is teaching, people do not like to go in for it. Consequently, mathematics education is facing many problems. Amoo (2002), still revealed that inadequate recruitment of qualified teachers is one of the problems facing the teaching and learning of mathematics. This may start from the number of teachers employed down to the type or treatment teachers receive. The teacher employed to teach mathematics may not qualify at all, but because there is lack of teachers in the field, the “imported” teacher will teach his subject willy-

30 nilly (Usman, 2003). For instance, it is considered normal for teachers with Nigeria Certificate in

Education (NCE) in Economics/Geography, or Ordinary National Diploma (OND) in Accounting and Engineering to teach mathematics in our schools, thus denying our students the opportunity of having the proper ideas and background of some technicalities in learning mathematics/geometry.

One can agree that the education of a country is generally evaluated in part, from the quality of the teachers. This depends on the training received both at the academic and professional levels. Commenting on the need for qualified teachers in Nigeria, Fafunwa, cited in Anih (2000), stated that of all education problems that beset African countries today, none is as persistent and agonizing as the one relating to the training of competent teachers.

Lack of knowledge of the usage of some of the technological equipment for teaching mathematics especially geometry contributes immensely to the problems facing teaching and learning of mathematics at different levels of our school system. This agrees with the assertion by

Ani cited in Anih (2000), that mathematics teachers should be given regular in-service training to update their knowledge of mathematics. This is supported too by Usman (2002), in his study for the need to retrain in-service mathematics teachers; that the training of the teachers should precede the planning of educational programme since the teachers are the soul and heart of any educational programme.Usman further expressed that if the results are to be taken seriously, that the current in- service mathematics teachers should be retrained to meet the challenges of the Universal Basic

Education (UBE) and the new national curriculum on mathematics. Educational institutions have the role of reshaping a nation through moulding the individuals. This training if embarked upon will help the teachers to keep abreast with mathematics/geometrical concepts and their application in teaching and learning. The poor/inadequate use of teaching materials constitutes immensely to the problem teaching and learning of mathematics/geometry. The teachers are duty-bound to give the best if trained regularly, with other incentives as the teachers will be alert and can conveniently

31 stand before the learners and do all within their power to arouse the learners’ interest, enhance retention in mathematics/geometry and also reaffirm the students confidence in the subject.

Over-loaded and unrealistic nature of the curriculum (Adebayo, 2000), is also one of the problems facing teaching and learning of mathematics/geometry. In recent past, substantial changes have taken place in the mathematics curriculum particularly at the secondary school level.

Changes in content have often been accompanied by recommendations for improving the teaching of mathematics (Badmus, 2005). Unfortunately, new curricula in Nigeria are not often given appropriate trial-testing before full-scale adoption. Students do not often get the needed aids from their predecessors because the students are not familiar with the new curriculum contents. And sometimes teachers, whose pre-service training is at variance with the content and methods of the new curriculum, find it difficult to teach the contents to the students. As a result, most children feel frustrated and develop lack of interest, poor retention and under achievement in the subject. Lack of interest between school mathematics/geometry and socio-cultural context of the society (Amoo,

2002), also constitutes a problem of teaching and learning of mathematics/geometry. The general public should at this time rise to give mathematics/geometry its place in the scheme of things in the society. There have been series of diagnosis and countless prescriptions for the cure of the low standard of achievement in mathematics in schools and this is where the Mathematical Association of Nigeria (MAN) should come to the rescue. The association can do a lot in infusing interest and love of mathematics into the secondary school students by way of individual encouragement, organization of quiz competitions, debates and symposia, in mathematics for students and teachers accordingly, and outstanding efforts should be rewarded reasonably.

At the secondary school (Junior and Senior), the broad mathematics concepts covered include arithmetic, algebra, geometry, statistics, trigonometry and calculus. In all these branches of mathematics, geometry lends itself to more of practical work. In the view of Dangoli (1999), geometry is the gate way to mathematics. It is a branch of mathematics where visualization and

32 analysis come together very well, and logical thinking is enhanced. No wonder Plato, one of the

Greek philosophers asserted that a person ignorant of geometry is not worth talking to (Lassa,

2012).

Geometry, developed centuries ago, is still very useful today. It is used in measuring farm land. It is important in architecture, construction, navigation, art and design, physics, chemistry and astronomy. It can be used at home with carpet, wall paper, hanging pictures, tiling or fence construction. Up till today geometry is an integral part of mathematics which man has to depend more on as language of science and technology. It is a special branch of mathematics and it follows that if teachers of mathematics do not possess adequate knowledge of geometry, the teaching and learning of mathematics is likely to be seriously deficient.

Despite, the importance of geometry and its usefulness in everyday life, students’ performance in it is worrisome. According to Chief Examiner’s reports of West African

Examinations Council (2003, 2004 and 2005), students performed poorly on questions involving geometry. This statement was confirmed by Fiase (2009), who traced the poor performance to students’ inadequate mastery of the basic principles of geometry and the general fear of the subject as being difficult. The present study therefore, aims at addressing these inadequacies.

Concept of Instructional Materials, Types and Uses

The term ‘instructional materials’ is otherwise called apparatus, teaching aids, educational media, media materials, instructional aids, instructional curriculum materials, equipment for teaching, educational technology, audio visual aids and so on by various people. According to Eya

(2004), all of them refer to same set of materials, which a classroom teacher uses to extend the range of vicarious experiences of the learner.

In the same vein, Nwideeduh (2003), stated that instructional media is an exciting new world revolutionized by the computer, yet retaining all the former applications in the use of graphic materials, non-projected pictures, projected still pictures, television, audio, and three-dimensional

33 materials. The author went further to state, that terms like “teaching aids”, “visual aids” audio- visual aids, have been used in former times to refer to the concept. This concept is mainly a teacher’s complementary resource for greater, effective communication so as to advance learning and improve learner’s achievement. Due to the diversification inherent in the employment of most effective “tools’ or “artifacts” for the communication of teaching, those former terms become too limited in scope. The term “curriculum materials” or “instructional materials”, referring to all educational materials, have gained greater acceptability (Nwideeduh, 2003). This is because it not only refers to the object but also incorporates all the learning resources, techniques and devices. It refers to the mental processes as well as the physical equipment, all of which are employed to enhance learning. Similarly, Obodo (2004), used the terms interchangeably as instructional materials. The instructional materials, according to the researcher, refers to the same concept. What these terms share in common is that, these are all resources or materials used by the mathematics teacher in the classroom for the purpose of enhancing effective teaching and learning. Instructional materials are message carriers, a sure and dependable way of the teacher attaining instructional objectives in teaching and learning situations. The naming therefore, has no different intentions outside the purpose of teaching, that is eliciting desired behavioural change in the target audience.

In his attempt to define instructional materials, (Odili, 2006), related it to instructional development design. Instructional development, according to Gaff in Odili (2006), is “the systematic and continuous application of learning principles and educational technology to develop the most effective and efficient learning experiences for students’ activities that are relevant, evaluating the results of these activities and taking remedial action if necessary”. The researcher added that materials performing or supporting the teacher to perform one or more of these functions are called instructional materials.

Contributing, Eya (2004), defined instructional materials as resources which a teacher utilizes in the course of presenting a lesson to the learner to understand. It is also viewed as a

34 representation of alternative channel of communication which mathematics teacher can use to compress and present information in a more formal way to the learner. Thomas (2000), pointed that instructional materials are those devices developed or acquired to assist teachers in transmitting organized knowledge, skills and attitudes by learners within an instructional situation. It is directed towards learning and acquisition of skills for work. Supporting, Nwideeduh (2003), asserted that instructional materials can be referred to as wide variety of equipment and materials used for teaching/learning by teachers to stimulate self activity on the part of the students. Such equipment includes pictures, charts, graphs, real objects, cutout shapes, chalkboards, specimens and models, maps and globes, television, computers, mock ups, slide projectors, mathematical instruments, projected and non projected materials, textbooks, geoboards, games et cetera. These devices, according to Obafemi (1999) and Obafemi (2005), when presented in different varieties, stimulate, motivate and arouse learner’s interest. Everything which a teacher uses in instruction is a teaching aid (Akaninwor, 1999).

Instructional materials have been described as information carrying technologies that can be used for instruction (Ike, 1997). Instructional materials are always held out in their different ways, the bright hope of delivering educational information and experiences widely, quickly, vividly with realism and immediacy that printed media could hardly achieve. For instance, a teacher can describe a basket or racket but it is very hard to tell the students exactly how the basket or racket looks like without either the real or picture of the basket or racket for clarity. This real or picture of the basket or racket is an instructional material which could help students to understand the lesson.

Betiku (2000, 2002), explained that the term instructional materials comprise all available and accessible theoretical, practical and skill-oriented resources which facilitate learning, acquisition and evaluation of vocational technical skills. According to the researcher, instructional materials integrate all the devices that assist teachers in transmitting the facts, skills, attitudes and knowledge to the learners within the instructional system and as may be applied in the world of work. This

35 supports the position of Akaninwor (1999), who pointed out that without the use of some materials, tools and facilities in teaching technical subjects in schools, certain skills that might be required for entry into some vocational occupational areas might not be imparted. This is applicable to mathematics as a subject, since mathematics is the bedrock of all sciences and technological societies.

The implication of the foregoing is that mathematics teachers should as much as possible use instructional materials in teaching and learning situations. Put differently, a good mathematics teacher should possess the skill of designing, developing and utilizing instructional materials to bring meaning to the door posts of the learners. Contributing on this, Umo (2005), asserted that when learners come face to face with the teacher through the proper use of instructional materials, the lesson is always effective. Most of the instructional materials are available in schools, homes, markets, information centers and libraries but it requires a carefully dedicated and conscientious teacher to discover what material is meant for which group, the researcher added. Regrettably, many inexperienced and unqualified teachers find it difficult to identify some of these materials.

This study therefore reveals the activity-oriented nature of fishing tools and thus provides additional relevant, concrete and useful instructional materials to mathematics teachers.

Instructional materials can be classified or grouped into visual materials, audio materials, audio-visual materials, software, hardware and projected materials (Umo, 2005). Teaching aids, according to Akaninwor (1999), can be classified into four broad categories.

(i) Projected aids: Overhead projectors, slides (various types and sizes) Motion Pictures

(8mm, super-8, 16mm, et cetera) Opaque Projectors and so on.

(ii) Non-Projected Aids: Objects, Models, Photographs: maps, folio, charts, graphs, posters,

boards (various types).

(iii) Sound Aids: Tape Recorders (Reel to Reel) Cassette Tape Recorders, Record Players,

Radio Sets.

36

(iv) Aids combining sound and pictures: Motion Pictures, Television, Slide Series, Video

Systems

According to Ojoko (2003), and Ogbonna (2007), constructivism is the instructional approach, which holds the view that knowledge is individually reconstructed by a learner based on the learner’s prior knowledge or experiences. It is a set of beliefs about knowing and learning that emphasizes the active role of learners in constructing their own knowledge (Von Glaserfeld, 1989).

In this view, the learner constructs knowledge in an attempt to integrate existing knowledge with new experiences. When a learner is presented with new information, the learner will reformulate the existing cognitive structure only if the new information is connected to the knowledge already in memory. The learner must actively construct knowledge into learner’s existing mental framework for meaningful learning to occur and retention facilitated.

Still contributing on importance of instructional materials, Bruner (1961), noted that, from the use of instructional materials, there will be: enhancement of the memory processing; an increase in general intellectual potency; an increase in motivation via shift from extrinsic to intrinsic; and motivation and the acquisition of the heuristics of discovery.

In a similar view, Akaninwor (1999), stated that many years of research works have proved that when teaching aids are properly integrated into the lesson plan, and used in classrooms, the instructional materials offer the following advantages;

(i) Attract the interest and attention of the students

(ii) Help the students to learn easier and retain longer, various tasks, meanings and

concepts.

(iii) Clarify and give the correct meaning to verbal descriptions. Without them, each student

attaches the student’s own personal interpretation to a particular topic, based on the

student’s own knowledge and experience.

(iv) Enhance faster learning, thus saving time for the teachers and students.

37

(v) Help to alleviate the problems and difficulties arising in learning, due to personal

differences.

(vi) Help a teacher to expand his/her teaching process and

(vii) Give students the opportunity to develop projects individually which would help them

to better comprehend and digest the lessons.

Instructional materials are therefore as essential for the mathematics teacher as spices are for the chef. Instructional materials are necessary extra ingredients that make teaching and learning of mathematics a pleasant and satisfying experience since mathematics is an abstract logical science. The instructional materials help reduce the level of abstraction involved in the teaching and learning of a concept. Instructional resources concretize the abstract concepts of mathematics and thus make them more meaningful. Contributing, Obodo (2004), asserted that the ability of the teacher to use instructional materials for teaching serves to strengthen the degree of the students understanding. The use of instructional materials makes teaching interesting, real and full of activities for the students. Obodo further observed that efficient use of instructional materials helps the students to develop originality, creativity and curiosity. The use of such concrete materials contributes greatly to students’ retention of knowledge long after it has been acquired. The effectiveness of any instructional materials according to the researcher depends upon the extent to which it is properly selected for a given purpose.

Furthermore, instructional materials keep the students busy and active. Instructional materials make room for active participation of the learners during lessons. Instructional materials also stimulate students’ interest and help in the provision of diagnostic and remedial tools to teachers. Instructional materials also help to place teachers in a better position to observe and analyze learning process outcome. The more relevant and concrete the material to be learned is to the learners’ everyday experiences, the higher the chances of their being engaged.

38

An appropriate instructional material also enhances communication between the teacher and the learner. According to Umeano (2005), today’s successful teachers of mathematics are able to communicate ideas, build students curiosity, direct independent study, pose challenging questions, plan review and reinforcement experiences. Use of appropriate instructional materials, not only brightens the classroom, and brings variety; instructional materials are very effective in establishing the sense of spirit of team work. Instructional materials also help learners to develop continuity in thoughts, stimulate self-activity on the part of the students to overcome physical limitation during the presentation of subject matter. On this, the researcher reported that anecdotal records show that a student taught with appropriate teaching materials becomes actively involved in the learning process and the student is presumably highly motivated than a student who is merely a passive recipient of information. This is in line with the findings of the California Miller

Mathematics improvement program. The findings according to Odili (2006), pointed out that

“students at all grade levels achieved better and had improved attitudes when taught by teachers who had specific training in the use of mathematics laboratories and manipulative materials”.

The implication of the above discussion is that teachers of mathematics should endeavour to make use of appropriate and adequate instructional materials in teaching and learning process.

Moreover, in this age of information explosion that is engendered by the invention of newer and more sophisticated technologies, the very foundation of most societies and the people’s cultural patterns experience radical transformation. To achieve some degree of success and make the adjustment process smooth and alluring, appropriate instructional materials should be integrated into mathematics teaching and learning. Ekpo-Eloma and Udosen (2008), opined that the present changes in the society and innovations, occasioned by advances in science and technology, have profoundly altered all what was, providing new challenges, most of which have never been anticipated or contemplated. Anyone refusing to learn and relearn, is in danger of becoming obsolete, irrelevant and a nuisance.

39

A number of instructional materials have been developed and used for the teaching and learning of mathematics in general and geometry in particular. Such materials include geoboard, models, mathematical sets, charts, and so on, yet, students’ achievement in the area of geometry is still not encouraging as earlier cited. The present research therefore, exposes the effectiveness of fishing tools as alternative /more useful, relevant and concrete instructional materials that can enhance the teaching and learning of geometry and mathematics in general.

Fishing Tools as Mathematics Teaching Resources

Instructional resources are those resources (human and material), that are used to stimulate and maintain students’ interest in mathematics learning as well as facilitate their understanding of mathematical topics such as geometry of two- and three dimensional shapes, among others, based on the students’ environment and cultural background. Instructional resources help in the formation of concepts in students’ minds. Mere telling without exposing the learners to the concrete and relevant materials does not enhance learning. A creative mathematics teacher therefore, needs to know what materials are available or can be provided to enrich the teaching and learning of mathematical concepts (Okafor and Anaduaka, 2013).

Mathematical activity is a multifaceted human activity, very different from the stereotypes often attached to it in popular culture. Quality mathematics education must therefore reflect that diversity in the different mathematics content gradually encountered by students(UNESCO, 2012: 11). Thus, there cannot be any quality mathematics education for all unless quality resources are produced for students and for teachers (UNESCO, 2012: 36), such as fishing tools instructional approach.

The Concept and Perspective of Fishing Tools

Fishing is an ancient practice that dates back to, at least, the beginning of the Paleolithic period about 40,000 years ago (Wikipedia, 2009). Archaeological features such as shell middens, discarded fish bones and cave painting show that sea foods were important for survival and consumed in significant quantities.

40

The ancient river Nile was full of fish; fresh and dried fish were a staple food for much of the population.

Fishing as an example of extractive occupation, is concerned with making available raw materials (fishes) from sea, river, creek, lake, or pond to consumers. Extractive occupation is concerned with making available raw materials and natural products from the land and sea.

Occupation could therefore be defined as any economic or productive activities which people engage in to create and produce goods and services in order to make a living (Longe, 2012).

Fishing is the activity of trying to catch fish. Fishing tools (tackle) is a general term that refers to the equipment used by fishermen when fishing. Almost any equipment or gear used for fishing can be called fishing tackle. Some examples are hooks, lines, sinkers, floats, rods, reels, baits, lures, spears, nets, gaffs, traps, waders and tackle boxes. Tackle that is attached to the end of the fishing line is called terminal tackle. This includes hooks, sinkers, floats, leaders, swivels, split rings and wire, shapes, beads, spoons, blades, spinners and clevises to attach spinner blades to fishing lures.

Fishing tackle can be contrasted with fishing techniques. Fishing tackle refers to the physical equipment that is used when fishing, whereas fishing techniques refers to the ways the tackle is used in fishing. There are many fishing techniques or methods (for catching fish). The term can also be applied to methods for catching other aquatic animals such as mollusks (shell – fish, squid, octopus) and edible marine invertebrates.

Fishing techniques include hand gathering, spear fishing, netting, angling and trapping.

Recreational, commercial and artisanal fishers use different techniques, and also, sometimes, same techniques. Recreational fishers fish for pleasure or sport, while commercial fishers fish for profit.

Artisanal fishers use traditional low-tech methods, for survival in third-world countries and as a cultural heritage in other countries (Wikipedia, 2009). Mostly, recreational fishers use angling methods and commercial fishers use netting methods.

41

There is an intricate link between various fishing techniques and knowledge about the fish and their behaviour including migration, foraging and habitat. The effective use of fishing techniques often depends on this additional knowledge

However, fishing tools that are considered in this study include thread, twine (rope), floats

(buoys), net, racket and lead (sinkers). Again, fishing is done in ocean, sea, river, creek, lake and fish pond using different fishing vessels such as trawlers, speed boats, dugout boats, canoes and so on. In addition, fish farming, as the principal form of aquaculture, involves raising fish commercially in tanks or enclosures, usually for food. Though, there are many fishing techniques, this study considers fishing with various kinds of nets and some associated fishing tools.

Besides, these fishing tools are geometrical in shape. While net meshes, racket and lead

(sinkers) are two-dimensional; a bundle of twine, thread, rope and a float (buoy) are solids and three-dimensional (Sidhu, 2006). Fishing as the activity of trying to catch fish, has cultural impact among others. A good knowledge of these fishing tools and their applications can enhance students’ understanding and motivation of mathematics, especially geometry of two-and three- dimensional shapes. For instance, net, lead, rackets, fishing lines, among others, can be used in teaching mathematics concepts like straight lines, parallel lines, diagonals, angles, rectangles, squares, rhombus, parallelogram, perimeter, area, and so on, in two-dimensional shapes. While a bundle of rope (twine or thread), pyramidal (terminal) fishing float, conical fishing trap, among others, can be used in teaching mathematics concepts, such as circle, radius, diameter, pi (
), arc, chord, circumference, angle, perpendicularity, symmetry, surface area, volume, cylinder, pyramid, and so on, in three-dimensional shapes.

A fishing net or fishnet is a net used for fishing. Nets are devices made from fibers woven in a grid-like structure. Fishing nets are usually meshes formed by knotting a relatively thin thread.

Fishing nets are well documented in antiquity.

42

Ropes and lines are made of fibre lengths, twisted or braided together to provide tensile strength.

These fishing lines are used for pulling, but not for pushing. The availability of reliable and durable ropes and lines has had many consequences for the development and utility of fishing nets, and influences particularly the scale at which the nets can be deployed (United Nations Educational,

Scientific and Cultural Organizations (UNESCO, 2009). Some fishing lines include;

Twine, Braided fishing line, multifilament fishing line, Monofilament fishing line, fishing line,

Manila rope and Abaca rope. Twine is a light string or strong thread composed of two or more strands or yarns twisted together.

Some types of fishing nets, like seine and trammel, need to be kept hanging vertically in the water by means of floats attached to the net at the top. Various light “corkwood” – type woods have been used around the world as fishing floats. Floats come in different sizes and shapes. These days, floats are often brightly coloured for easy seeing (spotting). Small floats were usually made of cork, but fishermen in places where cork was not available used other materials, like birch bark

(Wikipedia, 2011). Glass floats were large glass balls for long oceanic nets, now substituted by hard plastic. Floats are used not only to keep fishing nets afloat, but also for dropline and longline fishing. Often larger floats have marker flags for easy spotting (locating) (UNESCO, 2009).

In addition, weights in various shapes and sizes as well as anchors are used in fishing.

Nowadays, lead (designed in the form of small rectangles or squares) is commonly used as sinkers and is usually attached to the bottom of the fishing nets. However, fishing nets are of various types and techniques. The fishing net includes:

Bottom trawl, cast (throw) net, coracle net, drag net, drift, drive-in, fyke, gill, ghost, hand, landing, lave, lift, mid water trawl, plankton, purse seine, seine net, shore operated stationary lift nets, shrimp net, stake net, surrounding net, tangle net and trammel nets.

43

Meaning and Types of Fishing Tools

Fishing tools are synonymous with Fishing Tackle. Fishing tackle is a general term that refers to the equipment used by fishermen when fishing. Almost any equipment or gear used for fishing can be called fishing tackle. Some examples are hooks, lines, sinkers, floats, rods, reels, baits, lures, spears, nets, gaffs, traps, waders and tackle boxes. Tackle that is attached to the end of a fishing line is called terminal tackle. In the same way, tackle attached to the middle of a fishing line is termed middle tackle. This includes hooks, sinkers, floats, leaders, swivels, split rings and wire, shapes, beads, spoons, blades, spinners and clevises to attach spinner blades to fishing lures.

Fishing tackle can be contrasted with fishing techniques. Fishing tackle refers to the physical equipment that is used when fishing, whereas fishing techniques refers to the ways the tackle is used when fishing. However, a fishing net or fishnet is a net used for fishing. Nets are devices made from fibers woven in a grid-like structure. Fishing nets are usually meshes formed by knotting a relatively thin thread (nylon). Fishing nets have been used widely in the past, including the stone age societies. The oldest known fishing net is the net of Antrea, found with other fishing equipment in the Karehan town of Antrea in United Kingdom (UK). The remnants of another fishing net dates back to the late Mesolithic, and were found together with sinkers at the bottom of a sea.

For fishing lines, ropes and lines are made of fibre lengths, twisted or braided together to provide tensile strength. These fishing lines are used for pulling, but not for pushing. The availability of reliable and durable ropes and lines has had many consequences for the development and utility of fishing nets, and influences particularly the scale at which the nets can be deployed.

Twine is a light-string or strong thread composed of two or more strands or yarns twisted together.

More generally, the term can be applied to a cord (Wikipedia, 2011), braided fishing line, multifilament fishing line, monofilament fishing line, fishing line manila rope and abaca rope

44

For Floats, some types of fishing nets, like seine and trammel, need to be kept hanging vertically in the water by means of floats attached to the nets at the top. Various light “corkwood”

– type woods have been used around the world as fishing floats. Floats come in different sizes and shapes. These days, floats are often brightly coloured for easy identification. In time past, stones, ceramic materials of various shapes and sizes and shells of some fishes like cockle were used as the weights or sinkers for fishing nets. Nowadays lead is commonly used as sinker for fishing nets.

Rackets and baskets are other fishing tools which could be locally made with materials from red mangrove shoots, cane and plantain or banana stem. The rackets and baskets are of various sizes, used for drying and storing fishes, respectively.

As stated earlier, various types of fishing nets and techniques include the following.

Bottom Trawl: A trawl is a large net, conical in shape, designed to be towed along the sea bottom.

The trawl is pulled through water by one or more boats, called trawlers or draggers. The activity of pulling the trawl through the water is called trawling or dragging. Bottom trawling has a serious environmental impact resulting in a lot of bycatch and damage of sea floor. In fact, the 2005 report of the United Nations (UN) Millennium Project, recommended the elimination of bottom trawling on the high seas by 2006 to protect seamounts and other ecologically sensitive habitats.

Consequently, in mid October 2006, the then United States of America (USA) President Bush, joined other world leaders calling for a moratorium on deep-sea trawling (Wikipedia, April, 2011).

However, bottom trawl fishing is still in practice.

Cast net: Cast or throw net is small round net with weights on the edges which is thrown by the fisher. Sizes vary up to about four metres in diameter. The net is thrown by hand in such a manner that it spreads out on the water and sinks. Fish are caught as the net is hauled back in.

Coracle net: Coracle fishing is performed by two persons, each seated in a coracle, plying his paddle with one hand and holding a shared net with the other. When a fish is caught, each hauls up his end of the net until the two coracles are brought to touch and the fish is secured.

45

Dragnet: is any net dragged or hauled across a river or along the bottom of a lake, sea, or creek.

Drift net: The drift net is a net that is not anchored, but is drifting with the current.

Drive-in net: A drive-in net is another fixed net, used by small-scale fishermen in some fisheries in

Japan and South Asia, particularly in the Philippines. It is used to catch schooling forage fish such as fusiliers and other reef fish. The front part of the net is laid along the seabed. The fishermen either wait until a school swims into the net, or the fishermen drive fish into it by creating some sort of commotion. Then the net is closed by lifting the front end so the fish cannot escape

(Wikipedia, 2011).

Fyke net: Fyke nets are bag-shaped nets which are held open by hoops. These can be linked together in long chains, and are used to catch eels in rivers.

Gillnet: The gillnet catches fish which try to pass through it by snagging on the gill covers. Thus trapped, the fish can neither advance through the net nor retreat. It is a system of nets with floats and weights. The nets are anchored to the sea floor and allowed to float at the surface.

Ghost net: Ghost nets are nets that have been lost at sea. The nets may continue to be a menace to marine life for many years.

Hand net: Hand nets are held open by a hoop and are possibly on the end of a long stiff handle.

Landing net: When an angler uses a hand net to help land a fish, it is known as a landing net.

Lave net: This is a special form of large hand net, now used in very few locations on the River

Severn in England and Wales. The lave net is set in the water and the fisherman waits till a fish hits against the mesh and the net is then lifted. Fish as large as sturgeons are caught in lave nets.

Lift net: A lift net has an opening which faces upwards. The net is first submerged to a desired depth, and then lifted or hauled from the water. It can be lifted either manually or mechanically, and can be operated on a boat or from a shore.

Midwater trawl: In midwater trawling, a cone-shaped net is towed behind a single boat and spread by trawl doors (image), or it can be towed behind two boats (pair trawling) which act as the

46 spreading device. Here, pelagic fish such as anchovies, shrimp, tuna and mackerel are the target fish. However, midwater trawling is relatively benign compared to the damage bottom trawling can inflict on the sea bottom

Plankton net: Research vessels collect plankton from the ocean using fine mesh plankton nets. The vessels either tow the nets through the sea or pump sea water on board and then pass it through the net.

Purse seine: The purse seine, widely used by commercial fishermen, is an evolution of the surround net, which in turn is an evolution of the seine net. It is a large and long net used to surround fish, typically an entire fish school, on all sides. The bottom of net is then closed by pulling a line arranged like a draw string used to close the mouth of a purse. This completely traps the fish.

Seine net: A seine is a large fishing net that may be arranged in number of different ways. In purse seine fishing, the net hangs vertically in the water by attaching weights along the bottom edge and floats along the top edge of the net. As simple and commonly used fishing technique is beach seining, where the seine net is operated from the shore. Danish seine is a method which has some similarities with trawling. In the United Kingdom (UK), seine netting for salmon and sea-trout in coastal water is only permitted in very few locations and where it is permitted, one end of the seine must remain fixed and the other end is then waded out and returns to the fixed point. This variant is called Wade netting and is strictly controlled by law in UK.

Shore Operational Stationary Lift Nets: These are held horizontally by a large fixed structure and periodically lowered into the water. Huge mechanical contrivances hold out horizontal nets with diameters of twenty metres or more. The nets are dipped into the water and raised again, but otherwise cannot be moved. The nets may hold bait or be fitted with lights to attract more fish. The most famous examples are found at Kochi, India, where they are known as Chinese fishing nets

(Cheenavala). Despite this name, this technique is used all over the world. These nets are also

47 widely used on the Atlantic coast of France, where the nets are operated from small huts built over the water on stilts, known as carrelets (Wikipedia, 2011).

Shrimp net: A shrimp net has small strong meshes used mainly in catching, shrimps and prawns in shallow part of the Atlantic Ocean, rivers and creeks. The shrimp net that has a stake across its front part is used by an individual close to the sea shore and river bank.

Stake net: A stake net is a form of net for catching fish in shallow inter-tidal zones. It consists of a sheet of network stretched on stakes fixed into the ground, generally in rivers or where the sea ebbs or flows, for entangling and catching fish.

Surrounding net: A surrounding net surrounds fish on all sides. It is an evolution of the seine, and is typically used by commercial fishers in the sea or river.

Tangle net: Tangle nets, also known as tooth nets, are similar to gillnets except these nets have a smaller mesh size designed to catch fish by the teeth or upper jaw bone instead of by the gills.

Trammel: A trammel is fishing net with three layers of netting that is used to entangle fish or crustaceans. A slack central layer with a small mesh is sandwiched between two taut outer layers with a much larger mesh. The net is kept vertical by the floats fixed on the headrope and weights on the bottom rope of the net (Wikipedia, 2011).

Construction of Some Fishing Tools

There are various fishing tools constructed and used in fishing. Different materials used in construction includes; iron gauge, iron, rod, thread, twine, rope, stick, red mangrove shoots, cane, plantain or banana stem, tree trunks and roots. However, hooks, lines, sinkers, floats, rods, reels, bails, lures, spears, nets, gaffs, traps, waders, and tackle boxes are some examples of fishing tools.

Fishing nets are usually meshes formed by knotting a relatively thin thread. Early nets were woven from grasses, flaxes and other fibrous plant materials. Later, cotton was used. Modern nets are usually made of artificial polyamides like nylon, although nets of organic polyamides such as wool or silk thread were common until recently and are still in use.

48

Fishing lines are ropes and lines made of fibre lengths, twisted or braided together to provide tensile strength. The availability of reliable and durable ropes and lines has had many consequences for the development and utility of fishing nets, and influences particularly the scale at which the nets can be deployed.

Twine is a light string or strong thread composed of two or more strands or yarns twisted together. More generally, the term can be applied to a cord.

Natural fibres used for making twine includes; cotton, sisal, jute, hemp, henequen, and coir. A variety of synthetic fibres may also be used. Fishing lines include thread, twine, braided fishing line, multifilament fishing line, monofilament fishing line, fishing line, manila rope and abaca rope.

Weights and anchors of various shapes and sizes used as sinkers are attached to fishing nets. Apart from anchors usually constructed with iron, stone or blocks, many fishermen use lead constructed in rectangular and square shapes as sinkers for the fishing nets.

Various light “corkwood” – type woods have been used around the world as fishing floats. Floats come in different sizes and shapes. These days, floats are often brightly coloured for easy seeing

(spotting).

Small floats were usually made of cork, but fishermen in places where cork was not available used other materials, like birch bark in Finland and Russia, as well as the

Pneumatophores of Sonneratia Caseolaris in Southeast Asia and other parts of the world

(UNESCO, 2009). These materials have now largely been replaced by plastic form.

Subsistence fishermen in some areas of southeast Asia make corks for fishing nets by shaping the

Pneumatophores of Sonneratia Caseolaris into small floats.

The Entelea wood was used by Maori for the floats of fishing nets, while Native Hawaiians made fishing nets floats from low density Wiliwili wood. Glass floats were large glass balls for long oceanic nets, now substituted by hard plastic. Glass floats are used not only to keep fishing nets

49 afloat, but also for dropline and longline fishing. Often larger floats have marker flags for easy spotting. Glass floats are popular collector’s items. The glass floats were once used by fishermen in many parts of the world to keep fishing nets, as well as longlines or droplines afloat (Wikipedia,

2011).

However, some fishing tools are constructed locally using materials from the environment.

Baskets of various sizes and shapes are constructed using cane from the bush. Baskets could be in the forms of hemisphere, frustum, sphere, open cylinder, cylinder or tray. But rackets in form of circle, are constructed with red mangrove shoots from mangrove swamp (forest) and cane from the nearby bush as well as plantain or banana stem used as rope in the construction.

Only craftsmen and women who are very skillful can do the construction of these fishing tools especially “local cork”, (pyramidal fishing float), lead (sinker), basket and racket. In most cases, these fishing tools are geometry of two-or three-dimensional shapes. The present researcher is not aware of any study involving fishing tools. Hence, the need of the study.

Uses of Fishing Tools in Teaching/Learning of Some Geometrical Shapes

Fishing tools are geometrical shapes that have various uses in fishing occupation. Fishing nets are devices made from fibers, woven in grid-like structures, used in catching fishes. Fishing nets are usually meshes formed by knotting relatively thin threads. Net meshes determine the size of fish caught. Nets with small meshes, in most cases, catch small fishes while nets having large

(big) meshes that are strong catch big fishes. Net meshes are plane geometry.

Fishing lines as stated earlier, are ropes and lines made of fibre lengths, twisted or braided together to provide tensile strength. The fishing lines are used for pulling, but not for pushing. The availability of reliable and durable ropes and lines has had many consequences for the development and utility of fishing nets, and influences particularly the scale at which the nets can be deployed.

Twine is a light string or strong thread composed of two or more strands of yarns twisted together.

Natural fibres used for making twine include cotton, sisal, jute, hemp, henequen, and coir. A

50 variety of synthetic fibres may also be used (UNESCO, 2009). Like fishing lines, twines (thread) are two dimensional shapes. Of course, thread is used in mending net meshes.

Rackets used in drying fish are locally constructed by racket experts. Shoots of red mangrove in mangrove swamp (forest) and cane from the nearby bush or forest as well as plantain or banana stem are used in the construction. Rackets are two-dimensional objects.

