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UNIVERSITY OF EDUCATION, WINNEBA
EXPLORING THE COMPETENCIES OF BASIC SCHOOL SUPERVISORS IN MATHEMATICS: THE CASE OF KWAHU EAST DISTRICT OF THE EASTERN REGION
AHMED TIJANI
2018
University of Education,Winneba http://ir.uew.edu.gh
UNIVERSITY OF EDUCATION, WINNEBA
EXPLORING THE COMPETENCIES OF BASIC SCHOOL SUPERVISORS IN MATHEMATICS: THE CASE OF KWAHU EAST DISTRICT OF THE EASTERN REGION
AHMED TIJANI (8130110001)
A Thesis In The Department of MATHEMATICS EDUCATION, Faculty of SCIENCE EDUCATION, Submitted to the SCHOOL OF GRADUATE STUDIES, in partial fulfilment of the requirements for the award of the degree of MASTER OF PHILOSOPHY (MATHEMATICS EDUCATION)
in the university of Education, Winneba.
SEPTEMBER, 2019 University of Education,Winneba http://ir.uew.edu.gh
DECLARATION
CANDIDATE’S DECLARATION
I, Ahmed Tijani, declare that this thesis, with the exception of quotations and references contained in published works which have all been identified and duly acknowledged, is entirely my own original work, and it has not been submitted, either in part or whole, for another degree elsewhere.
SIGNATURE:……..……………………….
DATE:………...……………………………
SUPERVISOR’S DECLARATION
I hereby declare that the preparation and presentation of this work was supervised in accordance with the guidelines for supervision of thesis as laid down by the
University of Education, Winneba.
Supervisor’s Name: Asso. Prof. Michael J. NABIE
Signature:……………………………
Date:……….…………………………
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DEDICATION
This thesis is dedicated to my father, Alhaji Alfah Cidi, my uncle, Alhaji Salfu
Soalley and my grandfather, Alhaji Ahmed-Tijani Abdul-Rahman for their support and encouragement during the most difficult period of my life.
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ACKNOWLEDGEMENT
I would like to express my deepest appreciation to a number of people who have supported me throughout my study. Second degree cannot be obtained without the sacrifice and support of other persons. My gratitude goes to my supervisor, Asso.
Prof. M. J. Nabie, whose scholarly insight, patience and academic rigor helped me develop a better understanding of issues involved in this work. I am grateful to Cyril
A. Titty and to my former headmaster, Mr. J. Y. Boafo, for encouraging me to pursue this course. My appreciations also go to the Kwahu – East District Director of
Education, the Assistant Director in charge of supervision and monitoring, the circuit supervisors, the headteachers and the mathematics teachers of the Junior High
Schools in the Kwahu – East District for their tolerance and willingness with which they assisted me throughout the writing of this thesis.
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TABLE OF CONTENT
CONTENT Page DECLARATION ii
DEDICATION iii
ACKNOWLEDGEMENT iv
TABLE OF CONTENT v
LIST OF TABLES ix
LIST OF FIGURE x
ABSTRACT xi
CHAPTER ONE: INTRODUCTION 1
1.0 Overview: 1
1.1 Background 1
1.2 Statement of the Problem 5
1.3 Purpose of the Study 8
1.4 Research Objectives 8
1.5 Research Questions 9
1.6 Hypotheses 9
1.7 Significance of the Study 10
1.8 Delimitation 11
1.9 Limitations of the Study 11
1.10 Organization of the Study 12
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CHAPTER TWO: LITERATURE REVIEW 14
2.1 Overview 14
2.2 Conceptual Framework 14
2.3 The Concept of Competence 18
2.4 Mathematical Competence 19
2.5 Concept of Supervision 22
2.6 Types of Supervision 28
2.6.1 Autocratic or Authoritarian Supervision 30
2.6.2 Laissez-faire or Free-rein Supervision 31
2.6.3 Democratic Supervision 31
2.6.4 Bureaucratic Supervision 32
2.6.5 Companionable Supervision 32
2.6.6 Synergistic Supervision 32
2.6.7 Traditional Supervision 33
2.6.8 Clinical Supervision 34
2.7 Educational Stakeholders View of Supervision 34
2.8 Qualities of a Good Instructional Supervisor 37
2.9 Challenges and Problems of Instructional Supervision in Ghana 38
CHAPTER THREE: METHODOLOGY 41
3.0 Overview 41
3.1 Research Design 41
3.2 Research Setting 43
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3.3 Population 46
3.4 Sample 47
3.4 Sampling Techniques 48
3.5 Research Instruments 50
3.5.1 The Questionnaire 50
3.5.1.1 Teacher Questionnaire 51
3.5.1.2 Supervisor Questionnaire 52
3.6 Pilot Study 53
3.6.1 Validity 54
3.6.2 Reliability 55
3.7 Data Collection Procedure 56
3.8 Data Analysis 57
3.9. Ethical Consideration 62
3.9.1 Confidentiality 62
3.9.2 Anonymity 63
CHAPTER FOUR: RESULTS AND DISCUSSION 64
4.0 Overview: 64
4.2 Demographic Characteristics of the Participants 65
4.3 Findings related to Research Questions 68
Research Question 1 68
Research Question 2 79
Research Question 3 87
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Research Question 4 94
Hypothesis Testing 99
CHAPTER FIVE: SUMMARY OF FINDINGS, CONCLUSIONS AND
RECOMMENDATIONS 109
5.1 Summary 109
5.2 Summary of Key Findings 111
5.3 Conclusion 118
5.4 Recommendation 119
5.5 Suggestions for Further Study 121
REFERENCES 122
APPENDIX A 132
APPENDIX B 137
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LIST OF TABLES
1: BECE Results in Mathematics, Kwahu East 7
2: Summary of educational institutions in the Kwahu East District 45
3: Demographic Characteristics of Kwahu East District Mathematics Teacher Participants (Total = 150) 65
4: Demographic characteristics of Kwahu East District Mathematics Supervisors (n = 35) 67
5: Descriptive Statistics of Mathematics Teachers’ Perceptions of the Competency Level (first group) of Supervisors in Kwahu East District. 70
6: Descriptive Statistics of Mathematics Supervisors’ Perceptions of their Competency Level (first group) in ensuring teaching and learning of mathematics 80
7: Descriptive Statistics and Rank of Mathematics Supervisors’ Competent of ensuring teaching and learning of Mathematics 85
8: Descriptive Statistics of Teachers’ Perceptions of the Various Supervision Styles of Supervisors in Kwahu East District 89
9: Descriptive Statistics of Challenges Facing Supervisors in Kwahu East District 95
10: Descriptive statistics of mathematics teachers by gender 105
11: Independent-samples t-test of Basic School Mathematics Teachers’ perception of styles of supervision practices. 105
12: Descriptive statistics of respondents’ perceptions on supervisors’ competency 100
13: Independent-samples t-test of respondents’ perceptions on supervisors’ competency 102
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LIST OF FIGURE
1: A visual representation-the “KOM flower”-of the eight mathematical
competencies (Source: Niss & Jensen, 2002, p. 46) 15
2: District Map of Kwahu East 44
3: The neutral position on the five-point Likert-type scale 61
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ABSTRACT
The study sought to explore and examine the competence basic school mathematics supervisors possess in ensuring effective mathematics education delivery in the Ghanaian basic schools. A cross sectional descriptive survey research design was undertaken with an adopted conceptual framework from Niss and Jensen (2002). The conceptual framework enumerates the kinds of competence expected of a mathematics student, teacher or supervisors. The sample for the study comprised mathematics teachers and supervisors (n = 185) in the Kwahu East District. Multistage sampling techniques which included convenient, purposive and simple random sampling techniques were employed to sample the participants. The instruments used to gather data for the study were self-structured questionnaires. The data was analyzed using descriptive statistics and independent sampled t-test. The findings revealed that the mathematics teachers viewed most of their instructional supervisors as not competent enough to guide them to achieve the mathematics curriculum goal. The supervisors, on the other hand were of the view that they were very competent on all the parameters used in this study. The hypothesis tested on the difference of the claims of both mathematics teachers and supervisors indicated a significant difference. It also emerged from the study that most supervisors in the district employ the democratic style of supervision. Again, it was evident that a number of challenges were militating against the effective delivery of instructional supervision. Among others, the study concluded that to some extent the supervisors were averagely competent but needed more help to improve their performance. It was concluded again that the supervisors employ modern recommended styles of supervision in the face of many challenges. Therefore, the study recommended among others that training institutions should organize regular workshops, pre-service and in- service training programs for supervisors on desired competencies of modern-day instructional supervisor. Furthermore, it is recommended that Ghana Education Service should provide training for supervisors on modern day supervision styles as part of their induction process after their appointments. Finally, stakeholders of education must put their ‘shoulders to the wheel’ to ensure that they provide the necessary support to the basic schools supervisors to ensure effectiveness.
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CHAPTER ONE
INTRODUCTION
1.0 Overview
This chapter is the introductory section of the study which presents the general background of the study, statement of the problem, purpose of the study, research objectives, research questions, significance of the study, delimitations and limitations of the study and the organizational plan of the study.
1.1 Background
An educated population is a vital resource for national growth. Improvement in standards demands increasing need for qualified human resources, which in turn requires improvement in the quality of education. A fundamental subject which has the potential of adding value to the quality of a country’s human resource is mathematics. Mathematics is one of the core subjects of study at the Junior High
School (JHS) level whose importance in industry and technology cannot be underestimated. A nation’s development in science and technology requires her citizens’ acquisition of mathematical knowledge. The amount and rate of scientific and technological development of a nation determines the amount and type of mathematical knowledge acquired by her citizens.
The amount and type of mathematical knowledge for a nation’s development agenda is provided for by the mathematics curriculum. In Ghana, the Ministry of
Education (MOE) through the Ghana Education Service (GES) design and implement a curriculum to achieve a set of mathematical goals. The mathematical knowledge taught and learnt is determined by these set of goals.
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The Junior High School (J.H.S.) mathematics curriculum is designed to achieve the following goals: To
• Develop pupils’ skills of selecting and applying criteria for classification and
generalization.
• Communicate effectively using mathematical terms, symbols and explanations
through logical reasoning.
• Use mathematics in daily life by recognizing and applying appropriate
mathematical problem-solving strategies.
• Understand the process of measurement and use appropriate measuring
instruments.
• Develop the ability and willingness to perform investigations using various
mathematical ideas and operations.1 • Work co-operatively with other students in carrying out activities and projects
in mathematics.
• Develop the values and personal qualities of diligence, perseverance,
confidence, patriotism and tolerance through the study of mathematics.
• Use the calculator and the computer for problem solving and investigations of
real life situations.
• Develop interest in studying mathematics to a higher level in preparation for
professions and careers in science, technology, commerce, industry and a
variety of work areas (Ministry of Education, 2012).
For these goals to be realized and achieved, there is the need for a well organized and structured interactions between and among students, teachers, school administrators and external education officials. One of such organized and structured interaction provided in education delievery is instructional supervision. Mathematical
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instructional supervision and other important educational activities are aimed at providing quality mathematics education to all learners. Instructional supervision has been identified as a critical component in the development and successful implementation of any educational program in both developed and developing countries, since it enhances teaching and learning in schools (Too, Kimutai &
Zachariah, 2012). Supervision is further considered as one of the major factors that contribute to the effective delivery of quality basic education, therefore in a school setting where teaching and learning takes place, effective supervision plays a very crucial role in ensuring quality education by improving students’ academic performance. The Ministry of Education (2012) identified school supervision as vital without which the huge financial investment made in education will not yield the expected result.
In Ghana, the responsibility of supervision of public basic school teachers and instruction is vested in the hands of personnel from the Ghana Education Service
(GES), which include headteachers, circuit supervisors, the inspectorate board among others (Ghana Education Service, 2002). According to Mankoe (2006), supervision of teaching in schools is supposed to be a daily function of the circuit supervisor. Many basic school mathematics teachers, especially the untrained and the newly trained recruited teachers may not have mastery over or developed sufficient skills for effective teaching. Therefore, these categories of teachers need to be supervised continuously during teaching in their respective classrooms in order to develop their skills of teaching. Nakpodia (2006) as cited in Manas, (2013) asserted that instructional supervision in this modern era centers on the improvement of the teaching and learning situation for the benefits of both teachers and learners. It helps in the identification of areas of strengths and weaknesses of teachers, provides follow-
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up activities that should be directed at the improvement of identified areas of teachers’ weaknesses and give recognition to the teachers. Moreover, supervision creates a cordial working atmosphere based on good human relations. Finally, supervision helps the teachers in terms of self–discovery particularly in the areas of improvisation and use of modern teaching aids as a basis for improving teaching strategies. In this regard, basic school mathematics teaching and learning activities must be constantly monitored and revised to enable mathematics teachers meet the ever-changing developmental needs of the learner and the nation at large.
According to the Circuit Supervisors’ Handbook, the mathematics supervisor is charged with the role of being a: curriculum advisor; teacher supporter and evaluator of teaching and learning in the basic schools (Ghana Education Service,
2002). As curriculum advisor and teacher supporter, the Circuit Supervisor is to support teachers and headteachers through the provision of professional guidance and advice. The Circuit Supervisor is expected to work as a friend and colleague with headteachers and teachers to improve school management and classroom instruction as well as enhancing teaching and learning. As an evaluator of teaching and learning, the Circuit Supervisor is to monitor classroom teaching and learning and the teachers’ professional competencies, specifically, pupils’ performance in classroom assessment in Mathematics to ascertain their level of learning achievement (Ghana Education
Service, 2002).
The Ministry of Education considers school supervisors as curriculum advisors who help to improve the quality of teaching and learning in the classrooms and assigned roles to guide effective supervision. Supervisors are to organize assessment conference to determine the level of progress in attaining performance standards, monitor classroom teaching and learning, evaluate teachers’ professional
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competency, assess teacher performance and provide the needed support (Ghana
Education Service, 2002). By these roles, the basic schools’ mathematics supervisor is expected to ensure that the mathematics teacher exhibits mathematical content and pedagogical knowledge, best assessment practices and professional skills in the process of inducing learning in the mathematics classroom. This include mastery of subject matter, effective classroom management – class control, well distribution of questions among students, judicious use of time and teaching and learning materials, child centered strategies, and the application of mathematics in real life context.
Generally, the identified roles assigned to mathematics supervisors are aimed at not only improving academic performance of learners in mathematics, but it is also to ensure effective mathematics delivery and also to develop problem solvers and critical thinkers in the nation. It implies therefore that should mathematics supervisors undertake their professional duties as expected of them, classroom mathematics teachers are going to be effective and competent implementers of the basic school mathematics curriculum which will lead to high academic achievement on the part of the learners and education will achieve its ultimate goal.
1.2 Statement of the Problem
The success or failure of any educational policy is judged on the outcome of the results produced by schools at the end of every examination year. Factors affecting academic performance have thus become a subject of investigation to educational stakeholders in Ghana. A study of such factors affecting pupils’ academic performance revealed that effective supervision of instruction contributes to high academic performance of pupils (Okyerefo, Fiaveh & Lamptey, 2011). This implies that effective instructional supervision has the potential of helping school authorities
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achieve quality basic education. In recent years however, the Basic Education
Certificate Examination (BECE) results constantly show downward trend in students’ performance.
Among the subjects that most students fail, Mathematics was the worst affected (Gatsi, 2018). As a result, many parents, guardians and other stakeholders in education have expressed concern about the future of mathematics education in the country. In most cases the poor academic performance is attributed to ineffective school, teacher and instructional supervision in schools (Agbodza, 2017; Kuyini,
2011; Nkansah, 2010; Opare, 1999). Some of the reasons advanced for placing a potion of the blame on the door steps of mathematics supervisors is that, some of the supervisors lack practical training, have poor mathematical content knowlegde, lack of confidence and lack of an agreed upon set of professional skills which have remained remarkably undefined and random in Ghana Education Service (Adu, 2008).
Mankoe (2007) on his part enumerates the following as prevailing supervisory issues in basic schools: supervisors not being mobile, economic constraints make supervisors and teachers face the problem of making ends meet, academic qualification and professional development training for supervisors, headmasters, teachers; and some supervisors not able to demonstrate in teaching but always admonishing teachers towards effective teaching. The effect of the above-mentioned flaws in Ghana’s basic schools is ineffective supervision on the part of circuit supervisors. This also leads to poor teaching and learning resulting in massive failure by students during their basic education certificate examinations.
The academic performance of students in the Basic Education Certificate
Examinations in the Kwahu – East District is not very much encouraging from that of the country as a whole. Records as presented by the District Director of Education,
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Boafo (2017), suggests that almost half of the students who sit for the Basic
Education Certificate Examinations (BECE) in the district failed their examination.
The statistics showed that the most failure was recoreded in mathematics. The poor academic performance in the district has been tied to several factors including poor educational infrustructure, inadequate teaching and learning logistics, bad roads network to schools, inadequate teachers and lack of quality supervison practices among others (Aboagye, 2017; Boafo, 2017). Table 1.1 shows the Basic Education
Certificate Examinations (BECE) results in mathematics recorded for the period 2014 to 2017 in the Kwahu – East District.
Table 1. 1 BECE Results in Mathematics, Kwahu - East Year No. of Students Registed No. of Students who % of Students who Passed Passed 2014 1040 468 45.0% 2015 890 430 48.3% 2016 1026 482 47.0% 2017 1066 575 53.9% Total 4022 1955 48.6% Source: Kwahu East Education Directorate (2018)
Academic performance of students in Table 1.1 reveal that in 2014, 1040 basic school students were registered to sit for the final examination (Basic Education
Certificate Examinations). Out of this number, 468 students representing 45% passed the examinations. It is clear also that 48.3% representing 430 students passed the exams in 2015. Also, the district with a registered students pupolation of 1026 in the year 2016, recoreded a passed rate of 47%. And finally, 53.9% of the 1066 students registered in the 2017 academic year passed the Basic Education Certificate
Examinations. The table shows that an overall passed rate of 48.61% was recorded over the years under review.
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It is on the basis of the poor academic performance trend that Ankomah and
Hope (2011) and Zachariah (2013) recommended that studies be conducted on supervision as a factor that influence students’ performance and instructional effectiveness. In Ghana, there has been research works on academic achievement and supervision of instruction by some researchers (Adane, 2013; Okyerefo, Fiaveh &
Lamptey, 2011; Baffour - Awuah, 2011; Arthur, 2011; Opare, 1999). However, there is little or no published empirical study in Ghana exploring the competencies of school supervisors to carry out supervision of mathematics teachers in public basic schools. Hence the need for the current study to explore and examine the competencies of public basic school supervisors in mathematics education in the
Kwahu East District.
1.3 Purpose of the Study
The study sought to explore the level of competency of basic school mathematics supervisors in ensuring effective mathematics education delivery in
Ghanaian basic schools. Specifically, the study sought to: explore the competency of basic school mathematics supervisors in ensuring effective delivery of mathematics education in Kwahu East District; explore the view of basic school mathematics teachers on the impact of supervision on their classroom practices; identify the challenges facing school supervisors in supervising mathematics teachers in public basic schools.
1.4 Research Objectives
The purpose of the study was achieved through the following specific objectives:
1. Exploring the teachers’ views of the level of competence supervisors have in
ensuring effective teaching and learning of mathematics in basic schools in the
Kwahu East District.
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2. Exploring supervisors’ perceptions of their own competencies in ensuring
effective teaching and learning of mathematics in basic schools in the Kwahu East
District.
3. Identifying the styles of supervision of Junior High School mathematics teachers
experience in the Kwahu East District.
4. Enumerating some of the challenges school supervisors face in ensuring effective
mathematics education delivery in basic schools in the Kwahu East District.
1.5 Research Questions
The study sought to find answers to the following research questions:
1. What are mathematics teachers perceptions of the competence supervisors
have in ensuring effective teaching and learning of mathematics in basic
schools in the Kwahu East District?
2. How do supervisors perceive their competencies in ensuring effective teaching
and learning of mathematics in basic schools in the Kwahu East District?
3. What styles of school supervision do Junior High School mathematics teachers
in the Kwahu East District experience?
4. What inherent challenges do supervisors in the Kwahu East District face in
ensuring effective mathematics education delivery in basic schools?
1.6 Hypotheses
The following hypotheses were formulated to guide the study and were tested at 0.05 level of significance:
푯02: There is no statistical significant difference between mathematics teachers’ and supervisors’ perceptions of mathematics supervision competence of supervisors in the
Kwahu East District
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H01: There is no statistical significant difference between male and female mathematics teachers’ perceptions of styles of school supervision they experience in the Kwahu East District
1.7 Significance of the Study
The study explored and examined the level of competencies of basic school mathematics supervisors in ensuring effective mathematics education delivery in
Ghanaian basic schools. It is expected that:
The findings of the study will provide feedback about how supervision of mathematics instruction is being carried out in public basic schools in Kwahu East
District. In order words it may give feedback about how the established practices of instructional supervision is perceived and practiced by supervisors in the Kwahu East
District and how the practiced supervision is experienced by classroom mathematics teachers.
The results of the study may guide the mathematics supervisors to perceive how the instructional supervision implemented is experienced by the basic school mathematics teachers. In turn, what instructional supervision is and is not practiced and implemented together with what is and is not experienced can be determined and the reasons for the differences among the intended, perceived, implemented and experienced instructional supervision can be recognized and appropriate steps taken.
The findings of this study may help the Inspectorate Division of the Ghana
Education Service to revisit the various policies and guidelines formulated to guide basic school mathematics supervision. The results of the study intend to help direct the Ghana Education Service on the need and the kind of in – service training to be given to the school supervisors of public basic schools in Ghana.
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The study findings are geared to guide the circuit supervisors involved in the studies who wish to upgrade their pedagogical content knowledge in mathematics education supervision and monitoring. The study result is aimed at benefiting Non-
Governmental Organizations (NGOs) interested in improving students’ performance through valid and reliable instructional supervision.
Finally, the findings of the study is aimed at being a record for future researchers to rely on in their attempt to improve teacher supervision and thereby improving performance in mathematics at the basic schools in Ghana.
1.8 Delimitation
The study was delimitated to the basic school mathematics supervisors and teachers who were sampled for the study in the Kwahu East District. Although the
Eastern Region has 20 districts, only one district was used for the study in order to include the variables of interest and to reach out to all information rich respondents.
With regards to content, the scope of supervision as it is in basic school is evidently wide; consequently, the study focused only on mathematics supervisors’ competences in ensuring effective mathematics curriculum implementation. The perception of the supervisors and mathematics teachers on instructional activities has a role in promoting students’ learning and teachers’ teaching.
1.9 Limitations of the Study
According to Best and Kahn (2006), limitations are conditions beyond the control of the researcher that will place restriction on the validity of the study. Kwahu
– East District is a developing district with a number of remote areas. This made the
Junior High Schools in the study district scattered and difficult to get to the participants in their various schools and circuits. Also, the supervisors (Circuits
Supervisors and Headteachers) sampled for the study were not observed while
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supervising teaching and learning in their respective circuits and schools. As such, the findings of this research were based on completed questionnaires administered by the researcher.
In this regard, it is suggested that future researchers should include observation if possible, in their methodology. Another limitation to this study is that there is a possibility that some respondents might have faked some responses or even been subjective instead of being objective. In spite of the limitation pointed above, the study has been able to point out some areas of instructional supervision needed by teachers and their perceptions about these aspects of instructional supervision. Also the numbers of the responses were good enough for meaningful generalization of the result.
1.10 Organization of the Study
The study was organized into five chapters. The first chapter of the thesis included the general background of the study, statement of the problem, purpose of the study, research objectives, research questions, significance of the study, delimitations and limitations of the study, the organization of the study. The second chapter of the dissertation expands upon the review of literature associated with theoretical framework, theoretical and empirical review relating to topic understudy.
