Chapter-I INTRODUCTION

Background of Study

The term ‘Mathematics’ has been interpreted and explained in various ways. According to Oxford Dictionary, “Mathematics is the science of number and space’’. A famous 20th century mathematician Albert Einstein defined, ‘Mathematics is a free invention of human intellect. Similarly, Sidhu ( 2002, pg.2) writes, “Mathematics is the numerical and calculation part of man’s life and knowledge. It helps the man to give exact interpretation to his ideas and conclusions. It deals with quantitative facts and relationship as well as with problems involving space and form. Thus, mathematics as an expression of the human mind and reflects the active will the contemplative reason, and desire for aesthetic perfection. Mathematicians seek out patterns and formulate new conjunctives. Mathematician reside the truth or falsity of conjunctives by Mathematical proof”.

Basnet, D.B. (2003 pg.3) writes, “Mathematics has been used throughout the world as an essential tool in many fields, including natural science, engineering, medicine and social science. Applied mathematics (the branch of mathematics concerned with application of mathematical knowledge to other field) inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new mathematical discipline such as statistics and a game theory”.

Similarly, Gautam, D. (2005 pg.2) writes, “Mathematics also engages pure mathematics or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, and practical application for what began as pure mathematics are often discovered. Mathematics and mathematics education are too separate disciplines in the field of education. Mathematics primarily focuses on the process and products of

1 what mathematician does. This is the obstruction of thinking and process as mathematician applies in creating mathematics. The focus of mathematics in on creating mathematics with understanding is its basic structure. It does not give much concern about the mathematics should be thought, who can learn mathematics and why one cannot learn mathematics like issues. Mathematics education deals with mathematics from prospective of education. It is concerned with the development and implementation of appropriate curriculum and with all issues associated with the teaching and learning mathematics. Mathematics education covers the learners of all ages and at all levels from early childhood to adult. Thus, mathematics education is not solely concerned with curriculum, classrooms teachers and learners in school, nevertheless issues associated with school mathematics will be a major focus. The areas of mathematics education are curriculum, teaching, learning, and education. Five foundations:- Philosophy, Psychology, Sociology, Mathematics and technology guide, these are the areas. Improvement of school mathematics education is the primary concern of mathematics education, but it does not mean that it is limited to school education. What mathematics, what teaching methods and what learning strategies for the students of higher education would be appropriate are also the area of mathematics education. Hence, mathematics education is an applied discipline that deals with the wider application of mathematics is different sectors and fields”.

“The main objective of mathematics education is to prepare well-qualified mathematics teachers in both methods and contents. Mathematics education is the synthesis of what (content) and how (method). A mathematics education cannot afford the luxury of being a student of subject matter only, or students of the process transmitting subject matter only. We cannot concern ourselves with one of these to exclusion of the other. We must concern ourselves with both the process and product, the how of teaching and what of teaching.

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Geometry is one of the most useful and important branch of mathematics. Geometry includes an enormous range of ideas and can be viewed in many different ways. It has been interlocked with many other subjects and different views of human activity. The basic ideas of mathematics system originated in geometry some 22 or 23 hundred years ago” (Kelly & Ladd, 1989). Furthermore, Kelly & Ladd writes, “It is not certain who first had the ideas of typing to prove mathematics rule by reasoning rather than typing to prove it in different cases. Although both Thales (640-546 BC) and Pythagoras (Born 572 BC) have been given credit for the idea, originated in Greece around the sixth century BC, once the idea of this mathematical method has been discovered or invented the mathematics of geometry grew with astonishing speed. By 300 BC, a large body of geometric knowledge was in existence. At this time, the mathematician Euclid brought together and unified this knowledge by constructing the first definite, formal system of mathematics in his treaties ‘The Element’. It is probable that ‘Euclid’s Elements’ is highly successful of earlier writers; Euclid’s Element is not devoted theory and geometric algebra. The work is composed of 13 books with 465 propositions (Eves, 1986)”.

Geometry concerned with the properties of configurations of geometric objects, points, lines and circles. The word ‘Geometry’ is derived from the Greek word ‘Geomertorn’ that means geo (Earth) and metron (Measure), which points to its practical roots. According to Oxford Advanced Learners Dictionary (7th Ed.) ‘Geometry is the branch of mathematics that deals with the measurement and relationships of lines, angles, surfaces and solids. Similarly, Pandit (2002, pg3) noted, “Geometry is the growing body knowledge with ever widening applications and inherent beauty in its systematic structure and organization”.

Furthermore, shorting the importance of geometry, Malkevith(1998) writes, “Geometry considered a tool for understanding, describing, and interacting with the space in which we live , in perhaps the most intuitive, concrete and reality linked part of mathematics. On the on hand geometry as discipline, rest

3 on an expensive formulization process which has been carried out for over 2000 years at increasing levels of rigor, abstraction and generally thus, geometry is the best means of stimulating the spirit of inquiry and intuition. It is one of the most universal and useful tool in all parts of mathematics. It is also vital catalyst for effective use or study of any branch of mathematics”.

In Nepal, Mathematics has been taught as one of the major subjects in secondary education since the beginning of modern education. Secondary education level general mathematics has three components: Arithmetic, Algebra, and Geometry. In the past, these three components of mathematics taught separately. Now, there are more than these three areas such as Arithmetic, Algebra, Geometry, Trigonometry, Statics and Linear Programming.