Lead is a chemical element whose symbol is Pb. It is a heavy soft grey metal used as weight or sinker attached at the bottom of fishing nets. It is prepared or cut into shapes and sizes that are rectangular and square before being used as sinkers in sustaining fishing nets in water. This, again is a plane geometry.

Floats of different sizes and shapes are attached or fixed to the top of the fishing nets to sustain the fishing nets vertically in water. Various light “corkwood” type woods have been used around the world as fishing floats. Often, larger floats attached to the two ends of the fishing nets and middle for easy spotting or locating are termed “terminal” and “middle tackle” respectively.

Floats are three-dimensional objects and could be used in teaching and learning cylinders, pyramids as concepts in geometry among others.

Baskets of various sizes and shapes are constructed by craftsmen and women with cane sourced from the environment (forest). Like floats, baskets are solids. Baskets are used in collecting and storing fish. Traps and hooks are also used in catching fish. While traps are solids, hooks are two dimensional.

Such geometrical shapes include the following: straight lines, angles, triangles, circles, quadrilaterals like rectangle, square, rhombus, parallelogram, trapezium, kite and solids like cylinder, cone, frustum, pyramid, sphere and hemisphere.

Fishing tools could therefore be used in teaching and learning many concepts of two and three- dimensional shapes in geometry. The researcher is not aware of any study involving fishing tools.

Hence, the need for this study.

51

Retention and Achievement in Geometry

Retention is the continued possession of something or the continued existence of something

(Hornby, 2010). Retention is the ability to remember what has been learnt. Retention therefore involves the amount of a learning experience that is correctly remembered at a later time. Students’ ability to retain what they learnt for a long period of time aids the students overall performance in a subject. Visual materials aid the retention of information. This implies that retention cannot take place in a vacuum. In other words, before retention comes into play, learning must have taken place.

Learning can be defined as a relatively permanent change in thought or in behaviour that results from experience (Osborne & Dillon, 2010). Similarly, when a person engages in practice or training activities and when observation of the person’s performance shows that the performance has changed, learning is usually assumed to have occurred, the change in thought or behaviour being the result of a combination of practice operation with practice conditions (Ogbonna, 2007).

Simply put, learning is an observable change in thought or behaviour and when one is able to recall what has been learnt as the need arises, then, it is said that retention has taken place.

Chauhan (2010), stated that retention is direct correlate of positive transfer of learning, the latter of which is of primary essence in education. Consequently, it is pertinent to discuss some concepts aimed at clarifying the meaning of retention among learners. These concepts are: trace change, decay, and forgetting.

Concept of Trace Change

In trace change, memory of what has been learned tends to change steadily in specific ways. This often results in the loss of experience of the property of the original and more perfect trace. Change in the trace for original learning causes loss in the retention of the learned information. This implies that retention cannot take place if one has no good memory. Memory is the mind’s storehouse, the reservoir of accumulated learning of an organism. To a psychologist,

52 memory is any indication that learning has persisted over time. It is an ability to store and retrieve information (Myers, 1998: 269). Memory is also defined as, the ability to remember things.

Santrock (2005), viewed memory as the retention of information over time. Hence, there are different stages of memory storage. These include:

(i) Long term memory (LTM)

(ii) Short term memory (STM), and

(iii) Iconic memory (IM)

These stages of memory storage, according to Ogbonna (2007), provided sufficient background for understanding the problems of forgetting or lack of retention. Literature shows that there is an amount of information a subject is capable of holding in iconic, short or long term memory and each of these three types of memory has a different capacity.

(i) Long term memory storage: The capacity appears to be nearly infinite. A material that

attains LTM does not seem to push previously stored material out of LTM. There is

enough room in which to store raw information in LTM while still retaining most of the

old information.

(ii) Short Term Memory Storage: Here, the capacity is limited to 5 – 9 items of information.

STM has a limited capacity and once this limit is reached, the new information begins to

push the old one out of STM.

(iii) Iconic Memory Storage: Here, the capacity is less than 5. After a very brief presentation,

subjects usually recall only 3 or 4 items. However, information capacity of the memory

system is sometimes being exceeded. This brings to mind the concept of decay.

Concept of Decay or Disuse: This concept was held by Thorndike (1913). According to Ogbonna

(2007), Thorndike believed that the bond between stimulus and its response “weakened” over time simply because it was not used. In other words, learning leaves a “trace” in the brain, that is, the memory trace, which involves some sort of physical change that was not present prior to learning.

53

With the passage of time, normal metabolic processes of the brain cause a fading or decay of the memory so that the traces of the material once learned, gradually, disintegrate and eventually disappear altogether. Moreover, studies have shown that decay is quite prevalent in STM much more than in LTM. In the same vein, Cermack (1970), opined that an interaction of decay and interference contributes to the rate of retention loss in STM.

Concept of forgetting: It is not so much the passage of time that determines the cause of forgetting but what is done in the interval between learning and recall. New learning may interfere with prior learning. The interference of new learning with the old one is known as retroactive inhibition. On the other hand, the principle that maintains that prior learning may interfere with the learning and recall of new materials is called proactive inhibition. Adding, the trace change concept explains that the “memory trace” is a hypothetical construct. It is not something that can be pointed in the brain. Rather, it refers to whatever representation of an experience that persists in the nervous system. When memory trace “fades” or that something else happens to it, what emerges when attempt is made to recall learned material is different from experience that was originally registered. The process of retrieval involves locating learned materials when needed. Thus, forgetting can be explained as a retrieval failure. According to retrieval failure concept, forgetting is very often temporary, rather than permanent phenomenon. It is not loosing something but rather is more like being unable to locate and find it. When cues that were available at the time of learning are not available at the time of recall, retention suffers.

Another factor that can help retention is motivation. The concept of motivation, according to Agumuoh (2009), saw the degree of happiness or pleasantness, which the motive caused, as a crucial determination of retention of such motive. On the other hand, an unpleasant motive tended to be quickly regressed and eventually lost in the memory. A more recent explanation on forgetting is that of consolidation concept, which is of the view that the undisturbed period of memory tends to become durable and permanent. It states that if the newly formed traces are disturbed and no

54 time is given for its consolidation, the traces will be wiped out as the memory traces; otherwise, the memory traces unit remains.

Besides, psychologists have identified five signs of good memory:

Rapidity: It means how rapidly the learner recalls the past experiences. If one recalls

rapidly, it means he possesses a good memory.

Accuracy: The second sign of good memory is the accuracy of the facts and experience

recalled.

Length of time: How long one can retain the past experiences and recalling them is also

a sign of good memory.

Promptness: It refers to the revival of the detail of past experiences.

Serviceableness: It refers to the recall of right thing at the right time and place

(Chauhan, 2010; 243 – 244).

However, some concrete strategies for improving memory according to Myers

(1998: 302), include the following:

(i) Study repeatedly to boost long-term recall. Over learn.

(ii) Spend more time rehearsing or actively thinking about the material. Rehearsal and critical

reflection help more as it pays to study actively.

(iii) Make the material personally meaningful. To build a network of retrieval cues, take

thorough text and class notes in a learner’s own words. Better to form images, understand

and organize information, relate the material to what the learner already knows or has

experienced, and put it in the learner’s own words. To increase retrieval cues, form as

many associations as possible.

(iv) To remember a list of unfamiliar items, use mnemonic devices. Associate items with peg-

words. Make up a story that incorporates vivid images of the items. Chunk information

into acronyms.

55

(v) Refresh memory by activating retrieval cues. Mentally recreate the situation and the

mood in which the original learning occurred. Return to the same location; jogging

memory by allowing one thought to cue the next.

(vi) Recall events while they are fresh, before encountering possible misinformation. Record

memory when it is fresh to avoid distortion or misinformation.

(vii) Minimize interference. Study before sleeping. Don’t study in close proximity topics that

are likely to interfere with each other, such as Spanish and French.

(viii) Test a learner’s own knowledge, both to rehearse it and to help determine what the learner

does not yet know. If the learner must later recall information, he should not be lulled into

overconfidence of his ability to recognize it. The learner has to test his ability to recall by

defining concepts already learned before referring to the definitions in the text. The

learner should also take practice tests; and study guides in various texts.

The above concepts show that retention is a factor which depends on many variables. These variables include time interval between learning and retrieval, intervening experiences, specific subject involved, instructional strategies, environment and instructional materials. Retention can also be improved through the organizations of materials in some meaningful fashion. The faster and the more efficiently a person can organize incoming information, the more the person will be able to process and retain it (Ogbonna, 2007). This implies that, to perform this rapid organizational process, it is imperative that the person be able to analyze the attributes of whatever the person has to process, encode, retain and retrieve. Analysis involves identification of several dimensions of the material or item, such as physical attributes, conceptual attributes and so on.

This type of analysis that determines how information is to be organized in memory and provides cues for retrieval is referred to as encoding stages.

Another important technique that improves retention is self-recitation. Studies have shown that reciting materials to oneself increases retention better than simply reading and reading the

56 material. One can read a material once and spend five-sixths of the time asking oneself questions about the materials read. Active recall or self-recitation would be better than re-reading several times (Kalra, 2008, and Chauhan, 2010). Moreover, the self-recitation method in ordinary learning, forces the learner to define and select to-be-remembered (TBR). Recitation represents practice in the retrieval of information in the form likely to be required later on. In other words, time spent in active recall with the material out of sight, is time well spent.

Over learning is another technique that increases retention. This means learning something well beyond the point of bare recall. That is, learning in which repetition or practice has proceeded beyond the point necessary for the retention or recall required. Such over learning may, however, be necessary for the retention of recall required and in view of factors necessary to affect recall which are bound to enter encoding processes at various levels. This means that a moderate amount of over learning aids retention. This implies that, if one were to retain new learning over a considerable period of time, one would be wise to over learn the material beyond bare mastery of it. In the same vein, Kalra (2008), asserted that repetition beyond the criterion of initial correctness is necessary to ensure maximum retention of materials learned. Like other studies, retention is aided by over-learning, From the foregoing, it is evident that retention has a strong tie with achievement and that inappropriate instructional material leads to lack of understanding of concepts and this invariably leads to forgetting and poor retention. To facilitate retention of mathematical concepts especially in geometry, therefore, innovative instructional strategy and materials such as fishing tools instructional approach need to be explored, hence, the need for this study.

57

Interest and Achievement in Geometry

Interest, according to Oxford Advanced Learner’s Dictionary, 7th Edition (2010), is the feeling that a person has when the person wants to know or learn more about something. The quality that something has when it attracts somebody’s attention or makes him want to know more about it. Similarly, according to Ezike and Obodo (2004), interest is the feeling of intent, concern or curiosity about something. It is regarded as the condition of wanting to know or learn about something. Interest is a very strong factor in teaching and learning of Mathematics. The degree and direction of attitudes towards mathematics are largely determined by the kind of interest developed by students for mathematics. Thus, a student with positive attitude studies mathematics because of the fact that the student enjoys or likes it. The student gets satisfaction from acquiring mathematical ideas and finds mathematical activities very rewarding, the researchers maintained.

Many factors have been found to influence students’ interest in mathematics. These factors include; the ability of the teacher to allow students’ responses to drive lessons, shift instructional strategies and alter content (Ogbonna, 2004). Interest and curiosity are related. Curiosity could be defined as a tendency to be interested in a wide range of areas (Pintrich, 2003). There are two kinds of interests – personal (individual) and situational. Personal or individual interests are more enduring aspects of the person (Woolfolk, Hughes & Walkup, 2008). Learners with individual interests in learning in general, seek new information and have more positive attitudes towards schooling. Situational interests are more short-lived aspects of the activity, text or materials that catch and keep the learner’s attention. Both personal and situational interests are related to learning. From texts, greater interest leads to more positive emotional responses to the material, then to greater persistence, deeper processing better remembering of the material and higher achievement (Woolfolk, Hughes and Walkup, 2008). Interests increase when learners feel competent, so even if individuals are not initially interested in a subject or activity, the learners may develop interests as they experience success (Stipek, 2002).

58

One of the qualities of an effective science teacher is the ability to motivate the students and sustain the students’ interest in learning science. To motivate is to stimulate the interest of somebody or cause somebody to have interest in something (Hornby, 2010). It is definitive to say that science educators are making spirited efforts to find ways of stimulating and sustaining the interest of students in science and mathematics learning. This is to help students understand and achieve well in science and mathematics. According to Davis (1999), if a teacher wants to stimulate students’ interest in learning, the teachers should create an atmosphere that is open and positive that helps students feel that they are valued members of a learning community. Similarly, teachers often associate students’ interest with success in teaching and learning. It is known also that teachers who cannot keep a class interested will be faced with serious disciplinary problems, inadequate students’ achievement, and perhaps students’ failure (Lassa, 2012). Interest is sometimes described as a tendency to be attracted to something (Lassa, 2012). Teachers cannot assume that their students want to learn whatever is presented to them. Ways to stimulate interest must be actively sought. As identified by Lassa (2012), six potential generators of students’ interest in mathematics are: goal of instruction, enrichment content, methodology of instruction, instructional resources, the evaluation of learning and qualification of the mathematics teacher.

However, the stimulation of students’ interest usually results from the blending of many of these ingredients. On the other hand, students’ negative attitude and lack of interest in Mathematics often results to poor performance (Adeniyi, 2012). The researcher stated that the “inability to do mathematics and not liking it seem to go together”. Supporting this, Soyemi (2003), noted that the inability of students to understand the basic mathematical principles, computation or logical facts and the underlying processes that gave rise to the mathematical facts in geometry and mensuration were as a result of lack of interest. This led to poor performance.

Interest has been known to relate with motivation and these constructs are correlates of achievement (Ezeh, 1992). The power of intrinsic motivation has been observed to be very

59 effective in mathematics learning. According to Agwagah (2008), students’ motivation is especially relevant to mathematics education in the light of recurring questions about how to get more students interested and involved in mathematics. The author added that interest can be deterred by the way teachers approach teaching and learning. This supports the observation of

Adeniyi (2012), who indicated that the cause of students’ lack of interest in mathematics is attributed to poor teaching method. In line with this, Ogbonna, (2007), pointed out that, the outdated and ineffective teaching methods adopted by teachers make students dread mathematics and loose interest in learning the subject. Since interest is a very strong factor in teaching and learning of mathematics, will the use of fishing tools instructional approach help to motivate and sustain the interest of the students towards higher achievement and retention in mathematics in general and geometry in particular?

Gender and Mathematics Achievement

The most significant factor influencing attitudes towards science and subject choice is gender- (Osborne & Dillon, 2010). As Gardner (1975), commented, ‘sex is probably the most significant variable related towards students’ attitude to science’ (p.22). This view is supported by

Schibeci’s (1984) extensive review of the literature, and meta-analyses of a range of research studies by Becker (1989) and Weinburgh (1995) covering the literature between 1970 and 1991.

Both the latter two papers summarized numerous research studies to show that boys had a consistently more positive attitude to science than did girls, though this effect was stronger in physics than in biology. A more recent review of the situation had been conducted by Murphy and

Whitelegg (2006), which confirmed this ongoing picture. Indeed, the enduring low participation of girls in the study of physical sciences (Murphy and Whitelegg, 2006), standing in stark contrast to their educational success in other domains, had led to renewed focus in research to address the problem which had proved resistant to the many initiatives that have been taken since the early

1980s.

60

What is clear from an extensive literature on the subject is that girls’ attitudes to science are significantly less positive than boys (Erickson and Erickson, 1984; Francis, 2000; Haste, 2004;

Head, 1985; Kelly, 1981; Smail and Kelly, 1984; Whitehead, 1996). A common thesis offered to explain this phenomenon was that it was consequence of cultural socialization which offered girls considerably less opportunity to tinker with technological devices and use common measuring instruments (Johnson, 1987, Kahle and Lakes, 1983; Smail and Kelly, 1984; Thomas, 1986). For instance, Kahle contended that her data showed there was a gap between young girls’ desire to observe common scientific phenomena and their opportunities to do so. More importantly, Kahle’s data showed conclusively that their science education did not remediate for this lack of experience and leads her to argue that “lack of experiences in science leads to a lack of understanding of science and contributes to negative attitudes to science (Kahle and Lakes, 1983, 135). Similarly,

Johnson argues from her data, measuring a range of common childhood experiences of children, that early established differences in the interests and activities of boys and girls result in parallel differences in their science performances (1987, 479). However, such data are contradicted by more recent findings from twin studies that there is no difference between girls’ and boys’ ability

(Haworth, Dale and Plomin, 2008) or interest (Pell and Javis, 2001).

In terms of achievement in science, Elwood and Comber (1995), had shown that the situation had reached a position where girls were doing as well, if not better than boys in biology and chemistry though boys still surpassed girls at age 16 in physics. These findings suggest that gender itself may now only contribute a minor part in the attribution of success. What remains an enigma is why girls choose not to pursue science even though the girls are competent and do believe in their capabilities to succeed.

Blickenstaff (2005), in a useful review of the issue, noted that nine hypotheses had been advanced to explain the phenomenon. These are:

(i) Biological differences between men and women

61

(ii) Girls’ lack of academic preparation for a science major/career.

(iii) Girls’ poor attitude toward science and lack of positive experiences with science in

childhood.

(iv) The absence of female scientists/engineers as role models

(v) Science curricula are irrelevant to many girls

(vi) The pedagogy of science classes favour male students

(vii) A ‘chilly climate’ exists for girls/women in science classes

(viii) Cultural pressure on girls/women to conform to traditional gender roles.

(ix) An inherent masculine worldview in scientific epistemology (Osborne and Dillon,

2010: 251).

Similarly, gender issues in education have formed an important focus of research for years now. In science, mathematics and technology, gender inequality has remained a contentious issue

(Alwarter, 1994; Baker and Leary, 1995). There tend to be more males than females in mathematics and mathematics related fields like science. For instance, Okeke (2002, 2007), reported the fewness of female in science and technology. Among the ancient mathematicians, the celebrated, names such as Euclid, Erastothenes, Pythagoras, Pascal, Chike Obi and others, were all men. One begins to ponder on the possible causes of such imbalance, (Olagunju, 1996).

Even in school curriculum, there existed gender differences for boys and girls, for example, girls were made to do subjects like needlework, home management, nutrition, domestic science, housewifery, languages and literature (Lassa, 1995, 2012). The implication is that these subjects would prepare the girls for their future roles as mothers and housewives. In this context, girls seemed to fail to think beyond becoming wives and mothers, which are societal expectations of the girls. Discussing gender as a factor in students attitude in mathematics, Obodo (2004), stated that sex stereotyping is a factor among others which portray how parents’ attitudes influence their children’s mathematical attitude. The researcher further explained that some parents encourage

62 differential activities for their boys and girls. Some of these activities according to Obodo, have advantages or disadvantages in learning mathematics.

Agreeing, Harbor-Peters (2001), asserted that gender issues in mathematics have been a source of aversion, and that mathematics has been male-stereotyped since it was regarded as abstract, difficult and has attributes which boys were attracted to. A number of researches have been done in this regard; some of the results were in favour of boys than girls while some showed that gender has no significant effect on students’ ability in understanding of mathematical concepts.

Educational researchers like Lassa (2000, 2012), and Steen (2003), for instance, had documented males superiority over females in special ability. In the same view, Osborne and

Dillon (2010) and Ogunkunle (2009), reported significant difference in favour of boys and indicated that boys have higher mathematics reasoning ability and performed better. However,

Haworth, Dale and Plomin (2008); ASA (2005), reported no significant difference in mathematics achievement of boys and girls. This supports the findings of Olagunju (1996), who observed no significant differences between the performances of male and female students in mathematics.

While some studies like Alio (1997), Meremikwu (2002, 2008), found among other things that the mathematics achievement of girls was significantly better than their male counterparts.

The above assertions show that there is still gender parity and disparity on students’ performance in mathematics. This gender parity and disparity has been attributed to some factors.

According to Okeke (2002, 2007), Osborne and Dillon (2010), gender difference has been attributed to natural, societal, cultural and psychological reasons among others. Socially, gender inequality is well pronounced in the characterization of school milieu, exemplifying the masculine nature of science. Also, school text and curriculum materials carry passive imagery of women in various examples. The illustrations and pronouns, which are used often, portray females as passive in nature (Harbor-Peters, 2001). In school activities, the expectations from boys and girls reinforce

63 sex roles further. Girls are encouraged to study feminine subjects like languages, home economics, history and literature, which will prepare them for the expected adult role while boys are encouraged to study science and mathematics.

On cultural dimension, certain careers are unfeminine and incompatible with marital demands. For instance, majority of science related careers have inbuilt inflexibility in working schedules and require those involved to be out of their homes most of the time.

These types of jobs are incompatible with responsibility to meet dual role demand of home and work. As a result, girls with potentials for science and mathematical skills are discouraged from pursuing them (Erinosho, 1994). The psychological dimension has to do with attitude, interest and self-concept, the researcher explained. In the upbringing, females are nurtured to develop capacity for emotion, concern and feeling of nature with minimal manipulation of the physical objects in the environment. This makes the females not to develop attributes, which are masculine in nature. In terms of self-concept, girls probably have poor perception of their worth because of various negative experiences which the girls are exposed to. No wonder, one of the Millennium Development Goals (MDGs) and the

Education for All (EFA) goals is to promote gender equality and empower women. The present research intends to investigate the effectiveness of fishing tools in bridging the existing gender disparity on students’ achievement in mathematics.

Figure 1: A schematic representation of the essential variables in the study.

Fishing Tools Gender Instructional Approach

Achievement Retention Interest

Fishing tools instructional approach and gender are independent variables upon which achievement, retention and interest are dependent. 64

Theoretical Framework

Piaget’s Theory of Cognitive Development

No topic is closer to the heart of psychology than learning, a relatively permanent change in an organism’s behaviour due to experience. Learning shapes the learner’s thought, language, motivations, emotions, personalities and attitudes (Myers, 1998: 243).

Learning is seen as a relatively permanent change in thought or in behaviour that results from experience (Osborne and Dillon, 2010). Learning theories if properly explained indicate the internal workings of “the mind” and predict behaviour. In the behavioural view, new behaviours themselves are learned whereas according to the cognitive view, knowledge is learned, and changes in knowledge make changes in behaviour possible (Woolfolk, Hughes & Walkup, 2008:

294). These learning theories open our eyes to other possibilities and ways of seeing the world.

According to Melin (1970), most design decisions are certainly based on the learning theories, but the function of instructional design is more of an application of theory rather than a theory itself. In the development of a curriculum for school mathematics, for instance, the nature of mathematics as a discipline and psychological theories of learning must be considered. Teachers need to know about the teaching-learning process. The researchers should be aware of effective teaching and successful classroom practices which provide guidelines that will help in choosing instructional approach and materials that work with learners. Intellectual (cognitive) ability and maturity of learner should also be considered. Cognitive development of the child, is concerned with how children learn and gain knowledge about the world around them (Alonge, 2011) .Cognitive development is the process by which the cognitive abilities and capabilities of learners are modified with time. For the purpose of this study, Piaget’s and Bruner’s theories of learning are reviewed. The theories of Piaget cognitive development propose that learning takes place through three main processes namely:

(i) Formation of mental concepts (structure)

65

(ii) Adaptation of concepts as a result of experience

(iii) Relating concepts to form a network (Piaget, 1964).

Piaget exposed that these learning processes can be carried out in four (4) stages of cognitive development. These are:

(i) Sensori-motor stage: (Ages of 0 – 2 years)

(ii) Pre-operational stage: (Ages of 2+ - 7 years)

(iii) Concrete operational stage: (Ages of 7+ - 12 years)

(iv) Formal operational stage: (Ages of 12+ and above)

The learning of mathematics at each stage according to Alonge (2011), can proceed through the three learning processes as earlier identified.

i. The sensori-motor stage (0 – 2 years): At this stage, the child uses his/her senses and

body movements or ‘kick’ to explore information which may be continuous repetitions

of actions. This stage is also called a psychomotor stage.

ii. Pre-operational stage (Ages of 2+ - 7 years): A child at this stage tends to concentrate

on one feature of a variable of an object at a time like drawing patterns of shape, jigsaw

adding and subtracting quantities of concrete objects. The child is not able to make

symbolic representations; may not be able to differentiate between a square and a

rectangle, a rhombus and a parallelogram and so on.

Towards the later stage, the child can find by “trial and modification method” that 20÷ 4

= 5 but may not reason that it is because four groups of five equals 20 so that 20÷ 4 = 5.

Towards the end of this stage, children begin to develop the concept of reversibility. This

stage usually coincides with the nursery and lower primary school levels

iii. The concrete operational stage (Ages of 7-12years): This period coincides with the senior

primary school and junior secondary school levels. Children at this stage can solve

problems based on concrete objects that can be observed and manipulated. The children

66

are capable of dealing with logical issues and relations but cannot deal with propositions

and hypothesis testing. For example, a child at this stage should be able to solve for

variable x in the relation of the form 2x = 10, but may experience difficulty in isolating

variable x from 2xy = 10. This is because the procedure of controlling the effect of the

other variable is beyond the child’s mental ability. Children at this stage can measure

angles, shapes, differentiate between plane shapes and solid shapes, differentiate between

triangles, rectangles, squares and so on from the other. The children can think

operationally or logically. For example the children are able to reason that 20÷ 4 = 5

because 4 x 5 = 20. Also, if y + 700 = 1800, then y = 1800 – 700 = 1100 and so on. The

children can solve problems based on objects such as beads, bottle tops, plane shapes, and

so on which can be manipulated and can draw conclusions from concrete evidence and so

learning activities at this stage can include “problem situations”.

iv. The formal operational stage (12 years and above): This last stage of Piaget’s cognitive

development coincides with the upper (senior) secondary and first year in tertiary

institutions. Children at this stage are capable of reflective and abstract thinking and are

able to isolate variables from such expression like 2xy = 10 by dividing both sides of the

equation by 2x, ie 2xy = 10 and arrive at y = 5 . The students can now understand 2x 2x x

more complex conceptual relationships, solve complex problems, control all variables

while testing one and are capable of using sound logical procedures in problem solving.

Piaget’s theory stresses the importance of activities in the learning process. The psychologist is of the view that mathematics teaching should involve activities and students should be made to interact with one another. More so, the teacher should make the classroom situations to be in such a way that there would be interplay between the teacher and students where they could be active participants, not passive listeners. Mathematics teachers should create more involvement for students, hopefully, leading the students to a mathematics practical situation in which there

67 could be maximum learning through participation and sharing, where instructions become

“learners’ centred”. The theory is of the view that learners must construct their own meanings rather than being passive receivers of information. This theory is closely related to the philosophy of social constructivism.

Social constructivism as a philosophy of mathematics is based on fastening opportunities for students to experience, discover, discuss and re-construct the socially negotiated nature of mathematics (Betts, 2005). According to Ojoko (2003), and Ogunkunle (2006), constructivist approach has a major impact on effective teaching and learning of mathematics. It also emphasizes that students do not passively accept and absorb what the students are told or experience, rather the students actively make sense of new experiences by relating it to what the students already know and understand.

However, Piaget’s theory of learning is very relevant to this study, as its construct elaborated mathematical models of the mental structures, which characterized the concrete and formal operational stages. Children cannot learn like adults as the children lack the ability to generalize, have a narrow vision in problem solving situations and require materials to form relevant concepts. Hence, there is the need to state the implications of Piaget’s theory for the act of teaching and learning mathematics. The implications of Piaget’s theory to mathematics/geometry teaching and learning, as pointed out by Alonge (2011), are as follows:

(i) Mathematics teachers should expose the students to wide variety of concrete

objects to stimulate the students’ senses and make use of concrete materials in

teaching mathematics/geometry

(ii) The curriculum materials to be learnt must be within the limits of the cognitive

development level of the learner.

(iii) Mathematics teacher should explain mathematical concepts with adequate

illustrations based on their basic principles.

68

(iv) The students must be given opportunities to explore and interact with their

environment.

(v) Since children learn by social interaction, they should be given opportunities to talk

freely, share experiences, discuss their discoveries and or give out their differences.

(vi) Children should have considerable control over their learning. Therefore, the

children should be given opportunities to make decisions concerning what they

should learn and how.

(vii) Mathematics teachers should always adopt the question and answer (Socratic)

method of teaching by exploring children’s thinking abilities.

Bruner’s Theory on Mathematics Instruction

As time went on, another American psychologist whose views also resemble those of

Piaget’s is Jerome Bruner in 1966. Bruner’s theory also projected the idea that every discipline has structure and the learner should be helped to see to the structure with the aim of meaningfully relating the contents and their various parts to previous learning. Bruner (1966), developed the discovery teaching model which strongly endorses aiding the learner to discover what is intended to be learnt through research, questioning, interaction with the environment, investigation and so on. The psychologist has presented a system of cognitive development that resembles that of

Piaget and has proposed that children’s thinking abilities develop in three stages which Adekanye

(2008), described as:

(i) Enactive (events represented through motor responses)

(ii) Iconic (events represented through mental images of the perceptual fields)

(iii) Symbolic (events represented through design features that represent remoteness and

arbitrariness)

These three stages, according to Lindgren (1976), consisted of the sequence action, image and words and corresponded appropriately to Piaget’s sensori-motor perceptual and abstraction

69 modes of cognitive functioning. A major theme in this theory is that learning is an active process in which learners construct new ideas or concepts based upon the children’s current/past knowledge.

Bruner’s theory as pointed out by Kearsley (1944b) could be applied to instruction by applying the following principles:

(i) Instruction must be concerned with the experiences and contests that make the students

willing and able to learn (readiness).

(ii) Instruction should be designed to facilitate extrapolation and or fill in the gaps (going

beyond the information given). This implies that meaningful learning can only occur if the

teacher uses appropriate teaching approach and materials that can motivate the students to

learn. This is because students are always excited and full of certainty anytime the students

are faced with instructional materials. The teacher guides the students on how to use the

materials. The students store up the discovered fact and use it to see its relationship or

connections with the new concepts in geometry.

Bruner’s theory is relevant to the present study, since it emphasizes discovery, readiness, intuition and analytic language. It also promotes the use of appropriate instructional materials which in turn, helps to promote creativity, cooperation between students and teachers. These activities also serve as a good evaluation technique.

Empirical Studies

Studies on Achievement in Mathematics

Review of related literature has consistently shown that students’ poor achievement in mathematics has been attributed to various variables. Adekanye (2008), studied the effect of students’ participation in instructional material production on achievement and interest in

Geometry. The purpose of the study was to determine the effect of students’ participation in the production of instructional materials on achievement and interest in some geometrical concepts by students at upper UBE level. Six research questions and six hypotheses guided the study. The

70 method adopted was quasi – experimental or non – equivalent control groups. One hundred and sixty six (166) JS1 students from two coeducational secondary schools were used for the study. In each school, two classes were selected for the study. Two classes for experimental and two classes for the control by random sampling. The students were treated for 4 weeks with conventional approach in teaching geometry for the control group and the students’ participation in the production of instructional materials for teaching geometry for experimental group. Geometry achievement test (GAT) and geometry interest inventory (GII) were used for data collection. Mean and standard deviation were used to answer the research questions while ANCOVA was used to analyze the hypotheses. The study showed that students in geometry classes based on conventional approach and those based on participation in the production of instructional materials differed in performance. Those taught geometry based on participation in the production of the instructional materials strategy had the highest mean of 55. 4878 while the mean score of those with conventional strategy for teaching geometry was 40. 1786. The observed difference between the mean score of the experimental and control groups was significant at 0.05 level of the study using

ANCOVA. This implies that experimental approach affected students achievement more positively than the conventional method. This study is similar to the present study to some extent. For instance, the concepts used for the study are the same but the subject and the content areas are not.

Secondly, their designs are the same, quasi – experimental. The two studies also are related in comparing achievement and interest of male and female students but differ in comparing retention.

The use of fishing tools produced similar results as in the above reviewed study

Onwuakpa and Akpan (2000), investigated secondary school students’ classroom learning environment in relation to the students’ mathematics achievement. One thousand, two hundred

(1200) students in senior secondary school class one in Imo State were used as sample. Forty senior secondary schools out of two hundred and ninety five senior secondary schools were randomly selected. A classroom learning environment inventory and mathematics achievement test

71 instruments were used for the purpose of collecting data. Percentages, mean, standard deviation and ANOVA were used in the analysis. The implication of this study is that the levels of difficulty or nature of class work, satisfaction with class work and physical environment of students, all work together, to improve on students academic achievement. The study reveals that mathematics teachers should make their classroom teaching to be very lively and stimulating for the students.

The use of effective teaching strategies and styles, understanding the individual differences of students should always be considered by the mathematics teachers during teaching/learning process. Thus, the use of concrete and relevant instructional materials like fishing tools improved students’ academic achievement.

The above study is relevant to the present study because it sought to establish the achievements of male and female students related to the learning environment. The present study has found out that the fishing tools instructional approach improved achievements of male and female students.

In another study, Iji (2003), explored the effects of Logo and Basic programs on achievement and retention in geometry of Junior secondary students. The study took place at

Ahoada Education Zone of Rivers State. The main purpose of the study was to determine the efficacy of the use of Logo and Basic program methods in teaching Junior Secondary Geometry in

Nigeria. The design of the study was quasi – experimental in nature and it took a sample of two hundred and eighty – five (285) JS1 students drawn from three out of six of the co – educational schools that have computers in Ahoada Education Zone. Two instruments were used for the study.

These were: The geometry achievement test (GAT) and geometry retention test (GRT).

Data analysis techniques employed for the study were Mean, Standard Deviation and

ANCOVA. The result revealed that students taught LPM and BPM achieved higher than those taught with CPM. Also, the low achievers improved on the level of their Geometry achievement among others. It was recommended among other things, that since the methods were relatively

72 new; the methods should be incorporated in the mathematics curriculum for the pre – service teachers program. This will help the teacher to learn and use the LPM and BPM in teaching. The above study is similar to some extent to the present study. In the first instance, the content areas and the subjects used for the study are almost equivalent. Secondly, their design, are the same – quasi- experimental. Also, the two are related in determining achievements and retention of male and female students. Thus the present study produced similar results as in the above reviewed study: Fishing tools instructional approach enhanced achievements and retention of male and female students.

Again Ogwuche (2002), investigated age and sex as correlates of logical reasoning and mathematics achievement in ratio and proportion tasks. This study was done in Zone C, Education

Zone of Benue State. The main purpose of the study was to correlate logical reasoning with pupils’ achievement in mathematical ratio and proportion tasks. The study adopted correlation design. It specifically sought to establish the relationship that existed between logical reasoning and mathematics achievement in ratio and proportion between primary six pupils and JSS1 students.