A summary of the literature review concludes chapter two. The third chapter of the study describes the methodology used in the study. It includes an overview of the methodology, research design, research setting, population, sample and sampling techniques, research instruments, pilot study, data collection, data analysis procedures and ethics considerations. The fourth chapter presents and discusses the results of the
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study. The last chapter contains an overview, summary of the results, and implications for practice and further research.
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CHAPTER TWO
LITERATURE REVIEW
2.1 Overview
In this chapter, literature was reviewed under the following sub-headings: conceptual framework, concept of supervision, the concept of mathematics competencies, evolution of supervision in Ghana, supervision models, roles and responsibilities of the supervisor, impact of teacher supervision in schools and challenges of school supervision.
2.2 Conceptual Framework
A sound and an effective classroom supervision practices must be rooted in a well-researched theoretical or conceptual framework. Authorities in the area of mathematics supervision agree that supervisors must be mathematically competent and this is a clearly recognizable and distinct, major constituent of mathematical competence (Niss & Jensen, 2002). In this study the researcher adopted the conceptual framework of Niss and Jensen (2002), the “KOM flower”, to identify the competencies of supervisors in education. According to Niss and Jensen (2002) there are eight competencies which can be said to form two groups. The first group of competencies is to do with the ability to ask and answer questions in and with mathematics which includes: Thinking mathematically; Posing and solving mathematical problems; Modelling mathematically and Reasoning mathematically.
The other group of competencies is to do with the ability to deal with and manage mathematical language and tools and they include: Representing mathematical entities; Handling mathematical symbols and formalisms; Communicating in, with,
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and about mathematics and Making use of aids and tools (IT included). The cyclical nature of assessment is diagrammatically presented in Figure 2.1
Figure 2. 1: A visual representation – the “KOM flower” – of the eight mathematical competencies (Source: Niss & Jensen, 2002, p. 46)
The mathematics competence is the main ingredient in a proposal by Mogens Niss for applying a set of mathematical competencies as a tool for developing mathematics education (Niss, 1999). The KOM project (Niss & Jensen, to appear), running from
2000 – 2002 and chaired by Mogens Niss with Tomas Højgaard Jensen as the academic secretary, thoroughly introduced, developed and exemplified this general idea at all educational levels from primary school to university (cf. Niss (2003) for an actual presentation of the project). The definition of the term “competence” in the
KOM project (Niss & Jensen, to appear, ch. 4) is semantically identical to the one we use: Competence is someone’s insightful readiness to act in response to the challenges of a given situation (cf. Blomhøj & Jensen, 2003). A consequence of this definition is that it makes competence headed for action, based on but identical to neither knowledge nor skills. Secondly, the situatedness should be noticed, since this defines
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competence development as a continuous process and highlights the absurdity of labelling anyone either incompetent or completely competent. The various groups of the conceptual framework of Niss and Jensen (2002), the “KOM flower”, is elaborated on in the following section
Group of Competencies
1. Thinking mathematically: The ability to relate to and deal with such issues
was called the mathematical thinking competency.
2. The second competency has to do with identifying, posing and solving
mathematical problems. Not surprising, this was called the mathematical
problem handling competency. It is part of the view of mathematics education
nurtured in most places in develop countries, that the place and role of
mathematics in other academic or practical domains are crucial to mathematics
education.
3. As the involvement of mathematics in extra-mathematical domains takes place
by way of explicit or implicit mathematical models and modelling,
individuals’ ability to deal with existing models and to engage in model 2
Mathematical Competencies and PISA 39 construction (active modelling) is
identified as a third independent competency, the mathematical modelling
competency.
4. The fourth and last of this group of competencies focuses on the ways in
which mathematical claims, answers and solutions are validated and justified
by mathematical reasoning. The ability to follow such reasoning as well as to
construct chains of arguments so as to justify claims, answers and solutions
was called the mathematical reasoning competency.
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5. The activation of each of these four competencies requires the ability to deal
with and utilize mathematical language and tools. Amongst these, various
representations of mathematical entities (i.e. objects, phenomena, relations,
processes, and situations) are of key significance. Typical examples of
mathematical representations take the form of symbols, graphs, diagrams,
charts, tables, and verbal descriptions of entities. The ability to interpret and
employ as well as to translate between such representations, whilst being
aware of the sort and amount of information contained in each representation,
was called the mathematical representation competency.
6. One of the most important categories of mathematical representations consists
of mathematical symbols, and expressions composed of symbols. The ability
to deal with mathematical symbolism—i.e. symbols, symbolic expressions,
and the rules that govern the manipulation of them—and related formalisms,
i.e. specific rule-based mathematical systems making extensive use of
symbolic expressions, e.g. matrix algebra, was called the mathematical
symbols and formalism competency.
7. Considering the fact that anyone who is learning or practicing mathematics
has to be engaged, in some way or another, in receptive or constructive
communication about matters mathematical, either by attempting to grasp
others’ written, oral, figurative or gestural mathematical communication or by
actively expressing oneself to others through various means, a mathematical
communication competency is important to include.
8. Finally, mathematics has always, today as in the past, made use of a variety of
physical objects, instruments or machinery, to represent mathematical entities
or to assist in carrying out mathematical processes. Counting stones (calculi),
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abaci, rulers, compasses, slide rulers, protractors, drawing instruments, tables,
calculators and computers, are just a few examples. The ability to handle such
physical aids and tools (mathematical technology in a broad sense) with
insight into their properties and limitations is an essential competency of
contemporary relevance, which was called the mathematical aids and tools
competency.
2.3 The Concept of Competence
In the view of Gilbert (2008), the term "competence" first appeared in an article authored by R.W. White in 1959 as a concept for performance motivation. In
1970, Craig C. Lundberg defined the concept in "Planning the Executive
Development Program". The term gained attraction when in 1973, David McClelland wrote a seminal paper entitled, "Testing for Competence Rather than for Intelligence".
It has since been popularized by Richard Boyatzis and many others, such as Gilbert
(2008) who used the concept in relationship to performance improvement. Its use varies widely, which leads to considerable misunderstanding. On face value, the term competence can be defined as the ability of an individual to do a job properly, or a set of defined behaviors that provide a structured guide enabling the identification, evaluation and development of the behaviors in individual employees. Some scholars see "competence" as a combination of practical and theoretical knowledge, cognitive skills, behavior and values used to improve performance; or as the state or quality of being adequately or well qualified, having the ability to perform a specific role. For instance, management competency might include systems thinking and emotional intelligence, and skills in influence and negotiation.
Competency is sometimes thought of as being shown in action in a situation and context that might be different the next time a person has to act. In emergencies,
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competent people may react to a situation following behaviors they have previously found to succeed. To be competent a person would need to be able to interpret the situation in the context and to have a repertoire of possible actions to take and have trained in the possible actions in the repertoire, if this is relevant. Regardless of training, competency would grow through experience and the extent of an individual to learn and adapt. Competency has different meanings, and remains one of the most diffuse terms in all of human endeavor including organizational and occupational literature. Competencies are also what people need to be successful in their jobs. Job competencies are not the same as job task. Competencies include all the related knowledge, skills, abilities, and attributes that form a person’s job (Raven &
Stephenson, 2001). This set of context-specific qualities is correlated with superior job performance and can be used as a standard against which to measure job performance as well as to develop, recruit, and hire employees.
2.4 Mathematical Competence
To master mathematics means to possess mathematical competence. To possess a competence (to be competent) in some domain of personal, professional or social life is to master (to a fair degree, modulo the conditions and circumstances) essential aspects of life in that domain (Niss, 1999). Mathematical competence according to European Parliament and The Council of 18 December 2006, (2006) is the ability to develop and apply mathematical thinking in order to solve a range of problems in everyday situations. Building on a sound mastery of numeracy, the emphasis is on process and activity, as well as knowledge. Mathematical competence involves, to different degrees, the ability and willingness to use mathematical modes of thought (logical and spatial thinking) and presentation (formulas, models, constructs, graphs, charts). Niss and Jensen, (2002) on the other hand also defined
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mathematical competence as to mean the ability to understand, judge, do, and use mathematics in a variety of intra- and extra-mathematical contexts and situations in which mathematics plays or could play a role. Necessary, but certainly not sufficient, prerequisites for mathematical competence are lots of factual knowledge and technical skills, in the same way as vocabulary, orthography, and grammar are necessary but not sufficient prerequisites for literacy.
Mathematical competence is the ability to develop and apply mathematical thinking in order to solve a range of problems in everyday situations. Building on a sound mastery of numeracy, the emphasis is on process and activity, as well as knowledge. Mathematical competence involves, to different degrees, the ability and willingness to use mathematical modes of thought (logical and spatial thinking) and presentation (formulas, models, constructs, graphs, charts).
Competence in science refers to the ability and willingness to use the body of knowledge and methodology employed to explain the natural world, in order to identify questions and to draw evidence-based conclusions. Competence in technology is viewed as the application of that knowledge and methodology in response to perceived human wants or needs. Competence in science and technology involves an understanding of the changes caused by human activity and responsibility as an individual citizen.
Necessary knowledge in mathematics includes a sound knowledge of numbers, measures and structures, basic operations and basic mathematical presentations, an understanding of mathematical terms and concepts, and an awareness of the questions to which mathematics can offer answers. An individual
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should have the skills to apply basic mathematical principles and processes in everyday contexts at home and work, and to follow and assess chains of arguments.
An individual should be able to reason mathematically, understand mathematical proof and communicate in mathematical language, and to use appropriate aids.
A positive attitude in mathematics is based on the respect of truth and willingness to look for reasons and to assess their validity. For science and technology, essential knowledge comprises the basic principles of the natural world, fundamental scientific concepts, principles and methods, technology and technological products and processes, as well as an understanding of the impact of science and technology on the natural world. These competences should enable individuals to better understand the advances, limitations and risks of scientific theories, applications and technology in societies at large (in relation to decision- making, values, moral questions, culture, etc).
Skills include the ability to use and handle technological tools and machines as well as scientific data to achieve a goal or to reach an evidence-based decision or conclusion. Individuals should also be able to recognize the essential features of scientific inquiry and have the ability to communicate the conclusions and reasoning that led to them. Competence includes an attitude of critical appreciation and curiosity, an interest in ethical issues and respect for both safety and sustainability, in particular as regards scientific and technological progress in relation to oneself, family, community and global issues.
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2.5 Concept of Supervision
The effective application of managerial principles in the schools to achieve educational goals is termed as educational management (Too, Kimutai & Zachariah,
2012). The success or failure of our educational goal is belived to be determined largely by the school climate found in our schools where education takes place. For the goals of education to be achieved, school administrators cannot but apply appropraite management skills. The school supervisors at the basic schools, therefore, have a crucial responsibility to see to it that appropraite managerial duties are discharged appropraitely to achieve the desired goal and improve performance standards in the basic schools which the society cries for.
Supervision of schools have been defined and interpreted by scholars from various points of views (Munemo & Tom , 2013). Range (2013) sees supervision as providing coaching to build teachers’ capacity. The central to all the definitions is that supervision is basically a service which aims at improving conditions of teaching and learning in schools (UNESCO, 2007). Thus, supervision is the vital personal link between the service provider, paid or unpaid and the organization. It is the interactive process in which the organizations goals and values are communicated and interpreted to workers and they, in turn, are guided and supported to help achieve those goals.
Supervision is considered as the dimension or phase in educational administration which is concerned with improving educational effectiveness. This statement is affirmed by the definition of supervision as the function in schools that draws together the discrete elements of instructional effectiveness into whole school action (Glickman, 1990). Thus, for a school to achieve its goals, the teachers have to unite, work as a team around a common goal and individually adopt the school’s goal
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to be theirs’ and work towards achieving it under the watch of the headmistress or the headteacher.
Olive (1984) describes supervision as a means of offering to teachers specialized help in improving instruction while Glickman (1990) taught of supervision as glue of a successful school. Glue because it is a process by which some person or group of people are responsible for providing a link between individual teacher’s needs and organizational goals so that individuals within the school can work in harmony toward their vision of what the school should be.
In a school, supervision is the process of ensuring that the prescribed principles, rules, regulations and methods of implementing and achieving the objectives of education are effectively caried out. Also, to supervise is to direct, oversee, guide or make sure that expected standards are met (Enaigbe, 2009).
Furtheremore, supervision could be seen to be an interaction which involve a kind of reletionship that is establihed among workers which is influenced by a defined set of rules and regulations in an establishement. Beaton states that supervision calls for personal relationships, non-threatening and trusting atmosphere (Mapolisa &
Tshabalala, 2013). In conclusion, among the guiding principles for supervision set out for supervisors by the Ghana Education Service were; the supervisor is to evaluate the teachers’ professional competence and provide the needed support to the teacher.
Suppose the supervisor was a ‘Maths phobia’ type during his or her school days what support will he or she offer to benefit this teacher. Studies show that supervision by non – specialist does not help the supervisee (Munemo and Tom, 2013).
Mathematics supervisor, according to Fajemidagba (1991) is an excellent resource person who has a wealth of experience, knowledge and ability in the
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professional development of new mathematics teacher. The mathematics supervisor is a help giver, a tolerant individual and has a potential for creativity in mathematics teaching and learning. He is not a “boss” but a “leader” in the development of mathematics learning materials, curriculum and instructional process that ultimately will enhance effective teaching and better achievement in mathematics. The mathematics supervisor, is familiar with the school situation, aware of many problems that teachers face and willing to help. Finally, the mathematics supervisor has a definite obligation to visit mathematics classrooms in order to help mathematics teachers develop professionally.
After a thorough review of the above definitions and explanations of supervision, the researcher is therefore of the view that for effective supervision, the supervisor must have control over the content knowledge, pedagogical content knowledge and curricular knowledge of the subject he or she is to supervise. Such a supervisor will best support and influence the development of concepts at both the lesson preparation and presentation levels. This will help improve the problem- solving skills of the mathematics teacher and hence, enhance the quality instruction in the mathematics classroom.
Researchers conceptualize effective supervision not as an end result or product, but rather as the collection of knowledge and skills that supervisors possess.
Okyerefo, Fiaveh and Lamptey (2011) revealed that effective supervision of instruction is associated with pupils’ high academic performance. Glickman, Gordon and Ross-Gordon (2004) posit that effective supervision requires well trained personnel with knowledge, interpersonal skills, and technical skills that are prepared to provide the necessary and appropriate guidance and support to the teaching staff.
According to them these personal attributes are applied through the supervisory roles
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of direct assistance to teachers, group development, professional development, and curriculum development and action research. They believe that “this adhesive pulls together organizational goals and teacher needs and provides for improved learning”.
To facilitate effective supervisory processes Glickman, Gordon and Ross-
Gordon (2004) propose that supervisors should perform the following roles: providing personal development by providing on-going contact with the individual teacher to observe and assist him/her in classroom instruction; ensuring professional development by providing the learning opportunities for faculty provided or supported by the school and school system; and providing group development through the gathering together of teachers to make decisions on mutual instructional concern.
Similarly, supervisors should support curriculum development through the revision and modification of content, plans and materials of classroom instruction.
Glickman, Gordon and Ross-Gordon (2004) also posit that supervisors should engage teachers in action research by systematically studying faculty to find out what is happening in the classroom and school with the aim of improving student learning.
Other researchers also share similar views as those upheld by Glickman and colleagues. For example, Glanz, Shulman and Sullivan (2006) believe that an effective principal possesses the following characteristics: he is situationally aware of details and undercuts in the school; has intellectual stimulation of current theories and practices; is a change agent; and, actively involves teachers in design and implementation of important decisions and policies.
They also believe that effective principals provide effective supervision. To them, an effective principal creates a culture of shared belief and sense of cooperation, monitors and evaluates the effectiveness of school practices, is
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resourceful and communicates and operates from strong ideas and beliefs about schooling. Blasé and Blasé (1999) propose a model of effective principal derived from data (findings) which consists of two major themes: talking with teachers to promote reflection and promoting professional growth. According to them, effective principals (supervisors) value dialogue that encourages teachers to critically reflect on their learning and professional practice through the following strategies: making suggestions, giving feedback, modeling, using inquiry and soliciting advice and opinions, and giving praise. They also argue that effective principals use six strategies to promote teachers' professional growth: emphasizing the study of teaching and learning; supporting collaboration efforts among educators; developing coaching relationships among educators; encouraging and supporting redesign of programs; applying the principles of adult learning, growth, and development to all phases of staff development; and implementing action research to inform instructional decision making. For effective supervision and evaluation that will be relevant to teachers and improve their instructional practice, Range (2013) suggests school leadership, comprehensive teacher supervision and evaluation scope and focusing more on supervision and less on evaluation as key.
School leadership is made up with the school leader (headteacher as in Ghana) and the district leader (circuit supervisor as in Ghana), hold the success or other wise of effective teacher supervision and evaluation (Range, 2013). Range is of the view that district leaders must adopt comprehensive and fair teacher supervision practice such that school leaders will conduct a daily as well as weekly supervision and evaluation of teachers’ instructional activities. This frequent visit of supervisors to classroom to supervise teachers’ instructional activities gives a clearer picture of the
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effectiveness of the teacher as well as exposes the teacher’s weakness for the supervisor to address.
Other researchers, on the other hand, believe that successful supervisors are those who link interpersonal skills with technical skills. Brennen (2008) notes an effective supervisor who links interpersonal with technical skills will be successful in improving instruction. He suggests that an effective supervisor should be able to build self-acceptance, moral, trust, and rapport between the two parties. Brennen suggests that the supervisor in an effective supervision process should not delve deeply into the role of a counselor. The focus is always on the teaching act, rather than matters affecting the teacher that are beyond the confines of the classroom. Objectivity, devoid of personal biases, should be the hallmark if supervision is to be effective, he asserts. It is for this reason that Brennen (2008) posits that effective supervision results when a supervisor clearly sets out the criteria to be used in the evaluative process and ensures that even if the final assessment is a negative one, the teacher will benefit from the exercise and leave with his self-esteem intact.
Although in the minority, Oghuvbu (2001) believes that effective supervision involves adherence to bureaucratic processes to control and guide teachers. He identifies common determinants of effective supervision as: teachers and students working rigidly according to school time table, following school regulations, neat and decent environment, proper student management and disciplined students. In addition there should be delegation of duties by school heads, and positive, cordial, social and professional relationship among teachers. He suggests also that there should be well- prepared current records and research findings in the school which the supervisor can use to guide teachers’ classroom practices.
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Reference made to the adherence of strict time table and school regulations by this researcher as determinants of effective supervision should be compromised. The reason for his stance may stem from his personal philosophy and/or the context within which the study was conducted. Bureaucratic procedures in supervision may be characteristic of some African and other developing countries. The definition presented by UNESCO (2007) testifies to this belief, since most of their studies have been conducted in this context.
As shown in this section, all researchers share the belief that supervision is effective if the supervisor possesses and exhibits qualities and characteristics related to knowledge, interpersonal and technical skills. They are silent, however, on the direct causal effect of such qualities on student performance.
2.6 Types of Supervision
Supervision permeates every aspect of our lives as human beings. Supervision of teachers by heads, assisstant heads and education officers is a common practice in
Ghanaian schools. Until recently, the concept of instructional supervision was known as inspection which referred to the specific occasion when the whole school was examined and evaluated as a place of learning (Acheson & Gall 1997). Supervision as a concept is given several definitions by various people. According to Giwa (1987) the term supervision is derived from the Latin words which means ‘over’ and ‘see’.
Several researchers such as Harris (1996) as cited in Bays (2001) argue that defining supervision has been a contentious issue in education. Harris also observes that current thoughts in the definition of supervision do not represent full consensus, but common themes that run through major definitions include supporting teaching and learning; responding to changing external realities; providing assistance and feedback to teachers; recognising teaching as the primary vehicle for facilitating school
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learning; and promoting new, improved and innovative practices. He however pointed out that, discrepancies exist when it comes to roles, relationships, positions, and even skills and functions as far as supervision is concern.
The definitions of supervision vary from a ‘custodial orientation’ to a
‘humanistic orientation’. The custodial orientation is aimed at helping teachers by finding their defects, it is also known as the traditional supervision. Humanistic orientation on the other hand is the clinical supervision which emphasises teacher growth (Adeel, 2010). According to Osakwe (2010), supervision is concerned with the provision of professional assistance and guidance to teachers and students geared towards the achievement of effective teaching and learning in the school. Bernard and
Goodyear (2008, p.1) perceive “supervision is an intervention that is provided by a senior member of a profession to a junior member or members of that same profession. This relationship is evaluative, extends over time, and has the simultaneous purposes of enhancing the professional functioning of the junior member(s), and monitoring the quality of professional services offered”. McNamara
(2014) asserts that supervision is the activity carried out by supervisors to oversee the productivity and progress of employees who report directly to the supervisor.
School supervision according to Eregie and Ogiamen (2007) is defined as a whole mechanism systematically designed to accomplish the end of public education so that internal structure of the school is determined by the functions which are carried on towards those ends. School supervision can be classified as Instructional
Supervision; which borders on the activities which are carried out with the purpose of making the teaching and learning activities better and more result oriented for the learners; and Administrative Supervision; which deals with the mobilization and
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motivation of the staff in the school towards effective performance of their duties and responsibilities (Adu, Akinloye & Olaoye, 2014).
A variety of supervision types can be perceived to lie on a continuum with two extremes. One extreme is a type of supervision in which the supervisors acts as a friend and provides a shoulder for the supervisee to lean on. At the other end of the continuum, supervision demands strict accountability from the supervisee. Here, the supervisor may be interested in fault-finding. According to Chand (2015) types of supervision are generally classified according to the behaviour of supervisors towards his subordinates. These are also called techniques of supervision. Chand (2015) outlined the following as the types of supervision.
2.6.1 Autocratic or Authoritarian Supervision
Under this type, the supervisor wields absolute power and wants complete obedience from his subordinates. It is based on the principle that all members of the team need constant supervision and help; basically, because people will attempt to work as little as possible unless someone monitors them carefully. His/her leadership style benefits employees who require close supervision. Authoritarian supervision typically works well with individuals who are immature and undependable to complete work task if left alone. This type of supervision is resorted to tackle indiscipline subordinates. Creative employees who thrive in group functions detest this leadership style.
This implies that teacher have to deliver their teaching performance in a lucid manner. For this they have to act in accordance to the rules and regulations of the modern principles of teaching lay down. Also supervisors who have their own principles of teaching which are not suitable compel the teachers to teach accordingly.
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This type of supervision leads to creation of misunderstanding in human relationship between the supervisor and the teacher.
2.6.2 Laissez-faire or Free-rein Supervision
This is also known as independent supervision. Under this type of supervision, maximum freedom is allowed to the subordinates. A laissez-faire leader lacks direct supervision of employees and fails to provide regular feedback to those under his supervision. The philosophy behind this practice is often expressed as, ‘Hire good people and then get out of their way’. The supervisor never interferes in the work of the subordinates. This is mostly used when supervisors feel team members should be free to use their own creativity and individual style to complete their job task. The supervisor only comes in when they encounter a situation they are unable to handle on their own. In other words, full freedom is given to workers to do their jobs.
Subordinates are encouraged to solve their problems themselves.
This type of supervision gives absolute freedom to the teachers to deliver their teaching in their own light that they feel is the best for students. There is no hard and fast rule for them to follow guidelines of a sound teaching programme and appropriate methods of teaching for different subjects.
2.6.3 Democratic Supervision
Under this type, supervisor acts according to the mutual consent and discussion or in other words they consult subordinates in the process of decision making. This is also known as participative or consultative supervision. Subordinates are encouraged to give suggestions, take initiative and exercise free judgment. This results in job satisfaction and improved morale of employees. This point out that
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overall development of teaching and learning is the responsibility of one and all who are directly or indirectly linked with this process.
So this supervision says that there will be no improvement of teaching and learning only through teachers. Rather the high level officers as the supervisory personnel have to actively participate in the teaching programme and help the teachers by giving suggestions for improvement if any in private.
2.6.4 Bureaucratic Supervision
Under this type certain working rules and regulations are laid down by the supervisor and all the subordinates are required to follow these rules and regulations very strictly. A serious note of the violation of these rules and regulations is taken by the supervisor. This brings about stability and uniformity in the organisation. But in actual practice it has been observed that there are delays and inefficiency in work due to bureaucratic supervision.