Ogwuche, took four hundred and eighty – eight (488) primary six pupils and JSS1 students from 16 schools in the area of the study. Two instruments were used for the study: Test of logical thinking

(TOLT), and mathematics achievement test on ratio and proportion.

In the study, it was found that in TOLT, the male students performed better than their female counterparts; that there was significant difference between the achievements of male and female students in mathematics achievement test on ratio and proportion. Specifically, male students performed significantly better than their female counterparts. It was recommended among other things, that workshops, seminars and conferences be organized to enable teachers implement the findings of study.

The above study is similar to some extent to the present study in the sense that the subjects used for the study are almost equivalent. On the other hand, the above reviewed study differs from

73 the present one in terms of design and method. The study also was not rooted on instructional material like fishing tools. However, the present study investigated the use of fishing tools instructional approach as a strategy with the view to determining whether the result would be in line with the above findings of significant difference in achievements of male and female students or not? Like the above findings, the use of fishing tools instructional approach enhanced male students more than female students in mathematics achievement.

Furthermore, Kurumeh (2006), worked on the effect of ethno – mathematics approach on students’ achievement in geometry and mensuration. Four hundred (400) JS1 students from one hundred and ten (110) single sex secondary schools in Ogidi and Aguata Education Zones of

Anambra State were used for the experiment. Two schools were purposively drawn from each

Zone, making a total of (4) single sex schools. From the schools sampled, two intact classes were randomly drawn by balloting treatment and classes. Each group has two hundred (200) male and female students. Two research questions and three hypotheses guided the study. The design was quasi – experimental. The two groups were given pre – test and post – test using a researcher – constructed instrument, mathematics achievement test on geometry and mensuration (MATGM).

Mean and standard deviation were used to answer the research questions while the three null hypotheses were analyzed of covariance (ANCOVA) at P < 0.05.

The result of the study revealed that there exists a significant difference between the experimental and control groups in favour of the experimental group. Also, the female students benefitted more significantly than their male counterparts. It was recommended among other things, that teachers should adopt ethno – mathematics approach in teaching mathematics topics / concepts, particularly, in female schools by linking instructions to the learners’ immediate environmental experiences, cultural background, past experiences and daily activities. This will make mathematics gain popularity, capture the learners’ interest and challenge their intellect and result in better performance. The study is similar to the present study in the sense that the content

74 areas and the subjects used are almost equivalent. Moreover, both are of the same experimental design. The two also are related in determining the achievements of male and female students. The question was, would the present study produce a similar result like the above reviewed study? The findings of the present study like the reviewed study, showed that fishing tools instructional approach improved the experimental group higher than the control group with male students having higher achievement than their female counterparts.

Researching on practical, meaningful and creative approaches to teaching and learning geometry, Ozigboh (1994), studied the effects of geoboard and rolleograph as instructional materials in teaching plane geometry in secondary school. A sample of three hundred and twenty four (324) students was used. An achievement test was administered and ANOVA was used in data analysis. The findings showed that instructional materials used were effective in improving achievement and interest in mathematics. The instructional materials raised the curiosity to learn than the conventional instructional strategies of not providing students with instructional materials.

This literature review did not say anything about fishing tools instructional approach and students’ achievement, retention and interest in mathematics/geometry. This creates an urgent need to find the effects of the instructional materials and how fishing tools instructional approach could enhance students’ achievement, retention and interest in mathematics/geometry

In another development, Musa and Agwagah (2006), explored the effect of incorporating practical into mathematics evaluation on senior secondary school students’ achievement in mathematics. Two research questions were posed and three hypotheses were formulated to guide the study. A sample of one hundred (100) SS1 students from a randomly selected school in

Akwanga Education Zone of Nasarawa State served as subjects of the study. Two instruments:

Theory Achievement Test (TAT) and Practical Achievement Test (PAT) were developed, validated and used for data collection. Mean, standard deviation, t – test and two – way ANOVA were used for analyzing the data. The result revealed that the inclusion of practical examination in

75 mathematics evaluation is more effective than using the current practice of theory (essay and objective) only; male students performed significantly better than the female students when examined using practical approach and there was significant interaction effect between mode of evaluation and gender, based on the findings. It was recommended, among others, that mathematics curriculum specialists should structure a mathematics curriculum that would incorporate practical examination as is obtainable in other science subjects. The mathematics examiners should construct standardized practical test items in mathematics using identified concrete materials / models as specimen. Fishing tools instructional approach is practical oriented in teaching/learning some geometrical concepts. The use of fishing tools instructional approach also produced positive effects, as the above reviewed literature.

Studies on Instructional Materials and Achievement in Mathematics

Usman and Obidoa (2005), conducted a study on the effects of teaching some geometrical concepts with origami on students’ achievement. A total of sixty (60) junior secondary school one

(JSS1) students in Rohs holiday camp at Queen of Rosary Secondary School Nsukka (during one of the long vacation holiday camps) were used for the study. These students were randomly divided into two equal, 30 (experimental) and 30 (control) groups.

The study used a pre – test / post – test control group experimental design. The pretest was administered to the two groups before the commencement of the treatment. The two researchers were involved in the teaching of the two groups, one for experimental and the other for control.

The experimental group were taught some geometrical concepts (lines, angles and plane shapes) using the origami, while the control group were taught the same concepts using conventional approach at the same time. At the end of the treatment, the post – test was administered on the two groups. Two hypotheses guided the study. The findings of the study revealed that there is a significant difference in the means of achievement score of group taught with origami and those taught with the conventional method in favour of the experimental group. Similarly, the mean

76 achievement score of the female students is greater than that of male students but the difference is not significant. It was recommended among other things, that improvisation should be the central theme of instructional materials. Origami as an instructional material, has added more to the pool of the available instructional materials, for the teaching and learning of mathematics and geometry in particular. Moreover, it can be easily improvised as the main ingredient is paper.

In the same vein, Obi (2014), explored the effect of origami on students’ achievement, interest and retention in geometry. In the study, six (6) research questions and nine (9) hypotheses were formulated to guide the study. A sample of 166 JSS1 students from two (2) coeducational institutions drawn from Nsukka Education Zone of Enugu State was used. Three instruments:

Geometry achievement test (GAT); geometry retention test (GRT); and geometry interest scale

(GIS) were developed, validated and used for data collection.

This study is similar to the present study in the sense that, the content areas and the subjects used are almost the same. Moreover, both are quasi – experimental. The two studies also are related in determining the achievements of male and female students in geometry. The question was, would the present study produce a similar result like the above reviewed study? The finding of the present study was the same like the reviewed study.

Adekanye (2008), studied the effect of students’ participation in instructional material production on achievement and interest in Geometry. The purpose of the study was to determine the effect of students’ participation in the production of instructional materials on achievement and interest in some geometrical concepts by students at upper UBE level. Another purpose was to determine the influence of gender on achievement and interest of students. The problem of the study was to bridge the gap of poor performance of students in geometry by adopting the practical approach of guiding students to discover facts for themselves. Six research questions and six hypotheses guided the study. The method adopted was quasi – experimental or non – equivalent control groups. One hundred and sixty six (166) JS1 students from two coeducational secondary

77 schools were used for the study. In each school, two classes were selected for the study. Two classes for experimental and two classes for the control by random sampling. The students were treated for 4 weeks with conventional approach in teaching geometry for the control group and the students’ participation in the production of instructional materials for teaching geometry for experimental group. Geometry achievement test (GAT) and geometry interest inventory (GII) were used for data collection. Mean and standard deviation were used to answer the research questions while ANCOVA was used to analyze the hypotheses. The study showed that students in geometry classes based on conventional approach and those based on participation in the production of instructional materials differed in performance. Those taught geometry based on participation in the production of the instructional materials strategy had the higher mean of 55. 4878 while the mean score of those with conventional strategy for teaching geometry was 40. 1786. The observed difference between the mean score of the experimental and control groups was to be significant at

0.05 level of the study using ANCOVA. This implies that experimental approach affected students achievement more positively than the conventional method. This study is similar to the present study to some extent. For instance, the concepts used for the study are the same but the subject and the content areas are not. Secondly, their designs are the same, quasi – experimental. Both studies use relevant and concrete instructional materials. The two studies also are related in comparing achievement and interest of male and female students but differ in comparing retention. Could the use of fishing tools instructional approach produce similar results as in the above reviewed study?

The findings of this study produced similar results as in the above reviewed study.

Retention as a Factor in Mathematics Achievement

Researching on retention and achievement in mathematics, Agwagah (1994), investigated the effect of instruction in mathematics reading on pupils’ achievement and retention in mathematics: implication for rural mathematics education. The main purpose of the study was to determine the effect of instruction in mathematics reading on the achievement and retention of

78 rural primary school pupils in addition and subtraction of numbers. Two hypotheses guided the study. The study was a quasi – experimental research. The sample for the study consisted of one hundred and forty – two (142) primary four pupils selected randomly from two rural primary schools (one each from Anambra and Enugu States of Nigeria). The instruments employed for the study – (Achievement Test in Addition and Subtraction of Number) (ATASN) and lesson plans were developed by the researcher and were validated and vetted respectively by experts. Data collected were analyzed using mean scores, standard deviation and ANCOVA.

The result of the study indicated that students who were taught mathematics reading achieved higher and retained more of the content taught. The above reviewed study is similar to the present study in terms of design and method of data analysis. Both studies however, differ in scope and sample.

In another study, Iji (2003), explored the effects of Logo and Basic programs on achievement and retention in geometry of junior secondary school students. The study took place in Ahoada Education Zone of Rivers State. The main purpose of the study was to determine the efficacy of the use of logo and basic program methods in teaching junior secondary geometry in

Nigeria. The design of the study was quasi – experimental in nature and it took a sample of 285

JSS1 students drawn from three out of six of the co – educational schools that have computers in

Ahoada Education Zone. Two instruments were used for the study: The geometry achievement test

(GAT) and geometry retention test (GRT). Data analysis techniques employed for the study were mean, standard deviation and ANCOVA. The result revealed that the students taught with LPM and BPM achieved higher than those taught with CPM. The Low achievers also improved in the level of their geometry achievement among others. It was recommended among other things, that since the methods were relatively new; the method should be incorporated in the mathematics curriculum for the pre – service teachers program. This will help them to learn and use the LPM and BPM in teaching mathematics especially geometry

79

The two studies are similar in the sense that both of them are rooted to relatively new approaches. Again, the studies are similar in terms of design, subjects and content areas. The two are also related in comparing achievement and retention of male and female students. Thus the present study produced similar results as in the above reviewed study.

In another development Ogbonna (2007), explored the effect of two constructivist instructional models on students’ achievement and retention in number and numeration. The study was conducted in Umuahia Education Zone of Abia Sate. The main purpose of the study was to determine empirically the effects of IEPT and TLC constructivist instructional models on junior secondary school students’ achievement and retention in mathematics. The design of the study was quasi – experimental and it took a sample of five hundred and seventy (570) JSS11 students drawn from three (3) out of thirty six (36) co-educational secondary schools in Umuahia Education Zone.

Three instruments were used for data collection, namely; pre-mathematics achievement test

(PREMAT), post mathematics achievement test (POSTMAT) and delayed post- test (DELPOST) or Mathematics Retention Test (MRT). Mean scores, standard deviation and ANCOVA were employed for data analysis.

The result revealed that the use of IET and TLC constructivist instructional models enhanced significantly students’ achievement and retention in mathematics. It was recommended among other things, that the two instructional models should be included in the mathematics method of teacher training institutions. This might help in no small measure in minimizing the mass failures of students being currently experienced all over the nation.

The above reviewed study is similar to the present study in terms of design and method of data analysis. The studies are also related in comparing achievement and retention of male and female students. However, the two studies differ in terms of subjects and content areas. Again, while Ogbonna (2007), concentrated on new instructional models, the present study is on relatively new instructional approach.

80

Also Anyor and Iji (2014), worked on the effect of integrated curriculum delivery strategy on secondary school students Achievement and Retention in Algebra in Benue State, Nigeria. The study adopted a quasi-experimental design and carried out in Makurdi Local Government. The population comprised 1368 SS I students. It purposively sampled 149 students of 1368.

Instruments of the study were Algebra Achievement Test (AAT) and Algebra Retention Test

(ART). Descriptive statistics of mean and standard deviation were used to answer the researchers’ questions asked, while ANCOVA inferential statistic was used to test the hypotheses formulated at

0.05 level of significance. The study found among other things that Integrated Curriculum Delivery

Strategy (ICDS) enhanced students’ achievement and retention in the Algebra taught during the period of this study. The reviewed study is similar to the present study in terms of design, method of data analysis and subject, but differs in content areas.

In summary, it has been observed that most of the reviewed works were mainly on teaching methods. The present researcher investigated the effects of fishing tools instructional approach on students’ achievement, retention and interest in mathematics/geometry.

Interest as a Factor in Mathematics Achievement

Researching on interest and achievement, Ogbonna (2004), investigated on the effects of constructivist instructional approach on senior secondary school students achievement and interest in mathematics. The study sought to determine the effect of the approach on the achievement of male and female students in mathematics. The sample for the study was two sampled intact classes from sampled schools in Umuahia Education Zone of the Abia State. Two instruments, mathematics achievement test and quadratic equation interest scale were used. The design was quasi – experimental design. The mean and ANCOVA were used to analyse the data. The result of the study indicated that sex was a significant factor in determining the interest of male and female students. The mean interest scores of male students were higher. The study also revealed that gender was not a significant factor on students’ achievement in mathematics.

81

The above reviewed study is similar to the present study in terms of design. The studies also sought to determine the effect of the approach on the achievement and interest of male and female students in mathematics. On the other hand, both studies differ in the areas of content coverage and subjects for the study. Moreover, the above reviewed study, unlike the present one, focused on instructional models while the present study is on instructional approach.

Still reviewing, Alio (2000), investigated the effect of Polya’s language technique in teaching problem solving in Mathematics. The researcher sampled three hundred and twenty (320)

SS11 students randomly in Enugu State for both experimental and control groups. The design was quasi – experimental. The researcher administered 25 items multiple choice achievement test with mathematics interest scale before and after the treatment to ascertain their interest in mathematics.

The results of the findings were analyzed using Analysis of covariance (ANCOVA). It was revealed among other things, that students’ interest towards problem solving in mathematics was significantly affected by being exposed to this new method Polya’s language technique. This means, according to this study, that this technique (Polya’s technique) in teaching problem solving is a significant factor in interest towards problem solving in mathematics. The two studies are similar in the type of research design but differ in scope and sample size. Also, unlike Alio (2000), this present study explored students’ retention relative to fishing tools instructional approach.

Iweka (2006), also investigated on the effect of inquiry and laboratory approaches of teaching geometry on students’ achievement and interest. The population of the study consisted of all the junior secondary school class 2 (JSSCII), students from twenty nine (29) secondary schools in the Ika Education Zone of Delta State. Intact classes were used through random sampling. The research instruments used for data collection were Geometry Achievement Test (GAT) and

Geometry Interest Scale (GIS). Mean, standard deviation and ANCOVA were used for data analysis. The study revealed that the laboratory approach was significantly better than the inquiry and conventional approaches in enhancing students’ achievement and interest in geometry. It was

82 recommended among other things, that mathematics teachers should endeavour to use the laboratory approach in teaching difficult mathematics concepts, since this approach enhances achievement and interest and has the potentials of developing critical thinking and creative abilities in the students.

The two studies are similar in terms of design, sample and sampling technique and also sought to determine the effects of the approaches on students’ achievement and interest but differ in the approaches and content area. The present study, unlike Iweka (2006), is concerned with fishing tools instructional approach.

Moreover, a number of empirical studies on interest and achievement in mathematics have been presented and there is none within the knowledge of the researcher on the use of fishing tools on students’ achievement, retention and interest in mathematics/geometry. It is then necessary to investigate on the fishing tools instructional approach on students’ achievement and interest in mathematics / geometry.

Gender as a Factor in Students’ Achievement in Mathematics

Discussing gender as a factor, Erinosho (1994), took a sample of sixteen thousand, eight hundred and six (16,806) students, made up of five thousand, five hundred and sixty four (5,564) boys and eleven thousand, two hundred and forty – two (11,242) girls from twenty five (25) out of forty – one (41) Federal Colleges in Nigeria. This consists of fifteen (15) all girls and ten (10) co- educational. The researcher discovered that between 1985 and 1990, the most significant disparities between boys and girls in WAEC results was in mathematics, with 55.5% boys scoring various grades up to pass grade and for the girls, it was 44.5%. It was found that among all science subjects, physics ranked first in terms of achievement among girls with mathematics ranking last.

For the boys, mathematics ranked first, followed by biology.

The study appears to be sectionalized. For instance, the researcher should have included some State owned schools in the sample. This would have given a wider scope and a more valid

83 generalization especially given the fact that Federal Government Schools have better infrastructures than State Schools. The study was also based on second hand data, that is, WAEC results. All these make the differences between it and the present study, which is focused on one aspect of mathematics, geometry, with a view to differentiating achievement along gender.

In another study, Harbor – Peters (2001), asserted that gender issues in mathematics have been a source of aversion. The researcher said that mathematics has been male – stereotyped since it was regarded as abstract, difficult and has attributes which boys were attracted to. In an attempt to explore the interaction effect of gender and achievement, it would be recalled that Harbor –

Peters (1993), designed a study in which male and female teachers taught male and female students. The result of the findings was that, male students performed significantly better than their female counterparts generally. It was also revealed that male students taught by a female teacher performed significantly better than the male students taught by male teachers. On the other hand, it was observed that female students taught by male teachers performed significantly better than those taught by a female teacher.

Contributing, Obi (2014), investigated the effect of origami on students’ achievement, interest and retention in geometry. The population of the study consisted of all the JSS1 students from five (5) co – educational secondary schools that have more than 180 students in Nsukka

Education Zone of Enugu State. Intact classes were used through random sampling. The research instruments used for data collection were Geometry Achievement Test (GAT), Geometry

Retention Test (GRT) and Geometry Interest Scale (GIS). Mean, standard deviation and ANCOVA were used for data analysis. The result revealed among other things, that male students achieved higher than the female students using origami and conventional approaches. The interaction effect of treatment and gender on students’ achievement was significant. It was recommended among others, that origami approach should be incorporated in the secondary schools mathematics curriculum as a technique in teaching geometry.

84

The above findings were buttressed by Kurumeh and Iji (2007), who found that the difference in mean achievement of males and females was statistically significant in favour of males. Many other research findings showed that, there were significant differences in mean achievement in favour of males. Such findings were observed in Okeke (2002, 2007); Orji (2002); Ojoko (2003);

Ogbonna (2004, 2007), Obi (2006,2014), and many others. One begins to wonder, whether the cause is in the type of method applied in teaching, interest generated problem, nature of the concepts, instructional materials applied or any other hidden factor.

Contradicting the above findings, Akukwe (1991), using four hundred and fifty (450) students in

Imo State with Continuous Assessment Cumulative Average Score (CACAS) as an instrument, found among other things, that girls achieved higher than boys. Contributing, Salva (2001), investigated the comparative effects of attending single sex and co – educational secondary schools on the female students’ achievement in mathematics. Ninety thousand one hundred and five

(90,105) students from three hundred and twelve (312) schools that sat for mathematics in senior secondary certificate examination (SSCE) between 1991 to 1995 were used as subjects. The country was stratified into six geographical zones and two states were randomly selected from each zone.

The relative performances of students in mathematics across the four types of schools were assessed using the frequency counts and percentages. The Cochran Q test was used in the test of significance of difference between pairs of proportions. The findings showed that the proportions of pass and above grade in mathematics for boys and girls in co – educational schools were significantly higher than those of their counterparts in single sex schools. In mathematics, girls performed better than boys irrespective of whether the students are in single sex or co – educational school. The above review is related to the present study in the sense that both sought to determine the gender difference. In addition, the studies are not similar in design, sample and sampling technique.

85

In another study on gender differences and mathematics achievement among secondary students in Southern Cross River State, Meremikwu (2002, 2008), found among other things, that the mathematics achievement of girls in single sex school was significantly better than male counterparts in single sex school. The researcher used an analysis of variance and t – test in analyzing his data. The implication of the findings is that single sex schools should be encouraged so as to maintain gender balance in science, technology and mathematics. The above study is similar to the present in terms of subjects. Both studies used secondary school students and also sought for gender difference, but differ in design and type of school. The question was, “would boys and girls experience the same achievement in the present study?” This is the focus of this study.

Still searching on gender difference and mathematics achievement, Ezema (2002), studied the effects of Keller instructional Model on students error minimization and interest in quadratic equation. Mean, standard deviation and analysis of covariance (ANCOVA) were used in analyzing the data.

It was found that, there was no significant interaction effect between gender and instructional method on students’ achievement and interest in quadratic equation. The above line of thought is in agreement with Sunday, Akanmu and Fajemidagba (2014), who worked on effects of target task mode of teaching students Geometrical construction in May/June 2003-2012 SSCE General

Mathematics in Nigeria. The study investigated the impact of this mode of teaching on students’ performance in Geometrical construction. Two coeducational senior secondary schools purposively selected participated in the study. A four (4) essay item Mathematics Performance Test (MPT) on geometrical construction drawn from WAEC past questions was used as the instrument for the study. Data generated based on the hypotheses formulated were analyzed using t-test statistic and analysis of covariance (ANCOVA). The findings, among others, indicated that both male and female students performed equally well when exposed to the treatment. Similarly, Ogbonna (2004),

86 investigated the effects of constructivist instructional approach on senior secondary school students’ achievement and interest in mathematics. The study adopted a quasi – experimental design. Two secondary schools were drawn for the study using simple random sampling technique.

Four research questions and six hypotheses guided the study. Mean, standard deviation and analysis of covariance (ANCOVA) were used in analyzing the data.

The study revealed that constructivist instructional approach has a differential effect on the achievement and interest of male and female students taught with the models. The study also showed that there was no significant interaction effect between gender and instructional approach on students’ interest in mathematics.

In the same vein, Ojoko (2003), investigated the effectiveness of a constructivist instructional strategy on senior secondary school students’ achievement in mathematics. The study, like the previous one (Ogbonna, 2004), adopted a quasi – experimental design. Six secondary schools (public and private) were drawn for the study using random sampling technique. Four research questions and six hypotheses guided the study. Mean, standard deviation and analysis of covariance (ANCOVA) were used for data analysis.

The study revealed that the constructivist instructional strategy has a differential effect on the achievement of male and female students taught with the strategy. The study also showed that there was no significant interaction effect between gender and instructional approaches on students’ interest in mathematics. The above studies (Ogbonna, 2004 and Ojoko 2003) are similar to the present study in the sense that, their designs and methods of data analysis are the same. Both also sought for gender differences. The difference is in the area of subjects and approaches. Unlike

Ogbonna (2004), and (Ojoko, 2003), the present study investigated gender difference and the use of fishing tools instructional approach on students’ achievement in mathematics/geometry.

However, all the lines of thought from the above literature are in agreement with Olagunju (2001), who in his study, found that there was no significant difference between the general performance

87 of boys and girls in mathematics. However, the researcher is of the opinion that women should be seen as nation builders and developers of persons who make for development. Women should therefore, be encouraged to study Science, Technology and Mathematics (STM) for according to the researcher, there tends to be more males than females in this field of study.

Women play vital roles in sustainable development both at the national and international levels (Nwosu, 2002). The implication of the above statement is that women should be encouraged to compete favorably in the field of science, technology and mathematics. Moreover, the United

Nations Millennium Development Goals (MDGs) and the Education For All (EFA) goals, both emphasized the desirability for gender parity, gender equality and empowerment of women

(UNESCO, 2007). Would the present study help in any way to achieve these noble goals? This was one of the concerns of this researcher. Thus, the present study helped to an extent, in achieving these noble goals as this was one of the concerns of this researcher.

Summary of Literature Review

This chapter has examined the literature of previous studies, suggestions and recommendations that are relevant to the present study. This was initiated by considering the theoretical and conceptual frameworks. Theories that are relevant to the study were reviewed.

Piaget’s and Bruner’s theories of learning were found most relevant and appropriate because of the level and age of the subjects used for the study, (SS1) students. More so, the study is interested in the use of innovative instructional approach and materials which the cognitive theories advocate.

The cognitive theories opine that the use of appropriate instructional materials holds the greatest potential for implementing the principles of educational technology. Consequently, the use of fishing tools instructional approach is therefore practical oriented, learner-centred, active and applicable to the local environment. Would the use of fishing tools instructional approach, aid students’ active participation in the teaching and learning of some geometrical concepts? The

88 conceptual framework, which aimed at emphasizing on the various concepts that were relevant to the study was discussed.

Ethnomathematics as a culturally influenced mathematics is the mathematics of the environment or community. Like ethnomathematics approach, fishing tools instructional approach is practical, learner-oriented, active and applicable to the local environment. Ethnomathematics therefore, is seeking or using the mathematics observed in the cultural activities of the people.

However, the use of fishing tools instructional approach and its relevant and concrete instructional materials are yet to be investigated in other fields of study and mathematics. Hence, the present study focused on investigating the fishing tools instructional approach on students’ achievement, retention and interest in senior secondary school geometry (mathematics). Besides, fishing tools as mathematics teaching resources could stimulate and maintain students’ interest in mathematics learning as well as facilitate the students’ understanding of mathematical concepts such as geometry of two- and three- dimensional shapes, among others, that is based on the students’ environment and cultural background was discussed. Also reviewed were concepts of retention, interest and achievement in mathematics/geometry. It was revealed that retention and interest have a strong tie with achievement and inappropriate instructional approach / materials leads to lack of understanding of concepts and this invariably leads to forgetting and under achievement. The literature revealed that, despite all recognition accorded mathematics at all levels of the educational system; students’ achievement is still not impressive. This under – achievement according to the literature review could be summarily attributed to students, curriculum, societal, psychological and teachers’ factors to mention but a few. The review emphasizes teachers’ incompetence and use of inappropriate teaching methods and instructional materials as one of the major contributory factors.

Since geometry is presented in an abstract form to the students, the need to seek for a more practical approach of teaching and learning geometry/ mathematics to the students based on their

89 environment and cultural background was therefore proposed by the researcher. Hence the need of the present study.

To facilitate interest and retention of mathematical concepts, innovative instructional strategy and instructional materials such as fishing tools instructional approach was proposed. This is the focus of this research. In the empirical studies, however, students’ achievement in mathematics was reviewed alongside with approaches and instructional materials adopted. It was asserted that since the search for variety of instructional materials could facilitate achievement, enhance interest and retention, it is evident that the mathematics and science educators are concerned with positive change in the method of instruction. It is based on this, therefore, that this study aims at complementing the earlier efforts, hence, the present study on fishing tools instructional approach. The review showed that there is no empirical evidence of any study on fishing tools instructional approach on students’ achievement, retention and interest in senior secondary school geometry which the present study seeks to investigate. The review also examined empirical studies on gender and achievement in mathematics. From the studies reviewed, it is very clear that the issues of gender and achievement of students are not yet closed, as researches at these points were inconclusive. There is therefore, room for further investigation mainly to determine gender related differences with respect to mathematics achievement, retention and interest.

90

CHAPTER THREE

RESEARCH METHOD

This chapter discussed the procedures and strategies adopted to achieve the purpose of the study. The procedures and strategies included: the design of the study, area of the study, population for the study, sample and sampling techniques, instruments for the study, validation of the instruments, reliability of the instruments, treatment/experimental procedures, control of extraneous variables, method of data collection and method of data analysis.

Design of the Study

The research design for this study was quasi-experimental. Quasi-experimental design is relatively easier to carry out than true experiment because it lends itself to use of measurement materials which yield precision and objectivity, Denga and Ali (1998). Specifically, the study was a non-equivalent control group design. The design was considered most appropriate because variables such as achievement, retention and interest lend themselves to the use of measurement materials which yield precision and objectivity. Also, intact classes were used instead of randomly composed samples. Also in this design, there was no random assignment of participants (subjects) to the experimental and control groups. (McMillan; 2012: 227). The use of intact classes were to ensure non alteration of regular periods since Rivers State Senior Secondary Schools Board does not allow alteration of lesson periods.

The study used one treatment group and one control group. The design was presented diagrammatically as shown below.

E: O
x O

C: O
− x O

Source: Nworgu (2015: 114).

Where: E stands for experimental group

C stands for control group

90

91

O1 stands for first observation or pre test

O2 stands for second observation or post test.

X stands for treatment or experimental variable.

-X stands for the control variable or no treatment.

Area of the Study

This study was carried out in Andoni Education Zone of Rivers state of Nigeria. Rivers state is situated in the southern part of the country and one of the states of the South - South geopolitical zone. Students in the state do perform very poorly in external examinations in science subjects especially mathematics as indicated in WASSCE Results 2007-2011 of Schools in Rivers

State-appendix J3 on page 220. Similarly, Andoni Local Government Area records poor achievement of students in Mathematics in Senior School Certificate Examinations (SSCE) year after year as shown in the WASSCE Results of 2007-2011 of Schools in Rivers State and for this reason, the area was chosen for this study.

Andoni Local Government Area of the State where the study was conducted is located very close to the Atlantic Ocean and comprises of rural communities. The major occupation of the people is fishing. The Local Government Area has twelve (12) senior secondary schools altogether that are public and co-educational. All the schools in Andoni Local Government Area have similar characteristics such as: being all co-educational, having about the same teacher/students ratio and using the same mathematics textbook. Besides, the students in both experimental and control groups shared a common environment.

Population for the Study

The target population is two thousand, five hundred and eighteen (2518) senior secondary one (SSI) students of 2014/2015 academic session in all the twelve (12) senior co-educational public secondary schools in Andoni Education Zone of Rivers State (Ministry of Education, Port

92

Harcourt, 2014) on page 230. The SSI students were used because the students were in the foundation stage of the senior school contact with the topics in geometry.

Sample and Sampling Technique

A sample size of two hundred (200) students was used for the study. A purposive sampling technique was employed to sample four (4) co-educational schools that have the highest population of Two hundred (200) students and above and with a minimal difference between the number of male and female students. Out of the four schools selected, the first two schools selected were randomly assigned to Fishing Tools Treatment Group (FTTG) and the other two were for the

Control Group (CG). G.S.S Ngo had five (5) classes, C.S.S Agwut Obolo had four (4) classes,

C.S.S Ekede had three (3) classes, and C.S.S Unyeada had four (4) classes. Altogether, there were sixteen (16) classes. Numbers 1-50 were written on ballot papers and others without any number.

The papers were folded and reshuffled very well before dropping in a bag for students to pick.

Thus, in each school, an intact class was drawn through simple random sampling technique. That is, simple balloting was used to select the intact classes from the schools.

Instruments for Data Collection

Two research instruments were used, namely;

(i) Geometry Achievement test (GAT) and geometry retention test (GRT)

(ii) Geometry Interest Scale (GIS)

Development of Geometry Achievement and Retention Tests

The Geometry Achievement Test (GAT) consisted of 50 multiple choice items which were developed by the researcher based on the geometry content/area which were taught during lessons

(Appendix A on pages 144-150).

The geometry contents taught were:

(i) Identification and properties of a rectangle, rhombus and other plane shapes.

(ii) Word problems involving rectangles, rhombuses and other plane shapes.

93

(iii) Identification and properties of a cylinder, pyramid and other solid shapes.

(iv) Word problems involving cylinders, pyramids and other solid shapes.

The Geometry Achievement Test (GAT) was administered both as pre-test and post-test. The

Pre-Geometry Achievement Test (Pre-GAT) was used to establish the level of Geometry

Achievement of the students before treatment. The Post-Geometry Achievement Test (Post-GAT) which was not different in content but different in organization from Pre-GAT was used to determine the extent of students’ Geometry Achievement after the students must have been exposed to fishing tools instructional approach. The Geometry Retention Test (GRT) was the same as the GAT but different in organization (Appendix B on pages 151-157). The GRT was used to determine the extent of the learnt materials that were retained after some time. Geometry Retention

Test (GRT) was administered to the two groups two weeks after the Post Geometry Achievement

Test (Post GAT) had been administered to assess the retention level of the students. Though short, the period of two weeks was considered because the researcher did not want to disrupt the affected schools activities further for the term.

To develop the instruments, a test blueprint or table of specification was constructed using the four units to be taught during the period of the study. The table of specification is presented in

Appendix K on page 219.

The items of the instruments were based on SS1 Mathematics identified in the New General

Mathematics Book 1on pages 145-155 by Macrae, Kalejaiye, Chima, Garba, Ademosu, Channon,

Smith and Head (2011). These identified units were drawn from Senior Secondary Schools

Mathematics Curriculum for SS1 (Federal Ministry of Education (FME), 2007)). These identified units were also drawn from past WAEC questions on these topics since questions are what students will be exposed to, at the end of their work in the Senior School Certificate Examination (SSCE).

The basic guiding principle that was employed in developing the test blue print were objectives of the content areas considered in the study.

94

The items of the instruments were developed to cover lower order questions on knowledge and comprehension of the cognitive domain and questions involving higher thinking processes covering application, and analysis, leaving synthesis and evaluation. Since the subjects of this study are SS1 students, and the test items are multiple choice type, only four levels of the cognitive domain of Bloom’s Educational Taxonomy are applicable (Sidhu, 2007: 87), namely: knowledge, comprehension, application and analysis.

Geometry Interest Scale (GIS)

The Geometry Interest Scale (GIS) was adapted from Aiken (1963) Mathematics Interest

Scale. This instrument was adapted in this study with some modifications. The GIS contained thirty (30) item interest scales. The instrument covered the four (4) dimensions of interest identified by Baggaley (1973). The dimensions are enjoyment in geometry, leisure in geometry, normality of mathematics and career interest in mathematics. This instrument was designed to assess students’ interest in geometry.

GIS was administered before the start of the experiment to determine the initial level of interest students had in geometry and the experiment was to find out to what extent students’ interest had been influenced by the treatment. In GIS, subjects were instructed to place a tick (√) in the column which best indicated their opinion on a 4-point Likert Scale ranging from Strongly

Agree (4), Agree (3), Disagree (2), to Strongly Disagree (1) in positive statements and Strongly

Disagree (4) to Strongly Agree (1) in negative statements. A student’s score was therefore the sum of the weighted alternatives he had selected. (Appendices E and F on pages 160 and 161).

Validation of the Instrument

The instruments were validated by adopting the following procedures during the study. The test-blue print was face validated by three experts in measurement and evaluation, and three (3) experts in mathematics education. The achievement test was also subjected to validation by the same experts’ specified above. The validation exercise was conducted in the following manner.

95

Copies of the title of the study, purpose of the study, research questions, hypotheses, the test blue print and the achievement test were sent to the above specified experts. These experts were requested to do the following:

(i) See whether the questions test the objectives of the lesson;

(ii) See whether the clarity of questions was ensured and the language appropriate to

class level;

(iii) Check whether the instruments were relevant and appropriate to the age and level of

students to be tested;

(iv) Add any other useful information which might help to ensure the validity of the

instruments.

The lesson plans, marking guides/schemes and achievement tests were sent to three (3) senior secondary school mathematics teachers for vetting and validation respectively. The 30 items in the original instrument of GIS after face validation by experts reduce to the 20 items that were used for this study. These teachers were requested to check the adequacy of the lesson plans with regard to the attainment level of the students and vet the marking guide. The advice of the experts and those of the teachers helped the researcher to delete, modify and select the final set of test items for the study. For example, there were sixty (60) items for validation in each parallel test initially, some of the items were grouped as lower order and vice versa. At the end of the exercise, fifty (50) items for each test were selected for study.

Reliability of the Instruments

The instruments for the study GAT, GRT and GIS were subjected to a trial testing to ascertain their reliability. The instruments were administered by the researcher to SS1 students of

Community Secondary School, Kalabiama, a co-educational secondary school situated in same environment where the study was carried out but was not involved in the study. Thirty (30) students altogether drawn randomly from Community Secondary School, Kalabiama in

96

Opobo/Nkoro Local Government Area of Rivers State were involved in trial testing the instruments.

The scores obtained from the trial testing were used to determine the internal consistency reliability co-efficient of the instruments. The internal consistency of GAT was determined using

Kuder-Richardson formula 20, (K – R 20). The internal consistency reliability co-efficient of GRT was also determined using the formula 20, (K –R20) while the internal consistency reliability index of GIS was determined using Cronbach Alpha (Appendix I on pages 211-215).

Kuder Richardson formula was used because the test items (GAT and GRT) were of multiple-choice types. The internal consistency reliability co-efficient of GAT was 0.82 and that of

GRT was 0.80.

The internal consistency of GIS was determined from the data collected from trial testing using Cronbach Alpha. This index was found to be 0.88. The necessary reliability co-efficient of the instruments were thus determined.

Experimental (Treatment) Procedures

The regular mathematics teachers of the selected schools for the study were coordinated to assist in the study. This was done for one week before the commencement of the study. The coordination exercise was based on: The purpose of the study, the content areas to be taught and the use of the lesson plans for the conduct of the study.

For the four regular mathematics teachers that were coordinated, one taught the treatment group (Fishing Tools) in each of the two schools, while the teachers were advised to observe the normal class-room procedures in each of the two schools for the control group. The teachers were advised to use the same length of time (four weeks) to teach the content to the groups.

Two instrumental approaches were used for this study; the first approach involved the use of fishing tools instructional approach while the second approach made use of conventional

(lecture) method of teaching the selected geometrical shapes. The two methods are identical in

97 terms of contents, basic instructional objectives and mode of evaluation. The only difference was in the instructional approach. The fishing tools instructional approach was used for the experimental group while the conventional method was used for the control group. Students in both experimental and control groups were given the pre-test on GAT and GIS before the experiment by their respective regular mathematics teachers. After the pre-test, the trained regular teachers for the study commenced the experiment in their respective schools adhering strictly to the lesson plans which were developed by the researcher and discussed during the training session that was conducted by the researcher.

The experiment was conducted during the normal school periods following the time table for four weeks. Each week contains five periods of forty minutes per period. This implies a total of twenty (20) periods (Appendices G and H on lesson plans on pages 162-210).

At the end of the experiment which lasted for four weeks, the teachers administered the post achievement test and GIS to the subjects in the two groups. Also, a delayed post test (retention test) was administered to the two groups two weeks after the post test had been administered to assess the retention level of the students.

Control of Extraneous Variables

The researcher adopted the following measures to ensure that extraneous variables which might introduce bias into the study were controlled.

Teachers’ Variable

In order to ensure that errors coming from teachers’ variables would not interfere with the findings of this study, the researcher organized a one week coordination exercise for the regular mathematics teachers of the classes that were selected from schools sampled for the study. Separate coordination was organized for mathematics teachers in the treatment and control groups. The coordination helped in establishing a common instructional standard among the mathematics teachers. The topics for the study were also treated in details during coordination. The researcher

98 used this coordination period to detect individual problems of the teachers that might introduce errors to the study. A regular supervision was made by the researcher during the period of the experiment, to ensure that the teachers did not deviate from the agreed pattern of instruction.

Instructional Situation Variable

Instructional situation was the same for all the groups, since intact classes from SS1 students were used and lesson plans bearing the same contents were also used. More so, the researcher issued out instructional guides to the teachers in all the groups. Teaching and testing were conducted in all the classes of SS1 in the various schools selected for the study and not just the intact classes drawn. This helped to avoid Hawthorne effect (a situation in which research subjects’ behaviours are affected not by the treatment per say, but by the subjects’ knowledge of participation in the study) and novelty effect (a situation where the subjects develop a sudden increase of interest, motivation or participation simply because the subjects are doing something different). Pre-test, post-test, delayed post test and GIS were administered to all the classes of SS1 students in the schools selected, but data for the study were restricted to the intact classes drawn for the study. The study was only restricted to four (4) intact classes of four (4) schools namely:

Government Secondary School, Ngo, Community Secondary School, Agwut Obolo, Community

Secondary School, Ekede and Community Secondary School, Unyeada.

Inter Group Variable

Since intact classes were used for the study, the inter group variable that would have been introduced as a result of intact classes was controlled by using analysis of co-variance (ANCOVA) for data analysis. This would correct the initial difference among the research students.

Subject Interaction

To avoid the possible interaction between the experimental and control groups, the researcher made sure one group was selected from each school participating. Mathematics teacher was also strongly instructed not to give test of any kind; not to give any assignment until the end of

99 the experiment. This helped to reduce the errors that would arise from interactions and exchange of ideas among research subjects from the two groups in the same school or home.

Instructional Variable

The variables that might be introduced as a result of misinterpretations of the instruments for data collection by the subjects were removed by trial testing the instruments before actual experimentation. Any ambiguity found was removed; the instruments used were validated by experts in the field.

Method of Data Collection

The Pre-Geometry Achievement Test (PRE-GAT) and the Geometry Interest Scale (GIS) were administered to the students in the two groups before the commencement of the experiment and no feedback on the test was given to the students. Scores of the students were recorded and kept aside for use after the experiment by the researcher. At the end of the experiment, post-test on

Geometry Achievement Test (POST-GAT) and Geometry Interest Scale (POST-GIS) were administered to the experimental and control groups. For each of the groups, data of pre-test and post-test were recorded separately. The delayed post-test (retention test) was administered two weeks after the post-test on GAT had been administered. The Geometry Achievement Test (GAT) and Geometry Retention Test (GRT) were scored out of a maximum mark of a 100% and a minimum of zero (0) using the marking guides (Appendices C and D for marking guides on pages

158 and 159).

Method of Data Analysis

Data collected were analyzed with respect to research questions and hypotheses formulated for the study. The six research questions were answered by computing the means and the standard deviations of the experimental and control group scores.

The analysis of covariance (ANCOVA) was used to test the nine hypotheses at P < 0.05 probability level.

100

CHAPTER FOUR

RESULTS

This chapter is concerned with the presentation of results from data analysis. The results are presented in tables according to the research questions and hypotheses that guided the study.

Research Question 1: What are the mean achievement scores of students taught geometry of two-and three-dimensional objects using the fishing tools instructional approach and those taught with conventional (lecture) method?

Table 1: Mean and Standard deviation of pretest and post test scores of students taught geometry of two- and three-dimensional objects using the fishing tools instructional approach and those taught with conventional (lecture) method.

Variable Pre test Posttest Mean gain N
̅ SD
̅ SD FTIA 100 14.40 4.09 35.35 7.12 20.95 Lecture method 100 14.12 4.01 14.48 2.57 0.36

The result presented in Table one (1) shows that, the students taught geometry of two- and three-dimensional objects using the fishing tools instructional approach (experimental group) had a pretest mean of 14.40 with a standard deviation of 4.09 and a post test mean of 35.35 with a standard deviation of 7.12. The difference between the pretest and posttest mean for the group taught using fishing tools instructional approach was 20.95. The group taught geometry of two- and three-dimensional objects using lecture method (control group) had a pretest mean of 14.12 with a standard deviation of 4.01 and a post test mean of 14.48 with a standard deviation of 2.57. The difference between the pretest and post test mean for the control group was 0.36. For each of the groups, the post test means were greater than the pretest mean with the experimental group having a higher mean gain.

100 101

Research Question 2: What are the mean retention scores of the students taught geometry of two - and three-dimensional objects using the fishing tools instructional approach and those taught with conventional (lecture) method?

Table 2: Mean and Standard deviation of retention scores of the students taught geometry of two - and three-dimensional objects using the fishing tools instructional approach and those taught with conventional (lecture) method.

Variable Posttest score Retention score Mean gain N
̅ SD
̅ SD FTIA 100 35.35 7.12 36.02 6.99 0.67 Lecture method 100 14.48 2.57 14.56 2.59 0.08

The result presented in Table two (2) shows that, the students taught geometry of two- and three-dimensional objects using the fishing tools instructional approach (experimental group) had a post test mean of 35.35 with a standard deviation of 7.12 and a retention mean of 36.02 with a standard deviation of 6.99. The difference between the post test and the retention for the group taught using fishing tools instructional approach was 0.67. The group taught geometry of two-and three-dimensional objects using lecture method (control group) had a post test mean of 14.48 with a standard deviation of 2.57 and a retention mean of 14.56 with a standard deviation of 2.59. The difference between the post test mean and retention mean for the control group was 0.08. For each of the groups, the retention means were greater than the post test mean with the experimental group having a higher mean gain.

Research Question 3: What are the mean interest scores of students taught geometry of two- and three-dimensional objects using the fishing tools instructional approach and those taught with conventional (lecture) method?

102

Table 3: Mean and Standard deviation of interest scores of students taught geometry of two-and three-dimensional objects using the fishing tools instructional approach and those taught with conventional (lecture) method.

Variable Pre test Posttest Mean gain N
̅ SD
̅ SD FTIA 100 50.02 9.64 64.50 5.36 14.48 Lecture method 100 49.02 9.76 51.25 4.34 2.23

The result presented in Table three (3) shows that, the students taught geometry of two- and three-dimensional objects using the fishing tools instructional approach (experimental group) had a pretest interest mean of 50.02 with a standard deviation of 9.64 and a post test mean of

64.50 with a standard deviation of 5.36. The difference between the pretest and post test interest mean for the group taught using fishing tools instructional approach was 14.48. The group taught geometry of two- and three-dimensional objects using lecture method (control group) had a pretest interest mean of 49.02 with a standard deviation of 9.76 and a post test mean of 51.25 with a standard deviation of 4.34. The difference between the pretest and post test interest mean for the control group was 2.23. For each of the groups, the post test interest means were greater than the pretest interest means with the experimental group having a higher mean gain.

Research Question 4: What are the mean achievement scores of male and female students taught geometry of two and three-dimensional objects using fishing tools instructional approach?

Table 4: Mean and Standard deviation of mean achievement scores of male and female students taught geometry of two-and three-dimensional objects using fishing tools instructional approach. Variable Pre test Posttest Mean gain Mean difference Gender N
̅ SD
̅ SD Male 52 14.92 3.75 36.96 7.81 22.04 Female 48 13.83 4.40 33.60 5.84 19.77 2.27

103

The result presented in Table four (4) shows that, the male group had a pretest mean of 14.92 with a standard deviation of 3.75 and a post test mean of 36.96 with a standard deviation of

7.81. The difference between the pretest and post test mean for male group is 22.04. The female group had a pretest mean of 13.83 with a standard deviation of 4.40 and a post test mean 33.60 with a standard deviation of 5.84. The difference between the pretest and post test means for female group is 19.77. For each of the two groups, the post test achievement means were greater than the pretest achievement means with the male group having higher mean achievement score of 3.36.

Research Question 5: What are the mean retention scores of male and female students taught geometry of two- and three-dimensional objects using fishing tools instructional approach?

Table 5: Mean and Standard deviation of retention scores of male and female students taught geometry of two-and three-dimensional objects using fishing tools instructional approach. Variable Post test Retention score Mean gain Mean difference Gender N
̅ SD
̅ SD Male 52 36.96 7.81 38.46 7.90 1.50 Female 48 33.60 5.84 34.46 5.53 0.86 0.64

The result presented in Table five (5) shows that, the male group had a post test mean of

36.96 with a standard deviation of 7.81 and a retention mean of 38.46 with a standard deviation of 7.90. The difference between the post test mean and retention mean for male group was 1.50. The female group had a post test mean of 33.60 with a standard deviation of

5.84 and a retention mean of 34.46 with a standard deviation of 5.53. The difference between the post test mean and retention mean for female group was 0.86. For the male group, the retention mean was higher than the post test mean while the female group, the retention mean was also higher than the post test mean. The difference between the mean retention score of

104 the male group and that of female group is 4.00 with the male group having higher mean retention score.

Research Question 6: What are the mean interest scores of male and female students taught geometry of two-and three-dimensional objects using fishing tools instructional approach?

Table 6: Mean and Standard deviation of interest scores of male and female students taught geometry of two-and three-dimensional objects using fishing tools instructional approach. Variable Pretest score Posttest Score Mean gain Gender N
̅ SD
̅ SD Male 52 57.38 3.76 65.08 5.49 7.70 Female 48 42.04 7.45 63.87 5.21 21.83

The result presented in Table six (6) shows that, the male group had a pretest interest mean of

57.38 with a standard deviation of 3.76 and a post test interest mean of 65.08 with a standard deviation of 5.49. The difference between the pretest and post test interest means for male group was 7.70. The female group had a pretest interest mean of 42.04 with a standard deviation of 7.45 and a post test interest mean 63.87 with a standard deviation of 5.21. The difference between the pretest and post test interest means for female group was 21.83. For each of the two groups, the post test interest means were greater than the pretest interest means with the female group having higher mean gain.

Hypothesis 1: There is no significant difference in the mean achievement scores of students taught geometry of two-and three-dimensional objects using the fishing tools instructional approach and those taught with conventional (lecture) method.

105

Table 7: Analysis of Covariance (ANCOVA) of the mean achievement scores of students taught geometry of two-and three-dimensional objects using the fishing tools instructional approach and those taught with conventional (lecture) method. Type III Sum Source of Squares df Mean Square f Sig. Corrected Model 25938.216a 4 6484.554 846.752 .000 Intercept 1222.611 1 1222.611 159.648 .000 Pretest Achievement 3842.869 1 3842.869 501.801 .000 Methods 20973.914 1 20973.914 2.739E3 .000 Gender 38.649 1 38.649 5.047 0.03 Methods * Gender 79.954 1 79.954 10.440 .001 Error 1493.339 195 7.658 Total 151583.000 200 Corrected Total 27431.555 199 a. R Squared = .946 (Adjusted R Squared = .944)

The result in Table seven (7) shows that an f-ratio of 2.739 with associated probability value of 0.00 was obtained with regards to the mean achievement scores of students taught geometry of two-and three-dimensional objects using the fishing tools instructional approach and those taught with conventional (lecture) method. Since the associated probability (0.00) was less than 0.05 set as level of significance, the null hypothesis (H01) which stated that there is no significant difference in the mean achievement scores of students taught geometry of two-and three-dimensional objects using the fishing tools instructional approach and those taught with conventional (lecture) method was rejected. Thus, there was a significant difference in the mean achievement scores of students taught geometry of two-and three- dimensional objects using the fishing tools instructional approach and those taught with conventional (lecture) method with those taught using fishing tools instructional approach having a higher mean gain.

Hypothesis 2: There is no significant difference in the mean retention scores of students taught geometry of two-and three-dimensional objects using the fishing tools instructional approach and those taught with conventional (lecture) method.

106

Table 8: Analysis of Covariance (ANCOVA) of the mean retention scores of students taught geometry of two-and three-dimensional objects using the fishing tools instructional approach and those taught with conventional (lecture) method. Type III Sum of Source Squares df Mean Square f Sig. Corrected Model 28471.998a 4 7118.000 2.1294 .000 Intercept 4.528 1 4.528 13.547 .000 Posttest score 5182.094 1 5182.094 1.5504 .000 Retention 8.007 1 8.007 23.955 .000 Gender 7.872 1 7.872 19.575 .003 Methods * 1.569 1 1.569 4.694 .031 Gender Error 65.182 195 .334 Total 156454.000 200 Corrected Total 28537.180 199 a. R Squared = .998 (Adjusted R Squared = .998)

The result in Table eight (8) shows that an f-ratio of 23.955 with associated probability value of 0.00 was obtained with regards to the mean retention scores of students taught geometry of two-and three-dimensional objects using the fishing tools instructional approach and those taught with conventional (lecture) method. Since the associated probability (0.00) was less than 0.05 set as level of significance, the null hypothesis (H02) which stated that there is no significant difference in the mean retention scores of students taught geometry of two-and three-dimensional objects using the fishing tools instructional approach and those taught with conventional (lecture) method was rejected. Thus, there was a significant difference in the mean retention scores of students taught geometry of two- and three-dimensional objects using the fishing tools instructional approach and those taught with conventional (lecture) method with those taught using fishing tools instructional approach having a higher mean gain.

107

Hypothesis 3: There is no significant difference in the mean interest scores of students taught geometry of two-and three-dimensional objects using the fishing tools instructional approach and those taught with conventional (lecture) method. Table 9: Analysis of Covariance (ANCOVA) of the mean interest scores of students taught geometry of two-and three-dimensional objects using the fishing tools instructional approach and those taught with conventional (lecture) method. Type III Sum Source of Squares df Mean Square f Sig. Corrected Model 11018.328a 4 2754.582 217.155 .000 Intercept 3385.850 1 3385.850 266.921 .000 Pretest interest 1229.145 1 1229.145 96.899 .000 Methods 8247.203 1 8247.203 650.161 .000 Gender 171.312 1 171.312 13.505 .000 Methods * Gender 281.146 1 281.146 22.164 .000 Error 2473.547 195 12.685 Total 683395.000 200 Corrected Total 13491.875 199 a. R Squared = .817 (Adjusted R Squared = .813)

The result in Table nine (9) shows that an f-ratio of 650.161 with associated probability value of 0.00 was obtained with regards to the mean interest scores of students taught geometry of two-and three-dimensional objects using the fishing tools instructional approach and those taught with conventional (lecture) method. Since the associated probability (0.00) was less than 0.05 set as level of significance, the null hypothesis (H03) which stated that there is no significant difference in the mean interest scores of students taught geometry of two-and three-dimensional objects using the fishing tools instructional approach and those taught with conventional (lecture) method was rejected. Thus, there was a significant difference in the mean interest scores of students taught geometry of two-and three-dimensional objects using the fishing tools instructional approach and those taught with conventional (lecture) method.

108

Hypothesis 4: There is no significant difference in the mean achievement scores of male and female students taught geometry of two-and three-dimensional objects using the fishing tools instructional approach.

The result for this hypothesis is presented in Table seven (7)

The result in Table seven (7) shows that an f-ratio of 5.047 with associated probability value of 0.03 was obtained with regards to the mean achievement scores of male and female students taught geometry of two-and three-dimensional objects using the fishing tools instructional approach. Since the associated probability (0.03) was less than 0.05 set as level of significance, the null hypothesis (H04) which stated that there is no significant difference in the mean achievement scores of male and female students taught geometry of two-and three- dimensional objects using the fishing tools instructional approach was rejected. Inference drawn therefore is that there was a significant difference in the mean achievement scores of male and female students taught geometry of two-and three-dimensional objects using the fishing tools instructional approach.

Hypothesis 5: There is no significant difference in the mean retention scores of male and female students taught geometry of two and three-dimensional objects using the fishing tools instructional approach.

The result for this hypothesis is presented in Table eight (8).

The result in Table eight (8) shows that an f-ratio of 19.575 with associated probability value of 0.00 was obtained with regards to the mean retention scores of male and female students taught geometry of two-and three-dimensional objects using the fishing tools instructional approach. Since the associated probability (0.00) was less than 0.05 set as level of significance, the null hypothesis (H05) which stated that there is no significant difference in the mean retention scores of male and female students taught geometry of two-and three- dimensional objects using the fishing tools instructional approach was rejected. Inference

109 drawn therefore is that there was a significant difference in the mean retention scores of male and female students taught geometry of two-and three-dimensional objects using the fishing tools instructional approach.

Hypothesis 6: There is no significant difference in the mean interest scores of male and female students taught geometry of two-and three-dimensional objects using the fishing tools instructional approach.

The result for this hypothesis is presented in Table nine (9).

The result in Table nine (9) shows that an f-ratio of 13.505 with associated probability value of 0.00 was obtained with regards to the mean interest scores of male and female students taught geometry of two-and three-dimensional objects using the fishing tools instructional approach. Since the associated probability (0.00) was less than 0.05 set as level of significance, the null hypothesis (H06) which stated that there is no significant difference in the mean interest scores of male and female students taught geometry of two-and three- dimensional objects using the fishing tools instructional approach was rejected. Inference drawn therefore is that there was a significant difference in the mean interest scores of male and female students taught geometry of two-and three-dimensional objects using the fishing tools instructional approach.

Hypothesis 7: There is no significant interaction effect between fishing tools instructional approach and gender on students’ achievement in geometry of two-and three-dimensional objects.

The result for this hypothesis is presented in Table seven (7).

The result in Table seven (7) shows that an f-ratio of 10.44 with associated probability value of 0.00 was obtained with regards to the interaction effect between method and gender on students’ achievement in geometry of two-and three-dimensional objects. Since the associated probability (0.00) was less than 0.05, the null hypothesis (H07) was rejected. Thus,

110

there was a significant interaction effect between fishing tools instructional approach and

gender on students’ achievement in geometry of two- and three-dimensional objects.

Hypothesis 8: There is no significant interaction effect between fishing tools instructional

approach and gender on students’ retention in geometry of two-and three-dimensional

objects.

The result for this hypothesis is presented in Table eight (8).

The result in Table eight (8) shows that an f-ratio of 4.694 with associated probability value

of 0.03 was obtained with regards to the interaction effect between method and gender on

students’ retention in geometry of two-and three-dimensional objects. Since the associated

probability (0.03) was less than 0.05, the null hypothesis (H08) was rejected. Thus, there was

a significant interaction effect between fishing tools instructional approach and gender on

students’ retention in geometry of two-and three-dimensional objects.

Hypothesis 9: There is no significant interaction effect between fishing tools instructional

approach and gender on students’ interest in geometry of two- and three-dimensional objects.

The result for this hypothesis is presented in Table nine (9).

The result in Table nine (9) shows that an f-ratio of 22.164 with associated probability value

of 0.00 was obtained with regards to the interaction effect between method and gender on

students’ interest in geometry of two- and three-dimensional objects. Since the associated

probability (0.00) was less than 0.05, the null hypothesis (H09) was rejected. Thus, there was

a significant interaction effect between fishing tools instructional approach and gender on

students’ interest in geometry of two- and three-dimensional objects.

Summary of Findings

The summary of the findings is presented below:

1. There was a significant difference in the mean achievement scores of students taught

geometry of two-and three-dimensional objects using the fishing tools instructional

111

approach and those taught with conventional (lecture) method with those taught using

fishing tools instructional approach having a higher mean gain. This is indicative that

fishing tools instructional approach improved students achievement in geometry of two-

and three- dimensional objects.

2. There was a significant difference in the mean retention scores of students taught geometry

of two-and three-dimensional objects using the fishing tools instructional approach and

those taught with conventional (lecture) method with those taught using fishing tools

instructional approach having a higher mean gain. This means that fishing tools

instructional approach improved students’ retention in geometry of two- and three-

dimensional objects.

3. There was a significant difference in the mean interest scores of students taught geometry

of two-and three-dimensional objects using the fishing tools instructional approach and

those taught with conventional (lecture) method with those taught using fishing tools

instructional approach having a higher mean gain. This is indicative that fishing tools

instructional approach improved students’ interest in geometry of two- and three-

dimensional objects.

4. There was a significant difference in the mean achievement scores of male and female

students taught geometry of two-and three-dimensional objects using the fishing tools

instructional approach. This is indicative that fishing tools instructional approach appears

to have improved the achievement scores of both male and female students.

5. There was a significant difference in the mean retention scores of male and female

students taught geometry of two-and three-dimensional objects using the fishing tools

instructional approach. This is indicative that fishing tools instructional approach appears

to have improved the retention scores of both male and female students.

112

6. There was a significant difference in the mean interest scores of male and female students

taught geometry of two-and three-dimensional objects using the fishing tools instructional

approach. This is indicative that fishing tools instructional approach appears to have

improved the interest score of female students more than their male counterparts.

7. There was a significant interaction effect between fishing tools instructional approach and

gender on students’ achievement in geometry of two-and three-dimensional objects. This

means that there was an interaction between fishing tools instructional approach and

gender on students’ achievement in geometry of two- and three- dimensional objects.

8. There was a significant interaction effect between fishing tools instructional approach and

gender on students’ retention in geometry of two-and three-dimensional objects. The

findings showed that there was an interaction between fishing tools instructional approach

and gender on students’ retention in geometry of two- and three- dimensional objects.

9. There was a significant interaction effect between fishing tools instructional approach and

gender on students’ interest in geometry of two-and three-dimensional objects. This means

that there was an interaction between fishing tools instructional approach and gender on

students’ interest in geometry of two- and three- dimensional objects.

113

CHAPTER FIVE

DISCUSSION, CONCLUSION AND SUMMARY

This chapter was organized under the following headings: discussion of findings, conclusion, educational implications, recommendations; limitations of the study; suggestions for further studies and summary of the study.

Discussion of Findings

The findings were discussed under the following subheadings:

v Students’ achievement in geometry

v Students’ retention in geometry

v Students’ interest in geometry

v Influence of gender on students’ achievement in geometry

v Students’ retention and interest in geometry due to gender.

v Interaction effects of method and gender on achievement, retention, and interest of students in geometry.

Students’ Achievement in Geometry

In Table one (1), the mean achievement score of the experimental group in post test is higher than the post test mean achievement score of the control group. This indicated that the use of fishing tools instructional approach in teaching geometry of two-and three-dimensional shapes improved students’ achievement in geometry.

This higher achievement may have been due to the fact that students were taught geometry of two-and three-dimensional shapes, using fishing tools instructional approach, which allowed the students to participate more effectively in the teaching and learning process. The result was confirmed by the result on Table seven (7), which revealed that the method was a significant factor on students’ achievement in geometry. Hence, students who were taught geometry of two-and three-dimensional shapes using fishing tools instructional

113 114 approach achieved higher than those taught using the conventional (lecture) method. The implication of this is that, the instructional approach used in teaching geometry can produce differential effects on students with respect to geometry achievement. This positive and higher achievement may have been as a result of the active and cooperative participation of the students due to the fact that the approach used was practical in nature, from the learner’s environment, project-oriented and therefore, ensured students’ activity. This confirms the views of Obodo (2004), Kurumeh (2004, 2007), and Uka (2006), who averred that teaching method should be practical, applicable and project oriented.

The findings of this study also support the findings of other previous researchers such as Ogbonna, (2004, 2007), and Kurumeh (2004, 2007), where experimental groups proved better than the control group. The above researchers used the constructivist and ethno- mathematics instructional approaches respectively. This finding equally agrees with other previous and similar study (Adekanye, 2008), who confirmed that appropriate method and instructional materials lead to students’ improvement in mathematics in general and geometry in particular. The use of this innovative instructional approach (Fishing Tools) must have helped the students to develop self-confidence and enthusiasm in solving problems in geometry. This type of exposure to practical and applicability of mathematics/geometry in concrete situation and learner’s cultural background made geometry easy to understand thereby resulting in higher achievement. This agreed with the findings of Kurumeh (2004,

2007) and Uka (2006).

Moreover, this active involvement of students may also have given rise to efficient learning that accounted for the observed significant effect in achievement in geometry of two-and three-dimensional shapes. This gain is in line with ethno-mathematics approach which is practical, learner-oriented, active and applicable to the local environment. The control group on the other hand may not have seen anything different in their teachers’

115 method of teaching geometry of two-and three-dimensional shapes at their present level of education with that of the previous level.

Students’ Retention in Geometry

Results of the study show that the students in the experimental group obtained higher mean retention score than those in the control group (Table 2). The mean retention score

(36.02) of the experimental group in table 2, is higher than that of the control group (14.56).

This was further confirmed by the ANCOVA result (Table 8) which shows that the experimental group significantly retained higher than the control group in the geometry of two-and three-dimensional objects taught using fishing tools instructional approach. The finding of this study is in accordance with those of Iji (2003), Ogbonna (2007), and Eze

(2008), who confirmed that the use of new practical approaches enhances students’ retention.

While Iji (2003), explored the effects of logo and basic programs on achievement and retention in geometry of junior secondary school students, Ogbonna (2007), explored the effects of two constructivist instructional models on students’ achievement and retention in number and numeration. The result of the study of Iji (2003), revealed that the students taught with LMP and BPM achieved higher than those taught with CPM. In the same vein, the result of the study of Ogbonna (2007), revealed that the use of IET and TLC constructivist instructional models enhanced significantly students’ achievement and retention in

Mathematics.

Also Anyor and Iji(2014), worked on the effect of integrated curriculum delivery, strategy on secondary school students’ achievement and retention in Algebra in Benue State,

Nigeria. The study found among other things, that integrated curriculum delivery strategy

(ICDS) enhanced students’ achievement and retention in the Algebra taught during the period of the study. The findings of these studies, are in agreement with that of the present study.

116

Students’ Interest in Geometry

The result in Table three (3) shows that the mean interest score of the students in the experimental group is almost the same as the mean interest score of those in the control group at PRE GIS. But at POST GIS, the mean interest score of the students in the experimental group is higher than that of the control group. This is further confirmed by the ANCOVA result (Table 9), which indicates that the experimental group recorded higher interest score than the control group. These findings confirm that the use of fishing tools instructional approach enhances students interest in geometry of two-and three-dimensional objects. The result of this study is also in accordance with other studies such as (Adekanye; 2008;

Kurumeh, 2004; 2007; and Uka, 2006), which confirmed that the use of appropriate instructional approach based on the learner’s cultural background enhances students’ interest in learning.

Moreover, the practical nature of fishing tools instructional approach explains the overall high mean interest score for the experimental group. The approach motivated and sustained students’ interest thereby evoked greater understanding which resulted to higher interest in geometry of two-and three-dimensional objects. Because of the learner’s oriented nature of fishing tools instructional approach, unnecessary fear in mathematics was driven away and geometry of two-and three-dimensional objects becomes meaningful and relevant to the learners. Thus, the teaching and learning process was learner-centred.

Influence of Gender on Students’ Achievement in Geometry

The result shown in Table four (4) reveals that male students recorded higher mean achievement score than the females in experimental post test. The mean difference was not statistically significant as revealed in the ANCOVA result (Table 7). This implies that there was a significant influence in the mean achievement scores of male and female students taught geometry of two-and three-dimensional objects. The finding of the study seems not to

117 agree with those of Ogbonna (2007), Adekanye (2008), whose studies found the females achieving higher than the males in mathematics and geometry.

The result of this present study is also not in compliance with the findings of Utin

(2005), and Ogbonna (2004), which revealed no significant influence of male and

female students’ achievement in mathematics. Still on gender differences and

Mathematics achievement among secondary students in Southern Cross River State,

Meremikwu(2002, 2008), found among other things, that the Mathematics

achievement of girls in single sex school was significantly better than male

counterparts in single sex school. Contributing, Salva(2001), investigated the

comparative effects of attending single sex and co-educational secondary schools on

the female students’ achievement in Mathematics. The findings showed that the

proportions of pass and above grade in Mathematics for boys and girls in co-

educational schools were significantly higher than those of their counterparts in single

sex school.

In another study, Harbour-Peters (2001), asserted that gender issues in Mathematics have been a source of aversion, and that Mathematics has been male-stereotyped since it was regarded as abstract, difficult and has attributes which boys were attracted to. In the same vein, educational researchers like Lassa (2000, 2012), and Steen (2003), for instance, had documented males superiority over females in special ability. Also, Osborne and Dillon

(2010) and Ogunkunle (2009), reported significant difference in favour of boys and indicated that boys have higher Mathematics reasoning ability and performed better. These findings are in agreement with the finding of this present study. However, Haworth, Dale and Plomin

(2008); ASA (2005), reported no significant difference in Mathematics achievement of boys and girls. This supports the findings of Olagunju (1996), who observed no significant

118 differences of male and female students in achievement in Mathematics. On the other hand, these findings are not in compliance with the finding of the present study.

Gender Influence on Students’ Retention and Interest in Geometry

Table five (5) reveals that male students in the experimental group, obtained higher mean retention score than their female counterparts. The Table also reveals that both male and female students in the experimental group improved in their mean retention scores as regards geometry of two-and three-dimensional objects covered during the study. However,

Table eight (8) shows that the gender is not significant in students’ retention as reflected in the outcome of geometry of two-and three-dimensional objects using fishing tools instructional approach.

The result of this study is in line with Iji (2003), who found gender not to be statistically significant in students’ retention in mathematics. On the other hand, the result of the study, does not agree with Ogbonna (2007), who pointed out that the gender was statistically significant in students’ retention in mathematics. The result of no significant difference may be attributed to the influence of fishing tools instructional approach which is practical in nature based on the students’ environment and rooted in the constructivist principles of teaching and learning.

Moreover, the ability of students to discover the relationship between mathematics real world and cultural diversity of daily life activities from the learner’s environment using fishing tools instructional approach, created new learning environment that exposed students to the applicability and practicability of mathematics in concrete situation. Again, both male and female students improved significantly in their mean retention scores as was observed from the difference that existed between the POST GAT and GRT.

On the other hand, Table six (6) revealed that female students have a higher mean interest score in the POST GIS than their male counterparts. The mean difference is however,

119 not statistically significant as revealed in Table 9 at P < 0.05 level of significance. This implies that the use of fishing tools instructional approach helped both female and male subjects to develop interest in geometry. In other words, gender did influence fishing tools instructional approach in geometry of two-and three-dimensional objects. Use of fishing tools instructional approach is culture-based and practical oriented. The finding of this study is in compliance with the suggestion of Davison (in Kurumeh, 2007), who noted that culture based instructions offer a better opportunity for girls education in particular.