2.6.5 Companionable Supervision
This is based principally on a friendly and laidback environment. Above all else, supervisors seek to be liked by all members and to create harmonious relationships among members; they avoid confronting members about poor job performance if it is possible. As a result it is common for members to set out of bounds.
2.6.6 Synergistic Supervision
This refers to a cooperative effort between the supervisor and members. All efforts are joined together and each member is recognized for the importance of his individual contribution. Supervision in this approach has a dual focus: accomplishment of the organization’s goal and support of the staff in the
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accomplishment of their personal and professional development goals. This approach to supervision emphasizes the identification of potential problems early; the supervisor and member then jointly develop strategies to prevent or ameliorate problem situations. This type of supervision is usually a successful one.
Mankoe (2007) postulate that there are two types of school supervision; the district-based supervision which is external (conducted by the Inspectorate division of the education service, especially circuit supervisors). External supervision according to Ghana Education Service (2002) is the one carried out by persons/officers who are not part of the particular institution and whose work is to compliment the role and duties of the internal supervisors by providing professional advice and guidance to teachers. External supervision therefore comes from outside the institution. Prominent among them are the circuit supervisors and inspectorate teams from the district education office. The second type is school-based supervision which is internal and conducted by headmasters and teachers. Adentwi (2000) has opinion that when supervision is carried out by a member of the team responsible for planning and implementing the programme being supervised or evaluated it is referred to as internal supervision. According to Ghana Education Service (2002), there are two types of supervision. These are traditional and clinical supervision.
2.6.7 Traditional Supervision
This type of supervision is geared towards fault-finding; and the supervisors usually act as an inspector. Supervisors provide suggestions to the teacher after the lesson delivery which the later often, don’t find it helpful. The basic problem is that supervisors usually provide information and suggestions on problems they themselves are concerned with but not on the problem experienced by the teachers in their classroom. Besides, the supervisory conference tends towards a pattern in which the
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supervisor talks while the teacher listens. It casts supervision in the role of a superior telling the teacher (subordinate) what needs to be changed and how.
2.6.8 Clinical Supervision
A working definition of clinical supervision has been given by Goldhammer,
Anderson and Krajewski (1993), they believe clinical supervision is that aspect of instructional supervision which draws upon data from direct first hand observation of actual teaching, or other professional events, and involves face-to-face and other associated instructions between the observer(s) and the person(s) observed in the course of analysing the observed professional behaviours and activities and seeking to define and/or develop next steps toward improved performance.
Ghana Education Service (2002) describes clinical supervision as a process that aims at helping the teacher identify and clarifies problems, receive data from the supervisor and develop solutions with the aid of the supervisor. This process is made up of five steps which are similar to the initial model of clinical supervision outlined by Goldhammer (1969). These steps are;
1. Pre-observation conference
2. Observation
3. Analysis and strategy
4. Supervision conference or Post-observation conference
5. Post-conference analysis
2.7 Educational Stakeholders View of Supervision
One of the most respected professions in the world is teaching. Teachers are mostly role models and consciously imitated by people. According to Panda and
Mohanty (2003) the teacher is the pivot of any education system. According to Cole
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(2005) the personalities, approaches and the motives of the supervisor are major determinants of employees’ perception about supervision. Teachers usually associated supervision with the rating of teachers. The educational implication of this is that teachers see a typical supervisor as a threat. Harris (1985) observes that there is a general belief that teachers tend to associate instructional supervision with fault- finding. However it is meant to assist teachers improve their teaching skills because there is this generally believed that if teachers are left to themselves they may not try to develop their teaching skills.
Sullivan and Glanz (2000) described that teachers view supervision for the sake of evaluation as often being anything other than up lifting. In a study of supervision and teacher satisfaction, Fraser (1980) stated that "the improvement of the teaching learning process was dependent upon teacher attitudes toward supervision"
(p. 224). The writer noted that unless teachers perceive supervision as a process of promoting professional growth and student learning, the supervisory practice will not bring the desired effect.
The relationship between the teacher and the supervisor is expected to be collegial rather than authoritarian. In a study of supervisory behavior and teacher satisfaction Glatthorn (2007) found that the improvement of the teacher-learning process was dependent upon teacher attitudes towards supervision. According to
Glatthorn (1990), unless teachers view supervision as a process of promoting professional growth and student learning the supervisory exercise would not have the desired effect. Where the teachers’ views on supervision are negative, it is most likely that teachers may view observations as the perfect platforms for the supervisor to attack them (Reepen & Barr, 2010). As a result, it is argued that most teachers tend to become anxious and resentful of the process of supervision.
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Tshabalala (2013) posits that most teachers are aware of the basic aims of instructional supervision. They also appreciated the supervision process if it was done in the right manner and with the objective of improving the learning process and the promotion of teacher growth. With this objective in mind, they will not be inhibited by the supervisors’ presence in their classroom. Acheson and Gall (1997) said that the hostility of teachers is not towards supervision but the supervisory styles teachers typically receive. Thus, selecting and applying supervisory models aimed at teachers' instructional improvement and professional growth is imperative to develop a sense of trust, autonomy, and professional learning culture (Hargreaves & Fullan,
2012).
Finding from the study of Cogan (1987) revealed that experienced teachers felt that they must be left to do what they knew. Majority of the teachers did not want the supervisors’ inputs in lesson planning as happened in clinical supervision. Only a few untrained teachers indicated that they would welcome the help from the supervisor in planning lessons.
Whether we supervise teachers for the purposes of retention, review, dismissal, promotion, reward, or reprimand, our efforts need not be viewed as negative or unproductive. “no matter how capable are designated supervisors, as long as supervision is viewed as doing something to teachers and for teachers, its potential to improve schools will not be fully realized” (Sergiovanni & Starratt, 2007, p. 5). All teachers want supervisory practice which promises real assistance (Tshabalala, 2013).
Therefore, the supervisors are to play complementary roles with the teachers in order to ensure a qualitative education for the nation.
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2.8 Qualities of a Good Instructional Supervisor
A supervisor is someone in position of authority or leadership who possesses the skills and ability (competence) to provide supervision to the school in terms of perceiving desirable objectives, maintaining a balance of the curriculum and rendering help to the teachers regarding the methods and other instructional problems that they encounter. Ogunsaju (1983) sees a supervisor as one formally designated to the organization to interact with teachers in order to improve the quality of learning by students. He is an instructional leader who has as his ultimate objective to ensure that teachers are performing the duties for which they are scheduled.
Oshungboye (2001) identified some qualities of a good instructional supervisor. He said; a good instructional supervisor must be strong-willed, consistent and fair in his dealings with other people. He must be cooperative and view his job as a team-type service. He must be true to his own ideals but at the same time be flexible, needs loyal and respectful of the beliefs and dignity of those around him. He must assist teachers to evolve various approaches and techniques like individualized instruction, grouping, testing and evaluation. He must be sincere, firm, approachable and ready to help people solve their problems. He must be versed in the principles and practices of current educational trends and innovations and interpret these to teachers.
He must be open in his decision-making and respect people’s opinion on matters affecting the school system. He must assist in the organization and proper administration of co-curricular activities for students. He must help to clarify educational objectives and goals and enlighten teachers on their implications. He must maintain, around himself, a relaxing atmosphere that will encourage, stimulate and inspire people around him to work harmoniously to achieve the organizational goal.
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And lastly that he must be large-hearted and be prepared for oppositions without malice.
2.9 Challenges and Problems of Instructional Supervision in Ghana
Though supervision is one of the oldest form of educational leadership, its position is still one of the most controversial to the extent of it being used interchangeably with inspection especially in Ghana and most African countries. The implication is that most people still apply the principles of inspection as perceived during the colonial and early part of the postcolonial Ghana. This has not improved instructional services nor has it led to professional growth of teachers, because it does not encourage collegiality or colleagueship.
Another problem of supervision of instruction in schools is the inadequacy of supervisory personnel. Mankoe (2006) said there is insufficient number of supervisors in most states of Ghana. He maintained that insufficient number of supervisory personnel has militated against effective supervision of instruction in pre-tertiary schools as the few available ones are unable to reach out to all the schools as expected within the supervisory period. Thus in some cases, some schools are not visited by instructional supervisors for period of one term or a whole session. This sometimes sterns from the fact that few supervisors are assigned to many schools and when it becomes humanly impossible to reach out to all the schools, they only visit few schools around. When this happens, the idea of giving professional assistance and stimulating development in teachers is not achieved.
Another problem is lack of proper training of our supervisors. As identified by
Okoro (1999) and Ogbonnaya (1997), both shared the opinion that administrators of education in some African countries do not consider proper training of supervisory staff to carry out supervisory services. Ogbonnaya maintained that the criteria for
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appointing supervisors are basically the possession of a first degree in education and some years of teaching experiences. He further said that some supervisors are also appointed simply because “they know some officers at the headquarters” this leads to the placement of “wrong pegs in right holes”. The implication is that those who are not exposed to the supervisory techniques and approaches are made to handle the job and thus haphazard result will be achieved.
Another problem militating against effective supervision of instruction in our schools is lack of motivation of the teachers and supervisory staff. It has been observed that poor or lack of motivation has been responsible for the skeletal or poor supervisory services available in our schools. The few available supervisory staff is not adequately motivated as some of them are owed salary arrears for several months.
Some of them fail to penetrate into the interior schools as they claim they are not mobile while there is no provision for their transport allowance to these schools.
Sharing this view, William in Okoro (1999) maintains that teachers and principals are allowed to toil year in year out without corresponding remuneration and incentives.
Ogbonnaya (1997) maintained that supervisors are not sufficiently motivated in the execution of their functions. With the above views one therefore need not expect these supervisors to perform miracle and hence the poor supervisory services we experience.
Also, poor leadership style, resistance to change and innovation coupled with the supervisee’s negative attitude to supervision all constitute serious problems or constraints to supervision of instruction in schools. Ezeocha in Okoro (1999) and
Ogbonnaya (1997) hold the belief that most supervisory staff are not exposed to democratic culture and thus adopt the old form of inspection. The claim that some supervisors do not run open-door policy by way of involving their clients in decision
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making especially when such decision affect them. They also maintained that some supervisors and their clients are resistant to innovations and prefer to preserve the status quo. They maintained that old and experienced teachers tend to resist change and innovation. This thus make supervision very difficult, they tend to stick to the biblical injunction “as it was in the beginning, is now and ever shall it be”.
Another problem against effective supervision of instruction in our school is the social gap that exists between the supervisor and the supervisees. There seems to be an imaginary gap that socially separates the supervisors and their clients. This stems from the fact that some supervisors of instruction see themselves and their positions as sacred and as such distance themselves from their subordinates both in principles and action. In support of this, Okoro (1999) maintains that many supervisory personnel do not see the need for them to make themselves available to their clients for assistance because of the above problem.
Finally, the problem of fund and communication has featured prominently.
There is gross inadequate financial allocation needed to procure facilities for supervision. This thus lead to the problem of communication as the supervisors find it difficult to even relay any information to the supervisees by way of workshop, seminars, bulletins. Akin to this problem is that of the absence of finance to send supervisors and supervisees for in-service training where knowledge is updated.
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CHAPTER THREE
METHODOLOGY
3.0 Overview
This chapter presents the methodology of the study. The chapter is organized under the following headings: research design, research setting, population, sample and sampling techniques and research instruments. The chapter is further divided under: pilot study, data collection, data analysis procedures and ethics considerations.
3.1 Research Design
A research design is the conceptual structure within which research is conducted; it constitutes the blueprint for the collection, measurement and analysis of data (Kothari & Garg, 2014). In this study, a cross sectional descriptive survey research design was adopted to gather descriptive and comparative data on the level of competencies of basic school supervisors in ensuring effective mathematics education delivery in Ghanaian schools. The design was adopted for the purpose of describing some characteristics of Kwahu East District Junior High School mathematics teachers and their supervisors. Survey design was also adopted for the study to helped gather quantitative data in order to understand indepth the concept understudy. Avoke (2005) citing Blaxter, Hughes and Tight (1996), indicated that survey research in education involves collection of information from members of a group of students, teachers or other persons associated with educational issues.
Babbie, (2007) is of the view that, survey research provides a quantitative or numeric description of trends, attitudes, or opinions of a population by studying a sample of that population. It includes cross-sectional and longitudinal studies using questionnaires or structured interviews for data collection, with the intent of
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generalizing from a sample to a population. According to Ary, Jacobs and Rezavieh
(2002), survey permits the researcher to gather information from a large sample of people relatively quickly and inexpensively. The descriptive survey was further considered the most appropriate design for conducting this study since it is the one that deals with things as they currently are (Creswell, 2003). Creswell further noted that a survey study can be done in a short time in which investigators administer a survey to a sample or to the entire population of people in order to describe the attitudes, opinions, behaviours or characteristics of the population. Again, information gathered from the descriptive research can be meaningful or useful in diagnosing a situation since it involves describing, recording, analyzing and interpreting conditions that exist. Most surveys are based on samples of a specified target population – the group of persons in whom interest is expressed. They are designed to provide a
‘snapshot of how things are at a specific time’. There is no attempt to control conditions or manipulate variables (Kelley, Clark, Brown & Sitzia 2003). Surveys, according to Mertens (2010), can be a powerful and useful tool for collecting data on human characteristics, such as their beliefs, attitudes, thoughts, and behavior. Hence, the survey design fit very well within the framework of the study. This design was also used by the researcher because it allows precise description of the phenomenon.
It allowed the researcher to study the competency level of the supervisors, JHS mathematics teachers’ perceptions of their supervisors’ competency, the dominant style of supervison in the district, the dominant challenges of school supervisors
(Headteachers and Circuit Supervisors) in the discharge of their duties as well as how the identified challenges facing the supervisors can be addressed in the Kwahu East
District. Survey is characterized by the use of a set of predetermined questions for all
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respondents and the oral or written responses to these questions becomes the principal data for the researcher.
The descriptive survey however is not without difficulties. Creswell (2002), noted that, survey data is self-reported information, reporting only what people think rather than what they do. Kelley, Clark, Brown and Sitzia (2003) also on their part, pointed out some demerits associated with its use. These include the danger that, the significance of the data can become neglected if the researcher focuses too much on the range of coverage to the exclusion of an adequate account of the implications of those data for relevant issues, problems, or theories. Also, the private affairs of respondents may be pried into and there is therefore the likelihood of generating unreliable responses and difficulty in assessing the clarity and precision of questions that elicit the desired responses (Fraenkel & Wallen, 2009). In order to offset these identified weakness, ethical consideration was paid to enhance the results and findings of the study. In spite of these demerits, the descriptive survey seemed appropriate.
This is because the breadth of coverage of many people or events means that it is more likely than some other approaches to obtain data based on a representative sample, and can therefore be generalisable to a population (Kelley, Clark, Brown &
Sitzia, 2003). Also, it has the potentiality of providing a lot of information that could be gathered from the respondents.
3.2 Research Setting
The study was conducted in the Kwahu East District in the Eastern Region of
Ghana. The Kwahu East District was carved out of the Kwahu South District through the Legislative Instrument (L.I) 1839 and inaugurated on 29th February 2008 with
Abetifi as the District capital. The District is situated on the northern part of the
Eastern Region. It shares common boundaries with the Kwahu North to the east,
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Kwahu South to the south and the Fanteakwa Districts to the southeast and Asante-
Akim North of the Ashanti Region to the north. Thus, the District is linked up with many Districts and this promotes commercial activities among the District capitals and other nearby communities. The total land size of the District is 623.31 square kilometers. A pictorial representation of the district is presented in Figure 3.1
Figure 3. 1: District Map of Kwahu East Source: Ghana Statistical Service (2013)
The district has a heterogeneous population in terms of ethnicity. The predominant ethnic groups are Akans representing 70.4 percent of the total population. The other significant tribes are Ewes (17.7%) and Ga-Adangbe (5.0%).
There are other minor ethnic groups with Northern origin alongside a number of
Nomadic Fulani Herdsmen mostly from Mali and Niger (Ghana Statistical Service
(GSS), 2013). Agriculture is the major economic activity in terms of employment in
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the District. About 55.1 percent of the working population is engaged in this sector, which constitutes the main source of household income in the district. There are two prominent types of farming activities in the District. These are food cropping and livestock farming. The most predominant of these is food crop farming with more of the farmers in the district taking to it. Livestock farming is carried out on a limited scale. The District population is largely youthful with 40 percent falling within that bracket. The 2010 National Population and Housing Census puts the District’s population at 67,498 with an intercensal growth rate of about 1.19 percent. The projected population for the year 2020 was therefore 76,603 comprising 51 percent females and 49 percent males (Ghana Statistical Service, 2013). The spatial distribution of population ranges from about 5000 in the urban settlements such as
Abetifi, the District Capital, Nkwatia and Kwahu Tafo to about 2000 or less in the rural settlements. Formal education in the Kwahu East District is provided by both public and private sectors. However, the public sector dominates. There are 258 educational institutions in the District ranging from KG, Primary, JHS, SHS, vocational/technical to Tertiary. The proceeding table (see overleaf) presents a summary of the various educational levels in the district.
Table 3. 1: Summary of educational institutions in the Kwahu East District No Level Public Private Total
1 KG 50 10 60 2 Basic 70 34 104 3 SHS 5 1 6 4 Technical/Voc. 3 0 3 5 Tertiary 1 3 4
Total 129 48 177
Source: District Directorate of Education (2017)
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Table 3.1 presents the breakdown of the various educational institutions in the district. The table reveals that, the district has 164 basic schools (both public and private), 9 second circles, and 4 tertiary schools. Generally, educational infrastructure in the district needs improvement. However, the situation is comparatively better in the second cycle and Tertiary institutions. It is worth noting that educational infrastructure in recent times has seen a major boost through the construction of new facilities and rehabilitation of dilapidated ones which will certainly contribute to improvement in academic performance. Apart from classroom infrastructure, the schools need Teacher accommodation especially in the rural areas to attract Teachers to help arrest the canker of zero percent in the results of some of the schools which currently stands at 7 districts wide.
3.3 Population
The population for the study is estimated to be around 1590 JHS mathematics teachers and supervisors in the Eastern Region of Ghana. The estimated population consists of 795 JHS mathematics teachers, 530 head teachers and 265 circuit supervisors and other educational supervisors. Population in research refers to the aggregate or totality of objects or individuals regarding which inferences are to be made in a sampling study (Seidu, 2007 cited in Arthur, 2011). Cecilia (2012) also, stated that population is a collection of all possible individuals, objects or measurement that have one or more characteristics in common that are of interest to the researcher. Finally, a research population is a large well-defined collection of individuals or objects having similar characteristics (Castillo, 2009). Castillo distinguishes between two types of population: the target population and the accessible population. The target population which is also known as the theoretical population refers to the group of individuals to which researchers are interested in
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generalizing the conclusions. Whilst the accessible population which is also known as the study population is the population in research to which the researchers can apply their conclusions. The target population for this study was all head teachers of both public and private basic schools, circuit supervisors and all mathematics teachers (N =
1590) in both public and private basic schools in the Eastern Region of Ghana.
However, the accessible population was all head teachers of both public and private basic schools, circuit supervisors and all mathematics teachers in both public and private basic schools in Kwahu East and West District in the Eastern Region of
Ghana. The estimated accessible population for the study was 274. This population was chosen because they possessed the characteristics and qualities the researcher was interested in studying. Beside this, they were also selected due to their proximity to the researcher and the willingness of the various groups and members of the group to accommodate the study.
3.4 Sample
A sample is a finite part of a statistical population whose attributes are studied to gain information about the larger population (Merriam-Webster, 2005). Cecilia,
(2012) also asserted that a sample is a representative of the population to the extent that it exhibits the same distribution of the characteristics as the population. The sample for the study was all head teachers, circuit supervisors and all mathematics teachers in public and private Junior High Schools in the Kwahu East District in the
Eastern Region of Ghana. The District has a total of one hundred and four (104)
Junior High Schools out of which thirty-four (34) are private and seventy (70) are public schools. The researcher used all the one hundred and four (104) public and private JHS for the study. Out of the hundred and four (104) schools sampled, 24 were in streams (some two and others three streams). The implication is that some of
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the schools will have more mathematics teachers than others. A total number of 192 consented mathematics teachers and supervisors took the questionnaires (teachers =
157 and supervisors = 35). However, 150 mathematics teachers completed and returned the questionnaire. This represented 95.5% respond and return rate. All the questionnaires from the supervisors were completed and returned. In essence 100% respond and return rate was achieved. Therefore, 185 participants took part in the current study.
3.4 Sampling Techniques
According to Castillo (2009), sampling techniques are the strategies applied by researchers during the sampling process. Sampling techniques and procedures refer to the methods or techinques used to select a sample from the population. The researcher used the multistage sampling techniques. Multistage sampling is where the researcher divides the population into stages, samples the stages and then resamples, repeating the process until the ultimate sampling units are selected at the last of the hierarchical levels (Goldstein as cited in Nafiu, 2012). Firstly, convenience sampling technique was used to select the district, that is, Kwahu East District. According to
Agyedu, Donkor and Obeng (2013), convenience sampling technique is an approach where a sample is selected according to the suitability of the researcher. In their view, the suitability may be in respect of availability of data, accessibility of the subjects, among others. Kwahu East District was conveniently chosen because of its proximity and accessibility to the researcher.
Secondly, purposive sampling technique was used to select all Junior High
Schools in the district. Purposive sampling starts with a purpose in mind of the researcher and the sample is thus selected to include participants of interest and exclude those who do not suite that purpose (Fraenkel, & Wallen, 2009). Patton
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(1990) suggested that the “logic of power of purposeful sampling lies in selecting information-rich cases for study in depth. Information-rich cases are those from which one can learn a great deal about issues of central importance to the purpose of the research, thus the term purposeful sampling” (p. 169). Because the study sought to explore and examine the level of competency of basic school mathematics supervisors in ensuring effective mathematics education delivery in basic schools in the Eastern
Region of Ghana, it was imperative to select information-rich-sample who are related to the central issue being studied.
The teachers in each of the one hundred and four (104) public and private were stratified into lower primary (BS 1-3), upper primary (BS 4-6) and Junior High
School (BS 7-9) teachers. Out of these three strata, the researcher purposively selected all the teachers in the third stratum (Junior High School) for the study. Junior High
School were selected for the study because external examinations are (e.g., Basic
Education Certificate Examination (BECE), National Education Assessment (NEA),
Early Grade Mathematics Assessment (EGMA) and Trends in International
Mathematics and Science Study (TIMSS)) carried out on learners at these levels. The researcher further stratified these teachers into mathematics teachers and non- mathematics teachers. All one hundred and ninety-two (192) public and private mathematics teachers and supervisors were selected for the study. A total number of
192 consented mathematics teachers and supervisors took the questionnaires (teachers
= 157 and supervisors = 35). However, 150 mathematics teachers completed and returned the questionnaire. This represented 95.5% respond and return rate. All the questionnaires from the supervisors were completed and returned. In essence 100% respond and return rate was achieved. Therefore, 185 participants took part in the current study.
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3.5 Research Instruments
In order to collect relevant data from Junior High School mathematics teachers and supervisors in Kwahu East District, questionnaire for Teachers and Supervisors were used as the instruments to collect the necessary data(see Appendix A and B).
3.5.1 The Questionnaire
A questionnaire is a written instrument that contains a series of questions or statements called items that attempt to collect information on a particular topic
(Agyedu, Donkor, & Obeng, 2013). Separate survey questionnaires designed for JHS mathematics teachers and their supervisors were the main data collection instruments used in this study. While designing the questionnaires, the research questions were taken into account and they were divided into subheadings/subscales accordingly.
Besides, while interpreting the results, it was important to diagnose the differences between mathematics supervisors’ and teachers’ perceptions of supervision practices in basic schools in the Kwahu East District. Therefore, attention was paid to keep these two questionnaires parallel to each other.