Interaction Effects of Method and Gender on Achievement, Retention and Interest in Geometry

The result in Table seven (7) shows that an f-ratio of 10.44 with associated probability value of 0.00 was obtained with regards to the interaction effect between method and gender on students’ achievement in geometry of two-and three-dimensional objects. Since the associated probability (0.00) was less than 0.05, the null hypothesis (H07) was rejected. Thus, there was a significant interaction effect between method and gender on students’ achievement in geometry of two-and three-dimensional objects. The finding of the study is in agreement with Kurumeh (2004, 2007), who found significant interaction effect of ethnomathematics and gender on students’ achievement in geometry and mensuration. This means that fishing tools instructional approach significantly improved the mean achievement scores of both male and female students in geometry of two-and three-dimensional objects.

Similarly, the result in Table eight (8) shows that an f-ratio of 4.694 with associated probability value of 0.03 was obtained with regards to the interaction effect between method and gender on students’ retention in geometry of two-and three-dimensional objects. Since the associated probability (0.03) was less than 0.05, the null hypothesis (H08) was rejected.

Thus, there was a significant interaction effect between method and gender on students’ retention in geometry of two-and three-dimensional objects. The result of this finding is in compliance with Iji (2003), and (Obi, 2014), who found a significant interaction effect of

120 instructional material and gender on students’ retention respectively. The implication of this finding is that, relevant and concrete instructional approach enhances retention, which in turn aids achievement. This means that, fishing tools instructional approach significantly improved the mean retention scores of male and female students in geometry of two-and three-dimensional objects.

In the same vein, the result in Table nine (9) shows that an f-ratio of 22.164 with associated probability value of 0.00 was obtained with regards to the interaction effect between method and gender on students’ interest in geometry of two-and three-dimensional objects. Since the associated probability (0.00) was less than 0.05, the null hypothesis (H09) was rejected. Thus, there was a significant interaction effect between method and gender on students’ interest in geometry of two- and three-dimensional objects. Based on this finding, there is a high interaction between gender and method in interest as was also found by Kurumeh (2004,

2007). It also shows that gender influences method (fishing tools instructional approach) positively and highly since the correlation coefficient is positive. It further implies that if more females and males are taught geometry of two-and three-dimensional objects using this method, their performance will be enhanced and more students will pass. This means that fishing tools instructional approach significantly enhanced the mean interest scores of both male and female students in geometry of two-and three-dimensional objects.

Conclusion

Based on the result obtained, the researcher draws the following conclusion

Fishing tools instructional approach improved students’ achievement in geometry of two-and three-dimensional objects.

Fishing tools instructional approach improved students’ retention in geometry of two- and three-dimensional objects.

121

Fishing tools instructional approach improved students’ interest in geometry of two- and three-dimensional objects.

There was significant influence on male and female students taught geometry of two- and three-dimensional objects on achievement, retention and interest.

There was significant interaction between fishing tools instructional approach and gender on students’ achievement, retention and interest in geometry of two-and three- dimensional objects taught.

Educational Implications of the Study

This study has shed light on the use of Fishing Tools Instructional Approach in the teaching of geometry of two-and three-dimensional objects such as rectangle, square, rhombus, parallelogram, cube, cuboid, cone, cylinder and pyramid.

The study revealed that the use of fishing tools instructional approach significantly enhanced students’ achievement in geometry of two-and three-dimensional objects when compared to the conventional (lecture) method. This study has shown that fishing tools instructional approach promoted students’ retention and interest in geometry of two-and three-dimensional objects.

These findings have far reaching implications for mathematics education. As can be seen from the results of the study, fishing tools instructional approach provides an entirely new strategy (though similar to Ethnomathematics approach) to tackle the problem of students’ low achievement in the subject of mathematics. When adopted, teachers will have an innovative approach in presenting geometry of two-and three-dimensional objects in SS I in such a way and manner that the students will understand it, appreciate it and participate actively in solving geometrical problems without much difficulty.

The study has also shown that the use of fishing tools instructional approach will create uniform learning conditions and awareness of mathematics of the local environment

122 and community (Ethnomathematics) based on the learners’ cultural background for both male and female students. Another obvious implication is that students will show more interest in the study of geometry, thereby increasing the overall achievement in mathematics.

This study is thus a major contribution towards the attainment of the global goal of mathematics for all. The cognitive skills acquired through the Fishing Tools Instructional

Approach, can be applied to other subjects.

Recommendations

The following recommendations are made based on the findings of this research.

(i) Curriculum planners in primary and secondary schools should include fishing tools

instructional approach as one of the necessary instructional approaches to the

teaching of mathematics, especially geometry.

(ii) Teacher training institutions such as institutes of education, faculties of education

and colleges of education should incorporate fishing tools instructional approach in

their courses, mathematics methods to ensure proper training of teachers in the

innovative approach;

(iii) Government through ministry of education should organize public lectures,

seminars and work-shops on fishing tools instructional approach in schools, as a

way of marketing the new approach in teaching and learning process;

(iv) Government and non governmental organizations (NGOs) like multinational

companies and well meaning individuals should sponsor further researches into the

possible application of fishing tools instructional approach in other aspects of

science and technology.

123

Limitations of the Study

The study is constrained by the following limitations:

(i) Even though the researcher trained the mathematics teachers used for the study, whose

academic qualifications are the same, other extraneous variables like teacher personality

and teaching environment may have affected the results of this study.

(ii) Only SS I students were used for the study and in addition, the number of students used

was not large enough when compared with number in the area of study.

(iii) Geometry Retention Test (GRT) was administered to the students two weeks after the

experiment. This period was short and may have affected the results of this study.

Suggestions for Further Study

The following suggestions for further research were made:

(i) A replication of the study using other content areas like prism, sphere, also using

other branches of mathematics like algebra, statistics, among others.

(ii) A study can be conducted to examine the comparative effects of Fishing Tools

Instructional Approach on school location and gender related to achievement,

retention and interest in mathematics.

(iii) Similar investigation needs to be carried out in other states of the federation.

(iv) Efforts should be made to conduct similar research at the primary, junior secondary

school and tertiary levels using other geometrical shapes like prism, sphere,

hemisphere, among others.

Summary of the Study

The study was carried out to determine the efficacy of fishing tools instructional approach and students’ achievement, retention and interest in geometry.

To guide the investigation, six research questions and nine hypotheses were formulated.

124

The study employed non-equivalent control group quasi experimental design involving pre-test, post-test and retention test for both experimental and control groups. Two hundred (200) SSI students (104 males and 96 females) from four public and co-educational secondary schools in Andoni education zone in Rivers State were used for the study. Four intact classes of SS I students of the secondary schools were used. Each of the intact classes was given the opportunity of being assigned randomly to either experimental or control group.

Students in the experimental group were taught geometry of two-and three- dimensional objects using fishing tools instructional approach, while the control group students were taught using the conventional (lecture) method. All the groups were pre-and post tested.

Data were collected using two different instruments. These were:

(i) The Geometry Achievement Test (GAT): This was used for both pre-test and post-

test. The delayed geometry achievement test (DEL GAT), geometry retention test

(GRT); and

(ii) The Geometry Interest Scale (GIS): This was used as both pre-interest and post-

interest scales.

Lesson plans were also developed and used by the researcher. To ensure content validity, a Table of specification was developed. The reliability indices of these three test instruments were established. The reliability indices of GAT (0.82) and DELGAT (0.80) were established using Kuder-Richardson’s formula, while that of GIS (0.88) was found using Cronbach Alpha. To analyze the data of the study, the research questions were answered using mean and standard deviation. The hypotheses were tested using 2-way analysis of covariance (ANCOVA).

125

The result showed that students taught with fishing tools instructional approach achieved higher than those taught with conventional (lecture) method. More so, male and female students in the experimental group improved in their mathematics achievement, retention and interest among others. These results however, have serious implications for mathematics teachers, authors of mathematics textbooks, teacher training institutions and other stakeholders in mathematics education. Recommendations were therefore made based on the highlighted implications. Limitations of the study were also highlighted while suggestions for further studies were made.

126

REFERENCES

Abakpa, B. O & Igwue, D. O. (2013). Effect of mastery learning approach on senior secondary school students’ achievement and interest in geometry in Makurdi, Benue State, Nigeria. ABACUS: The Journal of the Mathematical Association of Nigeria. 38(1), 163 – 176.

Aburime, F (2002). Information technology strategies for relating the curriculum to productive work. A Paper Presented at the 15th Conference of the Curriculum Organization of Nigeria from 17th to 20th September. Alvan Ikoku College of Education, Owerri, Imo State.

Aburime, F. E. (2003). Geometrical manipulative as mathematics resource for effective instruction in junior secondary schools. The Journal of World Council of Curriculum and Instruction (WCCI) Nigeria, 4(2), 73-77.

Aburime, F. E. (2005). Meeting the challenges of mathematics curriculum innovation through production and utilization of geometric manipulations. curriculum and media technology research. A Journal of CUDIMAC, Faculty of Education, University of Nigeria, Nsukka. 1(1), 288 – 295.

Adebayo, O. A (1997). Mathematics as a vehicle of national development. Journal of Education for National Development and International Co-operation. 1(1), 75-81.

Adebayo, O.A (1999). Problems of teaching and learning mathematics. Paper Presented at Workshop on Effective Teaching of Mathematics, LSDPC Magodo, Lagos.

Adebayo, O.A (2000). Availability of basic teaching/learning materials in mathematics in selected secondary schools in Lagos State. 41st Annual Conference Proceedings of STAN, 263 – 266.

Adebayo, O. A. (2001). The place of mathematics in Nigerian secondary schools: course on effective teaching of mathematics in secondary schools phases. Lagos State Public Service Staff Development Centre, Magodo, Lagos: 1-7.

Adedeji, T (2007). The impact of motivation on students’ academic achievement and learning outcomes in mathematics among secondary school students in Nigeria, Eurasia Journal of Mathematics, Science and Technology Education. 3(2), 149-156.

Adekanye, T.O (2008). Effect of students’ participation in instructional material production on achievement and interest in geometry. Unpublished M.Ed Thesis, University of Nigeria, Nsukka.

Adeniyi, N. E. (1988). Mathematics in the secondary school. The Journal of Mathematical Association of Nigeria. 18(1), 89 – 106.

Adeniyi, C. O. (2012). Effects of personalized system of instruction on senior school students’ performance in mathematics in Kwara South, Nigeria. Unpublished Ph.D. Thesis , University of Ilorin, Ilorin, Nigeria.

Agbo, F. O (2002). Motivation and interest. In Oyetunde, O.T. & Piwuna, C.(eds), curriculum and instruction. Insights and strategies for effective teaching. Jos: LECAPS Publishers.

127

Agumuoh, P. C (2009). Effects of PEDDA and TLC Constructivist Instructional Models on students’ conceptual change and retention in physics. Unpublished Ph.D Thesis, University of Nigeria, Nsukka.

Agwagah, U. N. V. (1993). Instruction in mathematics reading as a factor in achievement and interest in word problem-solving. Unpublished Ph.D Thesis, University of Nigeria, Nsukka.

Agwagah, U. N. V. (1994). The effect of instruction in mathematics reading on pupils’ achievement and retention in mathematics education. Journal of Quality Education. 1(1), 67-72.

Agwagah, U.N.V & Ezeugo, N.C (2000). Effect of concept mapping on students’ achievement in algebra. implication for secondary mathematics education in the 21st century. ABACUS: The Journal of the Mathematical Association of Nigeria. 25 (1), 1-12.

Agwagah, U.N.V (2001), Mathematics Games for Primary Schools. Nsukka: Mike Social Press.

Agwagah, U. N .V (2001): Making mathematical education self-reliant. Journal of Science and Computer Education. (3), 37.

Agwagah, U. N. V. (2002). Teaching mathematics for critical thinking, essential skill for effective living. ABACUS: The Journal of the Mathematical Association of Nigeria. 30 (1), 38-44.

Agwagah, U. N. V. (2004). Sustaining development in secondary school mathematics through constructivist framework: A model lesson plan, Journal of Mathematical Association of Nigeria (MAN). 29(1), 92 – 98.

Agwagah, U.N.V. (2005). Teaching mathematics for critical thinking, essential skills for effective Living. ABACUS: The Journal of the Mathematical Association of Nigeria (MAN). 30(1), 38-44.

Agwagah, U.N.V (2008). Creating and sustaining students’ interest in learning mathematics through origami: Journal of Education for Professional Growth: Association of Education for Professional Growth in Nigeria (ASEPGN 2008). 4 (1), 46 – 54.

Agwagah, U. N.V (2013). Improving the teaching of mathematics for attainment of seven point agenda: Implication for gender parity. ABACUS; The Journal of the Mathematical Association of Nigeria. 38, (1), 111 – 121.

Ainley, M; Hidi, S & Berndorf, D (2002). Interest, learning, and the psychological processes that mediate their relationship. Journal of Educational Psychology. 94, 545-561.

Akaninwor, G.I.K (1999). Educational Technology. Theory and practice. Port-Harcourt; Wilson Publishing Co.

Akinsola, M.K. (2000). Enriching science, technology, and mathematics education: effect of resource utilization on students’ achievement in geometry. Science Teachers Association of Nigeria (STAN), 41st Annual Conference Proceedings, 289 – 291.

Akinsola, M. K. & Popoola, A. A. (2004). A Comparative study of the effectiveness of two strategies of solving mathematics problems on the academic achievement of secondary

128

schools students. ABACUS: The Journal of the Mathematical Association of Nigeria (MAN). 29(1), 67-68.

Akor, E.A.P (2005). Effects of polya problem-solving strategy in teaching of Geometry on Secondary School Students’ Achievement and Interest. Unpublished M.Ed Thesis, University of Nigeria, Nsukka.

Akukwe, A. C. (1991). School location and school type as factors in senior school mathematics in Imo State. Unpublished M. Ed Thesis , University of Nigeria, Nsukka.

Ale, S. O (1989). Combating poor achievement in mathematics, ABACUS: Journal of Mathematical Association of Nigeria. 19(1), 26 – 40.

Ale, S.O (1989). A keynote address. War against poor performance in mathematics. ABACUS: 19(1), 3 – 9.

Ale, S.O (2002). An address of welcome for summit workshop at national mathematical centre, Abuja, 12th – 15th October.

Ale, S. O. & Adetula, L. O. (2010). The national mathematical centre and the mathematics improvement project in nation building. Journal of Mathematical Sciences Education. 1(1), 1 –19.

Ali, A (1998). Strategic Issues and Trends in Science Education in Africa. Onitsha, Nigeria: Cape Publishers International Ltd.

Ali, A (2006). Conducting Research in Education and the Social Sciences. Enugu. Tian Ventures.

Alio, B.C. (1997). Polya’s problem-solving strategy in secondary school students achievement and interest in mathematics. Unpublished Ph.D Thesis, University of Nigeria, Nsukka.

Alio, B.C (2001). Performance in mathematics of secondary schools taught by trained and untrained Teachers. Unpublished M. Ed. Thesis, University of Nigeria, Nsukka.

Alonge, M.F. (2011). Mathematics as tool for re-branding Nigeria. A Lead Paper Presented at the 48th Annual Conference of the MAN, 4th – 9th September, 2011. www.mathematicalassociationofnigeria.org

Alwarter, M.M (1994). Research in Cultural Diversity in the Classroom. In D.L. Gabel (ed). Handbook of research on science teaching and learning. New York Macmillan Publishing Company.

Amoo, S.A (2000). Secondary school mathematics teacher characteristics and teaching effectiveness. Journal of Primary Science LACOPED. 2 (1); 29 – 35.

Amoo, S.A (2000a). Mathematics teacher’s effectiveness in the new millennium. A Paper Presented to the 37th Annual National Conference of the Mathematical Association of Nigeria held at University of Lagos, Nigeria between 28th August and 1st September, 2000.

129

Amoo, S.A (2001). An appraisal of problems encountered in the teaching and learning of Mathematics in secondary schools. Annual State Conference of Lagos Chapter of the Mathematical Association of Nigeria (MAN), August 2001.

Amoo, S. A. (2002). Analysis of problems encountered in teaching and learning of mathematics in secondary schools. ABACUS: The Journal of the Mathematical Association of Nigeria. 27(1), 30-34.

Anaduaka, U.S. (2008). Effect of multiple intelligences teaching approach on students’ achievement and interest in geometry. Unpublished Ph.D Thesis, University of Nigeria, Nsukka.

Anaekwe, M. C & Nnaka, C. V (2006). Students’ enrolment and achievement in STM at senior secondary certificate examinations. Implications for availability and utilization of instructional resources. Proceedings of 47th Annual Conference of STAN, held at Calabar.

Anih, A.U (2000). Effect of methodical sequencing on students’ achievement and retention on quadratic equation. Unpublished M.Ed. Thesis, Enugu State University of Science and Technology (ESUT), Enugu.

Animalu, A. (2000). Causes of failure in mathematics identified. The Punch, April, 11.

Anyor, J.W. & Iji, C. O. (2014). Effect of integrated curriculum delivery strategy on secondary school students’ achievement and retention in algebra in Benue State, Nigeria. ABACUS: The Journal of the Mathematical Association of Nigeria. 39(1), 83-96.

Ascher, M. (1991). Ethnomathematics: A multicultural view of mathematical ideas. Pacific Grove, Calif: Brooks/Cole.

Association for Science Education (ASE) (2005). Education through science. Hatfield: ASE.

Ausubel, D. P. (1960). The use of advance organizer in the learning and retention of meaningful verbal material. Journal of Educational Psychology. 51, 267-272.

Ausubel, D.P. (1963). The psychology of meaningful (verbal learning). New York: Grume and Stratton.

Ausubel. D. P. (1968). Educational psychology: A cognitive view. London: Holt, Reinhant and Winston.

Awotunde, P. O. & Bot, T. D (2003). Using mastery learning approach to improve performance of students in geometry in the secondary school. Journal of Educational Studies. University of Jos 7(1), 2 – 14.

Ayeni, R.O. (2012): The quest for development: Why mathematics matters. 2012 Inaugural Lecture Series of the Ladoke Akintola University Technology. Ogbomoso. 20 September, 6-7.

Ayoola, E.O. (2011): Mathematics: A formidable vehicle for development. 2011 Inaugural lecture series of the university of Ibadan. Ibadan 8 September, 58-64.

130

Azuka, B.F (2000). Motivation in technological development, focus on the next millennium- implication for secondary education. ABACUS: The Journal of the Mathematical Association of Nigeria. 25 (1), 63-73.

Azuka, B.F, (2000): Mathematics in technological development: Focus on the next millennium- implication for secondary education. ABACUS; The Journal of the Mathematical Association of Nigeria. 25 (1), 74.

Azuka, B. F (2001). Mathematics: The language of the new millennium ABACUS: The Journal of the Mathematical Association of Nigeria. 26(1), 26-34.

Azuka, B.F (2002). Strategies for effective teaching of some mathematics topics. Proceeding of the Workshop for Training Mathematics Teachers 57 – 60 in Animalu, AD.E. and Harbor Peters, VFA (Eds). Abuja: Ucheakonam Foundation (Nig) Ltd.

Badmus, G. A (2005). Challenges in contents and teaching of school mathematics in Nigeria. Unpublished foundation postgraduate course mathematics education. A Workshop Paper Presented on 11th – 23rd April, National Mathematical Centre, Abuja, Unit II.

Baker, D & Leary, R (1995).Letting girls speak out about science, Journal of Research in Science Teaching. 32(1), 3 – 27.

Becker, B.J. (1989). Gender and science achievement: a reanalysis of students form two meta- analyses. Journal of Research in Science Teaching. 26: 141 – 69.

Betiku, O.F (2000) Improvisation in mathematics in FCT primary schools. How far? 41st Annual Conference Proceedings of STAN, 339 – 341.

Betiku, O.F (2002). Factors responsible for poor performance of the students in school mathematics: suggested remedies. 43rd Annual Conference Proceedings of STAN, 342 – 349.

Betiku, O.F. & Ochepa, L.A (2004). Causes of mass failure in mathematics examinations among students, what are the remedies? Journal of Curriculum Organization of Nigeria. 2(1), 248 – 255.

Betts, P. (2005). Toward how to add aesthetic image to mathematics education, [email protected].

Blickenstaff, J.C (2005). Women and science careers: Leaky pipeline or gender filter? 17(4): 369 – 86.

Bloom, B. S. (1988). Taxonomy of educational objectives. New York: David Mckay Company.

Bruner, J.S (1960). The process of education: New York: Alfred A. Knop Inc.

Bruner, J. S (1966). Towards a theory of instruction. New York: Norton.

Cermack, L.S. (1970). Decay of inference as a function of the inter-trail interval in short term memory. Journal of Experimental Psychology. 84, 499 – 501.

131

Chauhan, S. S. (2010). Advanced educational psychology, (7th ed). Vikas publishing house PVT Ltd.

Chief Examiner’s Reports (2003-2005). The West African Examinations Council, SSCE May/June.

Chukwu, J.O (2002). Promoting interest in mathematics learning through local games. International Journal of Arts and Technology Education. 2(1), 124 – 136.

D’ Ambrosio, .U. (1985). Ethnomathematics and its place in the history and pedagogy of mathematics. For the learning of mathematics, 5, 44-48. D’ Ambrosio, U. (1997). Ethnomathematics and its place in the history and pedagogy of mathematics. In A Powell & M. Frankenstem (eds). Ethnomathematics, challenging Eurocentrism in Mathematics Education 13 – 24. Albany: State University of New York Press.

D’ Ambrosio, U. (1999). Literacy, matheracy, and technoracy: A trivium for today. 1 (2), 131- 153.

D’Ambrosio, U. (2001). What is ethnomathematics and how can it help children in school? Teaching Children Mathematics, 7(6).

D’ Ambrosio, U. (2007a). Peace, social justice and ethnomathematics. The Montana Mathematics Enthusiast. Monograph 1, 25-34.

D’ Ambrosio, U. (2007b). Political issues in mathematics education. The Montana Mathematics Enthusiast. Monograph 3, 51 – 56.

D’Ambrosio, U. (2009). The role of mathematics in building a democratic Society. Retrieved on March 17, 2013, from www.maa.org/g/pg235-238pdf.

Dangoli, A. T(1999). Effect of guided inquiry teaching of students’ achievement in geometry. Unpublished M. Ed. Thesis, University of Nigeria, Nsukka.

Davis, B.G (1999). Motivating students, http.//Honolulu.hawaii.eduintranet/committees/Fac Dev.com/guidebk/teachtip/motiv.htm.

Demirel, O. (2004). Planning and evaluation in instruction. Art of teaching. Pegem publication.

Denga, D. I. & Ali, A. (1998). An introduction to research methods and statistics in education and social sciences (3rd ed). Calabar, Nigeria: Rapid Educational Publishers Ltd.

Ekpo – Eloma, E.O & Udosen, I.N. (2008). Media in life-long education for positive adjustment. Proceedings of First International Conference of the Faculty of Education, University of Nigeria, Nsukka (4) University Trust Publishers, Nsukka.

Ekwueme, C. O (1998). Error pattern and students’ performance in junior secondary three mathematics examination in Cross River State. Unpublished M. Ed Thesis, University of Calabar, Calabar.

Ekwueme, L (2001). The teacher in introduction. U.S.A MS Graw Hill Publishing Company.

132

Elwood, J. & Comber, C (1995). Gender differences in A-level examinations: The reinforcement of stereotypes. Paper Presented as Part of the Symposium. A New Era? New Contexts for Gender Equality, BERA Conference.

Emenalor, S.I. (1986). Mathematics phobia and the psychology of learning mathematics. A Seminar Paper Presented at Alvan Ikoku College of Education, Feb. 1 – 3.

Eraikhuemen, 1 (2003). Mathematics as an essential tool for universal basic education (UBE): Implications for primary school mathematics. ABACUS: The Journal of the Mathematical Association of Nigeria.

Erickson, G & Erickson, L (1984). Females and science achievement: Evidence, explanations and implications. Science Education, 68:63-89.

Erinosho, S.Y(1994).Girls and science education in Nigeria; Abeokuta; Ango Int. Publishers.

Etukudo, U. E. (2002). The effect of computer-assisted instruction on gender and performance of junior secondary school students in mathematics. ABACUS: The Journal of the Mathematical Association of Nigeria (MAN). 27 (1), 1-10.

Etukudo, U. E. & Utin, A. Y. (2006). The effect of interactive basic programme package on secondary school students performance in graphs of quadratic expression. ABACUS: The Journal of the Mathematical Association of Nigeria (MAN). 31 (1), 1-10.

Eya, P.E. (2004). Instructional materials in a challenged educational system. Paper Presented at the Annual Conference Organized by Curriculum Development and Instructional Materials Centre (CUDIMAC). University of Nigeria, Nsukka.

Eze, C. C (2008).Comparative effects of two questioning techniques on students’ achievement, retention and interest in chemistry. Unpublished M.Ed Thesis, University of Nigeria, Nsukka.

Eze, J.E (2005). The effect of mathematics games on primary school pupils achievement in mathematics. Multidisciplinary Journal of Research and Development. 6,(1), 112 – 116.

Ezeamenyi, O. & Alio, B.C (2004). The roles of mathematics in information technology: Implication for the society. ABACUS: The Journal of the Mathematical Association of Nigeria (MAN). 29(1), 7 – 8.

Ezeh, D.N (1992). Effects of study questions as advance organizer on students’ achievement, retention and interest in integrated science. Unpublished Ph.D Thesis, University of Nigeria, Nsukka.

Ezema, P (2002). Effects of keller instructional model on students error minimization and interest in quadratic equation. Unpublished M.Ed Thesis, University of Nigeria, Nsukka.

Ezike, R. O. & Obodo, G. C (1991). The teaching of mathematics in schools and colleges. Anambra: Division of general studies college of education, Eha – Amufu.

Ezike, R.O & Obodo, G.C (2004). The teaching of mathematics in schools and colleges. Eha- Amufu.

133

Fakuade, R. A. (1974). The teaching of quadratic functions and solution of quadratic equations. The Journal of the Science Teachers’ Association of Nigeria (STAN). 12 (3-4), 31-37.

Fakuade, R. A. (1981). Teaching arithmetic and mathematics primary school. Ibadan: University Press.

Federal Ministry of Education (2007). Senior secondary education curriculum mathematics for ss1 – 3. Abuja NERDC

Federal Republic of Nigeria (2004). National policy on education. Lagos: Federal Government Press.

Federal Republic of Nigeria (2013). National policy on education (4th Edition) Abuja: NERDC.

Fiase, G. A. (2009). Effect of analogies in enhancing achievement and interest in geometric concepts among technical school students in Benue State. Unpublished M. Ed Thesis, University of Nigeria, Nsukka.

Francis, B (2000). The gendered subject: Students’ subject preferences and discussions of gender and subject ability. Oxford Review of Education, 26(1): 35 – 48.

Francois, K. (2010). The role of ethnomathematics within mathematics education. Centre for Logic and Philosophy of Science, Free University Brussels New York: Springer.

Galadima, I (2002). The relative effects of heuristic problem solving instruction on secondary school students’ performance on algebraic word problems. ABACUS: The Journal of the Mathematical Association of Nigeria.

Galadima, I. & Yushau, M.A. (2007). An investigation into mathematics performance of senior secondary school students in Sokoto State.ABACUS: The Journal of the Mathematical Association of Nigeria (MAN). 32(1), 24-31

Galadima, I, & Okogbenini, A.A. (2012). The effect of mathematical games on academic performance and attitude of senior secondary students towards mathematics in selected schools in Sokoto State. ABACUS: The Journal of Mathematical Association of Nigeria.

Gardner, P.L (1975a). Attitudes to science, studies in science education, 2: 1 – 41.

Gardner, P.L (1995). Measuring attitudes to science. Research in Science Education, 25(3), 283 – 9.

Gbamanja, S.P.T (1991). Modern methods in science education in Africa. Abuja: Totan Publishers Ltd.

Goetzfridt, N. J (2008). Pacific ethnomathematics: A bibliographic study. Honolnlu: University of Hawaii Press.

Harbor-Peters, V.F (1987). The target task and formal methods of presenting some geometric concepts: The effects on retention. A Paper Presented at the International Conference/Workshop on Mathematics and its Applications. ABU, Zaria from March 1-14.

134

Harbor – Peters, V.F. (1993). Teacher gender by student gender interaction in senior secondary III students mathematics achievement. The Nigerian teacher today. Journal of Teacher Education Published by the National Commission of Colleges of Education.

Harbor-Peters, V. F. (2000). Andragogical inquiry: A pedagogical method for teaching mathematics within the next millennium. ABACUS: The Journal of the Mathematical Association of Nigeria. 25 (1), 64-72.

Harbor-Peters, V.F. (2001). Inaugural Lecture. “Unmasking some aversive aspects of school mathematics and strategies for averting them’’, Enugu Snap Press.

Harbor-Peters, V.F. (2002). Generating and sustaining interest in mathematics classroom. In Animalu, A.O.E. & Harbor-Peters, V.F.A (eds). Proceedings of the Workshop for Retraining Mathematics Teachers at the University of Nigeria Secondary School Nsukka (9th-11th December), Enugu.

Haste, H (2004). Science in my future: A study of the values and beliefs in relation to science and technology amongst 11 – 21 years olds. Nestle Social Research Programme.

Haworth, C.M.A; Dale, P & Plomin, R (2008). A twin study into the genetic and environmental influences on academic performance in science in nine-year-old boys and girls. International Journal of Science Education. 30(8), 1003 – 25.

Head, J. (1985). The personal response to science. Cambridge: Cambridge University Press.

Hornby, A. S. (2010). Oxford advanced learner’s dictionary. Oxford: Oxford University Press.

Ifeakor, A.C. (2005). Effects of commercially produced computer-assisted instruction package on students’ achievement in secondary school chemistry. Unpublished Ph.D Thesis, University of Nigeria, Nsukka.

Iji, C.O. (2003). Effects of logo and basic programs on the achievement and retention in geometry of JSS students. Unpublished Ph.D. Thesis University of Nigeria, Nsukka.

Ike, G.A. (1997). Graphic skills perceived and possessed by educational technology teachers in colleges of education. Unpublished Ph.D Thesis: Department of Vocational Teachers Education, University of Nigeria, Nsukka.

Ilori, A. (1986). Improving quality of mathematics instruction in our schools and Nigerian teacher today. Journal of Teachers Education. National Commission for Colleges of Education. 3(1), 46 – 49.

Imoko, I.B. & Agwagah, U.N.V. (2006). Improving students’ interest in mathematics through the concept mapping technique: A focus on gender. Journal of Research in Curriculum and Teaching. 1 (6794-7720), 30.

Iweka, S (2006). Effect of inquiry and laboratory approaches of teaching geometry on students’ achievement and interest. Unpublished M.Ed Thesis, University of Nigeria, Nsukka.

Johnson, S (1987). Gender differences in science: Parallel in interest, experience and performance, International Journal of Science Education. 9 (4), 467 – 81.

135

Kahle, J.B & Lakes, M.K (1983). The myth of equality in science classrooms. Journal of Research in Science Teaching. 20: 131 – 40.

Kalra, R.M (2008). Science education for teacher trainees and in-service teachers. New Delhi: PHI Learning Private Ltd.

Kearsely, G. (1944b). Constructivist theory. (J. Bruner) www.gwu.edu/2tip/bunner (Dec. 1999).

Kelly, A. (ed) (1981). The missing half: Girls and science education. Manchester: Manchester University Press.

Kolawole, E. B. & Oluwatayo, J. A. (2005). Mathematics for everyday living: implications for Nigerian secondary schools ABACUS: Journal of the Mathematical Association of Nigeria (MAN). 30 (1), 51-55.

Kurumeh, M. S. C. (2004). Effects of ethnomathematics approach on students’ achievement and interest in geometry and mensuration. Unpublished Ph.D Thesis. University of Nigeria, Nsukka.

Kurumeh, M. S. (2006). Mathematics club for secondary school students: A key to set us free. Makurdi: Azaben Printers and Publishers.

Kurumeh, M. S. (2007). Effect of ethnomathematics approach on students’ interest in geometry and mensuration. ABACUS: The Journal of the Mathematics Association of Nigeria (MAN). 32 (1), 103-112.

Lassa, P. N. (1995). Entrepreneurship education for socio-economic and industrial development in Nigeria. A keynote address presented during the National Conference on Entrepreneurship Education at F.C.E(T) Umunze.

Lassa, P. N. (2000): The relevance and role of mathematics and its application in the 21st century: Implication for secondary mathematics. A Paper Presented during the National Mathematical Science Summit and Annual Lecture held at the National Mathematical Centre held between 26th - 27th July.

Lassa, P.N. (2012). The teaching of mathematics for Nigerian secondary school, Jos: Fab Anieh Nigeria Ltd.

Lindgren, H. C. (1976). Educational psychology in the classroom. New York: John Wiley and Sons. Inc.

Longe, O. A. (2012). Essential commerce for senior secondary schools. Lagos; Tanad Publisher Ltd.

Macrae, M. F, Kalejaiye, A. O., Chima, Z. I., Garba, G. U, Ademosu, M. O., Channon, J. B., Smith A. M. & Head, H. C (2011), New general mathematics for senior secondary schools 1. England; Pearson Education Ltd.

Maduabum, M. A. & Odili, G. A. (2006). Analysis of students’ performance in mathematics from 1991-2002. Journal of Research in Curriculum and Teaching (JRCT). 1(1), 64-67.

McMillan, J.H (2012). Educational research (6th Edition). New York: Pearson Education, Inc.

136

Melin (1970). Learning theories. New York: Macmillan Publisher,

Meremikwu, A.N (2002). Gender differences and mathematics achievement among secondary school students. Unpublished M.Ed Thesis. University of Calabar.

Mitchell, M. (1993). Situational Interest: Its multifaceted structures in the secondary school mathematics classroom. Journal of Educational Psychology. 85, 424-436.

Murphy C, & Beggs, J (2003). Children’s attitudes towards school science. School science review 84 (308): 109 – 16.

Murphy, P &Whitelegg, E (2006). Girls in the physics classroom: A review of research of participation of girls in physics, London: Institute of Physics.

Myers, D.G. (1998). Psychology (Fifth Edition). New York: Worth Publishers.

Nwabueze, M. U. (2009). Effect of area tiles approach on students’ achievement and interest in quadratic equations at senior secondary school Level. Unpublished M. Ed Thesis, University of Nigeria, Nsukka.

Nwagu, E.K.N (1992). Evaluating affective behavior observational techniques in B.G. Nworgu (ed). Educational measurement and evaluation theory and practice. Nsukka: Hallman Publishers.

Nwideeduh, S.B (2003). Focus on effective teaching in schools. Port Harcourt: Paragraphics.

Nworgu, B. G. (2015). Educational research. Basic issues & methodology (Third Edition). Nsukka, Enugu: University Trust Publishers.

Nwosu, A. A. (2002). Inquiry skills acquisition, for enhancing women’s participation in sustainable development. Implication for Science Education Proceeds of 3rd Annual and Inaugural Conferences of CASTME Africa 2003, 98 – 100.

Obafemi, A. O. (1999). Professional skills needed by technical teachers for improved teaching in community secondary schools in Kogi State. Unpublished M. Ed Thesis, University of Nigeria, Nsukka.

Obafemi; D. T. A. (2005). A comparative analysis of attitudes towards physics in the university demonstration and unity secondary schools in Rivers State, Unpublished M. Ed Thesis, University of Port Harcourt.

Obasanjo, .O. (2000). Obasanjo economic direction 1999-2003: The Presidency Shehu Shagari Way, Abuja, April.

Obi, C. N (2006). Comparative study of the effects of two problems-solving models on students’ achievement and interest on word problems in algebra. Unpublished M. Ed Dissertation, University of Nigeria, Nsukka.

Obi, C. N & Agwagah, U. N. V (2013). Effects of origami on students’ achievement in geometry in Nsukka Local Government Area of Enugu State, Nigeria. Journal of Mathematical Sciences Education. 2(1), 344 – 354.

137

Obi, C. N (2014). Effect of origami on students’ achievement, interest and retention in geometry. Unpublished Ph.D Thesis, University of Nigeria, Nsukka.

Obioma, G. O. (1985). The development and validation of a diagnostic mathematics test for junior secondary school students. Unpublished Ph.D Thesis, University of Nigeria, Nsukka.

Obioma, G. O. (1991). Policies and strategies for the development of mathematics teaching and tearning at senior secondary level. Paper Presented at National Implementation Committee on Mathematics Education, National Mathematical Centre, Abuja held at Sheraton Hotel and Towers, February 21-22.

Obodo, G.C (1990). The different effects of three teaching models on performance of junior secondary school students in some algebraic concepts. Unpublished Ph.D Dissertation, Faculty of Education, University of Nigeria, Nsukka.

Obodo, G. C. & Onoh, D. O. (2000). The content validity of senior secondary school certificate multiple-choice questions in mathematics from 1988-1994. ABACUS: The Journal of the Mathematical Association of Nigeria. 26 (1), 17-25.

Obodo. G. C. & Onoh, D. O. (2001). Cognitive content validity of senior school certificate multiple choice questions in mathematics from 1988-1994. ABACUS: The Journal of the Mathematical Association of Nigeria. 20(1), 17-22.

Obodo, G.C (2004). Principles and practice of mathematics education in Nigeria (Rev. ed). Enugu: Floxtone Press.

Odili, G. A (2006). Mathematics in Nigerian secondary schools. A teaching perspective. Rex Charles and Patrick Limited in Association with Anachuna Education books.

Odogwu, H. N (1995). Effect of laboratory approach on the performance and retention of different ability groups, in ‘2’ and ‘3’ dimensional geometry. Journal of Studies in Curriculum. 5, 6 (1,2), 9-15.

Odogwu, H.N. (2002). Female students’ perception and attitude to mathematics: A bane to their SMT education. ABACUS: The Journal of the Mathematical Association of Nigeria. 27(1), 19-29.

Ogbonna, C.C (2004). Effects of constructivist instructional approach on senior secondary school students’ achievement and interest in mathematics. Unpublished M.Ed. Thesis, University of Nigeria, Nsukka.

Ogbonna, C.C (2007). Effects of two constructivist instructional models on students’ achievement and retention in number and numeration: Unpublished Ph.D. Thesis, University of Nigeria, Nsukka.

Ogunkunle, R.A. (1998). Resources in communicating STM: Teaching and learning of STM using computer instruction in schools. In A.O Olanrewaju (ed) communicating science, technology and mathematics (52 – 54), Proceedings of 39th Annual Conference of the Science Teachers Association of Nigeria, Ibadan: Heinemann.

138

Ogunkunle, R.A (2000a). Studies of perception of difficult areas in mathematics and the use of instructional materials in secondary school. Journal of Research in Contemporary Education. 1(1), 9 – 22.

Ogunkunle, R.A (2000b). Teaching of mathematics in schools: The laboratory approach. The Nigerian Teacher Today. 8(1&2), 178 – 180.

Ogunkunle, R.A (2006). Constructivism: An instructional strategy for repositioning the teaching and learning of mathematics in secondary school. Multidisciplinary Journal of Research Development. 7(7), 82 – 89.

Ogunkunle, R.A (2009). Effects of gender on the mathematics achievement of students in constructivist and non-constructivist groups in secondary schools. ABACUS: The Journal of the Mathematical Association of Nigeria (MAN). 32(1), 34 – 39.

Ogwuche, A. E. (2002). Age and sex as correlates of logical reasoning and mathematics achievement in ratio and proportion tasks. Unpublished M.Ed Thesis, University of Nigeria, Nsukka.

Ojerinde D. (1986). Ought mathematical vocabularies be taught before mathematics. An Experimental Verification Curriculum Organization of Nigeria Monograph Series, (4), 151-164.

Ojerinde, D (1998). Under achievement in school science in Nigeria: The way out. African Journal of Education. 1(1), 176 – 191.

Ojerinde, D. (2006). NECO release SSCE result, 26 percent made five credits. The Guardian, Thursday, October 19.

Ojo, J. O (1986). Improving mathematics teaching in our schools. ABACUS: The Journal of the Mathematical Association of Nigeria. 17 (1) 30 – 39.

Ojoko, S.E. (2003). Effectiveness of a constructivist instructional strategy for fostering development of mathematical function concept in Port-Harcourt secondary schools. Unpublished M.Ed. Thesis, Rivers State University of Science and Technology, Port Harcourt.

Ojoko, S.E. (2012). Mathematics in a nutshell. Port Harcourt: Minson Nigeria Ltd.

Okafor, C. F. & Anaduaka, U. S. (2013). Nigerian school children and their mathematics phobia: How the teacher can be of help. Journal of Mathematical Sciences Education, National Mathematical Centre, Abuja. 2(1), 294-303.

Okeke, E.A.C (1986). Attracting women into science based occupations: Problems and prospects. Science and Public Policy 13(3).

Okeke, E. A. C(2002). Gender and science. Technology and mathematics. A lead paper presented at the 1st Annual Conference of the Institute of Education, University of Uyo. March 13 - 16.

Okeke, E. A. C. (2007). Clarification and analysis of gender concepts. STAN National Workshop of Gender and STM panel. A Paper Presented in June 2007.

139

Olagunju, S.O. (1996). Sex, age, and performance in mathematics. Unpublished Ph.D Thesis, ICEEE, University of Ibadan.

Olikeze, F.C. (1997). Effect of computer-assisted instruction (CAI) on secondary school students’ cognitive achievement and interest in biology. Unpublished Ph.D: Thesis, University of Nigeria, Nsukka.

Olunloye, O. (2010). Mass failure in mathematics; A national disaster. Tribune of 07/02/2010 Retrieved from http/www.tribune.com.ng on 08/05/2011.

Onabanjo, I.O. & Akinsola, O.S (2000). An investigation into the utilization of the available resources in mathematics classrooms. 41st Annual Conference Proceedings of STAN, 284 – 288.

Onwuakpa, F & Akpan, B.B (2000). Journal of Science Teachers Association of Nigeria. 35 (1&2), 55 – 62.

Oriaifo, S.O (1987). Incidence of retention among secondary school chemistry students: A study of the effects of an instructional package approach. Journal of Nigeria Educational Research Association. 7 (1&2), 19-20.

Oriaifo, S. O (1997). Science as metaphor for development. Africa Inaugural Lecture Series. University of Benin, Benin city.

Oriaifo, S. O (2003). Strategies for teaching science, technology and mathematics for learners’ gain. In Oloruntegbe, K. O. (ed) strategies for enhancing the teaching and learning of science, technology and mathematics for learners gain. STAN, Ondo State, 1 – 13.

Orji, A.B.C (2002). Gender imbalance in science and technology based human resources development in Africa Conference and Inaugural Conference of CASTME: Africa 2002, 114 – 115.

Osafehinti, I.O. (1986). The problem of mathematics in Nigeria: Any solution? Journal of Science Teachers Association of Nigeria. 24 (2), 24.

Osafehinti, I. D (1990). The universality of mathematics. ABACUS: Journal of Mathematical Association of Nigeria. 20 (1), 47 – 56.

Osborne, J.F; Simon, S. & Collins, S (2003). Attitudes towards science: A review of the literature and its implications, International Journal of Science Education. 25 (9), 1049 – 79.

Osborne, J & Dillon, J (2010). Good practice in science teaching. New York: Open University Press.

Ozigboh, I. G. (1994). Effect of geoboard and rellograh as instructional material in teaching geometry in secondary schools. Unpublished M. Ed Thesis University of Nigeria, Nsukka.

Pell, T & Javis, T (2001). Developing attitude to science scales for use with children of ages from five to eleven years. International Journal of Science Education. 23(8), 847 – 62.

Piaget, J. & Inhelder, B (1960). The child’s conception of geometry. New York: Basic Books.

140

Piaget, J (1964). Development and learnings. Journal of Research in Science Teaching. 2(4), 176 – 186.

Piaget, J (1971). The science of education. London: Routledge & Kegan Paul.

Piaget, J & Inhelder, B (1972). The psychology of the child. New York: Basic Books.

Pintrich P. R. & Schunk, D. H. (2002). Motivation in education: Theory, research, and application (2nd ed). Upper Saddle River, N. J: Merrill/Prentice-Hall.

Pintrich, P.R. (2003). A motivational science perspective on the role of students motivation in learning and teaching. Journal of Educational Psychology. 95, 667 – 686.

Powell, A.B; & Marilyn, F (eds) (1997). Ethnomathematics: Challenging eurocentrism in mathematics education, Albany, N.Y: State University of New York Press ISBN 0-7914- 3351-x.

Powell, A. (2002). Ethnomathematics and the challenges of racism in mathematics education. In P. Valero &O. Skovsmose (eds), Mathematics education and society. Proceeding of the third International Mathematics Education and Society Conference, MES3, (see. Ed). 2; 17-30. Denmark: Centre for Research in Learning Mathematics.

Sanni, S. O. & Ochepa, I. A (2002). Effect of practical discussion outside the classroom on students’ performance in mathematics. ABACUS: The Journal of Mathematical Association of Nigeria (MAN). 27 (1), 45 – 49.

Santrock, J.W (2005). Educational psychology: University of Texas at Dallas Science Curriculum Implementation Study (197a) SCIS Teachers Handbook. Berkeley, C.A.

Schibeci, R.A (1984). Attitudes to science; An update, studies in science education, 11: 26 – 59.

Schraw, G & Lehman, S (2001). Situational interest: A review of the literature and directions for future research educational psychology, 13, 23-52.

Schunk, D. H (2000). Learning theories: An educational perspective (3rd ed), Columbus, OH: Merrill/Prentice-Hall.

Sidhu, K. S. (2006). The teaching of mathematics. (Revised and enlarged edition) New Delhi: Sterling Publishers Private Ltd.

Sidhu, K. S (2007). New approaches to measurement and evaluation. New Delhi: Sterling Publishers Private Ltd.

Smail, B and Kelly, A (1984). Sex differences in science and technology among 11 years old school Children: 11 – Affective, Research in science and Technology Education, 2: 87 – 106.

Soyemi, B.O (2003). Students’ dictionary of mathematics. Educare Foundations Project in Collaboration with OFS and Associates Ltd Publisher, Text and Lesson Publishing Co. Nigeria.

141

Steen, L.A (2003). Out from under achievement, issues in science and technology. Online retrieved on February 13, 2006. http:// www. issues.org/ 19.4 /updated/ stan.html.

Stipek, D. J. (1993). Motivation to learn (2nd ed). Boston: Allyn and Bacon.

Stipek, D. J. (2002). Motivation to learn: Integrating theory and practice (4th ed). Boston Allyn.

Suleiman, B (2010). Relative effect of problem solving models on school students’ performance in mathematics in Zamfara State. Unpublished Ph. D. Thesis, Department of Science Education, University of Ilorin, Nigeria.

Sunday, Y; Akanmu, M.A & Fajemidagba, M.O. (2014). Effects of target-task mode of teaching on students’ performance in geometrical construction: ABACUS: The Journal of the Mathematical Association of Nigeria. 39(1), 33-42.

Sztefka, B. (2002). A case study on the teaching of culture in a foreign language. Available from http://www.betaiatefl.hit.bg/pdfs/case-study.pdf.

Terrypage, A; Thomas, J. B; & Marshall, A. R. (eds) (1979). International Dictionary of Education. London: Kogan Page.

Thomas, D. B. (2000). Rapid assessment of the competence of undergraduates in the improvisation and utilization of resources to teach secondary school mathematics content. A case study of University of Jos. Science Teachers Association of National (STAN) 41st Annual Conference Proceedings, 256 – 262.

Thomas, G.E (1986). Cultivating the interest of women and minorities in high school mathematics and science, Science Education, 73(3), 243 – 9.

Thorn-Dike, E.L. (1913). Educational psychology. New York: Teachers College Press,

Timku, L (2004). Methods of teaching geometry in schools. In Oyetunde, T. O., Mallam, Y. A. & Andzayi, C. A. (eds). The Practice of Teaching Perspectives and Strategies. Jos: Leepas Publishers.

Tsue, E. A. & Anyor, J. W (2006) Relationship between students’ achievement in secondary school mathematics and the science subjects. Journal of Research in Curriculum and Teaching (JRCT). 1(1), 48 – 54.

Uka, N.K. (2006). Teachers mathematics attitude, ethnomathematics knowledge and primary pupils’ achievement in mathematics in Abia State, Nigeria. Unpublished Ph.D Thesis, Faculty of Education, University of Calabar, Calabar.

Ukwungwu, J. O. & Ugbaja, R. A. E. (1990). Assessing students interest in integrated science. Nigeria Research in Education, 5, 140-143.

Umeano, C.N (2005). Skills required of mathematics teachers for improvisation of instructional materials in secondary schools.Unpublished M.Ed Thesis, University of Nigeria, Nsukka.

Umo, U.C (2005). Production and use of instructional materials in language arts. A Journal of CUDIMAC, Faculty of Education, University of Nigeria, Nsukka.

142

UNESCO (2007). Education for all. Global monitoring report.

UNESCO (2009). International year of natural fibres.

UNESCO (2012). Challenges in basic mathematics education.

Usiskin, Z. (1986). Resolving the continuous dilemmas in school geometry. Department of education, University of Chicago.

Usman, K. O. (2002). The need to re-train In-service mathematics teachers for the attainment of the objectives of universal basic education (UBE). ABACUS: The Journal of the Mathematical Association of Nigeria (MAN). 27 (1), 37-40.

Usman, K. O. (2003). Influence of shortage of human resources on the effective instruction of mathematics in secondary schools. The Journal of World Council of Curriculum and Instruction (WCCI) Nigeria. 4(2), 176-184.

Usman, K. O. & Obidoa, M.A (2005). Effects of teaching some geometrical concepts with origami on students achievement. Curriculum and media technology research. A Journal of CUDIMAC, Faculty of Education, University of Nigeria, Nsukka. (1) 190-195.

Von Glaserfeld, E (1989). An exposition of constructivism: Why some like it Radical. In R. Davis, C. Maher & N. Noddings (eds.). Constructivists views on the teaching and learning of mathematics. Reston, VA: National Council of Teachers of Mathematics.

WAEC (2007 - 2013): Chief examiners reports on the performance of candidates in mathematics, West African Examinations Council, Yaba, Lagos.

Walberg, H. J. (ed.) (2000). The international academy of education (IAE). Educational Practices Series at Chicago University of Illinois.

Wasagu, M. A. (2009). Meeting the challenges of education and means of achieving sustainable development in Nigeria: A lead paper 2009 Annual National Conference Organized by Shehu Shagari College of Education, Sokoto.

Weinburgh, M (1995). Gender differences in student attitudes toward science: A meta-analysis of the literature from 1970 to 1991. Journal of Research in Science Teaching. 32(4), 387 – 98.

Whitehead, J.M (1996). Sex stereotypes, gender identity and subject choice at a level. Educational Research, 38(2), 147 – 60.

Wikipedia Encyclopedia (2008). Fishing Industry. Fisheries Section Food Agricultural Organization (FAO) United Nations Organization Glossary May, 28.

Wikipedia Encyclopedia (2009). First Direct Evidence of Substantial Fish Consumption by Early Modern Humans. Food Agricultural Organization (FAO) China: PhysOrg.com July 6.

Wikipedia Encyclopedia (2009). Fisheries and Aquaculture in our Changing Climate Policy. Food Agricultural Organization (FAO). Copenhagen: The UNFCCC COP-15 December .

Wikipedia (2011). The Free Encyclopedia.

143

Woolfolk, A. Hughes, M & Walkup, V (2008). Psychology in Education. England: Pearson Education Ltd.

Woolnough, B (1994). Effective science teaching. Buckingham: Open University Press.

Young, D. & Jones, J (1995). Perceptions of relevance of mathematics and science. An Australian study. Journal of Research in Science Education. 25(1), 3 – 18.

144

APPENDIX A GEOMETRY ACHIEVEMENT TEST (GAT) INSTRUCTIONS: Answer all questions Circle the correct answer, each question carries equal mark

Gender (tick one applicable) Male Female

1. One of these is not a good example of a fishing tool. (a) Cock (b) Cork (c) Paddle (d) Canoe.

2. A chord 8cm long is 3cm from the centre of a circular twine, calculate the radius of the circle. (a) 5cm (b) 6cm (c) 9cm (d) 10cm

3. Which of these fishing tools is a good example of a rhombus? (a) Hook (b) Racket (c) Net mesh (d) Net mending stick.

4. One of these fishing tools is not a plane shape? (a) Net mending stick (b) Lead (c) Sail (d) Bailer.

5. Which of these fishing tools is a good example of a right-angled triangle? (a) Net mending ruler (b) Sail (c) Float (d) Basket.

6. Which of these is not a property of a parallelogram? (a) The opposite sides are parallel (b) The diagonals bisect one another at right angle (c) The opposite angles are equal (d) The diagonals bisect one another

7. If the diagonal of a square net mesh is 8cm, what is the area of the square? (a) 64 cm2 (b) 5.66 cm2 (c) 32 cm2 (d) 16 cm2

8. Figure 1below is called …………. (a) Regular polygon (b) Convex polygon (c) Re-entrant polygon (d) Equilibrium polygon

Fig. 1

145

9. How many rectangles are found in the figure 2 below? (a) 4 (b) 6 (c) 8 (d) 5

Fig. 2 10. How many triangles are in the figure 3 below?

(a) 13 (b) 9 (c) 10 (d) 12

Fig. 3 11. Find the area of ∆ ABC in figure 4 below. A

(a) 108 cm2 (b) 26 cm2 2 (c) 168 cm 12 cm (d) 84 cm2 B C 9 cm D 5 cm Fig. 4 12. Calculate the perimeter of circular rope whose diameter is 56 cm (a) 176 cm (b) 167 cm (c) 2464 cm2 (d) 24600 cm2

13. Calculate the perimeter of a rectangular lead in figure 5 below whose length and width are 17cm and 11cm respectively

(a) 135 cm (b) 187 cm 17 cm (c) 56 cm (d) 82 cm 11c m

Fig. 5. 14. A rectangle has …………… lines of symmetry

(a) 3 (b) 4 (c) 2 (d) 1 15. One of these is not an example of prism (a) Cube (b) kite (c) cuboids (d) cylinder

16. One of the quadrilaterals has no line of symmetry (a) Square (b) Rectangle (c) Rhombus (d) trapezium

146

An isosceles triangle is such that each of the base angles is twice the vertical angle. Use the statement to answer questions 17 and 18.

17. Find the vertical angle of the triangle (a) 720 (b) 300 (c) 630 (d) 360

18. Find the base angle of the isosceles triangle (a) 1800 (b) 900 (c) 720 (d) 300

19. Figure 6 below is called a …………..

Fig. 6.

(a) Triangular Pyramid (b) Circular Pyramid (c) Rectangular Pyramid (d) Square Pyramid

20. Figure 7 below is best described as a ………… (a) Convex Polygon (b) Re-entrant polygon (c) Cylinder (d) Hexagon

Fig. 7. 21. Any closed shape which has three or more straight sides is called a/an _____ (a) Cone (b) Ellipse (c) Polygon (d) Pyramid

Use figure 8 below to answer question 22 and 23 4 cm

7 cm 10 cm

Fig. 8.

22. Calculate the perimeter of the shape (a) 26 cm (b) 62 cm (c) 280 cm (d) 21 cm

147

23. Find the area of the shape (a) 43 cm2 (b) 34 cm2 (c) 110 cm2 (d) 21 cm2 24. Find the volume of a spherical basket whose diameter is 15 cm (a) 176 cm3 (b) 1770 cm3 (c) 1767 cm3 (d) 1768 cm3

25. A pyramidal float on a base 10 m2 is 5 m long high. Find the volume of the pyramid. (a) 50 m3 (b) 150 m3 (c) 160 m3 (d) 100 m3

26. Find the volume of the figure 9 below if its base area is 30cm2

16cm

Fig. 9.

(a) 480cm3 (b) 800cm3 (c) 180cm3 (d) 48cm3

27. Calculate in terms of π the total surface area of a solid a cylindrical rope of radius 3 cm and height 4 cm. (a) 36 πcm2 (b) 12 πcm2 (c) 42 πcm2 (d) 24 πcm2

28. Figure 10 below is called a …………………..

Fig. 10.

(a) Block (b) Cuboid (C) Cube (d) Square

Use figure 11 below to answer questions 29 – 31 v

A D

o

C Fig. 11. B 29. VO is called a ……………….. (a) Vertex (b) Slope (c) Diagonal (d) Height

30. /VA/ = /VB/ = /VC/ = /VD/ are called ……….. (a) Diagonals (b) Vertex (c) Slant heights (d) Tangent

148

31. The diagram ABCDV is called a ………… (a) Triangular Pyramid (b) Square Pyramid (c) Rectangular Pyramid (b) Circular Pyramid

32. A rectangular pyramid has …………… faces (a) 4 (b) 8 (c) 6 (d) 5

33. How many vertices has a cube? (a) 6 (b) 8 (c) 12 (d) 10

34. A structure with a base and sloping sides meeting at a point which is not in the same plane as the base is known as a …………….. (a) Polygon (b) Cylinder (c) Cone (d) Pyramid

35. Figure 12 below is called a…………………..

(a) Pyramid Fig. 12. (b) Cone (c) Cube (d) Cubiod

36. A pyramidal float 8 cm high stands on a rectangular base 6 cm by 4 cm. calculate the volume of the pyramid. (a) 192 cm3 (b) 92 cm3 (c) 64 cm3 (d) 46 cm3

37. Find the volume of a conical fishing trap of base diameter 14 cm and height 6 cm (a) 154 cm3 (b) 308 cm3 (c) 462 cm3 (d) 460 cm3

38. Calculate in terms of π, the total surface area of the cone of base diameter 12 cm and height 8 cm in figure 13 below.

8 cm Lcm

Fig. 13. 12 (a) 96 π cm2 (b) 960 π cm2 (c) 1960 π cm2 (d) 196 πcm2

149

39. What is the volume of a cork whose length, width and depth are 25 cm, 20 cm and 15 cm respectively? (a) 750 cm3 (b) 1500 cm3 (c) 7500 cm3 (d) 60 cm3

40. Use figure 14 below to find angle

510 A

0 112 B 0 75

Fig. 14. C

(a) 2380 (b) 1220 (c) 750 (d) 1120

41. If the dimensions of a rectangular canoe bench are 8 cm by 6 cm by 5 cm, find its volume. (a) 48 cm3 (b) 480 cm3 (c) 240 cm3 (d) 140 cm3

42. If a pentomino is made by five connected squares that touch only a complete side, which of these shape is a pentomino?

(a) (b) (c) (d)

43. ……….. is an example of a regular polygon except. (a) Trapezium (b) Square (c) Equilateral triangle (d) Regular hexagon

44. Which of the following is a good example of a compound solid shape?

(a) (c) (b) (d)

45. If a tetromino is formed by connecting four squares so that connected squares share a complete side, which of these shape is not a tetromino?

(a) (b) (c) (d)

46. A triangular pyramid (tetrahedron) has ……………….. edges (a) 3 (b) 4 (c) 8 (d) 6 47. A terminal float with square base and a height of 8 cm has a volume of 1352 cm3. Find the length of a side of the base.

150

(a) 15 cm (b) 169 cm (c) 13.5 cm (d) 13 cm

48. The figure 15 below is an example of …………………

Fig. 15.

(a) Cylinder (b) Trapezium (c) Frustum (d) Rectangle

Use the information below to answer questions 49 and 50 A cone has a base radius of 5cm and a height of 12cm. Calculate: 49. Its slant height (a) 13cm (b) 17cm (c) 169cm (d) 7cm

50. The total surface area. Leave the answer in terms of π (a) 90πcm2 (b) 191 πcm2 (c) 190 πcm2 (d) 100 πcm2.

151

APPENDIX B GEOMETRY ACHIEVEMENT TEST (GAT) INSTRUCTIONS: Answer all questions Circle the correct answer, each question carries equal mark

Gender (tick one applicable) Male Female

1. One of these fishing tools is not a plane shape? (a) Net mending stick (b) Lead (c) Sail (d) Bailer.

2. Which of these is not a property of a parallelogram? (a) The opposite sides are parallel (b) The diagonals bisect one another at right angle (c) The opposite angles are equal (d) The diagonals bisect one another

3. Which of these fishing tools is a good example of a right angle triangle? (a) Net mending ruler (b) Sail (c) Float (d) Basket.

4. One of these is not a good example of fishing tool. (a) Cock (b) Cork (c) Paddle (d) Canoe.

5. Which of these fishing tools is a good example of a rhombus? (a) Hook (b) Racket (c) Net mesh (d) Net mending stick.

An isosceles triangle is such that each of the base angles is twice the vertical angle. Use the statement to answer questions 6 and 7.

6. Find the vertical angle of the triangle (a) 720 (b) 300 (c) 630 (d) 360

7. Find the base angle of the isosceles triangle (a) 1800 (b) 900 (c) 720 (d) 300

8. Calculate the perimeter of a circular rope whose diameter is 56 cm (a) 176 cm (b) 167 cm (c) 2464 cm2 (d) 24600 cm2

9. Find the area of ∆ ABC in figure 1 below A

(a) 108 cm2 (b) 26 cm2 (c) 168 cm2 12 cm (d) 84 cm2 B C 9 cm D 5 cm

Fig. 1.

152

10. Calculate the perimeter of a rectangular lead in figure 2 below whose length and width are 17cm and 11cm respectively

17cm

(a) 135 cm (b) 187 cm 11cm (b) 56 cm (d) 82 cm Fig. 2. 11. One of these is not an example of prism (a) Cube (b) kite (c) cuboids (d) cylinder

12. How many triangles are in the figure 3 below?

(a) 13 (b) 9 (c) 10 Fig. 3 (d) 12

13. A rectangle has …………… lines of symmetry (a) 3 (b) 4 (c) 2 (d) 1

14. One of the quadrilaterals has no line of symmetry (a) Square (b) Rectangle (c) Rhombus (d) trapezium

15. Figure 4 below is called a …………..

Fig. 4. (a) Triangular Pyramid (b) Circular Pyramid (c) Rectangular Pyramid (d) Square Pyramid

16. Any closed shape which has three or more straight sides is called a/an _____ (a) Cone (b) Ellipse (c) Polygon (d) Pyramid

153

Use figure 5 below to answer questions 17 and 18 4 cm

7 cm

10 cm

Fig. 5.

17. Calculate the perimeter of the shape (a) 26 cm (b) 62 cm (c) 280 cm (d) 21 cm

18. Find the area of the shape (a) 43 cm2 (b) 34 cm2 (c) 110 cm2 (d) 21 cm2

19. A pyramidal float on a base 10 m2 is 5 m long high. Find the volume of the pyramid. (a) 50 m3 (b) 150 m3 (c) 160 m3 (d) 100 m3

20. Calculate in terms of π, the total surface area of a cylindrical rope of radius 3 cm and height 4 cm. (a) 36πcm2 (b) 12 πcm2 (c) 42π cm2 (d) 24π cm2

21. Figure 6 below is best described as a ………… (a) Convex Polygon (b) Re-entrant polygon (c) Cylinder (d) Hexagon Fig. 6.

22. A structure with a base and sloping sides meeting at a point which is not in the same plane as the base is known as a …………….. (a) Polygon (b) Cylinder (c) Cone (d) Pyramid

23. What is the volume of a cork whose length, width and depth are 25 cm, 20 cm and 15 cm respectively? (a) 750 cm3 (b) 1500 cm3 (c) 7500 cm3 (d) 60 cm3

24. Calculate in terms of π, the total surface area of the cone of base diameter 12 cm and height 8 cm in figure 7 below

8 cm Lcm

12 cm Fig. 7. 154

(a) 96π cm2 (b) 960πcm2 (c) 1960 πcm2 (d) 196 πcm2

25. Figure 8 below is called a …………………..

(a) Pyramid (b) Cone (c) Cube Fig. 8. (d) Cubiod

26. Find the volume of a conical fishing trap of base diameter 14 cm and height 6 cm (a) 154 cm3 (b) 308 cm3 (c) 462 cm3 (d) 460 cm3

27. A pyramidal float 8cm high stands on a rectangular base 6 cm by 4 cm. calculate the volume of the pyramid. (a) 192 cm3 (b) 92 cm3 (c) 64 cm3 (d) 46 cm3

28. Figure 9 below is a/an………….

(a) Regular polygon (b) Convex polygon (c) Re-entrant polygon (d) Equilibrium polygon Fig. 9.

29. Find the volume of a spherical basket whose diameter is 15 cm (a) 176 cm3 (b) 1770 cm3 (c) 1767 cm3 (d) 1768 cm3

30. Find the volume of the figure 10 below if its base area is 30cm2

16cm

Fig. 10.

(a) 480cm3 (b) 800cm3 (c) 180cm3 (d) 48cm3

31. How many rectangles are found in the figure 11 below?

(a) 4 (b) 6 (c) 8 (d) 5 Fig. 11.

155

32. A terminal float with square base and a height of 8 cm has a volume of 1352 cm3. Find the length of a side of the base. (a) 15 cm (b) 169 cm (c) 13.5 cm (d) 13 cm

33. A triangular pyramid (tetrahedron) has ………….. edges (a) 3 (b) 4 (c) 8 (d) 6

34 . How many vertices has a cube? (a) 6 (b) 8 (c) 12 (d) 10

35. A rectangular pyramid has …………… faces (a) 4 (b) 8 (c) 6 (d) 5

Use the information below to answer questions 36 and 37 A cone has a base radius of 5cm and a height of 12cm. Calculate: 36. Its slant height (a) 13cm (b) 17cm (c) 169cm (d) 7cm 37. The total surface area. Leave the answer in terms of π. (a) 190 πcm2 (b) 90 πcm2 (c) 191 π cm2 (d) 100 πcm2

38. If the dimensions of a rectangular canoe bench are 8 cm by 6 cm by 5 cm, find its the volume. (a) 48 cm3 (b) 480 cm3 (c) 240 cm3 (d) 140 cm3

39. If a pentomino is made by five connected squares that touch only a complete side, which of these shapes is a pentomino?

(a) (b) (c) (d)

40. ……….. is an example of a regular polygon except. (a) Trapezium (b) Square (c) Equilateral triangle (d) Regular hexagon

41. Which of the following is a good example of a compound solid shape?

(a) (c) (b) (d)

42. Figure 12 below is an example of a …………………

Fig. 12. (a) Cylinder (b) Trapezium (c) Frustum (d) Rectangle

43. If a tetromino is formed by connecting four squares so that connected squares share a complete side, which of these shapes is not a tetromino?

A a

(a) ( b) (c) ( d) 156

44. Use figure 13 below to find angle

510 A

1120 B 750

0 0 0 0 (a) 238 (b) 122 C (c) 75 (d) 112

45. Figure 14 below is called a …………………..

Fig. 14. (a) Block (b) Cuboid (C) Cube (d) Square

Use Figure 15 below to answer questions 46– 48

v

A D

o Fig. 15. B C

46. VO is called ……………….. (a) Vertex (b) Slope (c) Diagonal (d) Height

47. /VA/ = /VB/ = /VC/ = /VD/ are called ……….. (a) Diagonals (b) Vertex (c) Slant heights (d) Tangent

48. The diagram ABCDV is called a …………………. (a) Triangular Pyramid (b) Square Pyramid (c) Rectangular Pyramid (b) Circular Pyramid

157

49. If the diagonal of a square net mesh is 8cm, what is the area of the square?(a) 64 cm2 (b) 5.66 cm2 (c) 32 cm2 (d) 16 cm2

50. A chord 8cm long is 3cm from the centre of a circular twine, calculate the radius of the circle. (a) 5cm (b) 6cm (c) 9cm (d) 10cm

158

APPENDIX C GEOMETRY ACHIEVEMENT TEST (GAT) MARKING SCHEME Each question carries equal (1) mark. Total: 50 Marks

1. A 26. A 2. A 27. C 3. C 28. C 4. D 29. D 5. B 30. C 6. B 31. B 7. C 32. D 8. B 33. B 9. C 34. D 10. A 35. D 11. D 36. A 12. A 37. B 13. C 38. A 14. C 39. C 15. B 40. B 16. D 41. C 17. D 42. C 18. C 43. A 19. C 44. D 20. B 45. B 21. C 46. D 22. A 47. D 23. B 48. C 24. D 49. A 25. A 50. A

159

APPENDIX D DELAYED GEOMETRY ACHIEVEMENT TEST MARKING SCHEME Each question carries equal (1) mark. Total: 50 Marks.