In this study, the researcher used the structured questionnaire to collect quantitative data on Kwahu East District Junior High School mathematics supervisors and teachers’ perceptions of supervisors’ competency in supervising instructional processes. The respondents were limited to a list of options from which they were to choose one as a respond to each item. This was done to collect numeric data to describe the respondents’ perceptions of their supervisors’ supervision competencies.
While designing the JHS teachers’ questionnaires, the related literature on the supervisors’ competency, styles and techniques of supervision, and the theories and practices in teaching in mathematics were taken into account. In the JHS teachers’ questionnaires, the strengths and limitations of the questionnaires used in other studies
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were considered, and the necessary changes were made to make them suitable for the purposes of the present study. Although JHS mathematics teachers and their supervisors’ questionnaires are parallel to one another, there are still some differences between them. It is because; there are differences between the two groups in terms of their knowledge, perceptions and experiences of supervisor’s competencies. In short, the mathematics supervisors are assumed to have more knowledge and experiences about the goals, content, instructional methods and evaluation procedures of the mathematics curriculum when compared with the teachers. Besides, the supervisors perceive the implementation of the mathematics curriculum from the teaching, learning and supervision points of view, whereas teachers perceive the mathematics curriculum from the teaching and learning dimension only.
3.5.1.1 Teacher Questionnaire
In order to achieve the purpose of the study, a self-developed questionnaire named Supervisors’ Competency Perception Index II (SCPI-II) (for Mathematics
Teachers) was used. The Supervisors’ Competency Perception Index II (SCPI-II) questionnaire was divided into three main sections (see Appendix A). The first section was captioned ‘Demographic Information’. The Demographic information section involves both close and open-ended questions. Items about the teachers’ background characteristics such as area of specialization if trained, age, gender, educational background, experience and professional status among others. The main purpose of this section was to determine the general profiles of the teachers taking part in the study. Besides, the results obtained from this section were used to determine whether these background characteristics produced differences in their perceptions of the competencies supervisors bring on board, which is another research hypothesis of the study. The second section of the Supervisors’ Competency Perception Index II (SCPI-
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II) questionnaires consisted of 22 Likert-type scale items. The second sub-section elicited responses from participants on the professional competences (Mathematical
Thinking Competency, Problem Handling Competency, Modelling Competency,
Reasoning Competency, Representation Competency, Symbols and Formalism
Competency, Communication Competency, and Aids and Tools Competency) of school supervisors to supervise mathematics instruction. All the 22 items were structured questions which were measured on a 4-point Likert-type scale. The second section’s Likert-type scale ranges from 1 to 4 (1 = strongly disagree and 4 = strongly agree). The third and last section on the Supervisors’ Competency Perception Index II
(SCPI-II) questionnaires was designed based on the three main traditional styles of supervision available in literature. The purpose of this section of the questionnaire was to document, using closed-ended items, the various head teachers’ supervisory styles. A total of twenty-seven (27) items were used in the third sub-section. All items measuring the head teachers’ supervisory styles were anchored on a 4-point Likert-
Scale (1 = strongly disagree to 4 = strongly agree).
3.5.1.2 Supervisor Questionnaire
The Supervisors’ Competency Perception Index I (SCPI-I) (for Headteachers) questionnaire was also divided into sections in order to ensure sequencing on the instrument for the supervisors. The Supervisors’ Competency Perception Index I
(SCPI-I) is also provided in Appendix B. The SCPI-I was also sub-divided into three main sections. The first seven items on the questionnaire are about the supervisors’ characteristics such as their gender, age, professional status, area of specialization, highest qualification, current position, experience gain as a result of being on current position and teaching experience. These questions were asked not only to determine the general profiles of the supervisors but also to examine whether these background
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characteristics create a difference in the supervisors’ experiences about the mathematics curriculum in terms of its goals, content, instructional and assessment procedures, which is one of the objectives of the study. The second section of the
Supervisors’ Competency Perception Index I measured the professional competency of the supervisors. The third section measured the supervision challenges supervisors face in the district. The second and third sections were anchored a -point Likert-scale which ranged from 1 to 4 (1 = strongly disagree and 4 = strongly agree).
3.6 Pilot Study
Wilson and MacLean (1994) suggested that, piloting is able to help in establishing the reliability, validity and practicability of the questionnaire because it serves among other things: to check the clarity of the questions, give feedback on validity of test items and also to make sure that the data required answered the research questions. Pilot-testing the instruments enabled the researcher to modify items that were difficult to understand, reduce ambiguities and incorporate new categories of responses that were identified as relevant to the study (Awanta, &
Asiedu-Addo, 2008). After the two questionnaires had being revised in light of experts’ and colleagues’ suggestions, the Supervisors’ Competency Perception Index I
(SCPI-I) (for Headteachers) and Supervisors’ Competency Perception Index II (SCPI-
II) (for Mathematics Teachers) questionnaires were pilot-tested in a nearby selected district – the Kwahu West District. The researcher chose the district because it was deemed to have exhibited the similar characteristics as the district of interest to the researcher. The pilot-test helped the researcher to ensure the validity and reliability of the questionnaire. After explaining the purpose and significance of the study, twenty- two Junior High School mathematics teachers (n = 15) and basic school supervisors (n
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= 7) agreed to participate in the pilot study. Later, each participant was interviewed and they were asked the following questions:
1. How long did it take for you to respond to the questionnaire?
2. What kind of problems did you have while answering the questions/items?
3. Are there any questions that you recommend to be changed? What are your
suggestions?
4. What other parts and questions should be included in the questionnaire?
5. Are there any overlapping parts or questions in the questionnaire?
After this process, the questionnaire was redesigned considering the respondents’ opinions, problems and suggestions. In the new questionnaire, some of the questions/items were deleted and the terminology used in some of the statements was changed in order to make it comprehensible for the main study in Kwahu East
District.
3.6.1 Validity
Validity is the most important consideration in developing and evaluation of measuring instruments (Ary, Jacobs, & Razavieh 2002). Validity of a research instrument is determined by how well it measures the concept(s) it is intended to measure (Awanta, & Asiedu-Addo, 2008; Ruland, Bakken, & Roislien, 2007). In order to establish the validity of the research instruments, the following validity test were carried out: Face, and Content validity.
After developing the research instruments, a group of graduate students from the University of Education, Winneba and other teachers from some basic schools in
Winneba, were requested to carefully and systematically scrutinize and assess the instrument for its relevance and face validity. The feedback from the graduate
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students and teachers were factored into the final preparation of the instrument. Issues such as length of the items and general format of the questionnaire were some of the concern pointed out to the researcher during the pilot stage.
Content validity of an instrument focuses on the extent to which the content of the instrument corresponds to the concepts it is design to measure (Agyedu, Donkor &
Obeng, 2013). They opine that, the usual process of establishing content validity is to examine the objectives of the instrument and compare to its content. Cooper and
Schindler (2008) suggested two ways of determining content validity. Firstly, the designer may determine it through a careful definition of the topic of concern, the items to be scaled and the scale to be used. Secondly, an expert may judge how well the instrument meets the standard. Based on this knowledge, relevant information from literature and suggestions from my supervisor and other lecturers who are experts in supervision and supervisory practices, were sought to content validated the instruments.
Once the experts’, basic school mathematics supervisors’ and mathematics teachers’ opinions, problems and suggestions about the questionnaire were taken, necessary changes were made and the final versions of the two questionnaires were produced. Following the final changes, the questionnaire was sent to the site by the researcher for the data collection stage to commence.
3.6.2 Reliability
The term Reliability concerns the degree to which an experiment, test, or any measuring procedure yields the same results on repeated trials (Ruland, Bakken, &
Roislien, 2007). A reliability analysis using Cronbach’s Alpha statistics was run to determine the internal consistency of the items on the Supervisors’ Competency
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Perception Index I (SCPI-I) (for Headteachers) and Supervisors’ Competency
Perception Index II (SCPI-II) (for Mathematics Teachers) questionnaires. Reliability of the questionnaires was determined through the use of the Statistical Package for
Services Solutions (SPSS) version 20. The reliability measurements for each section of the piloted instrument were calculated. For Supervisors’ Competency Perception
Index I questionnaire 훼 = 0.81. The alpha value for each sub-section was accounted for and the results were appreciable. For example, Mathematical Thinking
Competency 훼 = 0.81, Problem Handling Competency 훼 = 0.79, Modelling
Competency 훼 = 0.91, Reasoning Competency 훼 = 0.83, Representation Competency
훼 = 0.90, Symbols and Formalism Competency 훼 = 0.71, Communication
Competency 훼 = 0.92, and Aids and Tools Competency 훼 = 0.95.
The Cronbach’s Alpha of Supervisors’ Competency Perception Index II questionnaire was 훼 = 0.873. The individual sub-scales alpha values were also determined. They include: Mathematical Thinking Competency 훼 = 0.75, Problem
Handling Competency 훼 = 0.70, Modelling Competency 훼 = 0.83, Reasoning
Competency 훼 = 0.73, Representation Competency 훼 = 0.80, Symbols and Formalism
Competency 훼 = 0.91, Communication Competency 훼 = 0.82, and Aids and Tools
Competency 훼 = 0.90. According to Creswell (2007) Cronbach’s Alpha reliability coefficient values of 0.70 and above are considered reliable.
3.7 Data Collection Procedure
According to Creswell (2002), respecting the site where the research takes place and gaining permission before entering a site is very paramount in research. An introductory letter (see Appendix C) was obtained from the Department of
Mathematics Education, University of Education, stating the aims and purpose of the
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study and the need for the participants to give their consent and co-operation. The letter of permission to conduct the study in the Kwahu East District was sent to the district educational directorate and permission granted with another introductory letter
(see Appendix D). Letters from District Education officers was used to solicit permission from school heads to administer the questionnaire to the mathematics teachers and supervisors. Approvals were granted verbally and the headteachers introduced the researcher to the teachers. During these introductions the researcher gave a brief overview of the study, addressed any concerns that teachers had about the study. The researcher finally solicited consent for teachers to participate in the study.
Obtaining informed consent from participants is a vital process in ethical research practice. It is very important that participants are well informed about the research, its purpose, benefits, and risks and what is expected of them in the research process even before they can give their consent (Langenbach, Vaughn, & Aagaard, 1994). Those who agreed to participate were given the questionnaire to complete either in the presence of the researcher or on an agreed date (maximum of one week). The completed questionnaires were collected by the researcher where they were immediately checked for any accidental omissions.
3.8 Data Analysis
According to Burns and Grove (2003), data analysis refers to the systematic organization and synthesis of research data, and the testing of research hypotheses.
Data analysis therefore is the ordering and breaking down of data into constituent parts and performing of thematic analysis or statistical calculations with the raw data to provide answers to the research questions which guide the research. Creswell and
Plano (2007) postulated that although there are similarities in the data analysis process, that is, data preparation, data exploration, data analysis, representation and
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data validation, in research data analysis is dependent on the design of the study. As this study used the survey research design, the concurrent data analysis was employed.
The responses from the questionnaire items were coded (e. g. Strongly
Disagree = 1, Disagree = 2, Agree = 3, Strongly Agree = 4) and analyzed through the use of Statistical Package for Social Science (SPSS version 20). The SPSS software was chosen for the data analysis because it is reasonably user friendly and does most of the data analysis one need as far as quantitative analysis is concerned. SPSS is also by far is the most common statistical data analysis used in educational research
(Muijs, 2004). The data entries were done by the researcher in order to check the accuracy of the data.
The following illustrates how data were analyzed for each research question
1. Research Question 1: What are mathematics teachers perceptions of the
competence supervisors have in ensuring effective teaching and learning of
mathematics in basic schools in the Kwahu East District?
Data gathered with the help of Section B on the Supervisors’ Competency Perception
Index II (for teachers) instrument was used to answer research question one (1). The section was anchored on a four-point Likert scale. The data collected was analyzed using appropriate descriptive statistics (frequencies, percentages, means and standard deviations) which allowed the researcher to use numerical values to represent scores in the sample. According to Borg and Gall (1983) descriptive statistics not only allows the researcher to use numbers but also provides the researcher with data that allow for inferences on the population and directions for answering the research questions. An item-by-item analysis of data was conducted. The percentage and
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frequency of the total sample responding to each question was given. The use of standard deviation on the items indicate the extent to which participant agree or disagreed with the items (measure of dispersion). Finally, tables were presented with descriptions and discussions of some major aspects that addressed the research question raised.
Research Question 2: How do supervisors perceive their competencies in ensuring effective teaching and learning of mathematics in basic schools in the Kwahu East
District?
Quantitative data collected on the respondents with the help of Section B on the Supervisors’ Competency Perception Index I (for supervisors) instrument was used to provide answers to research question two (2). The section was anchored on a four-point Likert-type scale (Strongly Disagree = 1, Disagree = 2, Agree = 3, Strongly
Agree = 4). Numerical scores were assigned to them to indicate possible relationship in responses of the respondents and then frequency lists were drawn. Descriptive statistics such as frequencies, percentages, means and standard deviations were employed to help explore the perceptions of supervisors’ competencies in ensuring effective teaching and learning of mathematics.
Research Question 3: What styles of school supervision do Junior High School teachers in the Kwahu East District experience?
Research question 3 was addressed using quantitative data gathered from
Section C of the Supervisors’ Competency Perception Index II (for teachers) instrument. This section was anchored on a five point Likert-type scale (Strongly
Disagree = 1, Disagree = 2, Undecided = 3, Agree = 4, Strongly Agree = 5). The questionnaire instrument had its scales of measurement reduced/recoded from five
Likert-type scale to three Likert-type scale for easy analysis of the data. For instance,
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the researcher combined “Strongly Disagree” and “Disagree” to “Disagree” and also
“Strongly Agree” and “Agree” to “Agree” to project a unique response. This combination according to Best and Kahn (2006) is possible when using Likert-type scale to report percentages. The scores assigned to the responses were easily analyzed using frequency counts. Descriptive statistics (frequencies, percentages, means and standard deviations) was employed to help explore the styles of school supervision do
Junior High School teachers in the Kwahu East District experience.
Research Question 4: What inherent challenges do supervisors in the Kwahu East
District face in ensuring effective mathematics education delivery in basic schools?
The data collected on Section C of the Supervisors’ Competency Perception
Index I (for supervisors) instrument, was analysed using appropriate descriptive statistics such as frequencies, percentages, means and standard deviations which allowed the researcher to use numerical values to represent scores in the sample. The purpose of the section was to explore some of the major challenges supervisors face in ensuring effective mathematics education delivery in basic schools in the Kwahu East
District. Section C, was anchored on a five point Likert-type scale (Strongly Disagree
= 1, Disagree = 2, Undecided = 3, Agree = 4, Strongly Agree = 5). The questionnaire instrument had its scales of measurement reduced/recoded from five Likert-type scale to three Likert-type scale for easy analysis of the data. For instance, the researcher combined “Strongly Disagree” and “Disagree” to “Disagree” and also “Strongly
Agree” and “Agree” to “Agree” to project a unique response. Descriptive statistics such as frequencies, percentages, means and standard deviations were employed to help explore the Figure 3.1 indicates scales of measurement reduced/recoded from five Likert-type scale to three Likert-type scale.
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Neutral General Disagreement General Agreement
Strong Strong Disagreement Disagreement Agreement Agreement
1 2 3 4 5
Figure 3. 2: The neutral position on the five-point Likert-type scale
Research Hypothesis 1: 푯01 = There will be no statistical significant difference
between male and female teachers’ perceptions of styles of school supervision in the
Kwahu East District
The aim of the hypothesis was to explore the difference that might exist
between male and female teachers’ perceptions of the styles of school supervision in
the Kwahu East District. To test this hypothesis, mean differences between male and
female teacher respondents were calculated. An independent-sampled t-test was run to
determine gender was a differentiator when it came to exploring the styles of school
supervision in the Kwahu East District.
Research Hypothesis 2: There will be no statistical significant difference between
mathematics teachers’ and supervisors’ perceptions of mathematics supervisors’
competency in the Kwahu East District
Descriptive statistics, means and standard deviations, were calculated to
establish mathematics teachers’ and supervisors’ levels of agreement with
supervisors’ competency in the Kwahu East District. T-test was calculated to
determine if the levels of agreement between the teachers and head teachers were
significant.
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3.9. Ethical Consideration
Kusi (2012) opines that in educational research, ethics are the issues that are related to how the researchers conduct themselves or their practices and the consequences of these on the participants in the research. The awareness of ethical concerns in research is reflected in the growth of relevant literature and in the appearance of regulatory codes of research practice formulated by various agencies and professional bodies. A major ethical dilemma is that which requires researchers to strike a balance between the demands placed on them as professional scientists in pursuit of truth, and their subjects’ rights and values potentially threatened by the research. Cohen, Manion, and Morrison (2007) suggest two concerns to watch for in ethical considerations; first, the manner in which the research has been conducted in relation to the research subject (matters such as informed consent, confidentiality, and persons involved) and secondly, acknowledgement of the contribution of all the people who have been involved in the research and as well as open recognition of individuals whose research influenced this present study. Ethical issues that were considered in this study are the permission to collect data, confidentiality, anonymity and the protection of participants (Patton, 2002; Berg, 2001; Neuman, 2000;).
3.9.1 Confidentiality
The participants were assured that all the information obtained will be treated as a confidential report. That is, data will only be used for stated purposes and no other person will have access to interview data. The participants were informed that their names will be omitted and will not be attached to any of the data gathered
(Liamputtong & Ezzy, 2005; Patton, 2002). The participants were also guaranteed that if their anonymity were to be threatened, all the records would be destroyed. This was done in order to avoid biased responses from participants. Data were kept safely in
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case there were queries about them at a later date. Audio-tapes were locked away.
Computer data were protected by a password. At the end of the process, all documents will be shredded and tapes will be erased (Walliman, 2006). Data will only be destroyed after completion of the degree and when the data are no longer required by the university.
3.9.2 Anonymity
One of the important ethical consideration the researcher considered was
‘maintaining the anonymity of respondents’. Providing anonymity of information collected from research participants means that either the project does not collect identifying information of individual subjects (e.g., name, address, Email address, etc.), or the project cannot link individual responses with participants’ identities. In this study the researcher did not seek for any information that was likely to reveal the identity of the respondents. This was done to protect the identity of research respondents. Personal anonymity may be central to gaining reliable information and that the issue of anonymity was dealt with when one respondent asked whether they had to give their names on the questionnaire.
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CHAPTER FOUR
RESULTS AND DISCUSSION
4.0 Overview
This chapter presents the results and discussion of the analyses of the data.
The chapter is organized under the following: demographic characteristics of the respondents, results and discussion of analyses on each research question and the research hypotheses.
The purpose of the study was to explore and examine mathematics supervisors’ competence in ensuring effective mathematics teaching and learning in basic schools in Ghanaian schools. Specifically, the study sought to: examine the competencies of basic school mathematics supervisors in ensuring effective delivery of mathematics education in Kwahu East District; explore the view of basic school mathematics teachers on the impact of supervision on their classroom practices; identify the challenges facing school supervisors in supervising mathematics teachers in Junior High School; explore ways of addressing the challenges of school supervisors in supervising mathematics teachers in Junior High School in the Kwahu
East District. In this regard the following research questions guided the study:
2. What are mathematics teachers perceptions of the competence supervisors have in
ensuring effective teaching and learning of mathematics in basic schools in the
Kwahu East District?
3. How do supervisors perceive their competencies in ensuring effective teaching
and learning of mathematics in basic schools in the Kwahu East District?
4. What styles of school supervision do Junior High School teachers in the Kwahu
East District experience?
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5. What inherent challenges do supervisors in the Kwahu East District face in
ensuring effective mathematics education delivery in basic schools?
Hypothesis
푯0 = There will be no statistical significant difference between male and female teachers’ perceptions of styles of school supervision in the Kwahu East District
푯0a = There will be no statistical significant difference between mathematics teachers’ and supervisors’ perceptions of mathematics supervisors’ competency in the
Kwahu East District
4.2 Demographic Characteristics of the Participants
The demographic information about the teachers is in Table 4.1.
Table 4. 1: Demographic Characteristics of Kwahu East District Mathematics Teacher Participants (Total = 150) Variable Categories Frequency Percentage Male 96 64.0 Gender Female 54 36.0
18 – 25 11 7.3 26 – 35 43 28.7 Age 36 – 45 54 36.0 46 – 55 35 23.3 56 and above 7 4.7 Cert A. 6 4 Diploma 61 40.7 Teachers’ Academic Qualification Bachelor’s Degree 80 53.3 Master’s Degree 3 2 Senior Sup. II 42 28 Senior Sup. I 10 6.7 Prin. 92 61.3 Rank of Teachers Superintendent Assist. Direct II 4 2.7 Assist. Direct I 2 1.3 Deputy Direct I 0 0.00 Less than 2 years 12 8.0 2 – 5 years 25 16.7 Years Teaching Experience 6 – 10 years 55 36.7 11 – 15 years 35 23.3 Over 15 years 23 15.3
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Source: Field Data - Questionnaire
Table 4.1 shows that majority, 96 representing 64.0%, of the teachers participating in the study were males whiles 36.0% representing 54 respondents were female. The result on the gender variable of the sample indicates that both male and female were given opportunity to take part in the study. However, the results show skewness toward the male teachers. The age composition of the teachers revealed that majority of them (n = 54, 36.0%) were between 36 – 45 years, this was followed by
26 – 35 years (n = 43, 28.7%), the 46 – 55 years were also numbered around 35 representing 23.3%. Finally, the 56 and above years were 7 representing 4.7 %.
Academic qualification of the teachers indicates that more than one-half (n = 80,
53.3%) were Bachelor’s degree holders whereas 61 representing 40.7% were diploma holder, 6 representing 4% were post-secondary certificate holder and finally 3 of the respondents representing 2% were master’s degree holders.
Table 4.1 further reveals that a larger portion of the teacher respondents (n =
92, 61.3%) were Principal Superintendent, this was followed by Senior
Superintendent II (28%), Senior Superintendent I (6.7%), Assistant Director II
(2.7%), and Assistant Director I (1.3%). The rank distribution of the respondents implies that information collected would reflect rich views from different rank and experience. Finally, the demographic characteristics on the years of teaching experience of the respondents reveals that, 12 of them representing 8.0% had taught for less than 2 years, 25 (16.7%) indicated that they had taught for about 2 – 5 years, also 55 indicated that they had taught for about 6 to 10 years, 35 of the teachers also indicated that they had spent about 11 – 15 years in the teaching profession while 23 indicated that they have been teaching for over 15 years.
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The demographic information about the mathematics supervisors (Circuit
Supervisors and Head Teachers) answering the questionnaires is presented in Table
4.2.
Table 4. 2: Demographic characteristics of Kwahu East District Mathematics Supervisors (n = 35) Variables Level C.S Heads Male 3 21 Gender Female 2 9 Total 5 30 20 – 30 0 5 31 – 40 2 16 Age 41 - 50 3 8 51 and above 0 1 Total 5 30 Diploma 0 2 Professional Qualification Bachelor’s Degree 5 26 Master’s Degree 0 2 Total 5 30 Trained 5 28 Professional status Untrained 0 2 Total 5 30 Mathematics 0 11 Area of specialization Others 5 19 Total 5 30 1 – 5 4 21 No. of years on current position 6 – 10 0 8 11+ 1 1 Total 5 30 1 – 5 0 4 6 – 10 0 3 No. of years of teaching 11 – 15 0 10 16 – 20 2 4 21+ 3 9 Total 5 30 Source: Field Data - Questionnaire
The analysis as presented in Table 4.2 suggest that three (3) out of the five (5) circuit supervisors were male while 21 out of the 30 head teachers were males. The data on the age of the respondents indicates that 0 circuit supervisor and 5 head teachers respective were within the 20-30 year age range. 2 circuit supervisors and 16 head teachers also indicated they were within the 31 – 40 year age bracket. The table
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further reveals that the 41 – 50 age bracket recorded 3 circuit supervisors and 8 headteachers. Finally, on the age demographic data, only one (1) headteacher indicated that he/she was within the 51 and above age bracket. Professional qualification of the supervisors was also gathered. The result indicates that, 2 of the headteachers had Diploma, 5 circuit supervisors and 26 headteachers had bachelor’s degree and 2 head teachers had master’s degree. Table 4.2 again reveals that all the circuit supervisors were professionally trained (n = 5) while 28 out of the 30 head teachers asserted that they were also professionally trained. However, none of the circuit supervisors indicated that he/she was trained mathematically, while 11 out of the 30 head teachers indicated that they had specialty in mathematics. Among the 5 circuit supervisors in the district, 4 indicated they have been on their current job for between 1 – 5 years, while 1 person indicated that he/she had been on the current job for over 11 years. In the same regard, 21 of the head teachers indicated that they have
1 – 5 years of experience on the current job, 8 indicated they had been on their current job for over 6 – 10 years while 1 person indicated that he/she had been on the current job for over 11 years. Finally, the respondents indicated that they have teaching experience of one form or the other.