1. D 26. B 2. B 27. C 3. B 28. B 4. A 29. D 5. C 30. A 6. D 31. C 7. C 32. D 8. A 33. D 9. D 34. B 10. B 35. D 11. B 36. A 12. A 37. B 13. C 38. C 14. D 39. C 15. C 40. A 16. C 41. D 17. A 42. C 18. B 43. B 19. A 44. B 20. C 45. C 21. B 46. D 22. D 47. C 23. C 48. B 24. A 49. C 25. D 50. A

160

APPENDIX E PRE-GEOMETRY INTEREST SCALE (PRE-GIS)

INSTRUCTIONS: This instrument is designed to help you express your feelings towards two- and three- dimensional shapes in geometry. Consider each statement and tick against each number the point which best expresses your feelings or the extent you like the topic. The four points on the scale are: Strongly Agree = SA Disagree = D Agree = A Strongly Disagree = SD

Gender: Male Female

S/N Item SA A D SD 1. I enjoy solving problems involving geometry 2. I hate geometry topics in mathematics 3. I like geometry because it is practical and real 4. I find it difficult to prove theorems in geometry 5. I enjoy drawing geometric shapes 6. I discover that geometry is abstract 7. During exams, I always attempt questions on geometry 8. I always feel bored in geometry classes 9. I convince others to avoid attending geometry class 10. I cannot differentiate geometric shapes 11. I find it difficult to draw geometric shapes 12. I encourage others to attend geometry lesson 13. I find it difficult to prove geometric formulae 14. I discover that geometry is very important in science related subjects 15. I discover that geometry is not related to any subject 16. I like geometry because its shapes are seen everywhere 17. I put geometry on my personal reading timetable every day 18. I don’t include geometry on my personal reading timetable 19. I can differentiate a plane figure from a solid figure easily 20. Geometry lessons are very interesting.

161

APPENDIX F POST-GEOMETRY INTEREST SCALE (POST-GIS)

INSTRUCTIONS:

This instrument is designed to help you express your feelings towards two- and three- dimensional shapes in geometry. Consider each statement and tick against each number the point which best expresses your feelings or the extent you like the topic. The four points on the scale are: Strongly Agree = SA Disagree = D Agree = A Strongly Disagree = SD

Gender Male Female

S/N Item SA A D SD 1. I discover that geometry is not related to any subject 2. I cannot differentiate geometric shapes 3. I find it difficult to draw geometric shapes 4. I encourage others to attend geometry lesson 5. I find it difficult to prove geometric formulae 6. I discover that geometry is very important in science related subjects 7. I enjoy solving problems involving geometry 8. I like geometry because its shapes are seen everywhere 9. I put geometry on my personal reading timetable every day 10. I don’t include geometry on my personal reading timetable 11. I can differentiate a plane figure from a solid figure easily 12. I hate geometry topics in mathematics 13. Geometry lessons are very interesting. 14. I like geometry because it is practical and real 15. I find it difficult to prove theorems in geometry 16. I enjoy drawing geometric shapes 17. I discover that geometry is abstract 18. During exams, I always attempt questions on geometry 19. I always feel bored in geometry classes 20. I convince others to avoid attending geometry class

162

APPENDIX G 1

LESSON PLAN ON PLANE SHAPES USING FISHING TOOLS INSTRUCTIONAL APPROACH

Subject: Mathematics Topic: Rectangle, Rhombus and other plane shapes Number in Class: 50 Students Date: Average Age of Students: 16 Years Gender: Mixed Contents: Plane Shapes

Duration: 40 minutes per period Objectives: By the end of the lesson, the students should be able to: (1) Identify the properties of a rectangle (2) Identify the properties of a rhombus (3) Distinguish between a rectangle and a rhombus. (4) Construct a rectangle and a rhombus (5) Identify and distinguish properties of other plane shapes. Instructional Materials: Racket, net (meshes), lead and Mathematical set Entry Behavior: Students are supposed to be familiar with plane sheets of paper Presentation

Content/Step Time Teacher’s activities Students’ activities Instructional Strategies Step 1 The teacher draws and Students define Racket, net Introduction explain some plane shapes plane shapes and (meshes) and lead as students to see give examples from instructional the local materials environment Step 2 Teacher introduces fishing Students state the Highlight some Fishing Tools tools models – racket, net uses of these fishing mathematical models (meshes) and lead tools concepts involved with fishing tools such as racket, net (meshes) and lead using guided discovery,

163

demonstration and illustration. Step 3 Red mangrove shoot or The red mangrove or Guide the students Construction cane stick is used for the cane stick is used to to identify of racket construction with plantain construct the racket mathematical using local or banana stem prepared thus: concepts associated materials and dried as rope with the fishing tool. Help the *The rope is used to students practice the draw 2 or 3 straight construction of the lines at the middle of the shape fishing tool using

materials from the

environment. Use

illustration and

demonstration. The teacher improvises *The prepared red Help the students to mangrove shoot is Step 4 instructional materials understand some then used to fix or Construction when teaching arrange the bars with mathematical equal spacing. of racket concepts associated using local with the materials instructional

materials such as Circle *Finally, tie the bars well with the rope. parallelogram,

● ● ● ● ● ● ● ● rectangle, parallel

lines, squares, right ● ● ● ● ● ● ● ● angles, angles, line Rectangle

segment, straight line, area, arc, circle, π, Parallelogram circumference, and so on using guided discovery and demonstration.

164

Net (Mesh) Guide the students Step 5 The net (mesh) is either a to identify some Net (meshes) square or rhombus mathematical concepts involved such as angle, equality, diagonals, Square Net (mesh) is a area perimeter, lines rhombus of symmetry, and properties of a rhombus among others using Rhombus demonstration and discussion Step 6 Lead is prepared as a *Cut as a rectangle Students identify the Lead rectangle or square mathematical concepts involved *The rectangle is with the following carefully folded fishing tools, noting Rectangle equally lines of symmetry of the plane shapes angles, diagonals, *Lead cut as a area, perimeter as Rectangular fishing square well as properties of trap some quadrilaterals rectangle, square, *It is folded equally parallelogram, at the middle rhombus; using Square examples and

explanation.

165

Teacher writes as the Guide the students Step 7 students mention other and make fishing tools that are corrections where having plane shapes on the Students mention necessary. board. other fishing tools Fishing hanger is Other fishing that have plane used in carrying net tools e.g. shapes. and fish. Use Fishing Fishing hanger is a illustration and hanger, rectangle or a square demonstration. paddle. Rectangle or trapezium Paddle is used in paddling boats

(canoes). Use of examples and questioning. Trapezium A paddle

Square

Kite

Teachers shows the Guide students Step 8 students local materials identify Sail and used in constructing a mathematical materials for fishing sail and materials concepts associated mending net for mending net such as A fishing sail with sail used in (Net sticks that are erect and fishing such as right mending strong for sail and net angle, stick and net mending stick and ruler - cut three strong perpendicularity, mending respectively. sticks that are erect. triangle, square, ruler) - Fix a cloth or water rhombus, proof to match the parallelogram, sticks that are rectangle, straight traingular. line, line segment, - The third stick is a parallel lines and fork stick. Pythagoras theorem. Triangle

- Bambo is used in Hypothenuse constructing ruler for mending net. i.e. net Opposite Adjacent mending ruler.

166

- Net mending stick A strong stick locally called utook is used in - Cut the bambo. constructing it. - Smoothen the ‘Anwa’, another strong bambo. Use of examples, stick is also used. - Its width equals the illustrations, sides of the net demonstration and mesh. guided discovery.

Rectangle Net mending ruler

- Cut a strong stick - Carve it flat as shown Net mending stick (Uti-eri/ mbala)

Triangle

Step 9: A plane shape is a two Students copy the Teacher makes

dimensional object that has summary into their correction where Summary only length and breadth mathematics note necessary. (width). Examples of plane books. shapes are circle, triangle, square, rectangle, parallelogram, rhombus, trapezium and kite. The fishing tools models used in this lesson include racket, net (meshes); and lead. The fishing tools especially the racket has many mathematical concepts that could be used in teaching/learning process. Step 10: Teacher asks the following Students do the The teacher marks Evaluation questions: asignments and the notes and makes i) Distinguish between submit same for corrections where a rectangle and a marking. necessary. parallelogram ii) Differentiate between a square and a rhombus iii) State the common

167

features among the plane shapes drawn above. iv) With diagrams, name three other plane shapes v) Why are plane shapes called two – dimensional objects?

Step 11: Teacher notes the answers Students copy the Teacher notes the Conclusion of the above questions correction into their answers of the given by the students and note books. above questions makes corrections where given by the necessary. students and makes corrections where necessary.

168

APPENDIX G 2

LESSON PLAN ON WORD PROBLEMS ON PLANE SHAPES USING FISHING TOOLS INSTRUCTIONAL APPROACH SUBJECT: Mathematics TOPIC: Word problems on rectangles, rhombuses and other plane shapes Class: SS1 Number in Class: 50 students Date: Average Age of Students: 16 years Gender: Mixed Contents: Properties of plane shapes

Duration: 40 minutes Objectives: By the end of the lessons, the students should be able to: (1) Identify and state properties of a rectangle and a rhombus (2) Solve some word problems on rectangles and rhombuses such as perimeter, area and angles of the shapes (3) Identify and state properties of other plane shapes (4) Solve some word problems involving other plane shapes Instructional Materials: Racket, net (meshes) lead, chalk board and mathematical set. Entry Behavior: Students are supposed to be familiar with plane sheets of paper

Presentation: Content/Step Time Teacher’s activities Students’ Instructional activities Strategies Step 1 Teacher constructs rectangle, The students Guide the Construction parallelogram, square and rhombus construct various students using of plane for students to see. plane shapes the fishing tools shapes especially such as racket, rectangle, net (meshes), parallelogram, and lead for the square and use of rhombus on graph construction. paper Use of examples, questioning and illustration. Step 2 Teacher writes students down Students identify Use the fishing

169

Properties of properties of various plane shapes properties of tools –racket, plane shapes especially rectangle, parallelogram, various plane net (meshes) square and rhombus as identified by shapes. and lead to students. Students also identify the distinguish properties of Parallelogram: A parallelogram is between rectangle each plane a quadrilateral having the following and parallelogram; shape. Use properties (i) The opposite sides are parallel square and guided (ii) The opposites sides are equal rhombus etc. discovery and (iii) The opposite angles are equal (iv) The diagonals bisect one Students identify variety. another and copy

properties of plane

shapes into their

note books. Parallelogram

Rectangle: A rectangle is a quadrilateral having the following properties (i) The opposite sides are parallels (ii) The opposite sides are equal (iii) The opposite angles are equal (iv) The diagonals bisect one another (v) All the four angles are right angles (vi) The diagonals are equal

Rectangle

Rhombus: A rhombus is a quadrilateral with the following properties (i) All four sides are equal (ii) The opposite sides are parallel

170

(iii) The opposite angles are equal (iv) The diagonals bisect one another at right angles (v) It has four line of symmetry

Rhombus Square: A square is a quadrilateral that has the following properties. (i) All four sides are equal (ii) The opposite sides are parallel (iii) The opposite angles are equal (iv) The diagonals bisect one another at right angles (v) All four angles are right angles (vi) The diagonals are equal (vii) It has four lines of symmetry

Square Step 3 The teacher solves problems on The students Use the fishing Perimeter of perimeter and areas of plane shapes differentiate tools – racket, rectangle, between perimeter net (meshes) square, and area of plane and lead to parallelogram shapes solve word and rhombus problems involving plane shapes. Use of examples, questioning and problem solving.

171

The formulae for the perimeters and areas of common plane shapes are: Plane shape Perimeter Area Triangle: base b, height a+b+c ½ bh Parallelogram: base b, height h 2(l+b) bh Trapezium: height h, parallels a and b a+b+c+d ½ (a+b)h. Circle; radius r, diameter, d 2πr; πd πr2 Rectangle: length l, breadth b 2(l+b) lb. Rhombus 4s S2 Square 4s S2 Step 4 The teacher derives the formulae to Students use Correct any Area of find the perimeter and area of plane derived formulae misconception rectangle, shapes for students to see. to solve problems arising from the parallelogram, on plane shapes. examples, square and illustrations, rhombus and problem solving. Step 5 Teacher solves word problems on Students solve Guide and make Perimeter and plane shapes as examples for some words corrections area of other students to see. problems on where plane shapes 1. Calculate the perimeter of a perimeter and area necessary. rectangular net mending ruler whose of other plane Using examples length and breadth are 17cm and shapes and guided 11cm respectively. discovery.

Perimeter = L+b+L+b 17cm

= 2l+2b 11cm = 2(l+b) = 2(17 + 11)cm =2(28)cm = 56cm

2. Calculate the perimeter and area of a circular thread whose diameter is 28cm. (a) Perimeter of circle = πd 22 2/ 8/ × = 7/ 1 =88cm

172

(b) Area of circle = πr2 22 14 14 × × cm 2 7 1 1 = = 44×14cm 2 14cm = 616cm 2 3. Find the area of a triangular fishing sail whose base and height are 14m and 12m respectively . Area of ∆ = ½ base x height = ½ bh. = ½ x 14 x 12m2 = 84m2 12m

14m 4. Calculate the perimeter of a fishing hanger whose dimensions are shown 4m in the figure below 7m From the shape, 10m BC2 = 42 + 32 = 16 + 9 = 25 BC = 25 4m D A = 5m 7m 10m

4m C E 3m Perimeter of the shape B = (10 + 4 + 7 + 5)m = 26m 5. What is the perimeter and area of a net mesh (rhombus) with a side measuring 18cm? Perimeter of the rhombus = 18 + 18 + 18 + 18cm = 36 + 36cm = 72cm Area of the rhombus = 182cm2 = 18 x 18cm2 = 324cm2

18cm

173

Step 6: The teacher goes over the lesson Students copy the Teacher makes Summary briefly emphasizing the fishing tools summary into their correction instructional approach; mentions mathematics note where names of plane shapes, properties, books. necessary. formulas for calculating the perimeter and area of plane shapes as shown below. Pi (
) is a constant value that represents the ratio of the circumference to the diameter of any circle regardless of the size of the circle. i.e.
=


=

22 = 2

where
=
7 ,
=












,
=











=





Similarly, Area of a circle is found thus; A =



ℎ



=












, 22
=
7



=








ℎ






. Step 7 Teacher asks the students the Students do the Evaluation following questions. assignment and (i) Write down the common submit same to the property among the plane teacher for shapes. marking. (ii) Distinguish between a rectangle and a parallelogram (iii) Differentiate between a square and a rhombus. (iv) Give an example of each of the plane shapes (v) Calculate the perimeter and area of a rhombus whose sides 9cm. (vi) Calculate the perimeter and area of a rectangle whose length and width are 7cm and 5cm respectively.

(vii) Calculate the perimeter and area of the figure below

174

4cm

3cm 7cm Step 8 Teacher notes the answers of the Students copy the Teacher notes Conclusion questions above as given by students corrections into the answers and makes corrections where their note books. from the necessary. questions above answered by students making corrections where necessary

175

APPENDIX G 3 LESSON PLAN ON SOLIDS USING FISHING TOOLS INSTRUCTIONAL APPROACH Subject: Mathematics Topic: Cylinder, Pyramid and other solids Number in class: 50 students Date: Average Age of Students: Age of students: 16 years Gender: Mixed Contents: Solids

Duration: 40 minutes per period Objectives: By the end of the lessons, the students should be able to: (1) Identify the properties of a cylinder (2) Identify the properties of a pyramids (3) Distinguish between a cylinder and a pyramid (4) Identify properties of other solids (5) Draw the solids Instructional Materials: A bundle of rope (twine), a bundle of thread, a float, basket and mathematical set. Entry Behavior: Students are supposed to be familiar with tins of milk, tomatoes, ovaltin, milo, bournvita, bucket and funnel. Presentation Content/Step Time Teacher’s activities Students activities Instructional Strategies Step 1 Teacher draws different plane Students define plane Racket, net Definition/exp shapes. shapes as two- (meshes) and lanation of dimensional having lead. Use of plane shapes only length and breadth examples, (Revision) (width) e.g squares, illustrations, rectangle, rhombus, demonstration parallelogram, among and guided others. discovery.

Step 2 Teacher defines solids as 3- Students state the A bundle of dimensional shapes because difference between rope (twine), a Definition, they have length, (width) plane shapes and solids bundle of thread explanation of breadth and height (depth). and a float. solids Illustration and demonstration. Step 3 Teacher watches the students Students mention Identification Cylinder (A draw and cite examples from some properties of a and drawing of

176 bundle of the environment cylinder the solids. Use thread)/float Rope making of examples, (cork) - source for stick locally demonstration called “urot” and guided - Cut down the stick r - Clean the bark Cylinder discovery. - Remove the bark Rope (twine) is used in - Dry it fishing net - Weave it as rope. - used in making

fishing sail - It is fixed to anchor sinker for anchorage.

- it is sold for money.

A bundle of rope Step 4 Teacher observes as the Students mention and Identification Pyramid (A students draw and give state some properties of and drawing of pyramidal examples of solids a pyramid. For the solids. Use fishing float). instance, rope (twine) of integrated “olik” pyramidal strategies, fishing float- ‘ ekpe’. questioning, demonstration and guided discovery. Step 5 Teacher draws some solids Students identify Use fishing for students to see. Cylinder and similarities and tools pyramid differences between instructional the solids. models as

Cube guides to Net of some Solids highlight relationship. Net of a cube Use examples

Net of a cuboid and discussion.

Cuboid Net of a cylinder

177

Step 6 Teacher introduces the fishing Students are guided to Fishing Tools Fishing tools tools instructional models and construct the fishing models: a bundle of draw the shapes on the board tools models such as a instructional rope/thread and models for students to see. bundle of rope and the shape of a terminal fishing float terminal float. Use of models using materials from to highlight the the environment. concepts. Illustration and examples. Highlight the concepts using integrated strategies. Step 7 Teacher constructs pyramidal Students state uses of Students to Construction (terminal ) fishing float in the the models in fishing practice the of the solids class for students to see. and in classroom. procedure of Thread is used in constructing the mending net. Rope for models using anchorage. Float to materials from sustain net. the environment. Use illustration, examples and explanation. Step 8 A floating material such as Students source for Guide the Construction bamboo is used for the floating materials from students to of a pyramidal fishing float construction. environment and use construct the - smoothen the bamboo them, for the fishing tools - measure it and cut correctly. construction, following and identify - fix the base as a rectangle or the steps outlined by mathematical square the teacher . concepts -Join the diagonals and fix the involved. height Questioning and -Fix the slant heights use of examples accordingly and

178

-An attractive flag could be explanation. fixed at the apex of the Illustrations, terminal float to be seen at demonstration . . . . distance ...... Flag and guided discovery.

V

Slant height

Height A B 0 D C A pyramidal fishing float

Step 9 The teacher draws the solid. Students count faces, The teacher

Faces, edges edges and apexes of the guides and solids and supply the and apexes answers with examples corrects any

(vertices) of accordingly. For misconceptions. solids instance, a cube has 6 Use of Rectangular pyramid faces and 12 edges. integrated e..g dice, cubes of

sugar and magi. A strategies. cuboid has 6 faces and 12 edges e.g. match box, chalk box.

Square pyramid

Circular pyramid (cone)

Triangular Pyramid

179

Step 10 Students mention local Guide students Other solid Teacher shows students one materials used in draw various shapes – solid after another and asks constructing basket, forms of bailer, baskets them to mention local bailer. baskets materials used in construction Students state uses of - frustum, and their uses. the fishing tools. cylinder, Basket is used to store sphere, and fish or net while bailer hemisphere; is used to bail out water Bailer like from boat or canoe. hemisphere, sphere; use of examples, illustrations, demonstration and guided discovery.

Step 11 Cane stick sourced from Students observe as the Guide the Basket environment is used for the construction goes on. students to construction construction Students mention local identify some - Smoothen the cane stick materials used in mathematical very well. constructing the concepts - Split the cane stick to sizes. fishing tools and do the involved such - Engage the services of local practice themselves. as straight-lines, craft instructor. angles, squares, frustum, cylinder, sphere, hemisphere, fractions, rectangles, Cane sticks parallelogram, rhombus, parallel lines, bearing, circles, semi-circle, arc, circumference, radius, Split cane stick diameter; pii etc. Use of examples, illustrations, demonstration and guided A basket discovery.

180

Cone

Frustum

Sphere

Step 12 - Pluck mature calabash Use of Bailer - Cut into two equal parts The students mention examples, construction - Remove material inside and the uses of fishing illustrations, wash it bailer. demonstration Or and guided Use floating material Students practice the discovery. Carve it with a matchet or consrtuction of bailer knife. themselves.

A bailer

Step 13 Unlike plane shapes that have Students copy the Teacher makes Summary length and breadth (width), summary into their correction solids such as cube, cuboid, mathematics note where cylinder, cone, frustum, books. necessary. pyramid, prism, hemisphere and sphere are three Guided dimensional and have length, discovery, width and height (depth). illustrations and A pyramid is a discussion. structure with a base and sloping sides meeting at a Illustrations, point which is not in the same examples and plane as the base. demonstration. If the base is circle, it

181

is a circular pyramid or cone. If the base is a square, it is a square pyramid. If the base is a rectangle, it is a rectangular pyramid. If the base is a triangle, it is a triangular pyramid. The fishing tools used in the lesson plan have many mathematical concepts that could be easily employed in the teaching-learning process. A pyramid is a polyhedron with a base that is a polygon and lateral faces that are formed by connecting each vertex of the base to a single given point (the vertex of the pyramid) that is above or below the surface that contains the base. The lateral faces do not need to be congruent. But a prism is a polyhedron with two congruent (same size and shape) parallel bases that are polygons, and lateral faces (faces on the sides) that are parallelograms formed by connecting the corresponding vertices of the two bases. Lateral faces may also be rectangles, rhombi, or squares. A prism may also be seen as a solid which has uniform cross section e.g. cube, cuboid, and cylinder. Step 14 The teacher ask the students Evaluation the following questions Students answer the Guided (i) Name and draw five (5) questions and submit discovery. solids you know. same for marking. (ii) Distinguish between a pyramid and a prism (iii) Why are cylinders and pyramids among others

182

called solids? (iv) With diagrams, name four types of pyramids (v) State the difference between a cone and frustum and give two examples each. Step 15: Teacher notes the answers Students copy the Teacher notes Conclusion from the questions above by corrections into their the answers students making corrections notes. from the where necessary. questions above by students making corrections where necessary.

183

APPENDIX G 4 LESSON PLAN ON WORD PROBLEMS ON SOLIDS USING FISHING TOOLS INSTRUCTIONAL APPROACH Subject: Mathematics Topic: Word problems on cylinders, pyramids and other solids Number in Class: 50 students Date: Average Age of Students: 16 years Gender: Mixed Contents: Properties of a cylinder, pyramid and other solids Duration: 40 minutes each Objectives: By the end of the lesson, the students should be able to: (1) Identify and state the properties of a cylinder, pyramid and other solids (2) Calculate the surface areas and volumes of cylinders, pyramids and other solids. Instructional Materials: A bundle of rope or twine, a float, basket and mathematical set Entry Behaviour: Students are supposed to be familiar with tins of milk, ovaltin, tomatoes, bourn vita, bucket, and funnel. Presentation: Content/Ste Time Teacher’s activities Students’ Instructiona p activities l Strategies Step 1 The teacher writes on the board as the Students recall Guide the Revision students mention some plane shapes. methods of students on work on finding the use of plane shapes perimeter and Racket, net area of plane (meshes) and shapes. lead as fishing tools. Use of examples, illustration, and discussion. Step 2 Teacher draws cylinders and pyramids Students note Guide the Cylinders and that surface area students on pyramids and volume are the use of a calculated on bundle of solids. rope and a float as

184

fishing tools. Use of guided discovery. Step 3 Teacher helps students understand surface Students draws Guide Explanation areas and volumes of the solids. other solids students on of surface such as cube, relevant area, volume cuboid, cone, fishing tools of solids frustrum, sphere noting and prism. concepts involved. Use of demonstratio n and questioning. Step 4 Teacher introduces the fishing tools Students draw Identification Fishing tools instructional models, draws the shapes on and give and drawing. instructional the board and asks students to give examples examples from Use of models from their locality, using local names their local examples, (displayed) environment illustrations, using local and questioning English names. and guided discovery. Step 5 Teacher draws, labels, and identifies Students draw Problem Drawing and features of cylinder and pyramids. the shapes solving, use labeling of accordingly and of examples cylinders and ask questions and pyramids questioning (solids) and practice.

r Cylinder

185

Step 6 Teacher introduces surface area of cylinders Students note Use relevant Areas of and pyramid the explanation fishing tools cylinder, and solve – a bundle of pyramid problems rope (twine)

Cone (solids) accordingly and a float. Use of Conical fishing trap examples, illustrations, guided discovery Cast (Throw) net and Twine (rope) discussion. Step 7 Teacher introduces volumes of cylinders Students A bundle of Volume of and pyramids calculate rope and a cylinder and volumes of float as pyramid cylinders and instructional (solids) pyramids materials. Use of examples and Rectangular pyramid probing questions.

Square pyramid

186

Triangular Pyramid

Prism

Sphere Step 8 Teacher draws the solids on the board. Students draw Guide and Areas and cube, cuboid, correct volumes of cone, frustum, misconceptio other solids sphere and ns where like cube, prism and necessary. cuboids, calculate their Variety and cone, volumes and variation of frustum, surface areas. problem sphere and solving. prism Students count Questions of faces, edges and variety and apexes of every variation; simple regular application. solid. Step 9. Solid shapes are cube, cuboid, cylinder, Students use the The teacher Summary cone, pyramid, frustum, prism, sphere, formulae to should check hemisphere etc show their features (faces, solve problems their edges, apexes). Surface area is the sum of involving the assignments area of their faces. Volume is the product of solid shapes and make the length, width (breadth) and depth corrections

187

(height) of the solid. where Volume of cylinder is found by necessary V =


ℎ where V = volume, 22
=
7 , r = radius of circle, and h = height of the cylinder Total surface area of a cylinder = 2


+ 2

ℎ = 2



+ ℎ






.

height

r

Area of curved surface is S = 2

ℎ. Volume of cone =



ℎ
Area of curved surface of a cone i.e. S =


Total surface area of a cone =


+






+











Volume of a pyramid 1 i.e. V =
3











ℎ


ℎ
1
3bh.

height

r

Volume of a sphere =




The surface area of a sphere = 4


. 1 Volume of cone/pyramid/prism =
3 base area x height i.e. V =
bh.

188

Step 10:

Solid shape Area Volume Cube edge 6l2 l3 The Cylinder: radius r, height h Curved surface, Πr2h. formulae for S = 2πrh. the surface Total surface = areas and 2πrh + 2πr2 volumes of = 2πr(r+h) sq common unit solids are Prism: height h, base area A Ah 2 Cone: radius r height h slant height l Πrl + πr 1 πr 2 h. Πr (l+r) sq. unit 3 1 Pyramid 3 Ah 2 Sphere 4πr 4 3 3 πr

Solid shape Number of faces F Number of V – E+F Number of edges E vertices V Cube 6 square 12 8 Cuboid 6 rectangular 12 8 Cone 1 circular 1 1 Cylinder 2 flat circular 2 - Rectangular 5 Pyramid 5 8 Square 5 2 pyramid 5 8 Triangular pyramid 4 2 (Tetrahedron) 4 6 Sphere 1 - - 1

Prism i. Faces depend on the number of sides of the base polygon ii. If a prism has a triangular base, it is called a triangular prism iii. If a prism has a quadrilateral base, it is called a prism. iv. If a prism has a base that is not perpendicular to the lateral edges, it is called an oblique prism. v. If a prism has a base perpendicular to the lateral edges, it is called right

189

prism. vi. If a prism has a regular base, it is called a regular prism. In general, a prism with an n-sided base has i. n + 2 faces ii. 3n edges iii. 2n vertices V-E + F = 2 or V – E + F = 1 (for one surface solid).

Step 11 1. If the dimensions of a rectangular cork Examples of are 8cm by 6cm by 5cm, find its volume and Word its total surface area. Problems of solids. Volume of cork = Lxbxh cm3 = 8x6x5cm3 = 48x5cm3 = 240cm3

Total surface area of the cork = 2(lxb+lxh+bxh)cm2 = 2(8xx6 + 8x5+ 6x5)cm2 = 2(48 + 40 + 30)cm2 = 2x118cm2 = 236cm2 2. Calculate the total surface area of a cylindrical twine (thread) whose height and radius are 15cm and 13/4cm respectively. Total surface area of cylinder = 2πr (r+h)cm2 22 7 3 2 = 2x 7 x 4 (1 4 + 15)cm 7 2 =11x( 4 +15)cm 7+60 2 11( 4 )cm 67 2 =11x 4 cm 373 2 = 4 cm 1 2 = 184 4 cm = 184.25cm2 3. A pyramidal fishing float has a rectangular base ABCD and the vertex V is vertically above the point of intersection of the diagonal. Given that AB = 8cm, BC = 6cm and the slant height = 9cm. calculate (i) the height VO, and (ii) the volume of the pyramidal fishing

190 float.

(i) D 8cm C V 6cm O 9cm

D A C 2 2 2 AC = 8 + 6 O 6cm A = 64 + 36 8cm B =100 AC = 100 V = 10cm In ∆AVO, VO2 = AV2 – OV2 = 92 - 52 9cm = 81 – 25 O =56 A = ∴VO = 56 5cm = 7.483 = 7.5cm ∴the heightVO = 7.5cm 1 ii. Volume of the pyramid = 3 base area x height 1 = ×8× 6× 7 1 cm 3 3 2 1 2 1/5/ = × 8× 6/× cm 2 3/ 2/ 1 1 =120cm3. ∴thevolume of the pyramid=120cm3 4. A conical fishing trap has a base radius of 5cm and a height of 12cm. Calculate: (a) Its slant height (b) the total surface area. Leave the answer in terms of π. (a) L2 = h2 + r2 = 122 + 52 = 144 + 25 = 169 12cm L = 169 = 13cm 5cm (b) Total surface area = πrl + πr 2 = πr (l+r) = 5π (13 + 5) = 5π (18)

191

= 5π x 18 2 = 90πcm 5. Find the surface area and volume of a spherical basket whose diameter is 9cm. Surface area of the spherical basket = 4πr2 22 9 9 = 4/ × × × cm 2 7 2/ 2/ 22×81cm 2 = 7 1782cm 2 = 7 254 4 cm 2 = 7 = 254.57cm 2 . 4 Volume of spherical basket = πr 3 . 3 4 2/ 2/ 9 9 9 × × × × cm 3 3/ 7 2/ 2/ 2/ 33×81 = cm 3 7 2673 = cm 3 7 = 381.857cm3 = 381.86cm3 Students do the Step 12 (i) Draw cylinder, cube, cuboid, cone and assignment Evaluation pyramid and submit (ii) State how many faces has each of the some for solids. marking. (iii) State the formulae for calculating the total surface area of a cylinder and a cone. (iv) State the formulae to find volume of cube, cuboid, cylinder, cone, pyramid and sphere. (v) What is the volume of cylindrical twine of radius 7cm and height 3cm? (vi) Calculate the surface area of a cube whose side is 8cm. (vii) What is the volume of a cone of radius 14cm and slant height of 10cm? (viii) Calculate the volume of a spherical basket of radius 21cm. (ix) A pyramid on a base 100m2 is 15m high. Find the volume of the pyramid. (x) A pyramidal fishing float 8cm high stands on a rectangular base 6cm and 4cm, calculate the volume of the

192

pyramid. (xi) Find the volume of a conical net of base diameter 14cm and height 6cm. Step 13 The teacher notes the answers provided by Students copy The teacher Conclusion the students on the above questions and the corrections notes the make correction where necessary. into their notes. answers provided by the students on the above questions and make correction where necessary.

193

APPENDIX H 1 LESSON PLAN ON PLANE SHAPES USING CONVENTIONAL (LECTURE) METHOD

Subject: Mathematics Topic: Rectangle, Rhombus and other plane shapes Class: SS I Number in class: 50 Students Date: Average Age of Students: 16 Years Gender: Mixed Contents: Plane Shapes

Duration: 40 Minutes per period Objectives: By the end of the lessons, the students should be able to: (i) Identify the properties of a rectangle (ii) Identify the properties of a rhombus (iii) Distinguish between a rectangle and a rhombus (iv) Construct a rectangle and a rhombus (v) Identify and distinguish properties of other plane shapes. Instructional Materials: New General Mathematics SS 1, Graph paper and Mathematical set. Entry Behaviour: Students are supposed to be familiar with plane sheets of paper.

Presentation: Content/Step Time Teacher’s activities Students’ activities Instructional Strategies Step 1 The teacher defines Students watch the Definition of plane shapes and give teacher draw a plane plane shapes examples shape Step 2 The teacher draws and Students write down the Questioning. Rectangle mentions properties of properties of the plane a rectangle shape Step 3 The teacher draws and Students note properties Questioning Rhombus mention properties of of the plane shape a rhombus Step 4 The teacher gives Students note the Questions and answers. Similarities similarities and relationship. and differences between differences the two plane shapes Step 5. The teacher draws Students draw the plane Examples

194

other plane shapes and shapes into their writes their properties exercise books Step 6. The teacher draws Students identify some Questions and plane shapes and checks answers. Identification some plane shapes. same in their of plane mathematics texts. shapes in text book Circle

Rectangle

Parallelogram

Square

Rhombus

Step 7. The teacher identifies Students list down some Examples and illustrations some plane shapes in plane shapes found in the environment. the environment. Step 8. A plane shape is a Students copy the Teacher makes Summary two-dimensional summary into their correction where object that has only mathematics note books. necessary. length and breadth (width). Examples of plane shapes include circle, triangle, square, rectangle,

195

parallelogram, rhombus, trapezium and kite. Shapes that are plane are common in the environment. Step 9. Teacher writes Students do the The teacher marks Evaluation assignment on the asignments the notes and makes board for students. corrections where 1.Distinguish between necessary. a rectangle and a parallelogram 2. Differentiate between a square and a rhombus 3. State the common features among the plane shapes drawn above 4. With diagrams, name three other plane shapes. 5. Why are plane shapes called two- dimensional objects?

Step 10: Teacher notes the Students copy the Teacher notes the Conclusion answers of the above corrections into their answers of the above questions given by the notes. questions given by students and makes the students and correction where makes corrections necessary. where necessary.

196

APPENDIX H 2 LESSON PLAN ON WORD PROBLEMS ON PLANE SHAPES USING CONVENTIONAL (LECTURE) METHOD Subject: Mathematics Topic: Word problems on rectangles, rhombuses and other plane shapes Class: SS 1 Number in Class: 50 students Date: Average Age of Students: 16years Gender: Mixed Contents: Properties of plane shapes

Duration: 40 minutes per period Objectives: By the end of the lessons, the students should be able to: (1) Identify and state properties of a rectangle and a rhombus (2) Solve some word problems on rectangles and rhombuses such as perimeter, area and angles of the shapes (3) Identify and state properties of other plane shapes. (4) Solve some word problems involving other plane shapes.

Instructional Materials: New General Mathematics SS I and Mathematical set. Entry Behavior: Students are supposed to be familiar with plane sheets of paper.