4.3: Findings related to Research Questions
Research Question 1: What are mathematics teachers perceptions of the competence supervisors have in ensuring effective teaching and learning of mathematics in basic schools in the Kwahu East District?
Research question one sought to explore mathematics teachers’ perceptions of basic school supervisors’ competence in ensuring effective mathematics teaching and learning in basic schools in the Kwahu East District. The supervisors’ competency level was measured through the lens of Niss and Jensen’s (2003) conceptual
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framework named the “KOM flower” (KOM – in Danish stands for “Competencies and the Learning of Mathematics” (Niss, 2003)). According to Niss (2003) there are eight competencies which can be said to form two groups. The first group of competencies has to do with the ability to ask and answer questions in and with mathematics and the other group of competencies has to do with the ability to deal with and manage mathematical language and tools. As such the first research question was addressed based on the group of competencies. Thus, two separate tables (Table
4.3 and Table 4.3 con’t) were created for each of the competence examined. The quantitative data generated from the research question was analyzed using descriptive statistics (frequency counts, percentage, mean and standard deviation scores).
According to the Table 4.3 (see overleaf), the mean scores obtained for each statement reveals that the majority of the teachers believe that most of the supervisors were averagely competent in supervising the teaching and learning of mathematics in the district. Table 4.3 displays information about mathematics teachers’ perceptions of the competence of the supervisors with regards to “ability to ask and answer questions in and with mathematics”.
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Table 4. 3: Descriptive Statistics of Mathematics Teachers’ Perceptions of the Competency Level (first group) of Supervisors in Kwahu East District. Statement SD (%) D (%) A (%) SA (%) M(SD) SSM Mathematical Thinking Competency SSSD My supervisors are able to supervise teachers posing questions that are characteristic of 2(1.3) 66(44.0) 74(49.3) 8(5.3) 2.6(0.6) mathematics, and predict the kinds of answers that mathematics students may offer. Most supervisors in my school understand and are 2.6 able to supervise the scope and limitations of a 9(6.0) 58(38.7) 69(46.0) 14(9.3) 2.6(0.7) (1.3) given concept. Some external supervisors are able to extend the scope of a concept by abstracting some of its 1(0.7) 49(32.7) 92(61.3) 8(5.3) 2.7(0.6) properties and generalizing results to larger classes of objects during pre-observation conference. Problem Handling Competency SD (%) D (%) A (%) SA (%) M (SD) My supervisors are able to supervise teachers pose and specify different kinds of mathematical 5(3.3) 73(48.7) 68(45.0) 4(2.7) 2.4(0.6) problems – pure or applied; open-ended or closed- ended. 2.5 My supervisors are able to supervise teachers (1.0) solving different kinds of mathematical problems, 10(6.7) 73(48.7) 49(32.7) 18(12.0) 2.5(0.8) whether posed by others or by oneself, and, if appropriate, in different ways. Modelling Competency SD (%) D (%) A (%) SA (%) M (SD) External supervisors are able to supervise teachers when analyzing foundations and properties of 18(12.0) 62(41.3) 51(34.0) 19(12.7) 2.5(0.9) existing models, including assessing their range and validity. During pre-observation conference, supervisors are able to decode existing models, i.e. translating and 28(18.7) 52(34.7) 35(23.3) 35(23.3) 2.5(1.1) 2.4 interpreting model elements in terms of the (1.5) ‘reality’ modelled to teachers. My supervisors are able to supervise teachers performing active modelling in a given context - structuring the field – mathematising - working 5(3.3) 101(67.3 40(26.7) 4(2.7) 2.3(0.6) with(in) the model, including solving the problems it gives rise to etc. Reasoning Competency SD (%) D (%) A (%) SA (%) M (SD) Most external supervisors are able to supervise teachers when following and assessing chains of 13(8.7) 43(28.7) 86(57.3) 8(5.3) 2.6(0.7) arguments, put forward by students during mathematics lessons. Knowing what a mathematical proof is (not), and how it differs from other kinds of mathematical 26(17.3) 25(16.7) 81(54.0) 18(12.0) 2.6(0.9) 2.7 reasoning, e.g. heuristics, is one unique (1.3) characteristics of my supervisor. Mathematics supervisors have the ability to uncover the basic ideas in a given line of argument 3(2.0) 41(27.3) 97(64.7) 9(6.0) 2.8(0.6) (especially a proof), including distinguishing main lines from details and ideas from technicalities. Key: SD = Strongly Disagree, D = Disagree, A = Agree, SA = Strongly Agree, (%) = Percentage, M = Mean, SD = Std. Deviation, SSM = Sub-scale Mean, SSSD = Sub-scale Std. Deviation
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Table 4.3 (CON’T) Descriptive Statistics of Mathematics Teachers’ Perceptions of the Competency Level (second group) of Supervisors in Kwahu East District. Representation Competency SD (%) D (%) A (%) SA (%) M (SD) SSM Supervising teachers’ understanding and utilizing (decoding, interpreting, distinguishing between) of different sorts of representations of 2(1.3) 94(62.7) 41(27.3) 13(8.7) 2.4(0.7) mathematical objects, phenomena and situations is not a problem to my internal supervisors Supervising teachers when utilizing the relations between different representations of the same 2.5 entity, including knowing about their relative 28(18.7) 33(22.0) 84(56.0) 5(3.3) 2.4(0.8) (1.2) strengths and limitations are no problem to my supervisors My supervisors are able to supervise teachers choosing and switching between representations 10(6.7) 34(22.7) 106(70.7) 0(0) 2.6(0.6) when teaching mathematics. Symbols and Formalism Competency SD (%) D (%) A (%) SA (%) M (SD) Most pre or post conferences with supervisors are characterized with decoding and interpreting symbolic and formal mathematical language, 22(14.7) 73(48.7) 32(21.3) 23(15.3) 2.4(0.9) and understanding its relations to natural language. Understanding the nature and rules of formal 2.6 mathematical systems (both syntax and 2(1.3) 54(36.0) 87(58.0) 7(4.7) 2.7(0.6) (1.4) semantics) is no problem to most of my supervisors. My supervisors are able to supervise teachers in handling and manipulating statements and 1(0.7) 66(44.0) 79(52.7) 4(2.7) 2.6(0.6) expressions containing symbols and formulae. Communication Competency SD (%) D (%) A (%) SA (%) M (SD) Understanding others’ writings, visual or oral ‘texts’, in a variety of linguistic registers, about 2(1.3) 68(45.3) 73(48.7) 7(4.7) 2.6(0.6) matters having a mathematical content is not a challenge to most supervisors in my school 2.7 Expressing oneself, at different levels of (0.9) theoretical and technical precision, in oral, visual or written form, about such matters is a 4(2.7) 42(28.0) 81(54.0) 23(15.3) 2.8(0.7) unique characteristic of most supervisors in my school. Aids and Tools Competency SD (%) D (%) A (%) SA (%) M (SD) Most supervisors know the existence and properties of various teaching and learning tools 8(5.3) 74(49.3) 66(44.0) 2(1.3) 2.4(0.6) and aids for mathematical activity, and their range and limitations. Internal supervisors are able to supervise 2.4 teachers’ ability to prepare a standard teaching 4(2.7) 89(59.3) 56(37.3) 1(0.7) 2.4(0.6) and learning tools and aids for mathematical (1.2) activities for various level of learners. My supervisors are able to supervise teachers’ ability to reflectively use appropriate materials, 18(12.0) 86(57.3) 34(22.7) 12(8.0) 2.3(0.8) aids and tools in teaching. Key: SD = Strongly Disagree, D = Disagree, A = Agree, SA = Strongly Agree, (%) = Percentage, M = Mean, SD = Std. Deviation, SSM = Sub-scale Mean, SSSD = Sub-scale Std. Deviation
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The first three items on Table 4.3 provides information on the first sub-scale which is captioned ‘Mathematical Thinking Competency’. The first sub-scale recorded a total mean score of 2.6 (SD = 1.2). Table 4.3 indicates that a little above one-half of the mathematics teachers (n = 82, 54.6%, M = 2.6 and SD = 0.6) agreed (i.e. agreed and strongly agreed) that their supervisors are able to effectively supervise teachers posing questions that were characteristic of mathematics, and predict the kinds of answers that mathematics students may offer. Also, the table reveals that, majority of the teachers were of the view that most supervisors in their schools understood and were able to supervise the scope and limitations of a given concept (55.3% disagreeing/strongly disagreeing). The second item on the Mathematical Thinking
Competency of the supervisors attracted a mean score of 2.6 (SD = 0.7). Again, it is evident that a large number of the teachers (n = 100, 66.6%, M = 2.7 and SD = 0.6) believe that some external supervisors are able to extend the scope of a concept by abstracting some of its properties and generalizing results to larger classes of objects during pre-observation conference.
Under the second sub-scale ‘Problem Handling Competency’, two items were presented to the teacher respondents. The analysis according to Table 4.3 revealed that the sub-scale attracted a mean score value of 2.5 (SD = 1.0) making it the second least rated competency possessed by supervisors according to the mathematics teachers. The first item under this sub-scale sought to enquire whether supervisors were able to supervise teachers pose and specify different kinds of mathematical problems – pure or applied; open-ended or closed-ended and the analysis reveals that slightly above one-half of the teachers disagreed with the item meaning that most supervisors were able to supervise teachers pose and specify different kinds of mathematical problems – pure or applied; open-ended or closed-ended (n = 78, 52%
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disagreeing/strongly disagreeing). The item mean score was 2.4 (SD = 0.6). The last item on the ‘Problem Handling Competency’ sub-scale was ‘My supervisors are able to supervise teachers solving different kinds of mathematical problems, whether posed by others or by oneself, and, if appropriate, in different ways’ and 55.4% (n =
83) of the teachers disagreed (i.e. D and SD) with the statement. This item mean score was also 2.4 (SD = 0.8).
The third competency investigated in the district was the ‘Modelling
Competency’ of the mathematics supervisors. The mean score of this scale was 2.4
(SD = 1.5). The indication is that most teachers ranked the ‘Modelling Competency’ of the supervisors fifth in the range of the eight competencies. From the table it is evident that most teachers disagreed to all the items on this competency. For example,
‘External supervisors are able to supervise teachers when analyzing foundations and properties of existing models, including assessing their range and validity’ was the first item on the third subscale. The item attracted about 53.3% (n = 80) of the teachers either disagreeing or strongly disagreeing (M = 2.5, SD = 0.9). More so, the next item on the ‘Modelling Competency’ attracted about 53.4% (n = 80) disagreeing that during pre-observation conference, supervisors were able to decode existing models, i.e. translating and interpreting model elements in terms of the ‘reality’ modelled to teachers. Finally, the an over whelming majority of the mathematics teachers were of the view that most supervisors were unable to supervise teachers performing active modelling in a given context - structuring the field – mathematising
- working with (in) the model, including solving the problems it gives rise to among others (70.6% disagreeing/strongly disagreeing). As such the item mean score was 2.3
(SD = 0.6).
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The final competency on the first group of competencies was ‘Reasoning
Competency’ and this sub-scale recorded a total mean score of 2.7 (SD = 1.3). The mean score makes the ‘Reasoning Competency’ the better ranked among all the eight competencies investigated by the researcher. The implication may be that most of the teachers were of the view that most supervisors were competent in mathematics reasoning. The item mean value for each of the items were also quit high. For instance, the first item ‘Most external supervisors are able to supervise teachers when following and assessing chains of arguments, put forward by students during mathematics lessons’ recorded a mean score value of 2.6 (SD = 0.7). This shows that most of the teachers agreed (i.e. A or SD) with the item (62.6% agreeing/strongly agreeing). The second item also saw a large number of the respondents (n = 99,
66.0%, M = 2.6 and SD = 0.9) agreeing to the statement which sought to explore whether knowing what a mathematical proof is (not), and how it differs from other kinds of mathematical reasoning, e.g. heuristics, was a unique characteristic of supervisors in the district. As shown in Table 4.3, most mathematics teachers (n =
106, 70.7%, M = 2.8 and SD = 0.6) believe that most mathematics supervisors had the ability to uncover the basic ideas in a given line of argument (especially a proof), including distinguishing main lines from details and ideas from technicalities.
A close examination of Table 4.3 (CON’T) reveals that about 64.0% (n = 96) of the teachers indicated that supervising teachers’ understanding and utilizing
(decoding, interpreting, distinguishing between) of different sorts of representations of mathematical objects, phenomena and situations was a problem to their internal supervisors. Actually, 59.3% representing 89 teacher respondents indicated that they agreed with the item which suggested that supervising teachers when utilizing the relations between different representations of the same entity, including knowing
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about their relative strengths and limitations was not a problem to their supervisors.
And finally, majority of the teachers agreed that their supervisors were able to supervise teachers choosing and switching between representations when teaching mathematics (70.7% agreeing). The first three items discussed so far clustered around the first sub-scale under the second group of competencies investigated named
‘Representation Competency’. This competence attracted a mean score of 2.5 (SD =
1.2) making it the fourth most competency attribute most supervisors possessed in the district.
‘Symbols and Formalism Competency’ was the second major class of competency investigated under the second group of competencies. The scale mean score was 2.6 (SD = 1.4). The first item under the ‘Symbols and Formalism
Competency’ sub-scale was ‘Most pre or post conferences with supervisors are characterized with decoding and interpreting symbolic and formal mathematical language, and understanding its relations to natural language’ and this item saw majority of the teachers disagreeing (63.4%, n = 95). Again, a most of the teachers (n
= 94, 62.7%, M = 2.7 and SD = 0.6) revealed that understanding the nature and rules of formal mathematical systems (both syntax and semantics) was no problem to most of their supervisors in the district. And finally, about 55.4% (n = 83) of the teacher agreed that their supervisors were able to supervise teachers in handling and manipulating statements and expressions containing mathematics symbols and formulae. The item mean score was 2.6 with a standard deviation of 0.6.
The third competency explored was the Communication Competency of the supervisors. This attribute was rank fourth among the eight competencies by the teachers (M = 2.7, SD = 1.0) as a quality been possessed by the supervisors. An examination of the table reveals that slightly above one-half of the respondents (n =
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80, 53.4%, M = 2.6 and SD = 0.6) indicated that they agreed that understanding others’ writings, visual or oral ‘texts’, in a variety of linguistic registers, about matters having a mathematical content was not a challenge to most supervisors in their school.
Secondly, about 69.3% of the respondents representing 104 teachers agreed (i.e. A or
AD) that expressing oneself, at different levels of theoretical and technical precision, in oral, visual or written form, and about such matters was a unique characteristic of most supervisors in their school and district.
The final set of competence which was investigated was under the name ‘Aids and Tools Competency’. The three sets of items under the ‘Aids and Tools
Competency’ sought to explore supervisors’ competence in the area of teaching and learning materials. The sub-scale was ranked sixth (M = 2.4, SD = 1.2) among the list of supervisors’ competency attribute by the teachers. The analysis reveals that about
54.6% of the teachers asserted that most supervisors did not know the existence and properties of various teaching and learning tools and aids for mathematical activity, and their range and limitations (n = 82 disagreeing/strongly disagreeing). The analysis further reveals that majority of the mathematics teachers (n = 93, 62.0%, M = 2.4 and
SD = 0.6) stated that they disagreed (i.e. D or SD) with the assertion that internal supervisors were able to supervise teachers’ ability to prepare a standard teaching and learning tools and aids for mathematical activities for various level of learners. And finally, a significant number of the participants (n = 104, 69.3%, M = 2.3 and SD =
0.8) indicated that they disagreed with the statement that their supervisors were able to supervise teachers’ ability to reflectively use appropriate materials, aids and tools in teaching.
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Discussion
The issue of teaching and learning of mathematics in our basic schools and for that matter supervision of the subject have been a growing phenomenon and concern to major stakeholders in the field of mathematics education over the past few decades.
It is in this vein that the study sought to explore the competencies supervisors possess in ensuring the effective teaching and learning of mathematics in basic schools in
Ghana. The first research question therefore sought to investigate basic school teachers’ perceptions of the level of competence supervisors have in ensuring effective teaching and learning of mathematics in basic schools in the Kwahu East
District. The questionnaire which was designed structured the competencies of the supervisors into eight categories which included; mathematics thinking competency, problem handing competency, modelling competency, reasoning competency, representation competency, symbols and formalism competency, communication competency, and aids and tools competency. The study’s results indicated that the mathematics teachers rated their supervisors above average in two of the competency, average in two of the competency and below average in two of the competency. This shows that the supervisors in the district had a fair level of competency in supervising the teaching and learning of mathematics in basic schools in the Kwahu East District.
Reasoning and communication competencies received the highest mean score of 2.7.
This was closely followed by mathematics thinking and symbols and formalism with a mean score of 2.6. Problem handling and representation competency had a mean of
2.5. Finally, modelling and aid and tools competency had a mean score of 2.4 respectively. In order to establish a clearer picture of the predominant competency of the supervisors, the researcher believed it was vital to scrutinise the statements within each category as shown in the reporting of the major findings. Nevertheless, the
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findings support the previous literature and the contention that these perceptions are well-known position among many teachers of mathematics (Atkins, & Wood, 2002;
Niss & Jensen, 2002; Cobb, Gresalfi & Hodge, 2009; Gresalfi, Martin, Hand &
Greeno, 2009; Horn, 2008).
For teachers to achieve the laudable goals and objectives of basic school education as entrenched in the National Policy on Education (Ghana Education
Service, 2004), their positive perception about the competence of supervisor is greatly needed, because this will make them exploit maximally the usefulness, essence and benefits of having instructional supervisors which is to help them improve class instruction which will invariably improve their class performance and students’ class performance. In the current study the possible reason for teachers’ negative perception could be due to the type of interaction that already exists between them and their instructional supervisors and the influence this has had over time. This finding is in agreement with the findings of Horn (2008) that supervision enables the abilities and qualities of individual teachers to be identified which makes classroom visitation very important, also that through supervision individual potentials are developed. The findings on the competency can be compared to the findings of previous research by
Austin, Shah and Muncer, who also used the set of competency measure as used in the present study (Austin, Shah & Muncer, 2005). They found that the most supervisors were, in the view of tutors and other peers, competent in the area of mathematical thinking competency, aid and tool competency and communication competency. Austin, Shah and Muncer, again found that superverses were not competent in the area of symbols and formalism modelling competency. Although, in the present study it was only mathematical thinking competency, and communication competency that teachers claimed their supervisors were competent in, they indicated
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that their supervisors were not modelling and tools and aids competencies. The current findings also support that of a previous research which has identified high competency of supervisors on mathematical thinking competency. (Heinsman, 2008;
Viswesvaran, Schmidt, & Ones, 2005).
Research Question 2: How do supervisors perceive their competencies in ensuring effective teaching and learning of mathematics in basic schools in the Kwahu East
District?
Research question two sought to explore supervisors’ perceptions of their own competencies in ensuring effective mathematics teaching and learning in basic schools in the Kwahu East District. Similar to research question one, question two measured the perceptions of supervisors through the lens of Niss and Jensen’s (2003) conceptual framework named the “KOM flower”. Niss (2003) asserted that there are eight competencies which can be said to form two groups. The first set of competencies has to do with the ability to ask and answer questions in and with mathematics (i.e. Mathematical Thinking Competency, Problem Handling
Competency, Modelling Competency, and Reasoning Competency) and the other set of competencies has to do with the ability to deal with and manage mathematical language and tools (i.e. Representation Competency, Symbols and Formalism
Competency, Communication Competency, and Aids and Tools Competency). The quantitative data which was generated from the questionnaire was analyzed using descriptive statistics (mean and standard deviation scores). According to the Table 4.4
(see overleaf), the mean scores obtained for each statement reveals that majority of the supervisors believe that they are very competent in ensuring effective mathematics teaching and learning in basic schools in the Kwahu East District. The results of the quantitative analysis is presented in Tables 4.4 and Tables 4.4 (CON’T) based on the
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two competency division as presented by Niss (2003). A summary of the competencies is presented in Table 4.5.
Table 4. 4: Descriptive Statistics of Mathematics Supervisors’ Perceptions of their Competency Level (first group) in ensuring teaching and learning of mathematics Statement SD (%) D (%) A (%) SA (%) M(SD) Mathematical Thinking Competency I am able to supervise teachers posing questions that are characteristic of mathematics, and predict 0(0) 10(28.6) 16(45.7) 9(25.7) 3.0(0.8) the kinds of answers that mathematics students may offer. Most teachers in my school would say I understand and am able to supervise the scope and limitations 0(0) 10(28.6) 22(62.9) 3(8.6) 2.8(0.6) of a given concept. I am able to extend the scope of a concept by abstracting some of its properties and generalizing 0(0) 9(25.7) 23(65.7) 3(8.6) 2.8(0.6) results to larger classes of objects during pre- observation conference with teachers. Problem Handling Competency SD (%) D (%) A (%) SA (%) M (SD) My teachers will agree that am able to supervise teachers posing and specifying different kinds of 0(0) 8(22.9) 20(57.1) 7(20.0) 3.0(0.6) mathematical problems – pure or applied; open- ended or closed-ended. I am able to supervise teachers solving different kinds of mathematical problems, whether posed by 0(0) 8(22.9) 16(45.7) 11(31.4) 3.1(0.7) others or by oneself, and, if appropriate, in different ways. Modelling Competency SD (%) D (%) A (%) SA (%) M (SD) I am able to supervise teachers when analyzing foundations and properties of existing models, 1(2.9) 15(42.9) 13(37.1) 6(17.1) 2.7(0.8) including assessing their range and validity. During pre-observation conference, I am able to decode existing models, i.e. translating and 0(0) 10(28.6) 8(22.9) 17(48.6) 3.2(0.9) interpreting model elements in terms of the ‘reality’ modelled to teachers. My teacher believe that I am able to supervise them performing active modelling in a given context - 0(0) 12(34.3) 17(48.6) 6(17.1) 2.8(0.7) structuring the field – mathematising - working with(in) the model, including solving the problems it gives rise to etc. Reasoning Competency SD (%) D (%) A (%) SA (%) M (SD) I am able to follow and assess teachers when chains of arguments, are put forward by students during 0(0) 7(20) 24(68.6) 4(11.4) 2.9(0.6) mathematics lessons. Knowing what a mathematical proof is (not), and how it differs from other kinds of mathematical 0(0) 8(22.9) 21(60.0) 6(17.1) 2.9(0.6) reasoning, e.g. heuristics, is one unique characteristics I possess. I have the ability to uncover the basic ideas in a given line of argument (especially a proof), 0(0) 9(25.7) 23(65.7) 3(8.6) 2.8(0.6) including distinguishing main lines from details and ideas from technicalities. Key: SD = Strongly Disagree, D = Disagree, A = Agree, SA = Strongly Agree, (%) = Percentage, M = Mean, SD = Std. Deviation, SSM = Sub-scale Mean, SSSD = Sub-scale Std. Deviation
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Table 4.4 (CON’T): Descriptive Statistics of Mathematics Supervisors’ Perceptions of their Competency Level (second group) in ensuring teaching and learning of mathematics Representation Competency SD (%) D (%) A (%) SA (%) M (SD) Supervising teachers’ understanding and utilizing (decoding, interpreting, distinguishing between) of different sorts of representations of 0(0) 11(31.4) 18(51.4) 6(17.1) 2.9(0.7) mathematical objects, phenomena and situations is not a problem to me at all Supervising teachers when utilizing the relations between different representations of the same entity, including knowing about their 0(0) 6(17.1) 28(80.0) 1(2.9) 2.9(0.4) relative strengths and limitations is not my problem I am able to supervise teachers choosing and 0(0) 8(22.9) 25(71.4) 2(5.7) 2.8(0.5) switching between representations when teaching mathematics. Symbols and Formalism Competency SD (%) D (%) A (%) SA (%) M (SD) Most pre or post conferences with my teachers are characterized with decoding and interpreting symbols and formal mathematical 0(0) 9(25.7) 18(51.4) 8(22.9) 3.0(0.7) language, and understanding its relations to natural language. I am able to understanding the nature and rules of formal mathematical systems (both syntax 0(0) 8(22.9) 24(68.6) 3(8.6) 2.9(0.6) and semantics) I am able to supervise teachers in handling and 0(0) 9(25.7) 21(60.0) 5(14.3) 2.9(0.6) manipulating statements and expressions containing symbols and formulae. Communication Competency SD (%) D (%) A (%) SA (%) M (SD) Understanding others’ writings, visual or oral ‘texts’, in a variety of linguistic registers, about 0(0) 7(20.0) 15(42.9) 13(37.1) 3.2(0.8) matters having a mathematical content is not a challenge me Expressing myself, at different levels of theoretical and technical precision, in oral, 0(0) 3(8.6) 17(48.6) 15(42.9) 3.3(0.6) visual or written form, about such matters is a unique characteristic I possess Aids and Tools Competency SD (%) D (%) A (%) SA (%) M (SD) I know the existence and properties of various teaching and learning tools and aids for 0(0) 3(8.6) 25(71.4) 7(20.0) 3.1(0.5) mathematical activity, and their range and limitations. I am able to supervise teachers’ ability to prepare a standard teaching and learning tools 0(0) 8(22.9) 22(62.9) 5(14.3) 3.0(0.6) and aids for mathematical activities for various level of learners. I am able to supervise teachers’ ability to 0(0) 1(2.9) 19(54.3) 15(42.9) 3.4(0.6) reflectively use appropriate materials, aids and tools in teaching. Key: SD = Strongly Disagree, D = Disagree, A = Agree, SA = Strongly Agree, (%) = Percentage, M = Mean, and SD = Std. Deviation
Table 4.4 reports the findings regarding supervisors’ perceptions of their competencies in ensuring effective mathematics teaching and learning in basic
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schools in the Kwahu East District. It is evident from the table that majority of the participants (71.4%, n = 25, M = 3.0, SD = 0.8) agreed or strongly agreed that they were capable of supervising teachers posing questions that were characteristic of mathematics, and predict the kinds of answers that mathematics students may offer.
Again, it can be seen from the results presented on the table that 25 of the respondents representing 71.5% agreed or strongly agreed that most teachers in their schools would attest that they, the supervisors, understood and were able to supervise the scope and limitations of a given concept in the mathematics classroom. For item 3,
74.3% (n = 26, M 2.8, SD = 0.6) of the 35 supervisors who participated in the study agreed or strongly agreed that they were able to extend the scope of a concept by abstracting some of its properties and generalizing results to larger classes of objects during pre-observation conference with mathematics teachers.
Cumulatively, 77.1% (n = 27, M 3.0, SD = 0.6) of the participants agreed or strongly agreed that teachers would agree that they were able to supervise teachers posing and specifying different kinds of mathematical problems – pure or applied; open-ended or closed-ended. Furthermore, it is also evident from Table 4.4 that most supervisors were of the view that they were able to supervise teachers solve different kinds of mathematical problems, whether posed by others or by oneself, and, if appropriate, in different ways (n = 27 disagreeing/strongly disagreeing). A large number of the respondents (n = 19, 54.2%, M 2.7, SD = 0.8) agreed or strongly agreed that they were able to supervise teachers when analyzing foundations and properties of existing models, including assessing their range and validity. In the same regard, a significantly large number of the mathematics supervisors conjectured that during pre- observation conference, they were able to decode existing models, i.e. translating and interpreting model elements in terms of the ‘reality’ modelled to teachers (n = 25,
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71.5%, M = 3.2, SD = 0.9). It is further revealed in the table that majority of the supervisors who took part in the study indicated that most their teachers believe that they were capable of supervising them performing active modelling in a given context
- structuring the field – mathematising - working with(in) the model, including solving the problems it gives rise to etc.
Additionally, 80.0% (n = 28) of the participants agreed or strongly agreed that they were competent in following and assessing teachers when chains of arguments, are put forward by students during mathematics lessons (M = 2.9 and SD = 0.6).
“Knowing what a mathematical proof is (not), and how it differs from other kinds of mathematical reasoning, e.g. heuristics, is one unique characteristics I possess” attracted about 77.1% of the respondents representing 27 agreeing or strongly agreeing. Finally, the last but not the least item on Table 4.4 reveals that majority (n =
26, 74.3%, M = 2.8, SD = 0.6) of the supervisors agreed or strongly agreed to the statement that they had the ability to uncover the basic ideas in a given line of argument (especially a proof), including distinguishing main lines from details and ideas from technicalities.
The second set of competencies that was explored on the supervisors has to do with their ability to deal with and manage mathematical language and tools (i.e.
Representation Competency, Symbols and Formalism Competency, Communication
Competency, and Aids and Tools Competency). With regards to the second research question, results collected on the second group of competence ‘the ability to deal with and manage mathematical language and tools’ are displaced in Table 4.4 (CONT).
The information shows that majority of the supervisors perceived themselves as competent.
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As it is displayed in Table 4.4 (CONT), majority of the supervisors (68.5%, M
= 2.9, SD = 0.7) were of the view that supervising teachers’ understanding and utilizing (decoding, interpreting, distinguishing between) of different sorts of representations of mathematical objects, phenomena and situations were not a problem to them at all. It is again evident from the table that the participants were of the view that supervising teachers when utilizing the relations between different representations of the same entity, including knowing about their relative strengths and limitations was not a problem to them (82.9% agreeing/strongly agreeing). The table revealed that most respondents’ opinions did not differed on the third (3rd) item
“I am able to supervise teachers choosing and switching between representations when teaching mathematics” (77.1%, n = 27 agreeing/strongly agreeing).
Again, considering the second research question, Table 4.4 (CONT) reveals information that 74.3% (M = 3.0, SD = 0.7) of the 35 supervisors who took part in the study were of the view that most pre or post conferences with their teachers were characterized with decoding and interpreting symbols and formal mathematical language, and understanding its relations to natural language. In addition, a little above two-thirds (77.2%, n = 27, M = 2.9, SD = 0.6) of the participants agreed or strongly agreed that they were able to understand the nature and rules of formal mathematical systems (both syntax and semantics). Out of the 35 supervisors who participated in the study, 74.3% representing 26 respondents agreed or strongly agreed that they were able to supervise teachers in handling and manipulating statements and expressions containing symbols and formulae. Notably, a significantly high number of the participants (80.0%, n = 28, M = 3.2, SD = 0.8) indicated that understanding others’ writings, visual or oral ‘texts’, in a variety of linguistic registers, about matters having a mathematical content is not a challenge them. In the
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same vein, majority were of the view that expressing themselves, at different levels of theoretical and technical precision, in oral, visual or written form, about such matters is a unique characteristic they possessed (91.5%, n = 32, agreeing/strongly agreeing).
The next item on the table “I know the existence and properties of various teaching and learning tools and aids for mathematical activity, and their range and limitations” attracted more of the supervisors (91.4%, n = 32, M = 3.1, SD = 0.5) agreeing or strongly agreeing to the statement.
In the same regard, about 77.2% of the supervisors agreed (A or SD) that they were able to supervise teachers’ ability to prepare a standard teaching and learning tools and aids for mathematical activities for various level of learners. And finally, all but one (1) of the supervisors agreed or strongly agreed that they were able to able to supervise teachers’ ability to reflectively use appropriate materials, aids and tools in teaching basic school learners. A summary of various sub-scales under the supervisors’ competence and their mean ranking is presented in Table 4.5. The purpose of the table summary (Table 4.5) was to document how the supervisors ranked their supervision competence in order of proficiencies.
Table 4. 5: Descriptive Statistics and Rank of Mathematics Supervisors’ Competent of ensuring teaching and learning of Mathematics. Sub-scale Sample (n) Mean (M) SD Rank Mathematical Thinking Competency 35 2.87 1.2 6 Problem Handling Competency 35 3.05 0.9 3 Modelling Competency 35 2.90 1.3 5 Reasoning Competency 35 2.87 1.1 6 Representation Competency 35 2.87 0.9 6 Symbols and Formalism 35 2.93 0.9 4 Competency Communication Competency 35 3.25 1.0 1 Aids and Tools Competency 35 3.17 1.1 2 Source: Field Data – Questionnaire
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The research results in Table 4.5 reveals that “Aids and Tools Competency” sub-scale attracted the highest mean rating (M = 9.43, SD = 1.1) from the respondents.
This indicates that most of the mathematics supervisors were of the view that they are competent in supervising teachers in the preparation and use of mathematics aids and tool in the classroom. The second most rated sub-scale among the competencies was
“Modelling Competency”. This sub-scale attracted a mean (M) score of 8.71 and a standard deviation (SD) of 1.3. The table further reveals that “Symbols and Formalism
Competency” was the third most rated proficiency the supervisors claimed they possessed. A mean (M) of 8.70 and standard deviation (SD) of 0.9 was recorded for the Symbols and Formalism Competency theme.
Again, information from Table 4.5 shows that the fourth most ranked supervision competence the supervisors asserted they were proficient in was the
“Reasoning Competency” (M = 8.69, SD = 1.1). Moreover, “Mathematical Thinking
Competency” was adjudged the fifth highest proficiency the supervisors asserted they possessed. The mean and standard deviation of the sub-scale were 8.60 and 1.2 respectively. Additionally, the mathematics supervisors, according to the table, were of the view that their expertise in “Representation Competency” sub-scale was sixth in a chronological order (M = 8.54, SD = 0.9). The mathematics “Communication
Competency” of the respondent was ranked seventh and had a mean and standard deviation of 6.51 and 1.0 respectively. And finally, most of the participants
(supervisors) revealed that their major challenge was “Problem Handling
Competency”. Thus, this sub-scale was ranked last by majority of the respondents (M
= 6.06, SD = 0.9).
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Discussion
Supervisors make use of different competencies in their work and this is supported by the literature (Truxaw & DeFranco, 2008; Lampert & Cobb,
2003; Niss & Jensen, 2002). This study structured the competencies of the supervisors into eight categories which included; mathematics thinking competency, problem handing competency, modelling competency, reasoning competency, representation competency, symbols and formalism competency, communication competency, and aids and tools competency. The results on the supervisors’ competencies as presented in the aforementioned tables and subsequent reporting indicates that the supervisors were of the view that they were highly competent in supervising and ensuring the effective teaching and learning of mathematics in basic schools in the study area. On all of the competencies investigated, the supervisors indicated that they had the capacity in ensuring its realization in the process of mathematics supervision. This is in support of Wedege, (2000) view when he opines that supervisor perceive themselves as capable of carrying out their professionally assigned duties in most educational institutions. In the same vain, Niss, (2003) found that most mathematics teachers and supervisors believe that mathematics competence was a trait they possess and that the competencies were needed in their quest to help learners acquire the necessary mathematical skills and ability.
Research Question 3: What styles of school supervision do Junior High School teachers in the Kwahu East District experience?
The purpose of this research question was to explore the various supervision styles that mathematics teachers in the Kwahu East District experience as part of their engagement with supervisors. In relation to the third research question, Table 4.6 presents information about mathematics teachers’ perceptions of the supervision
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styles their educational supervisors employ in their various schools in the Kwahu East
District. The supervision styles include the Autocratic Supervision styles, Democratic
Supervision styles and Laissez-Faire Supervision styles. Questionnaire items 1, 4, 7,
10, 13 and 16 were measuring Autocratic Supervision styles, items 2, 5, 8, 11, 14, and
17 were also measuring Democratic Supervision styles and finally, questionnaire items 3, 6, 9, 12, 15, and 18 were measuring Laissez-Faire Supervision styles.
According to the table, the mean scores obtained for each item/statement and sub- scale revealed that majority of the teachers believe that their supervisors employ democratic supervision style (sub-scale Mean = 3.8, sub-scale Standard Deviation =
0.5), this was followed by autocratic supervision style (sub-scale Mean = 3.9, sub- scale Standard Deviation = 0.3). Finally, according to the teacher respondents the least supervision style which was practiced by various supervisors was the laissez- faire supervision styles (sub-scale Mean = 2.8, sub-scale Standard Deviation = 0.7)
Table 4.6 is presented as follows:
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Table 4. 6: Descriptive Statistics of Teachers’ Perceptions of the Various Supervision Styles of Supervisors in Kwahu East District. D U A M SSM No Statement (%) (%) (%) (SD) (SSSD) My supervisor believes that supervisees need to be 14 16 120 3.7 1 supervised closely, or they are not likely to do their work. (9.3) (10.7) (80.0) (0.6) Most supervisors in my school believes that it is fair to say 90 26 34 2.6 4 that most supervisees in the general population are lazy (60.0) (17.3) (22.7) (0.8) Some supervisors are of the view that as a rule, supervisees 11 6 132 3.8 7 must be given rewards or punishments in order to motivate them to achieve organizational objectives (7.4) (4.0) (88.6) (0.6) 3.5 Most supervisors in my school believes that most 19 30 101 3.6 (0.5) 10 supervisees feel insecure about their work and need direction (12.7) (20.0) (67.3) (0.7) Most supervisors in my school believe that the supervisor is 22 18 110 3.6 13 the chief judge of the achievement of members of the group. (14.7) (12.0) (73.3) (0.7) My supervisor believes that effective supervisors give orders 6 9 135 3.9 16 and clarify procedures to their supervisees (4.0) (6.0) (90.0) (0.5) Most supervisors in my school believes that supervisees 4 3 143 3.9 2 want to be part of decision making process (2.7) (2.0) (95.3) (0.4) Some supervisors are of the view that providing guidance 23 14 113 3.6 5 without pressure is the key to being a good supervisor (15.3) (9.3) (75.3) (0.7) 3.7 My supervisor believes that most supervisees want frequent 1 9 140 3.9 (0.3) 8 and supportive information from their supervisors (0.7) (6.0) (93.3) (0.3) My supervisor believes that supervisors need to help 2 7 141 3.9 11 supervisees accept responsibility for completing their task (1.3) (4.7) (94.0) (0.3) It is the believe of my supervisor that it is the supervisor’s 26 24 100 3.5 14 job to help supervisees find their "passion" (17.3) (16.0) (66.7) (0.7) Some supervisors are of the view that supervisees are 31 25 94 3.4 17 basically competent and if given a task will do a good job (20.7) (16.7) (62.7) (0.8) My supervisor believes that in complex situations, 84 19 47 2.8 3 supervisors should let supervisees work problems out on their own (65.0) (12.7) (31.3) (0.9)
My supervisor believes that supervision requires staying out 95 18 37 2.6 6 of the way of supervisees as they do their work (63.3) (12.0) (24.7) (0.9) Some supervisors in my school believes that as a rule, 63 26 61 3.0 9 supervisors should allow supervisees to appraise their own work (42.0) (17.3) (40.7) (0.9) 2.9 Some authorities in my school are of the view that (0.7) 73 23 54 2.9 12 supervisors should give supervisees complete freedom to solve problems on their own (48.7) (15.3) (36.0) (0.9)
Most supervisors in my school believes that in most 38 20 92 3.4 15 situations, supervisees prefer little inputs from their supervisors (25.3) (13.3) (61.3) (0.9)
Most supervisors in my school believes that in general, it is 116 14 20 2.4 18 best to leave supervisees alone (77.3) (9.3) (13.3) (0.7) Key: D = Disagree, U = Undecided, A = Agree, (%) = Percentage, M = Mean, SD = Std. Deviation, SSM = Sub-scale Mean, SSSD = Sub-scale Std. Deviation
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The first sub-scale, Autocratic Supervision styles, attracted a sub-scale mean score of
3.5 (SD = 0.5). This mean score and standard deviation values placed this supervision style second on the spectrum of the supervision styles in the district. The position as expressed by the sub-scale mean is subsequently reflected in the various items making up the scale. For example, result from Table 4.6 reveals that more than three-fourth of the respondents (80.0%) agreed that their supervisors believe that supervisees need to be supervised closely or they are not likely to do their work. Again, 60% of the respondents representing 90 asserted that most supervisors in their schools believe that it is fair to say that most supervisees in the general population are lazy.
In addition, more than three-fourths of the participants (n = 132, 88.6%) claimed that some supervisors are of the view that as a rule, supervisees must be given rewards or punishments in order to motivate them to achieve organizational objectives. Moreover, a little more than one-half of the teachers (n = 101, 67.3%) opined that most supervisors in their schools believe that most supervisees feel insecure about their work and need direction. Although there were a few mathematics teachers (n = 22, 14.7%) who revealed that most supervisors in their schools did not believes that the supervisors are the chief judge of the achievement of members of a group, majority (n = 110, 73.3%) believed that their supervisor saw themselves as the supervisors are the chief judge of the achievement of members of the group. Finally, almost all the participants (n = 135, 90%) indicated that their supervisors believed that effective supervisors give orders and clarify procedures to their supervisees.
The second sub-scale, Democratic Supervision styles, was rated first and best among the three main supervision styles that the participants were allowed to respond to. This supervision style attracted a mean score of 3.7 with a standard deviation of
0.3. This high mean score indicates that most of the mathematics teachers indicated
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that majority of their supervisors do practices the democratic supervision style in their supervision. As such the outcomes are visibly indicated in the various items that compose the sub-scale. Results from Table 4.6 indicates that the overwhelming majority of the mathematics teachers (n = 143, 95.3%) indicated that most supervisors in their schools believes that supervisees want to be part of decision making process.
Likewise, majority of them felt that some supervisors are of the view that providing guidance without pressure is the key to being a good supervisor (75.4% agreed/strongly agreed). Again, it was indicated in item 8 (under Democratic
Supervision styles) that 140 (93.3%) of the mathematics teachers agreed that their supervisor believes that most supervisees want frequent and supportive information from their them while 1 representing 0.7% disagreed with the item and 9 representing
6.0% were undecided on the item.
In the same manner, item 11 attracted most of the mathematics teachers to agree (n = 141, 94.0%) that their supervisor believes that supervisors need to help supervisees accept responsibility for completing their task. However, 2 of the respondents representing 1.3% disagreed with statement and 7 representing 4.7% were undecided. Item 14, ‘It is that believe of my supervisor that it is the supervisor’s job to help supervisees find their "passion"’ recorded 100 (66.7%) mathematics teachers agreeing, 26 (17.3%) disagreeing and 24 (16.0%) unsure of the stand.
Finally, the sub-scale’s last but not the least item (item 17) chronicled as much as 94 mathematics teachers representing 62.7% agreeing that some supervisors are of the view that supervisees are basically competent and if given a task will do a good job,
31 (20.7%) disagreed and 25 (16.7%) were unsure of their stand.
The least practiced supervision style by school supervisors, according to the mathematics teachers who participated in the study, was the Laissez-Faire
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Supervision styles. The sub-scale recorded a mean score value of 2.9 with a standard deviation of 0.7. The respondents were mostly torn between agreeing and disagreeing on the items under this sub-scale. For example, as many as 65.0% of the respondents disagreed that their supervisors believe that in complex situations, supervisors should let supervisees work problems out on their own. In like manner, 63.3% representing
95 participants opined that their supervisor believe that supervision requires staying out of the way of supervisees as they do their work. Interestingly, the participants were spilt on the next statement (item 9) which states that ‘Some supervisors in my school believes that as a rule, supervisors should allow supervisees to appraise their own work’. The item attracted 63 respondents representing 42.0% disagreeing while
40.7% representing 61 participants agreed and 17.3% of them were undecided about the item.
The next sentence (item 12) ‘Some authorities in my school are of the view that supervisors should give supervisees complete freedom to solve problems on their own’ attracted more mathematics teachers disagreeing (n = 73, 48.7%), 23 representing 15.3% were undecided while as 54 representing 36.0% agreed with the statement. While most of the participants (66.7%, n = 100) indicated that, it is the belief of their supervisors that it is the supervisor’s job to help supervisees find their
"passion", minority (17.3%, n = 26) disagreed with that assertion while 16.0% representing 24 were undecided about the statement. Information provided by most of the respondents (61.3%, n = 92) in the study further revealed that most supervisors in basic schools believes that in most situations, supervisees prefer little inputs from their supervisors. Finally, it can be observed from Table 4.6 that item 18 ‘Most supervisors in my school believes that in general, it is best to leave supervisees alone’
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attracted an overwhelming majority (77.3%) disagreeing with the statement while
13.3% of the participant agreed with the statement.
Discussion
All these styles of supervision and how they are being experienced by supervisees and some of the above-mentioned examples associated with them have already been identified and raised in studies conducted to investigate types and styles of supervision which basic school supervisors practice and are experienced by their mathematics teachers. Specifically, other studies have already found that the main and basic styles of supervision in our basic/elementary school are the autocratic, democratic and laissez-faire styles of supervision (Chand, 2015; Adu, Akinloye &
Olaoye, 2014). This study’s findings was in contrast with Okoro (1999) and
Ogbonnaya (1997) hold the belief that most supervisory staff are not exposed to democratic culture and thus adopt the old form of inspection. The claim that some supervisors do not run open-door policy by way of involving their clients in decision making especially when such decision affect them. They also maintained that some supervisors and their clients are resistant to innovations and prefer to preserve the status quo. They maintained that old and experienced teachers tend to resist change and innovation. This thus make supervision very difficult, they tend to stick to the biblical injunction “as it was in the beginning, is now and ever shall it be”. However, this study’s findings supports Mankoe, (2007) proposal which states that, one other way of improving instructional supervision is that of embracing democratic culture of supervisors in their leadership style. The supervisors should include their subordinates in decision making especially when such decisions affect them. The morale of teacher grows if he has a part to play in decision making process. Involving subordinates in the supervisory practices boost their morale and make them feel they belong to the
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system and worthy of contributing to the development and growth of the educational system in the area.
Research Question 4: What inherent challenges do supervisors in the Kwahu East
District face in ensuring effective mathematics education delivery in basic schools?
According to Glatthorn, (1990) supervision is the service provided to help teachers in order to facilitate their own professional development so that the goals of the school might be better attained. However, there are several factors which tend to militate against effective supervision of mathematics instruction in basic schools.
Therefore, the purpose of the fourth research question was to explore challenges basic school mathematics supervisors face in ensuring effective mathematics education delivery in basic schools in the Kwahu East District. The question was explored through the perspective of supervisors in the Kwahu East District. To enhance computation, the options were weighted on the 3-point Likert rating scale thus:
Disagree (D) – 1 points; Undecided (U) – 2; and Agree (A) – 3 points. The midpoint for the scale is 2.0. Therefore, only means scores of 2.0 and above were accepted as indications of great extent of problem, while mean scores below 2.0 were regarded as indications of low extent of problems. Some of challenges as identified in literature are presented in Table 4.7.