Content/Step Time Teacher’s activities Students’ Instructional Strategies activities Step 1 Teacher constructs various Students Questions and answers. Construction plane shapes especially observe the of plane rectangle, parallelogram, teacher shapes square and rhombus on the construct board. rectangle, parallelogram, square and rhombus on graph paper. Step 2 The teacher writes down the Students Questioning properties of various plane Properties of distinguish shapes especially rectangle, plane shapes parallelogram, square an between

197 rhombus. rectangle and Parallelogram: A parallelogram; parallelogram is a quadrilateral having the square and following properties rhombus; (v) The opposite sides are parallel trapezium and (vi) The opposites sides are kite. equal (vii) The opposite angles are equal Students copy (viii) The diagonals bisect one another the properties

of the plane

shapes into

Parallelogram their notes.

Rectangle: A rectangle is a quadrilateral having the following properties (i) The opposite sides are parallels (ii) The opposite sides are equal (iii) The opposite angles are equal (iv) The diagonals bisect one another (v) All the four angles are right angles (vi) The diagonals are equal

Rectangle Rhombus: A rhombus is a quadrilateral with the following properties (i) All four sides are equal (ii) The opposite sides are parallel (iii) The opposite angles are equal (iv) The diagonals bisect one another at right

198

angles (v) It has four line of symmetry

Rhombus Square: A square is a quadrilateral that has the following properties. (i) All four sides are equal (ii) The opposite sides are parallel (iii) The opposite angles are equal (iv) The diagonals bisect one another at right angles (v) All four angles are right angles (vi) The diagonals are equal (vii) It has four lines of symmetry

Square

Step 3 Teacher differentiates Students solve Questioning Perimeter of between perimeter and area problems on rectangle, of plane shapes. perimeter and square, area of plane parallelogram shapes. and rhombus The formulae for the perimeters and areas of common plane shapes are: Plane shape Perimeter Area Triangle: base b, height a+b+c ½ bh Parallelogram: base b, height 2(l+b) bh

199

h Trapezium: height h, a+b+c+d ½ (a+b)h. parallels a and b Circle; radius r, diameter, d 2πr; πd πr2 Rectangle: length l, breadth 2(l+b) lb. b Rhombus 4s S2 Square 4s S2 Step 4 The teacher derives the Students use Questions and answers. Area of formulas to solve problems. the formulas rectangle, to find the parallelogram, perimeter and square and area of plane rhombus shapes through reasoning. Step 5 Teacher solves some word Students copy Perimeter and problems on perimeter and worked area of other area of other plane shapes as examples into plane shapes examples. their notes. Step 6 The teacher goes over the Students copy Teacher makes correction Summary lesson briefly. the summary where necessary. into their mathematics note books. Step 7 Teacher asks the students Students Teacher makes corrections Evaluation the following questions. provides where necessary. (i) Write down the answers common property (solutions) to among the plane the questions shapes. and submit (ii) Distinguish between a same for rectangle and a marking. parallelogram (iii) Differentiate between a square and a rhombus. (iv) Give an example of each of the plane shapes (v) Calculate the perimeter and area of a rhombus whose side is 9cm.

200

(vi) Calculate the perimeter and area of a rectangle whose length and width are 7cm and 5cm respectively (vii) Calculate the perimeter and area of the figure below

4cm

3cm 7cm

Step 8 Teacher notes the answers Students copy Teacher notes the answers Conclusion from the questions below by the from the questions below by students making corrections corrections students making corrections where necessary. into their where necessary. While perimeter is the notes. While perimeter is distance around a two – the distance around a two – dimensional shape, area Students copy dimensional shape, area describes the region inside a the summary describes the region inside a shape. For instance, the into their shape. For instance, the circumference of a circle is mathematics circumference of a circle is its perimeter. notebooks. its perimeter. Pi (π) is a constant value that Pi (π) is a constant value that represents the ratio of the represents the ratio of the circumference to the circumference to the diameter of any circle diameter of any circle regardless of the size of the regardless of the size of the circle. circle. i.e.
=
i.e.
=



=


=

= 2

where
= = 2

where
= 22 22
7 ,
=
7 ,
=












,
=












,
=











=

















=





Similarly, Area of a circle is Similarly, Area of a circle is found thus; found thus; A =



ℎ



= A =



ℎ



=












,












, 22 22
=
7




=
7



=








ℎ






. =








ℎ






.

201

APPENDIX H 3 LESSON PLAN ON SOLIDS USING CONVENTIONAL (LECTURE) METHOD Subject: Mathematics Topic: Cylinder, Pyramid and other solids Class: SS1 Number in class: 50 students Date: Average Age of students: 16 years Gender: Mixed Contents: Solids Duration: 40 minutes per period Objectives: By the end of the lessons, the students should be able to: (1) Identify the properties of a cylinder (2) Identify the properties of a pyramid (3) Distinguish between a cylinder and pyramid (4) Identify properties of other solids (5) Draw the solids

Instructional Materials: Ovaltin and Mathematical set. Entry Behavior: Students are supposed to be familiar with tins of milk, tomatoes, ovaltin, milo, bournvita, bucket and funnel. Presentation: Content/Step Time Teacher’s activities Students activities Instructional Strategies Step 1 The teacher defines and explains Students write Definition/expla plane shapes giving examples from down the nation of plane environment explanations into shapes their exercise books. Step 2 Solids are 3-dimesnional shapes The students Questioning Definition and because they have length, breadth observe the explanation of and height (depth). difference between solids plane shapes and solids Step 3 The teacher mentions some Students copy into Use of examples Cylinder properties of a cylinder . exercise books the properties. Step 4 The teacher mentions and states Students write Questions and answers. Pyramid some properties of pyramids down the properties into exercise books

202

Step 5 The teacher identifies similarities Students note down Questioning Cylinder and and differences between the solids the relationship. pyramid

r Cylinder

Circular pyramid (cone)

Rectangular pyramid

Square pyramid

Triangular pyramid

Step 6 The teacher draws the solids on the Students draw Drawing of board. solids into their Solids note books. Step 7 The teacher mentions other solids Students write Questions and answers. Other solids like cube, cuboid, cone, frustum, down names of

203

sphere and prism. other solids into their exercise books noting their properties. Step 8 The teacher counts faces, edges and Students note down Use of illustrations Faces, edges apexes of the solids the answers and and apexes of accordingly. explanations. solids Step 9. Unlike plane shapes that have Students copy the Teacher Summary length and breadth (width), solids summary into their makes such as cube, cuboid, cylinder, mathematics note corrections cone, frustum, pyramid, prism, books. where hemisphere and sphere are three necessary. dimensional and have length, width and height (depth). A pyramid is a structure with a base and sloping sides meeting at a point which is not in the same plane as the base. If the base is circle, it is a circular pyramid or cone. If the base is a square, it s a square pyramid. If the base is a rectangle, it is a rectangular pyramid. If the base is a triangle, it is a triangular pyramid. The fishing tools used in the lesson plan have many mathematical concepts that could be easily employed in the teaching-learning process. A pyramid is a polyhedron with a base that is a polygon and lateral faces that are formed by connecting each vertex of the base to a single given point (the vertex of the pyramid) that is above or below the surface that contains the base. The lateral faces do not need to be congruent. But a prism is a polyhedron with two congruent (same size and shape) parallel bases that are polygons, and lateral faces (faces on the sides) that are parallelograms formed by connecting the

204

corresponding vertices of the two bases. Lateral faces may also be rectangles, rhombi, or squares. Step 10. The teacher asks the students the following questions Evaluation (i) Name and draw five (5) solids you know. (ii) Distinguish between a pyramid and a prism (iii) Why are cylinders and pyramids among others called solids? (iv) With diagrams, name four types of pyramids (v) State the difference between a cone and frustum and give two examples each. Step 11 Teacher notes the answers from the Students do the Teacher notes Conclusion questions above by students making assignment and the answers corrections where necessary. submit same for from the marking. questions above by students making corrections where necessary.

205

APPENDIX H 4 LESSON PLAN ON WORD PROBLEMS ON SOLIDS USING CONVENTIONAL (LECTURE) METHOD Subject: Mathematics Topic: Word Problems on Cylinders, Pyramids and other Solids Class: SS1 Number in Class: 50 Students Date: Average Age of Students: 16 years Gender: Mixed Contents: Properties of cylinder, pyramid and other solids Duration: 40 minutes per period. Objective: By the end of the lessons, the students should be able to: (1) Identify and state the properties of cylinder, pyramid and other solids (2) Calculate the surface areas and volumes of cylinders, pyramids and other solids

Instructional Materials: Bournvita tin and mathematical set. Entry Behaviour: Students are supposed to be familiar with tins of milk, ovaltin, tomatoes, bournvita; bucket and funnel Presentation:

Content/Step Time Teacher’s activities Students Instructional activities Strategies Step 1 The teacher writes names of Students name Use of plane shapes on the board. illustrations. Revision work some plane on plane shapes shapes and recall methods of finding perimeter and area of plane shapes. Step 2 The teacher draws cylinder Students draw Questions and and pyramid on the board. answers. Cylinders and cylinder and pyramids pyramid in their exercise books. Step 3 The teacher draws other solids Students draw Questioning on the board. Explanation of other solids such Teacher explains surface areas surface area and and volumes of solids. as cube, cuboid, volume of solids cone, frustum, sphere and prism.

206

Students copy explanation into their note books. Step 4 Teacher writes the examples Students draw Questions and on the board. answers. and give examples from their environment. Step 5 The teacher draws, labels and Students draw the Questioning identifies features of cylinder Drawing and shapes and pyramids labeling of accordingly cylinders, pyramids (solids) Step 6 Teacher introduces surface Students note the Questions and area of cylinders and pyramids answers. Areas of explanation and cylinder and solve problems pyramid (solids)

r Cylinder Step 7 Teacher introduces volume of Students are Examples and cylinders and pyramids illustrations. Volume of helped to cylinder and calculate volume pyramid (solid) of cylinder and

pyramid

Cone

Conical fishing trap

Step 8 The teacher counts faces, edges Students draw a Use of examples,

207

Areas and and apexes of the solids after cube, cuboid, illustrations and drawing the shapes on the explanations. volumes of cone, frustum, board. other solids like sphere and prism cube, cuboid, and count their cone, frustum, faces, edges and sphere and apexes prism themselves. Rectangular pyramid

Square pyramid

Prism

Sphere

Basket

Step 9 The teacher explains to the The students Questioning Derivation of students how the formulas are write down the formulas derived formulas and use them to solve word problems Step 10 The teacher explains to the The teacher gives Questions and answers. Revision of the students how the formulas are more word

208 formulas being derived and solves more problems to the derivation problems using the formulas students to solve using the formulas. Step 11 Solid shapes are cube, cuboid, Students copy the Summary cylinder, cone, pyramid, summary into frustum, prism, sphere, their note books. hemisphere etc show their features (faces, edges, apexes). Surface area is the sum of area of their faces. Volume is the product of the length, width (breadth) and depth (height) of the solid.

Volume of cylinder is found by V =


ℎ where V = volume, 22
=
7 , r = radius of circle, and h = height of the cylinder Total surface area of a cylinder =


ℎ+ 2

ℎ = 2



+ ℎ






. Area of curved surface is S = 2

ℎ.

height

r

Area of curved surface is S = 2

ℎ. Volume of cone =



ℎ
Area of curved surface of a cone i.e. S =


Total surface area of a cone =


+






+

height

r

209

Volume of a pyramid 1 i.e. V =
3








⊥

ℎ


ℎ
1 =
3bh. Volume of a sphere =




The surface area of a sphere = 4


. Volume of cone/pyramid/prism 1 =
3 base area x height i.e. V =
bh.

Step 12 (i) Draw cylinder, cube, Students do the Evaluation cuboid, cone and exercise and pyramid submit same for (ii) State how many faces marking. has each of the solids. (iii) State the formulae for calculating the total surface area of a cylinder and a cone. (iv) State the formulae to find volume of cube, cuboid, cylinder, cone, pyramid and sphere. (v) What is the volume of cylindrical twine of radius 7cm and height 3cm? (vi) Calculate the surface area of a cube whose side is 8cm. (vii) What is the volume of a cone of radius 14cm and slant height of 10cm? (viii) Calculate the volume of a spherical basket of radius 21cm. (ix) A pyramid on a base 100m2 is 15m high. Find

210

the volume of the pyramid. (x) A pyramidal fishing float 8cm high stands on a rectangular base 6cm and 4cm, calculate the volume of the pyramid. (xi) Find the volume of a cone of base diameter 14cm and height 6cm. Step 13 The teacher notes the answers Students copy The teacher Conclusion provided by the students on the corrections into notes the above questions and make their note books. answers correction where necessary. provided by the students on the above questions and make correction where necessary.

211

APPENDIX I Computation of the Reliability of Geometry Achievement Test (GAT)

S/N R W P Q PQ 1 24 6 0.80 0.20 0.16 2 26 4 0.87 0.13 0.12 3 14 16 0.47 0.53 0.25 4 16 14 0.53 0.47 0.25 5 12 18 0.40 0.60 0.24 6 17 13 0.57 0.43 0.25 7 15 15 0.50 0.50 0.25 8 17 13 0.57 0.43 0.25 9 15 15 0.50 0.50 0.25 10 9 21 0.30 0.70 0.21 11 8 22 0.27 0.73 0.20 12 21 9 0.70 0.30 0.21 13 14 16 0.47 0.53 0.25 14 16 14 0.53 0.47 0.25 15 20 10 0.67 0.33 0.22 16 16 14 0.53 0.47 0.25 17 17 13 0.57 0.43 0.25 18 15 15 0.50 0.50 0.25 19 12 18 0.40 0.60 0.24 20 19 11 0.63 0.37 0.23 21 25 5 0.83 0.17 0.14 22 8 22 0.27 0.73 0.20 23 12 18 0.40 0.60 0.24 24 13 17 0.43 0.57 0.25 25 23 7 0.77 0.23 0.18 26 24 6 0.80 0.20 0.18 27 10 20 0.33 0.67 0.22 28 27 3 0.90 0.10 0.09 29 18 12 0.06 0.40 0.24 30 16 14 0.53 0.47 0.25 31 16 14 0.53 0.47 0.25 32 6 24 0.20 0.80 0.16 33 11 19 0.37 0.63 0.23 34 13 17 0.43 0.57 0.25 35 16 14 0.53 0.47 0.25 36 21 9 0.70 0.30 0.21 37 15 15 0.50 0.50 0.25 38 26 4 0.87 0.13 0.12

212

39 19 11 0.63 0.37 0.23 40 16 14 0.53 0.47 0.25 41 24 6 0.80 0.20 0.16 42 26 4 0.87 0.13 0.12 43 14 16 0.47 0.53 0.25 44 20 10 0.67 0.33 0.22 45 21 9 0.70 0.30 0.21 46 17 13 0.57 0.43 0.25 47 15 15 0.50 0.50 0.25 48 16 14 0.53 0.47 0.25 49 18 12 0.60 0.40 0.24 50 25 5 0.83 0.17 0.14 10.84 R = Number of Examinees that choose correct option W = Number of examinees that choose wrong options p = Proportion of examinees that choose correct option q = Proportion of examinees that choose wrong option pq = Product of proportion of those that choose correct option and those that choose wrong options 2 S1 = Variance of total item n  ∑ pq rA = 1 2  n −1 S 1  b  50  10.84 = 1−  50−1 54.69 50 = (1− 0.20)) 49 =1.0(0.80) = 0.82

213

APPENDIX I2 Computation of the Reliability of Geometry Retention Test (GRT)

S/N R W P Q PQ 1 19 11 0.63 0.37 0.23 2 21 9 0.70 0.30 0.21 3 19 11 0.63 0.37 0.23 4 27 3 0.90 0.10 0.09 5 23 7 0.77 0.23 0.18 6 16 14 0.53 0.47 0.25 7 17 13 0.57 0.43 0.25 8 19 11 0.63 0.37 0.23 9 15 15 0.50 0.50 0.25 10 14 16 0.47 0.53 0.25 11 21 9 0.70 0.30 0.21 12 11 19 0.37 0.63 0.23 13 24 6 0.80 0.20 0.16 14 23 7 0.77 0.23 0.18 15 15 15 0.50 0.50 0.25 16 22 8 0.73 0.27 0.20 17 14 16 0.47 0.53 0.25 18 19 11 0.63 0.37 0.23 19 25 5 0.83 0.17 0.14 20 16 14 0.53 0.47 0.25 21 14 16 0.47 0.53 0.25 22 19 11 0.63 0.37 0.23 23 24 6 0.80 0.20 0.16 24 26 4 0.87 0.13 0.12 25 19 11 0.63 0.37 0.23 26 17 13 0.57 0.43 0.25 27 6 24 0.20 0.80 0.16 28 18 12 0.60 0.40 0.24 29 12 18 0.40 0.60 0.24 30 21 9 0.70 0.30 0.21 31 16 14 0.53 0.47 0.25 32 12 18 0.40 0.60 0.24 33 21 9 0.70 0.30 0.21 34 21 9 0.70 0.30 0.21 35 12 18 0.40 0.60 0.24 36 18 12 0.60 0.40 0.24 37 20 10 0.67 0.33 0.22 38 27 3 0.90 0.10 0.09

214

39 23 7 0.77 0.23 0.18 40 15 15 0.50 0.50 0.25 41 14 16 0.47 0.53 0.25 42 17 13 0.57 0.43 0.25 43 16 14 0.53 0.47 0.25 44 16 14 0.53 0.47 0.25 45 24 6 0.80 0.20 0.16 46 21 9 0.70 0.30 0.21 47 22 8 0.73 0.27 0.20 48 24 6 0.80 0.20 0.16 49 13 17 0.43 0.57 0.25 50 24 6 0.80 0.20 0.16 10.63

R = Number of Examinees that choose correct option W = Number of examinees that choose wrong options P = proportion of examinees that choose wrong option P = proportion of examinees that choose wrong option Pq = Product of proportion of those that choose correct option and those that Choose wrong options 2 St = variance of total item.   n  ∑ Pq  rA = 1− 2  n−1  S   a1  50  10.63  = 1−  50−1 47.34 50 = (1−0.22) 49 =1.02(0.78) =0.80

215

APPENDIX I3 RELIABILITY COMPUTATION USING CRONBACH ALPHA Geometric Interest Scale (GIS) Reliability SCALE: ALL VARIABLES Case Processing Summary N % Cases valid 30 100.0 Excludeda 0 .0 Total 30 100.0 a.Listwise deletion based on all variables in the procedure: Reliability Statistics Cronbach’s N of Items Alpha .876 20

216

APPENDIX J1 Analysis of WAEC from 2000-2004 Adapted from Kurumeh (2006)

Year No of Entry % Pass/Credit % Failure 2000 643, 371 32.81 67.19 2001 1,023,102 36.55 63.45 2002 1,078, 901 34.50 65.50 2003 939,506 36.91 63.09 2004 844,525 34.52 65.48

217

APPENDIX J2 THE WEST AFRICAN EXAMINATIONS COUNCIL COUNTRY: NIGERIA WEST AFRICAN SSC EXAMINATION STATISTICS OF RESULTS BY GRADES FOR ALL CANDIDATES

NO. OF NO. OF CANDS. CANDS. SUBJECT THAT THAT ENTERED SATE ABS 1-6 7-8 9 MAY/JUNE 2005 MATHEMATICS 1092511 1066538 25973 408283 269898 367716 % 97.62 2.37 38.28 25.30 34.47

MAY/JUNE 2006 MATHEMATICS 1184180 1162335 21845 482869 36756 293565 % 98.15 1.84 41.54 31.62 25.25

MAY/JUNE 2007 MATHEMATICS 1275839 1254492 21347 588486 335581 304550 % 98.32 1.67 46.91 26.91 24.27

MAY/JUNE 2008 MATHEMATICS 1369124 1340906 28218 763994 318218 228808 % 97.93 2.06 56.97 23.73 17.06

MAY/JUNE 2009 MATHEMATICS 1348832 1323247 25585 552848 372560 366431 % 98.10 1.89 45.49 25.75 23.97

MAY/JUNE 2010 MATHEMATICS 1348832 1323247 25585 552848 377560 366431 % 98.10 1.89 41.77 28.15 27.69

MAY/JUNE 2011 MATHEMATICS 1540177 1509220 30957 597384 469057 420318 % 97.99 2.00 39.58 31.07 27.85 97.78 2.21 50.60 28.85 18.02

MAY/JUNE 2012 MATHEMATICS 1695301 1657757 37544 838845 478420 298848 97.78 2.21 50.60 28.85 18.02 %

MAY/JUNE 2013 MATHEMATICS 1688087 1657612 30475 898524 462555 245670 98.19 1.80 54.20 27.90 14.82 %

218

APPENDIX J3 REVIEW OF WEST AFRICAN SCHOOL CERTIFICATE EXAMINATION RESULTS IN RIVERS STATE 2007 – 2011 Table IV: Analysis of 5-year students’ performance. In WASSCE in Rivers State 2007 – 2011

Year 2007 2008 2009 2010 2011

No of schools 442 464 513 495 527

No of students who sat for examination (Public & 86, 895 87, 912 81, 618 43,126 61429

Private)

No with minimum of 5 credits including English and 43, 911 47, 211 39.601 13,715 30670

Mathematics

% of performance in relation to the total number 50.47% 53.70% 48.52% 31.80% 50.22% registered

219

APPENDIX K Table of Specification or Test Blue Print on Geometry Achievement Test (GAT) EDUCATIONAL OBJECTIVES Week LOWER ORDER HIGHER ORDER QUESTIONS Content Percenta QUESTIONS ge KNOW- COMPR APPLI- ANALYS SYN- EVA- TOTAL weightinLEDGE E- CATION IS THESIS LUATIO 100% g 40% HENSI 20% 15% 0% N ON 0% 25% Identificati on and 1 25 5 3 3 2 - - 13 properties (1,3,4,5 (8,14,1 (`20,21, (43,45) of a ,6) 6) 42) rectangle, a rhombus and other plane shapes Some word 1 25 5 3 3 1 - - 12 problems (2,7,9,1 (12,13, (18,22,2 (40) involving 0,11) 17) 3) rectangles, rhombuses and other plane shapes Identificati on and 1 25 5 3 3 2 - - 13 properties (15,19, (31,32, (34,35,4 (46,48) of a 28,29,3 33) 4) cylinder, a 0) pyramid and other solid shapes Some word 1 25 5 3 3 1 - - 12 problems (24,25, (37,38, (41,47,4 (50) involving 26,27,3 39) 9) cylinders, 6) pyramids and other solid shapes Total 4 100 20 12 12 6 - - 50

220

APPENDIX L SOME FISHING TOOLS TWO– DIMENSIONAL SHAPES Concepts Concepts: ● ● ● ● ● ● ● ● i. Straight lines ● ● i) Straight lines ● ● ii. Parallel lines ● ● ii) Diagonals ● ● iii. Parallelogram ● ● ● iii) Perpendicularity ● ● ● iv. Rectangle iv) Symmetry RACKET v. Right angles. v) Perimeter vi. Semi circle vi) Area vii. Radius NET MESH vii) Square viii. Diameter viii) Parallelogram ix. Arc.

x. Chord ix) Kite x) Rhombus xi. Perimeter xi) Angle xii. Area xii) Right angle xiii. Perpendicularity NET MESH xiii) Parallel lines xiv.

(
)

xv.





xvi. Square xvii. Angle Concepts: THREE – DIMENSIONAL SHAPES (i) Straight lines Concepts: (ii) Rectangle (iii) Diagonals (i)
(ii) Radius (iv) Height (iii) Diameter (v) Slant height (iv) Circle (vi) Perpendicular

(v) Arc lines (vi) chord (vii) Symmetry (vii) Circumference (viii) Surface area

(viii) Surface area (ix) Volume TERMINAL (ix) Volume (PYRAMIDAL) (x) Rectangular base (x) Perpendicularity FISHING FLOAT (xi) Total surface areas A BUNDLE OF ROPE (xi) Total surface areas (xii) Triangular base (TWINE) (xii) Cylinder (xiii) Circular base (xiv) Angle (xiii) Angle (xv) Square base

221

SOME FISHING TOOLS 1. Thread, twine or rope

2. Float, buoy (cork)

● ● ● ● ● ● ● ● 3. Racket ● ● ● ● ● ● ● ● ● ● ● ● ● ●

4. Lead

5. Net meshes

6. Baskets

222

7. Bailer (ewop)

8. Canoe (uji)

9. Canoe bench (agọm)

11. Conical fishing trap 10. Hand gathering net (ukpuuk) (Oket)

12. Rectangular fishing trap (edek) 13. Trap (nkata)

14. Net mending stick 15. Paddle (uti- eri/mbala) uran

16. Fishing Hook (ukọọk) 223

17. Net mending ruler (abada)

18. Water stirring stick (akigbo)

19. Crab stick (uti uka)

20. Fishing sail (awala) •

21. Net with fish 22. Landing Net

224

APPENDIX M

TYPES OF FISHES WITH PICTURES

225

226

227

228229

APPENDIX N SENIOR SECONDARY 1 STUDENTS’ POPULATION OF SCHOOLS AS AT 2014/2015 ACADEMIC SESSION IN ANDONI LOCAL GOVERNMENT AREA

SS I S/No Name of School Male Female 1 Government Secondary School, Ngo 185 184 2 Community Secondary School, Agwut Obolo 143 142 3 Community Secondary School, Ekede 129 127 4 Community Secondary School, Ebukuma 100 92 5 Government Secondary School, Asarama 122 120 6 Community Secondary School, Unyeada 142 141 7 Government Comprehensive High School 84 83 Ataba 8 Community Secondary School, Ibot Irem 95 85 9 Community Secondary School, Dema 116 110 10 Community Secondary School, Ikuru Town 62 55 11 Community High School, Egbormung 58 50 12 Community Secondary School, Okoroboile 53 40 Total 1290 1228 Grand Total 25 18 Source: Ministry of Education, Port-Harcourt.

229 229

APPENDIX O ANCOVA FOR GAT OUTPUT

Between-Subjects Factors Value Label N Methods 1 FTIA 100 2 LECTURE 100 Gender 1 Male 104 2 Female 96

Descriptive Statistics Std. Methods Gender Mean Deviation N Pretest score FTIA Male 14.9231 3.75132 52 Female 13.8333 4.40180 48 Total 14.4000 4.09237 100 LECTURE Male 14.8077 3.88076 52 Female 13.3750 4.04562 48 Total 14.1200 4.00575 100 Total Male 14.8654 3.79846 104 Female 13.6042 4.21146 96 Total 14.2600 4.04154 200 Posttest FTIA Male 36.9615 7.81141 52 score Female 33.6042 5.84458 48 Total 35.3500 7.10580 100 LECTURE Male 15.0577 2.63769 52 Female 13.8542 2.36993 48 Total 14.4800 2.57211 100 Total Male 26.0096 12.44053 104 Female 23.7292 10.87293 96 Total 24.9150 11.74083 200

230 229

Tests of Between-Subjects Effects Dependent Variable: Posttest score Type III Sum Source of Squares Df Mean Square F Sig. Corrected Model 25938.216a 4 6484.554 846.752 .000 Intercept 1222.611 1 1222.611 159.648 .000 Pretest score 3842.869 1 3842.869 501.801 .000 Methods 20973.914 1 20973.914 2.739E3 .000 Gender 38.649 1 38.649 5.047 .026 Methods * 79.954 1 79.954 10.440 .001 Gender Error 1493.339 195 7.658 Total 151583.000 200 Corrected Total 27431.555 199 a. R Squared = .946 (Adjusted R Squared = .944) Estimated Marginal Means 1. Grand Mean Dependent Variable: Posttest score 95% Confidence Interval Mean Std. Error Lower Bound Upper Bound 24.897a .196 24.511 25.283 a. Covariates appearing in the model are evaluated at the following values: Pretest score = 14.2600. 2. Methods Dependent Variable: Posttest score 95% Confidence Interval Methods Mean Std. Error Lower Bound Upper Bound FTIA 35.153a .277 34.606 35.699 LECTURE 14.642a .277 14.095 15.188 a. Covariates appearing in the model are evaluated at the following values: Pretest score = 14.2600.

231229

3. Gender Dependent Variable: Posttest score 95% Confidence Interval Gender Mean Std. Error Lower Bound Upper Bound Male 25.343a .273 24.804 25.881 Female 24.452a .284 23.891 25.012 a. Covariates appearing in the model are evaluated at the following values: Pretest score = 14.2600.

4. Methods * Gender Dependent Variable: Posttest score 95% Confidence Interval Methods Gender Mean Std. Error Lower Bound Upper Bound FTIA Male 36.231a .385 35.471 36.991 Female 34.074a .400 33.285 34.863 LECTURE Male 14.454a .385 13.696 15.213 Female 14.829a .402 14.037 15.622 a. Covariates appearing in the model are evaluated at the following values: Pretest score = 14.2600.

ANCOVA FOR RENTENTION

Between-Subjects Factors Value Label N Methods 1 FTIA 100 2 LECTURE 100 Gender 1 Male 104 2 Female 96

Descriptive Statistics Std. Methods Gender Mean Deviation N Posttest FTIA Male 36.9615 7.81141 52 score Female 33.6042 5.84458 48 Total 35.3500 7.10580 100

232 229

LECTURE Male 15.0577 2.63769 52 Female 13.8542 2.36993 48 Total 14.4800 2.57211 100 Total Male 26.0096 12.44053 104 Female 23.7292 10.87293 96 Total 24.9150 11.74083 200 Retention FTIA Male 38.4615 7.90002 52 Female 34.4583 5.52733 48 Total 36.0200 6.99492 100 LECTURE Male 15.1538 2.62256 52 Female 13.9167 2.43060 48 Total 14.5600 2.59494 100 Total Male 26.3077 12.64610 104 Female 24.1875 11.16415 96 Total 25.2900 11.97510 200

233229

Tests of Between-Subjects Effects Dependent Variable: Retention Type III Sum Source of Squares Df Mean Square F Sig. Corrected Model 28471.998a 4 7118.000 2.1294 .000 Intercept 4.528 1 4.528 13.547 .000 Posttest score 5182.094 1 5182.094 1.5504 .000 Methods 8.007 1 8.007 23.955 .000 Gender 7.872 1 7.872 19.575 .003 Methods * 1.569 1 1.569 4.694 .031 Gender Error 65.182 195 .334 Total 156454.000 200 Corrected Total 28537.180 199 a. R Squared = .998 (Adjusted R Squared = .998)

Estimated Marginal Means

1. Grand Mean Dependent Variable: Retention 95% Confidence Interval Mean Std. Error Lower Bound Upper Bound 25.293a .041 25.212 25.373 a. Covariates appearing in the model are evaluated at the following values: Posttest score = 24.9150.

2. Methods Dependent Variable: Retention 95% Confidence Interval Methods Mean Std. Error Lower Bound Upper Bound FTIA 25.743a .100 25.545 25.941 LECTURE 24.842a .101 24.643 25.041 a. Covariates appearing in the model are evaluated at the following values: Posttest score = 24.9150.

234 229

3. Gender Dependent Variable: Retention 95% Confidence Interval Gender Mean Std. Error Lower Bound Upper Bound Male 25.229a .057 25.116 25.342 Female 25.356a .060 25.238 25.474 a. Covariates appearing in the model are evaluated at the following values: Posttest score = 24.9150.

4. Methods * Gender Dependent Variable: Retention 95% Confidence Interval Methods Gender Mean Std. Error Lower Bound Upper Bound FTIA Male 25.590a .125 25.345 25.836 Female 25.896a .108 25.682 26.109 LECTURE Male 24.868a .112 24.647 25.088 Female 24.817a .121 24.578 25.055 a. Covariates appearing in the model are evaluated at the following values: Posttest score = 24.9150.

ANCOVA FOR INTEREST

Between-Subjects Factors Value Label N Methods 1 FTIA 100 2 LECTURE 100 Gender 1 Male 104 2 Female 96

235 229

Descriptive Statistics Std. Methods Gender Mean Deviation N Pretestint FTIA Male 57.3846 3.76336 52 Female 42.0417 7.44614 48 Total 50.0200 9.64206 100 LECTURE Male 56.7115 3.33923 52 Female 40.6875 7.22924 48 Total 49.0200 9.76179 100 Total Male 57.0481 3.55642 104 Female 41.3646 7.33143 96 Total 49.5200 9.69067 200 Posttestint FTIA Male 65.0769 5.49811 52 Female 63.8750 5.20893 48 Total 64.5000 5.36826 100 LECTURE Male 54.2500 2.61875 52 Female 48.0000 3.37702 48 Total 51.2500 4.33537 100 Total Male 59.6635 6.92485 104 Female 55.9375 9.09576 96 Total 57.8750 8.23398 200

236 229

Tests of Between-Subjects Effects Dependent Variable: Posttestint Type III Sum Source of Squares Df Mean Square F Sig. Corrected Model 11018.328a 4 2754.582 217.155 .000 Intercept 3385.850 1 3385.850 266.921 .000 Pretestint 1229.145 1 1229.145 96.899 .000 Methods 8247.203 1 8247.203 650.161 .000 Gender 171.312 1 171.312 13.505 .000 Methods * 281.146 1 281.146 22.164 .000 Gender Error 2473.547 195 12.685 Total 683395.000 200 Corrected Total 13491.875 199 a. R Squared = .817 (Adjusted R Squared = .813)

Estimated Marginal Means

1. Grand Mean Dependent Variable: Posttestint 95% Confidence Interval Mean Std. Error Lower Bound Upper Bound 57.938a .252 57.441 58.436 a. Covariates appearing in the model are evaluated at the following values: Pretestint = 49.5200.

2. Methods Dependent Variable: Posttestint 95% Confidence Interval Methods Mean Std. Error Lower Bound Upper Bound FTIA 64.391a .357 63.688 65.094 LECTURE 51.486a .358 50.779 52.193 a. Covariates appearing in the model are evaluated at the following values: Pretestint = 49.5200.

237229

3. Gender Dependent Variable: Posttestint 95% Confidence Interval Gender Mean Std. Error Lower Bound Upper Bound Male 56.352a .485 55.396 57.309 Female 59.525a .515 58.510 60.540 a. Covariates appearing in the model are evaluated at the following values: Pretestint = 49.5200.

4. Methods * Gender Dependent Variable: Posttestint 95% Confidence Interval Methods Gender Mean Std. Error Lower Bound Upper Bound FTIA Male 61.618a .606 60.422 62.813 Female 67.164a .613 65.955 68.374 LECTURE Male 51.087a .589 49.925 52.249 Female 51.885a .648 50.607 53.163 a. Covariates appearing in the model are evaluated at the following values: Pretestint = 49.5200.