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Table 4. 7: Descriptive Statistics of Challenges Facing Supervisors in Kwahu East District. Statement D (%) U (%) A (%) M (SD) Majority of supervisors do not have relevant trainings in mathematics 10 (28.6%) 5 (14.3) 20 (57.1) 2.3 (1.0) education There are inadequate number of supervisors to assist the basic school 5 (14.3) 0 (0) 30 (85.7) 2.7 (0.5) mathematics teachers teach properly There are inadequate number of relevant supervision manuals in the 11 (42.9) 2 (5.7) 22 (51.4) 2.3 (1.1) district office and basic schools There is insufficient allocated budget for the supervisory program in the 0 (0) 2 (5.7) 33 (94.3) 2.9 (0.4) district. There is lack of follow up on the activities of supervisors by the 5 (14.3) 7 (20) 23 (65.7) 2.5 (1.0) superiors. Most mathematics supervisors’ use of supervision for administrative purposes 7(20) 0 (0) 28 (80) 2.6 (0.9) only. Most mathematics teachers’ lack of knowledge about the concept of 9 (25.7) 4 (11.4) 22 (51.4) 2.3 (1.0) supervision is a big challenge to the supervision process Basic school mathematics teachers perceive supervisors as a fault finder 0 (0) 0 (0) 35 (100) 3.0 (0.1) rather than assisting them. Lack of training for supervisors and lack of support for supervisors from 8 (22.9) 5 (14.3) 22 (62.9) 2.4 (1.0) higher offices affect the supervisory practice in the district Routine administrative burden makes it hard for supervisors to find time to 2 (5.7) 3 (8.6) 30 (85.7) 2.8 (0.4) visit classrooms and observe how mathematics teachers are teaching Key: D = Disagree, U = Undecided, A = Agree, (%) = Percentage, M = Mean, and SD = Std.
Deviation
An inspection of the table reveals that majority of the suggested indicators, if not all, were of a great challenge to the supervisors in the Kwahu East District. In fact, a simple majority of the respondents believe that most of supervisors did not have relevant trainings in mathematics education to enable them supervise the teaching and learning effectively (n = 20, 57.1%, M = 2.3, SD = 1.0). Again, a large majority of the
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respondents indicated that they agreed that, there were inadequate number of supervisors to assist the basic school mathematics teachers teach properly (n = 30,
85.7% agreeing). The supervisors were also asked about adequacy of relevant supervision manuals in the districts and about a half of them (n = 22, 51.4%, M = 2.3,
SD = 1.1) asserted that, the materials were inadequate.
Furthermore, a large number of the supervisors revealed that there was insufficient allocated budget for the supervisory program in the district (n = 33,
94.3%, M = 2.9, SD = 0.4). Similarly, 65.7% (n = 23) of the participants indicated that there was lack of follow up on the supervision activities of supervisors by the superiors. Most mathematics supervisors used of supervision for administrative purposes only was also another indicator which received high agreement level by the supervisors (n = 28, 80.0%, M = 2.6, SD = 0.9). Additionally, about one-half of the respondents asserted that most mathematics teachers’ lack of knowledge about the concept of supervision was a big challenge to the supervision process (n = 22, 51.4%,
M = 2.3, SD = 1.0). The next item which was considered was, ‘basic school mathematics teachers perceive supervisors as a fault finder rather than assisting them’ also received an overwhelming endorsement from the respondent (n = 35, 100%, M =
3.0, SD = 0.1).
The table further indicated that, majority of the respondents believed that lack of training for supervisors and lack of support for supervisors from higher offices affected the supervisory practice significantly in the district (62.9%, n = 22). Finally, the participants indicated that routine administrative burden made it hard for supervisors to find time to visit classrooms and observe how mathematics teachers were teaching effectively (n = 30, 85.7%, M = 2.8, SD = 0.4).
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Discussion
The findings of this study with respect to research question 4, implies that supervisors were really facing a lot of challenges in the course of undertaking their professional duties. Most of these challenges have been discussed in literature. Some of the identified challenges which are noted in supervision literature and have been corroborated in this study are discussed as follows:
Though supervision is one of the oldest form of educational leadership, its position is still one of the most controversial to the extent of it being used interchangeably with inspection especially in Ghana. The implication is that most people still apply the principles of inspection as perceived during the colonial and early part of the postcolonial Ghana. This has not improved instructional services nor has it led to professional growth of teachers, because it does not encourage collegiality or colleagueship.
Another problem of supervision of instruction in schools is the inadequacy of supervisory personnel. Mankoe, (2007) said there is insufficient number of supervisors in most educational district in Ghana. He maintained that insufficient number of supervisory personnel has militated against effective supervision of instruction in schools as the few available ones are unable to reach out to all the schools as expected within the supervisory period. Thus in some cases, some schools are not visited by instructional supervisors for period of one term or a whole session.
This sometimes sterns from the fact that few supervisors are assigned to many schools and when it becomes humanly impossible to reach out to all the schools, they only visit few schools around. When this happens, the idea of giving professional assistance and stimulating development in teachers is not achieved.
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Another problem is lack of proper training of our supervisors. As identified by
Atta, Agyenim-Boateng, and Baafi-Frimpong, (2000) and Antwi, (1992) both shared the opinion that administrators of education in Ghana do not consider proper training of supervisory staff to carry out supervisory services. Atta, Agyenim-Boateng, and
Baafi-Frimpong, maintained that the criteria for appointing supervisors are basically the possession of a first degree in education and some years of teaching experiences.
They further said that some supervisors are also appointed simply because “they know some officers at the headquarters” this leads to the placement of “wrong pegs in right holes”. The implication is that those who are not exposed to the supervisory techniques and approaches are made to handle the job and thus haphazard result will be achieved.
Another problem militating against effective supervision of instruction in our schools is lack of motivation of the teachers and supervisory staff. It has been observed that poor or lack of motivation has been responsible for the skeletal or poor supervisor services available in our schools. The few available supervisory staff is not adequately motivated as some of them are owed salary arrears for several months.
Some of them fail to penetrate into the interior schools as they claim they are not mobile while there is no provision for their transport allowance to these schools.
Sharing this view, William in Okoro (1999) maintains that teachers and principals are allowed to toil year in year out without corresponding remuneration and incentives.
Ogbonnaya (1997) maintained that supervisors are not sufficiently motivated in the execution of their functions.
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Hypothesis Testing
푯01 = There is no statistical significant difference between mathematics teachers’ and supervisors’ perceptions of mathematics supervision competence of supervisors in the
Kwahu East District?
The aim of the second hypothesis was to compare the mean scores of basic school mathematics teachers and their supervisors on supervisors’ competencies in supervising mathematics teaching and learning in the Kwahu East District of Ghana.
To help address the research hypothesis, descriptive statistics (mean and standard deviation scores) and an independent samples t-test were used to analysis the differences that existed between basic school mathematics teachers and their supervisors’ perceptions of supervisors’ competencies in supervising mathematics teaching and learning in the Kwahu East District. The use of t-tests enabled the researcher to compare the two samples (mathematics teachers and supervisors) so inferences could be made about the population from which the sample was drawn from. Table 4.10 documents information on various sub-scales of supervisors’ competence (Mathematical Thinking Competency, Problem Handling Competency,
Modelling Competency, Reasoning Competency, Representation Competency,
Symbols and Formalism Competency, Communication Competency, and Aids and
Tools Competency), the various participants, the mean, standard deviation, and sampled size to each response sub-scale.
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Table 4. 8: Descriptive statistics of respondents’ perceptions on supervisors’ competency Sub–scale Participant Sample (n) Mean (M) SD Teacher 150 7.89 1.3 Mathematical Thinking Competency Supervisor 35 8.60 1.2 Teacher 150 4.97 1.0 Problem Handling Competency Supervisor 35 6.06 0.9 Teacher 150 7.27 1.5 Modelling Competency Supervisor 35 8.71 1.3 Teacher 150 7.95 1.3 Reasoning Competency Supervisor 35 8.69 1.1 Teacher 150 7.51 1.2 Representation Competency Supervisor 35 8.54 0.9 Symbols and Formalism Teacher 150 7.61 1.4 Competency Supervisor 35 8.71 0.9 Teacher 150 5.39 0.9 Communication Competency Supervisor 35 6.51 1.0 Teacher 150 7.04 1.2 Aids and Tools Competency Supervisor 35 9.43 1.1 Source: Field Data - Questionnaire
It is evident from Table 4.10 that, Mathematical Thinking Competency sub- scale attracted a mean and standard deviation scores of M = 7.89 (SD = 1.3) and M =
8.60 (SD = 1.2) from the mathematics teachers and supervisors respectively. Again it is also revealed from the table that the Problem Handling Competency sub-scale also attracted a mean and standard deviation rating of M = 4.97 (SD = 1.0) and M = 6.06
(SD = 0.9) respectively from the teacher and supervisor respondents. The Modelling
Competency theme in the same regard saw the supervisors rating high (M = 8.71, SD
= 1.3) the practices over the teachers’ assessment (M = 7.27, SD = 1.5). Furthermore, the supervisors mean score rating for Reasoning Competency sub-scale was M = 8.69
(SD = 1.1) and that of the teachers was M = 7.95 (SD = 1.3). The next sub-scale whose mean scores rating was sought was the Representation Competency sub-scale.
This theme was rated by the teachers and supervisors as M = 7.51 (SD = 1.2) and M =
8.54 (SD = 0.9) respectively. In fact, the teacher respondents ranked low (M = 7.61,
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SD = 1.4) supervisors’ competency in Symbols and Formalism Competency sub-scale than the supervisors’ themselves (M = 8.71, SD = 0.9). Communication competency of the supervisors was mean and standard deviation ranked by the two categories of the respondents (mathematics teachers and supervisors). The analysis indicated that the teachers rated their supervisors’ Communication Competency as M = 5.39 (SD =
0.9) while the supervisors themselves rated the Communication Competency as M =
6.51 (SD = 1.0). Finally, the Aids and Tools Competency also attracted a mean and standard deviation scores of M = 7.04 (SD = 1.2) and M = 9.43 (SD = 1.1) from the teachers and supervisors respectively.
An inspection of Table 4.10 reveals that there exist to some extent an amount of differences in the mean and standard deviation scores of teacher and supervisor participants’ responses. In order to examine the mean score’s statistical significant differences, the research carried out an independent samples t-test on the data set.
However, before the test was carried out, assumptions underlining independent samples t-test were carried out in order test the suitability of the data under study.
First and foremost, the assumption of independence of the scores was tested.
Field (2009) in explaining independence of the scores asserted that a person or case cannot appear in more than one category or group, and the data from one subject cannot influence the data from another. This assumption was met since the scores/data for this study came from different participants (mathematics teachers and supervisors). Another assumption that was tested was normality of the distributed.
According to Gravetter and Wallnau (2000) normal is used to describe a symmetrical, bell-shape curve, which has the greatest frequency of scores in the middle, with smaller frequencies toward the extremes. This normality can be expressed and assessed to some extent by obtaining the values of skewness and kurtosis of the
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distribution. The value of skewness and kurtosis of the distribution are also 1.21 and
0.75 respectively. Therefore, the assumption was met as the distribution scores were approximately non-normal.
Assumption of homogeneity of variance across the dependent variables
(Supervisors competency) was also assessed. The findings indicated that the assumption was not violated because Levene’s test for equality of Variances for each of the eight sub-scale supervisors’ competencies was non-significant. The Levene’s test statistics for each of the sub-scale are as follows: p = 0.281 (Mathematical
Thinking Competency); p = 0.672 (Problem Handling Competency); p = 0.275
(Modelling Competency); p = 0.239 (Reasoning Competency); p = 0.148
(Representation Competency); p = 0.100 (Symbols and Formalism Competency); p =
0.208 (Communication Competency), and p = 0.887 (Aids and Tools Competency). It can therefore be assumed that the variances are roughly equal and the assumption is tenable. The result as presented on the assumptions underlining Independent-samples t-test indicates that the analysis was tenable. Therefore, results of the independent- samples t-test is presented in Table 4.11.
Table 4. 9: Independent-samples t-test of respondents’ perceptions on supervisors’ competency. Mean 95% Confidence Interval Sub-scale t-value df Sig Difference of the Difference
Lower Upper
Mathematical Thinking Competency -3.1 183 0.002 -0.7 -1.168 -.259 Problem Handling Competency -5.7 183 0.000 -1.1 -1.457 -.711 Modelling Competency -5.1 183 0.000 -1.4 -1.995 -.887 Reasoning Competency -3.2 183 0.002 -0.7 -1.193 -.285 Representation Competency -4.6 183 0.000 -1.0 -1.469 -.590 Symbols and Formalism Competency -4.6 183 0.000 -1.1 -1.587 -.628 Communication Competency -6.5 183 0.000 -1.1 -1.470 -.785 Aids and Tools Competency -11.3 183 0.000 -2.4 -2.808 -1.969 Source: Field Data - Questionnaire
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Table 4.11 reflects results from the eight Independent samples t-tests, which were conducted by the researcher to determine if there were significant differences among supervisors’ competency by type of respondents (mathematics teachers and supervisors). It is evident from the table that all composite means yielded statistically significant differences (p < .05). For example, the results on the differences about perception of the respondents were significant on each of the sub-scale: Mathematical
Thinking Competency t(183) = -3.1, p < 0.002; Problem Handling Competency t(183)
= -5.7, p < 0.00; Modelling Competency t(183) = -5.1, p < 0.000; Reasoning
Competency t(183) = -3.2, p < 0.002; Representation Competency t(183) = -4.6, p <
0.000; Symbols and Formalism Competency t(183) = -4.6, p < 0.000; Communication
Competency t(183) = -6.5, p < 0.000 and Aids and Tools Competency t(183) = -11.3, p < 0.000.
Discussion
Most of the teacher respondents did not agree that mathematics supervisors possessed the requisite competence to improve professional qualities of mathematics teachers in the study area. This could be because, depending on individual supervisors, supervision has probably succeeded in bringing about the opposite and that it has strained relations instead.
푯02 = There is no statistical significant difference between male and female mathematics teachers’ perceptions of styles of school supervision in the Kwahu East
District?
In accordance with the first research hypothesis, an inferential statistic was employed on the data set to investigate whether the differences between teachers by background factor (gender) was statistically significant. In order to test research
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hypothesis one, descriptive statistics and an independent samples t-test were employed to determine the differences between male and female teachers’ perceptions of the various supervision practices that they experience in their various schools in the
Kwahu East District.
Independence samples t-test assumptions were assessed to ensure the appropriateness of using this statistic tool to explain the difference between male and female mathematics teachers on the various styles of school supervision. The first assumption that was considered was the independence of the scores obtained. The independence of scores means that each person or case should be counted only once.
Field (2009) asserted that a person or case cannot appear in more than one category or group, and the data from one subject cannot influence the data from another. This assumption was met because the scores/data for this study came from different participants that are male and female. The next assumption that was considered was normality of the distributed; this assumption was met as the distribution scores were approximately non-normal. This normality can be expressed and assessed to some extent by obtaining the values of skewness and kurtosis of the distribution. The value of skewness and kurtosis of the distribution are also 0.966 and 1.016 respectively.
Assumption of homogeneity of variance across the dependent variables (Styles of
Supervision) was also assessed. The findings indicated that the assumption was not violated because Levene’s test for equality of Variances for each of the three supervision styles was non-significant {p = 0.133 (Autocratic), p = 0.481
(Democratic) and p = 0.787 (Laissez-Faire)} it can therefore be assumed that the variances are roughly equal and the assumption is tenable. The result as presented on the assumptions underlining Independent-samples t-test indicates that the analysis was
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tenable. Therefore, Table 4.8 presents the results on the descriptive statistics of the analysis.
Table 4. 10: Descriptive statistics of mathematics teachers by gender Gender N Mean Std. Deviation Male 96 3.99 0.8 Autocratic Supervision Female 54 3.98 0.6 Male 96 4.29 0.6 Democratic Supervision Female 54 4.28 0.6 Male 96 2.75 0.8 Laissez-Faire Supervision Female 54 2.76 0.8 Source: Field Data - Questionnaire
It is evident from Table 4.8 that the mean score for autocratic style of supervision was 3.99 (SD = 0.8, n = 96) for male participants and 3.98 (SD = 0.6, n =
54) for female participants. Again, it is evident from the table that democratic style of supervision recorded a mean score value of 4.29 (SD = 0.6, n = 96) for male participants and that of female is 4.28 (SD = 0.6, n = 54). Finally, it is clear from the
Table 4.8 that Laissez-Faire style of supervision attracted a mean score of 2.75 (SD =
0.8, n = 96) for the male participants and 2.76 (SD = 0.8, n = 54). Table 4.9 presents the results of the t-test analysis.
Table 4. 11: Independent-samples t-test of Basic School Mathematics Teachers’ perception of styles of supervision practices. 95% Confidence Sig. Mean Std. Error t df Interval of the (2-tailed) Difference Difference Difference Lower Upper Autocratic Supervision 0.10 147 0.95 0.01 0.127 -0.244 0.259 Democratic Supervision 0.14 148 0.89 0.01 0.100 -0.183 0.211 Laissez-Faire Supervision -0.10 148 0.95 -0.01 0.138 -0.283 0.264 Source: Field Data - Questionnaire
The results as presented in Table 4.9 indicates that basic schools male mathematics teachers in the Kwahu East District perceived their supervisors as employers of autocratic supervision style was almost the same as (M = 3.99, SD = 0.8)
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their female (M = 3.98, SD = 0.6) counterparts in the districts. From the table, the result of the analysis indicates that there was no statistical significant difference between the two groups (t = 0.10, df = 147, p = 0.95). For the magnitude of the effect size, Mean differences and Cohen’s d (effect sizes) were computed between male basic school teachers and female basic school teachers’ assessment of the autocratic supervision styles employed by the supervisors. Cohen’s d was computed to compare the magnitude of differences between basic school teachers using, 푑= (Cohen,
1969; Thalheimer & Cook, 2002).
푑 =
푑 =
푑 = = 푑 = 0.017
The magnitude of the difference was very small based on Cohen’s effect size
(0.017 or 1.7%), results showed a non-significant discrepancy between male and female teachers’ assessment of autocratic supervision styles of supervisors. Cohen’s guidelines for effect size are as follows: Cohen’s d = 0.20 or less is considered small,
Cohen’s d = 0.50 is moderate, and Cohen’s d = 0.80 is considered large (Cohen,
1969).
The t-test analysis presented in Table 4.9 further reveals that majority of the male teachers asserted that their supervisors did employ democratic supervision styles
(M = 4.29, SD = 0.6). This assertion was also endorsed by the female teachers (M =
4.28, SD = 0.6) in the district. The difference between the perceptions of the two participants (male and female) in the study was not statistically significant (t = 0.14, df = 148, p = 0.89). Mean differences and Cohen’s d (effect sizes) were computed between male basic school teachers and female basic school teachers’ assessment of
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the democratic supervision styles employed by the supervisors. Cohen’s d was computed to compare the magnitude of differences between basic school teachers using, 푑= (Cohen, 1969; Thalheimer & Cook, 2002).
푑=
푑=
푑=
푑=0.023
Even though the magnitude of this difference was very small based on
Cohen’s effect size (0.023 or 2.3%), results showed a non-significant discrepancy between male and female teachers’ assessment of autocratic supervision styles of supervisors. Cohen’s guidelines for effect size are as follows: Cohen’s d = 0.20 or less is considered small, Cohen’s d = 0.50 is moderate, and Cohen’s d = 0.80 is considered large (Cohen, 1969).
Finally, the results in the table indicated that there was a slight difference in the observations of the participants when it came to Laissez-Faire supervision style.
The results indicated that female teachers (M = 2.76, SD = 0.8) were of the view that their supervisors did employ the Laissez-Faire supervision style often than their male
(M = 2.75, SD = 0.8) counterparts. The differences between their view about the supervision style was not statistically significant t(148) = -0.10, p = .95; however, it did also not represent a medium-sized effect Cohen’s d = 0.02 (1.2%).
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푑=
푑=
푑=
푑=0.016
Cohen’s guidelines for effect size are as follows: Cohen’s d = 0.20 or less is considered small, Cohen’s d = 0.50 is moderate, and Cohen’s d = 0.80 is considered large (Cohen, 1969).
These findings seem to be consistent with the related literature about the effect of certain background characteristics on teacher perceptions (Başkan, 2001; Wayne &
Youngs, 2003; Bennell and Akyeampong (2006). Bennell and Akyeampong (2006) in their study found that gender was not a differentiator when it came to perceptions on styles of supervision in Sub-Saharan Africa and Asia.
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CHAPTER FIVE
SUMMARY OF FINDINGS, CONCLUSIONS AND
RECOMMENDATIONS
5.1 Summary
The purpose of this survey research method was to explore and examine mathematics supervisors’ competence in ensuring effective mathematics teaching and learning in basic schools in Ghanaian schools. The study specifically sought to examine mathematics teachers and supervisors’ perceptions of the competence supervisors possess in ensuring effective mathematics teaching and learning in basic schools in Kwahu East District. The study adopted Niss and Jensen’s (2003) conceptual framework named the “KOM flower” (KOM – in Danish stands for
“Competencies and the Learning of Mathematics” (Niss, 2003). The study further sought to explore and examine the styles of supervision which mathematics teachers were being exposed to by school authorities in the Kwahu East District.
The target population for this study was all mathematics teachers and supervisors in the Eastern Region of Ghana. The accessible population was all head teachers of all JHS schools, circuit supervisors and all mathematics teachers in Junior
High Schools in Kwahu East and West District in the Eastern Region of Ghana. A total number of 192 consented mathematics teachers and supervisors took the questionnaires (teachers = 157 and supervisors = 35). However, 150 mathematics teachers completed and returned the questionnaire. This represented 95.5% return rate. The instruments used to gather data for the study were the Supervisors’
Competency Perception Index I (SCPI-I) (for Headteachers) and Supervisors’
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Competency Perception Index II (SCPI-II) (for Mathematics Teachers) questionnaires.
The study was guided by the following research questions and hypotheses:
1. What are mathematics teachers perceptions of the competence supervisors
have in ensuring effective teaching and learning of mathematics in basic
schools in the Kwahu East District?
2. How do supervisors perceive their competencies in ensuring effective teaching
and learning of mathematics in basic schools in the Kwahu East District?
3. What styles of school supervision do Junior High School teachers in the
Kwahu East District experience?
4. What inherent challenges do supervisors in the Kwahu East District face in
ensuring effective mathematics education delivery in basic schools?
Hypotheses
푯01 = There is be no statistical significant difference between mathematics teachers’ and supervisors’ perceptions of mathematics supervision competence of supervisors in the Kwahu East District
푯02 = There is be no statistical significant difference between male and female teachers’ perceptions of styles of school supervision in the Kwahu East District
Quantitative data was the grounding for this study. Statistical Product for
Services Solution (SPSS) was the statistical software packaged used in analyzing the quantitative data (data from questionnaire). Descriptive statistics (frequencies, percentages, means scores and standard deviations), were used to analyzed the research questions while inferential statistics (independent-sample t-test) was used to analyzed the two research hypotheses.
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5.2 Summary of Key Findings
5.2.1 Research Question 1: What are mathematics teachers perceptions of the competence supervisors have in ensuring effective teaching and learning of mathematics in basic schools in the Kwahu East District?
The Supervisors’ Competency Perception Index II (SCPI-II) questionnaire was used to measure basic school mathematics teachers’ perceptions of the mathematics competency of their supervisors. After conducting the 22-item survey, the author used previously identified perceptions sub-scales (Mathematical Thinking Competency,
Problem Handling Competency, Modelling Competency, Reasoning Competency,
Representation Competency, Symbols and Formalism Competency, Communication
Competency, and Aids and Tools Competency) to analyze the data. The findings in relation to research question 1 revealed that:
a. Majority of the teachers who participated in the study generally indicated that
their supervisors’ Mathematical Thinking Competency was just a little above
average. The result was an indication that the teacher respondents were of the
perception that their supervisors had some degree of competency in
supervising and helping them to develop their mathematical thinking capacity.
b. It was also evident that most teacher respondents who took part in the study
revealed that majority of their supervisors had an average competency in
problem handling ability. The finding shows that most of the respondents had
the perception that their mathematics supervisors in basic schools had some
degree of competency in supervising with regards to problem handling
competency.
c. Nevertheless, the study suggested that most basic school mathematics teachers
in the Kwahu East District asserted that their supervisors’ competency in
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mathematics modelling was below average. This outcome indicates that most
mathematics teachers are of the perceptions that their supervisors were not
very competent in supervising and helping them to develop mathematics
modelling competency. For example, most of them were of the view that most
supervisors are unable to decode existing models to mathematics teachers. d. It was established during the study also that most basic school teachers were
of the opinion that most supervisors’ mathematics Reasoning Competency was
above average. This to some extent meant that the teachers had the belief that
their supervisors were very capable of ensuring the implementation and
supervision of mathematics Reasoning Competency in basic schools. e. Again, the study’s findings revealed the teachers conjectured that their
supervisors’ ability in mathematics Representation Competency was average. f. Supervisors’ skills in Symbols and Formalism Competency, was the next sub-
scale been ranked by the teachers. The findings revealed that the teachers are
of the view that their supervisors’ skill in supervising Symbols and Formalism
during lessons was high above average. g. Furthermore, the results showed that the teachers’ view about their overseers’
competency in mathematics communication was well above average. This is
an indication that the supervisors were perceived to have the competency in
supervising and developing mathematics communication skills of the basic
school mathematics teacher. h. And finally, the study’s findings revealed that supervisors’ competency in
supervising the preparation and use of mathematics aids and tools in and out
of the classroom was way below average, as indicated by the teacher
respondents.
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5.2.2 Research Question 2: How do supervisors perceive their competencies in ensuring effective teaching and learning of mathematics in basic schools in the
Kwahu East District?
The first 22 survey item on the Supervisors’ Competency Perception Index I
(SCPI-I) was used to gather quantitative data on basic school mathematics supervisors’ perceptions of their competencies in ensuring effective teaching and learning of mathematics in the Kwahu East District. The conclusions in relation to the research question suggested that:
a. Majority of the supervisors believe that their competency in supervising and
developing Mathematical Thinking Competency in basic school teachers in
the Kwahu East District is well above average.
b. Most of the mathematics supervisors who took part in the study are of the
view that their competency in supervising problem handling skills of the basic
school teacher is also very high above average.
c. Furthermore, it is evident from the study that most supervisors conjectured
that their competency in supervising teachers’ modelling skill is also above
average.
d. Again, a bulk number of the supervisor respondents indicated that their skill in
supervising the mathematical reasoning competency of mathematics teachers
was high above average.
e. Another sub-scale whose composite mean was above average was the
Representation Competency. The indication is that, most supervisors were of
the perception that they had the need skills and competencies in supervising
basic school teachers’ mathematical representation skills and abilities.
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f. The findings further revealed that most supervisors were of the view that they
are most competent in supervising and develop mathematics teachers’ skills
and abilities in teaching with regards to Symbols and Formalism.
g. Supervisors’ Communication Competency was the next sub-scale explored in
the study. The result indicated that the supervisors indicated that they were
more competent in supervising and developing Communication Competency
in the mathematics teachers more than all the other construct measured. This
sub-scale scored the highest composite mean scores.
h. Finally, the study’s findings revealed that the supervisors indicated that their
skills in supervising and helping teachers in developing competency in aids
and tools is very high. This indicates that most supervisors believe they are
very competent in this and the other competency explored in this study.
5.2.3 Research Question 3: What styles of school supervision do Junior High School teachers in the Kwahu East District experience?
Research results in relation to the third research question suggested that:
a. Majority of the mathematics basic school teachers who participated in the
study believed that most supervisors in the district employ the democratic
style of supervision. This finding meant that most supervisors in the district
were adopting the modern-day approach to supervision. This assertion was
very much evident in the results generated on each item under the sub-scale.
For example, most of the teachers indicated that most supervisors their schools
believe that supervisees want to be part of decision making process and they
therefore allow them the space which is geared to horned the supervision and
leadership skill of the supervisee. Also, the respondents revealed that their
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supervisor believes that supervisors need to help supervisees accept
responsibility for completing their task.
b. The study results further indicated that some school authorities were found of
adopting the autocratic style of supervision in the quest to undertake the
supervisory role. Even though, this style of supervision has been projected in
literature as not being a friendly approach to supervision, authorities in this
area are of the view that, this style is still in use in most organization and it
may be producing the desired results. The stands taken by most of the
mathematics teachers indicate that most supervisors adopted the situational
style of supervision. This is clearly seen in the way the respondents have
arranged the two-main style of supervision.
c. Finally, the research findings indicated that some of the teacher respondents
are of the view that some of the supervisors were still engaged in adopting the
Laissez-Faire style of school supervision. This the teachers opined was evident
through activities such as ‘Some authorities in my school are of the view that
supervisors should give supervisees complete freedom to solve problems on
their own’ and ‘My supervisor believes that supervision requires staying out of
the way of supervisees as they do their work’.
5.2.4 Research Question 4: What inherent challenges do supervisors in the Kwahu
East District face in ensuring effective mathematics education delivery in basic schools?
Despite the numerus benefits inherent in educational supervision in general and mathematics supervision in specificity, the area has been found to be inundated with numerous challenges (Mankoe, 2007). Items on challenges facing instructional supervision in the Kwahu East District was administer to mathematics supervisors. A
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number of challenges were identified to have been responsible for militating against the delivery of effective instructional supervision of mathematics. In the Kwahu East
District some of the challenges include: lack of finance, inadequate relevant trainings in mathematics education, inadequate number of supervisors, inadequate number of relevant supervision manuals, insufficient allocated budget, lack of follow up on the activities of supervisors, erroneous impression of supervision by most mathematics teachers, lack of training for supervisors, routine administrative burden among others.
However, with the appropriate determination, the challenges of supervision of instruction of mathematics in our basic schools can be addressed if there is a stronger belief that a teacher is the most with long lasting influence on student. Therefore, their instructional activities must constantly be under the lenses of supervision in order to ensure that the best teaching and learning experiences are always transmitted to the student.
5.2.5 Research Hypothesis 1: There will be no statistical significant difference between mathematics teachers’ perceptions of supervision competence of supervisors in the Kwahu East District and their supervisors’ perceptions.
Concerning supervisors’ mathematics instructional competency; teacher and supervisor respondents gave their opinions. The result shows that the teacher and supervisor respondents have different views on the competencies of supervisors.
Mathematics supervisor respondents replied that their supervision competency in ensuring quality implementation of the mathematics curriculum in basic schools in the
Kwahu East District is above average. In order words the supervisors asserted that they had the requisite competency in supervising mathematics teachers in basic school in the study area. The supervision competency ranges from Mathematical Thinking
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Competency, Problem Handling Competency, Modelling Competency, Reasoning
Competency, Representation Competency, Symbols and Formalism Competency,
Communication Competency, and Aids and Tools Competency. On the contrary, the majority of teacher respondents asserted that their instructional supervisors did have, in some cases average in order cases below average competency in supervising them.
This indicates that most mathematics teachers in the Kwahu East District were of the view that their supervisors did not have the requisite competency in supervising them before, during and after mathematics instructions. The difference between the supervisors’ and teachers’ views for all the variables were statistical significant.
5.2.6 Research Hypothesis 2: There will be no statistical significant difference between male and female teachers’ perceptions of styles of school supervision in the
Kwahu East District.
Findings based on the background characteristic (gender) of the Junior High
School teachers were examined to establish if there exist any significant differences between their perceptions of the styles of school supervision. The findings on this research hypothesis suggest that, both male of female teachers in the Kwahu East
District did not differ significantly on the various styles of supervision school authorities employ in the school setting. For example, even though there was a difference in the perception of both male (M = 4.29, SD = 0.6) and female (M = 4.28,
SD = 0.6) mathematics teachers when it came to assessing the democratic style of supervision, the difference was not statistically significant. Furthermore, the results also show that, there was a slight difference between male (M = 3.99, SD = 0.8) and female (M = 3.98, SD = 0.6) teachers in terms of how they perceived school authorities in adopting the autocratic style of supervision. The identified difference
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was not statistically significant. Finally, the outcomes of the analysis based on the research question three reveal that females (M = 2.76, SD = 0.8) and males (M = 2.75,
SD = 0.8) teachers differed in the way they both perceived the laissez-faire style of supervision. This observed difference was not statistically significant.
5.3 Conclusion
Based on the findings of the study, the following conclusions were drawn:
The study brought to bear the importance of supervisors’ competencies on mathematics teachers’ perceptions which have a telling effect on their performance. It indicated that the effect of supervisors’ competency on staff perceptions and performance in the Kwahu East District Education Directorate is so crucial that attention has to be paid to develop it.
Among others it can be concluded based on the study result that the general feeling of the supervisor respondents particularly was that they were competent enough to supervise instructional implementation in basic schools in the Kwahu East
District Education Directorate. This finding was questionable in that most of the supervisors (both internal and external) indicated that they lack training in the field of mathematics (as shown in demographic data). It is therefore concluded that either the supervisors were not truthful during the study or they did not understand most of the items measuring their competency and therefore decided to respond to the survey anyhow.
As indicated in the findings, it can be concluded that the general feeling among the respondents is that the main styles of supervision adopted for practice by supervisors in the district’s basic school are democratic, autocratic and laissez-faire respectively. It can be inferred from the study’s results that most staff experienced
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democratic style of supervision more than any other type of supervision. The next style of supervision which seems to be predominating in the district was the autocratic style of supervision and finally followed by the laissez-faire style of supervision. It can also be concluded that teacher demography characteristics (gender) was not a differentiator when it came to the styles of supervision. It is therefore concluded that basic school authorities in the district should not employ one style for male teachers and different style for female teachers in our basic schools.
The results of the study discovered that supervision was negatively affected by many problems; such as: the incapability of school-based supervisors; the absence of in-service training programs to update supervisors; non-availability of supervision manual at school; an insufficient allocation of budget to carry out supervisory activities; the unavailability of experienced supervisors in schools and the heavy workload of school-based supervisors. As a result, school-based supervision was less supportive for effective teaching and learning process.
Supervisors should not be taken for granted, for their challenges are never ending. There may be weaknesses with their supervision, but it is the organization which would have to alleviate these weaknesses. They need to be properly managed to make them acquire the sense of working to improving performance.
Finally, this study is unique because it sought to examine the competency of public basic school supervisors to ensure effective delivery of mathematics education.
Unlike previous studies which dealt with the general supervision of instruction.
5.4 Recommendations
The following recommendations have been drawn based on the findings of the study, to minimize to the identified problems and prosed solutions that impede the
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competency of supervisors and practice of instructional supervision in Kwahu East
District:
1. The findings of the study based on mathematics teachers’ view point revealed
that, instructional supervisors do not have the requisite competency in
supervising mathematics teachers in the classroom in order to design and
implement appropriate instructions. It is therefore recommended that training
institutions such as University of Cape Coast (UCC), University of Education
Winneba (UEW) and Ghana Education Service (GES) through pre-service and
in-service training programmes must organize regular workshops for teachers,
headteachers and circuit supervisors on desired competencies of modern-day
instructional supervision. Again, since supervision is a process but not a
product, some aspects of modern-day instructional supervision could be
incorporated into the teacher training programmes at the diploma, degree and
masters’ levels to sensitize teachers’ about modern-day instructional
supervision competencies.
2. GES must take steps to provide training for Circuit Supervisors, Headmasters
and Heads of Departments in instructional supervision as part of their
induction process after their appointments. In addition, new developments in
the education system could be provided to headmasters through periodic in-
service-training to keep them abreast with current trends and practices.
3. The challenges of supervisors should be addressed by the Municipal Director
of Education and the Ministry of Education. These challenges include supply
of cars to the inspectorate division of the Municipal Directorate of Education
by the Ministry of Education to enhance their mobility and also serve as
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incentive. The Municipal Director of Education should ensure regular supply
of fuel to enable supervisors regularly visit their respective schools.
4. All stakeholders of education must put their shoulders to the wheel to ensure
that they provide the necessary support to the basic schools supervisors. For
example, accommodation should be provided to teachers on campus by the
government, PTA and Non-Governmental Organisations (NGOs) so that they
could be punctual and regular at school.
5. Supervisors should share findings of their supervision with supervisees and
also take steps to know what motivates them as individual teachers and at the
same time creating opportunities for staff to share personal accomplishments.
5.5 Suggestions for Further Study
The educational implications of the findings of the study calls for further research in the area of supervisors’ competency in the mathematics classroom. The following are recommended for further research:
Further studies on how supervision of mathematics instruction is done and what supervisors look out for during supervision of mathematics instruction is recommended.
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APPENDIX A
UNIVERSITY OF EDUCATION, WINNEBA
DEPARTMENT OF MATHEMATICS EDUCATION
SELF-ADMINISTER QUESTIONNAIRE ON:
EXPLORING THE COMPETENCIES OF BASIC SCHOOL SUPERVISORS IN THE MATHEMATICS CLASSROOMS: THE CASE OF KWAHU – EAST DISTRICT OF THE EASTERN REGION
SECTION A - BACKGROUND INFORMATION Please tick [ √ ] in the appropriate space provided below and supply answers where required. If you want to change an item you have already ticked, put a cross [ × ] over the selected item and tick the new item. 1. Gender a. Male [ ] b. Female [ ]
2. Age a. 18 - 30 [ ] b. 31 - 40 [ ] c. 41 - 50 [ ] d. 51 and above [ ]
3. Professional Qualification a. Cert A [ ] b. Diploma [ ] c. Bachelor’s Degree [ ] d. Master’s Degree [ ] e. Others [ ] f. Specify……………………………………………………
4. Rank of Teacher…………………………………………………
5 How long have you been teaching? a. 1 – 5 year(s) [ ] b. 6 – 10 years [ ] c. 11 – 15 years [ ] d. 16 – 20 years [ ] e. 21 years and above [ ] Please check ‘√’ in the appropriate box. If you want to change an item you have already ticked, put a cross [×] over the selected item and tick the new item.
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Scale: Strongly Disagree (SD = 1), Disagree (D = 2), Agree (A = 3), Strongly Agree (SA = 4) Statement SD D A SA Mathematical Thinking Competency My supervisors are able to supervise teachers posing questions that are characteristic of mathematics, and predict the kinds of answers that mathematics students may offer. Most supervisors in my school understand and are able to supervise the scope and limitations of a given concept. Some external supervisors are able to extend the scope of a concept by abstracting some of its properties and generalizing results to larger classes of objects during pre-observation conference. Problem Handling Competency SD D A SA My supervisors are able to supervise teachers pose and specify different kinds of mathematical problems – pure or applied; open-ended or closed-ended. My supervisors are able to supervise teachers solving different kinds of mathematical problems, whether posed by others or by oneself, and, if appropriate, in different ways. Modelling Competency SD D A SA External supervisors are able to supervise teachers when analyzing foundations and properties of existing models, including assessing their range and validity. During pre-observation conference, supervisors are able to decode existing models, i.e. translating and interpreting model elements in terms of the ‘reality’ modelled to teachers. My supervisors are able to supervise teachers performing active modelling in a given context - structuring the field
– mathematising - working with(in) the model, including solving the problems it gives rise to etc. Reasoning Competency SD D A SA Most external supervisors are able to supervise teachers when following and assessing chains of arguments, put forward by students during mathematics lessons. Knowing what a mathematical proof is (not), and how it differs from other kinds of mathematical reasoning, e.g. heuristics, is one unique characteristics of my supervisor. Mathematics supervisors have the ability to uncover the basic ideas in a given line of argument (especially a proof), including distinguishing main lines from details and ideas from technicalities. Representation Competency SD D A SA Supervising teachers’ understanding and utilizing (decoding, interpreting, distinguishing between) of different sorts of representations of mathematical objects,
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phenomena and situations is not a problem to my internal supervisors
Supervising teachers when utilizing the relations between different representations of the same entity, including knowing about their relative strengths and limitations are no problem to my supervisors My supervisors are able to supervise teachers choosing and switching between representations when teaching mathematics. Symbols and Formalism Competency SD D A SA Most pre or post conferences with supervisors are characterized with decoding and interpreting symbolic and formal mathematical language, and understanding its relations to natural language. Understanding the nature and rules of formal mathematical systems (both syntax and semantics) is no problem to most of my supervisors. My supervisors are able to supervise teachers in handling and manipulating statements and expressions containing symbols and formulae. Communication Competency SD D A SA Understanding others’ writings, visual or oral ‘texts’, in a variety of linguistic registers, about matters having a mathematical content is not a challenge to most supervisors in my school Expressing oneself, at different levels of theoretical and technical precision, in oral, visual or written form, about such matters is a unique characteristic of most supervisors in my school. Aids and Tools Competency SD D A SA Most supervisors know the existence and properties of various teaching and learning tools and aids for mathematical activity, and their range and limitations. Internal supervisors are able to supervise teachers’ ability to prepare a standard teaching and learning tools and aids for mathematical activities for various level of learners. My supervisors are able to supervise teachers’ ability to reflectively use appropriate materials, aids and tools in teaching. SECTION C: STYLES OF SUPERVISORS Please check ‘√’ in the appropriate box. If you want to change an item you have already ticked, put a cross [×] over the selected item and tick the new item. Scale: Strongly Disagree (SD = 1), Disagree (D = 2), Undecided (U = 3), Agree (A = 4), and Strongly Agree (SA = 5)
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Statement SD D U A SA My supervisor believes that supervisees need to be supervised closely, or they are not likely to do their work Most supervisors in my school believes that it is fair to say that most supervisees in the general population are lazy Some supervisors are of the view that as a rule, supervisees must be given rewards or punishments in order to motivate them to achieve organizational objectives Most supervisors in my school believes that most supervisees feel insecure about their work and need direction Most supervisors in my school believes that the supervisor is the chief judge of the achievement of members of the group. My supervisor believes that effective supervisors give orders and clarify procedures to their supervisees Most supervisors in my school believes that supervisees want to be part of decision making process Some supervisors are of the view that providing guidance without pressure is the key to being a good supervisor My supervisor believes that most supervisees want frequent and supportive information from their supervisors My supervisor believes that supervisors need to help supervisees accept responsibility for completing their task It is the believe of my supervisor that it is the supervisor’s job to help supervisees find their "passion" Some supervisors are of the view that supervisees are basically competent and if given a task will do a good job My supervisor believes that in complex situations, supervisors should let supervisees work problems out on their own My supervisor believes that supervision requires staying out of the way of supervisees as they do their work Some supervisors in my school believes that as a rule, supervisors should allow supervisees to appraise their own work Some authorities in my school are of the view that supervisors should give supervisees complete
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freedom to solve problems on their own Most supervisors in my school believes that in most situations, supervisees prefer little inputs from their supervisors Most supervisors in my school believes that in general, it is best to leave supervisees alone
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APPENDIX B
UNIVERSITY OF EDUCATION, WINNEBA
DEPARTMENT OF MATHEMATICS EDUCATION
SELF-ADMINISTER QUESTIONNAIRE ON:
EXPLORING THE COMPETENCIES OF BASIC SCHOOL SUPERVISORS IN THE MATHEMATICS CLASSROOMS: THE CASE OF KWAHU – EAST DISTRICT OF THE EASTERN REGION
SECTION A - BACKGROUND INFORMATION Please tick [ √ ] in the appropriate space provided below and supply answers where required. If you want to change an item you have already ticked, put a cross [ × ] over the selected item and tick the new item. 1. Gender a) Male [ ] b) Female [ ]
2. Age a) 20 - 30 [ ] b) 31 - 40 [ ] c) 41 - 50 [ ] d) 51 and above [ ]
3. Professional Qualification a) Cert A [ ] b) Diploma [ ] c) Bachelor’s Degree [ ] d) Master’s Degree [ ] e) Others [ ] f) Specify……………………………………………………
4. Professional status a) Trained b) Untrained 5. Area of specialization a) Mathematics b) Others 6. Number of years at current position………………………. 7. How long have you been teaching………………………….
Please check ‘√’in the appropriate box. . If you want to change an item you have already ticked, put a cross [×] over the selected item and tick the new item.
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Scale: Strongly Disagree (SD = 1), Disagree (D = 2), Agree (A = 3), Strongly Agree (SA = 4) Statement SD D A SA Mathematical Thinking Competency I am able to supervise teachers posing questions that are characteristic of mathematics, and predict the kinds of answers that mathematics students may offer. Most teachers in my school would say I understand and am able to supervise the scope and limitations of a given concept. I am able to extend the scope of a concept by abstracting some of its properties and generalizing results to larger classes of objects during pre-observation conference with teachers. Problem Handling Competency SD D A SA My teachers will agree that am able to supervise teachers posing and specifying different kinds of mathematical problems – pure or applied; open-ended or closed-ended. I am able to supervise teachers solving different kinds of mathematical problems, whether posed by others or by oneself, and, if appropriate, in different ways. Modelling Competency SD D A SA I am able to supervise teachers when analyzing foundations and properties of existing models, including assessing their range and validity. During pre-observation conference, I am able to decode existing models, i.e. translating and interpreting model elements in terms of the ‘reality’ modelled to teachers. My teacher believe that I am able to supervise them performing active modelling in a given context - structuring the field – mathematising - working with(in) the model, including solving the problems it gives rise to etc. Reasoning Competency SD D A SA I am able to follow and assess teachers when chains of arguments, are put forward by students during mathematics lessons. Knowing what a mathematical proof is (not), and how it differs from other kinds of mathematical reasoning, e.g. heuristics, is one unique characteristics I possess. I have the ability to uncover the basic ideas in a given line of argument (especially a proof), including distinguishing main lines from details and ideas from technicalities.
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Representation Competency SD D A SA Supervising teachers’ understanding and utilizing (decoding, interpreting, distinguishing between) of different sorts of representations of mathematical objects, phenomena and situations is not a problem to me at all Supervising teachers when utilizing the relations between different representations of the same entity, including knowing about their relative strengths and limitations is not my problem I am able to supervise teachers choosing and switching between representations when teaching mathematics. Symbols and Formalism Competency SD D A SA Most pre or post conferences with my teachers are characterized with decoding and interpreting symbols and formal mathematical language, and understanding its relations to natural language. I am able to understanding the nature and rules of formal mathematical systems (both syntax and semantics) I am able to supervise teachers in handling and manipulating statements and expressions containing symbols and formulae. Communication Competency SD D A SA Understanding others’ writings, visual or oral ‘texts’, in a variety of linguistic registers, about matters having a mathematical content is not a challenge me Expressing myself, at different levels of theoretical and technical precision, in oral, visual or written form, about such matters is a unique characteristic I possess Aids and Tools Competency SD D A SA I know the existence and properties of various teaching and learning tools and aids for mathematical activity, and their range and limitations. I am able to supervise teachers’ ability to prepare a standard teaching and learning tools and aids for mathematical activities for various level of learners. I am able to supervise teachers’ ability to reflectively use appropriate materials, aids and tools in teaching.
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SECTION C: CHALLENGES OF SUPERVISORS Please check ‘√’ in the appropriate box. . If you want to change an item you have already ticked, put a cross [×] over the selected item and tick the new item. Scale: Strongly Disagree (SD = 1), Disagree (D = 2), Undecided (U = 3), Agree (A = 4), and Strongly Agree (SA = 5) Statement SD D U A SA Majority of supervisors do not have relevant trainings in mathematics education There are inadequate number of supervisors to assist the basic school mathematics teachers teach properly There are inadequate number of relevant supervision manuals in the district office and basic schools There is insufficient allocated budget for the supervisory program in the district. There is lack of follow up on the activities of supervisors by the superiors. Most mathematics supervisors’ use of supervision for administrative purposes only. Most mathematics teachers’ lack of knowledge about the concept of supervision is a big challenge to the supervision process Basic school mathematics teachers perceive supervisors as a fault finder rather than assisting them. Lack of training for supervisors and lack of support for supervisors from higher offices affect the supervisory practice in the district Routine administrative burden makes it hard for supervisors to find time to visit classrooms and observe how mathematics teachers are teaching
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