“School mathematics curricula of Nepal have given emphasis on Geometry learning from beginning of school. The curricula aimed at developing students understanding of intended geometric concepts at primary, lower secondary and secondary level” (Luitel, 2005 pg.4). Similarly, according to NCTM, “geometry is one of the content standards of school mathematics, which aims at developing spatial reasoning, problem solving skills, and communication”. Moreover, about the important of thinking skills in geometry, A vision for School Geometry (2005) writes, “reasoning is fundamental to mathematical activity. Active learners question, examine conjecture and experiment. Mathematics programs should provide reasoning skills. Learners need varied experiences to construct arguments in problems settings and to evaluate the arguments of others” (VSG, 2005). Furthermore, MALATI believes “Geometry offers an excellent context for learners to experience, mathematical activity and that can be done at primary and secondary levels (Smith, 1997)”. Thus, geometry is regarded as a core content area of school mathematics program. It is the most important and integral part of school mathematics curricula.

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Showing the importance of geometry, Vance (1973) writes, “it is a way of modeling our physical environment and because there is a great abundance of models suitable for all levels, from kinder garden through graduate school. Geometry is a natural vehicle for developing intuition, creativity and a spirit of inquiry. Furthermore, geometry is a fertile source for interesting and challenging problems and geometrical methods are powerful tools in problems solving”.

Schacht (1996) put this idea in this way; perhaps the most important value of geometry for all students is the experience they get in building a logical system of thought. Learning to use correct reasoning in solving geometric problems should help to improve thinking habit generally. Similarly, Koman at al. (1986) characterized the place of geometry as uniting and making more precise all the objective approaches to mathematical knowledge. The geometry, therefore, plays a significant role in school mathematics. Moreover, it is our belief that geometry teaching for school students should be based on psychological, theoretical and practical considerations. Therefore, it is important that the subject matter presented to the pupils should be attractive and interesting to them. The content and methods of work in geometry should be influenced bye some practical motives.

Supporting this idea, Chernysheva et al. (1986) states “Geometry has many aspects which are directly linked with the school syllabus. Geometry plays a significant role in applied science, in technology and in production. It is geometric theory that it most likely to prove to be the best tool for the development of children’s logical thinking. School geometry becomes the focal point for developing the student’s scientific and theoretical thinking”.

The school geometry should be studied not only as a set of useful facts, but as a scientific system. Thus, to teach geometry effectively, teaches need to know the child’s spatial environment (Bishop, 1980) and they need to develop their skills

5 in geometry not only for future use in teaching but also as aids to their own study of mathematics. They particularly need to understand and to capitalize upon the interrelations among the several areas of mathematics. Furthermore, secondary school teachers need to develop each of the five basic skills in geometry. (Visual, verbal, drawing, logical, applied) at each of the five levels of mental development (recognition, analysis, ordering, deduction & rigor). (Meserve, 1986). Therefore, the prospective secondary school teachers need to broad preparation in teaching geometry. Thus, the geometry teachers should have sufficient background for teaching geometry.

However, the teachers of our secondary schools are troubled because most students have wrong impression about the geometry and dislike geometrical activities. There is sorts of hesitation for learning geometry in them. Therefore, the teachers have great problems to motivate the students in geometrical activities (Koirala, 1981). Furthermore, many high school teachers can attest to the difficulties they have teaching geometry of deductive nature. Despite the best efforts of teachers, learners continue to have difficulty with deduction and proof. Many learners simply memorize proofs or rules (VSG 2005)

Thus, no area of secondary school mathematics curriculum has received more critical study than has the geometry program (Albert, 1958). As a result, mortality is high school geometry has been high and this has been ascribed to various causes. Some have left it has been due to hardness of subject. Still some thinks, ‘students lose interest in geometry because of its abstract nature, which they regard as having no practical value. Admittedly, demonstrative geometry is not the easy subject to learn. It demands careful and sustained attention, perseverance, and measure of ingenuity. In order to attain real mystery of it most students have to do some hard work (Butter & Klren, 1965)

Furthermost, describing the real reason of the failure in growth, Butler & Klren (1965) writes, “there is however good reason to believe that in most cases that

6 real reason for much of the failure in geometry an a apathy towards the subject lies mainly in poor motivation and failure to provide clear insight in to the meaning and method of subject. Probably much of the unsatisfactory work in geometry and the dissatisfaction with the students views of the subject can the traced to the fact that it has not been taught to then in such a way as to excite their curiosity and present them with an intellectual challenge but just as a rather dull job to be done”.

Supporting this idea, CERID (1988) states, “most of the teaching in secondary school consists of lecturing, role memorization and group reciting. Students interaction and question answer technique are rarely practical little opportunity is provided for independent study, laboratory experience, community study, working with ones hand and son on. The causes responsible for this state of affairs are mostly connected with lack training among the teachers, large class size in urban areas and poor physical facilities in rural schools”. (CERID, 1986)

Therefore, it should be admitted that the present day of teaching mathematics (geometry) is far from being satisfactory. Everybody has complains about the teaching of mathematics. It is dull boring, difficult and useless from the point of view of learners. It is too remote from the interest of the student (Sidhu, 2002). About the issues of geometry, teaching and learning, Luitel (2005) has stated three major issues as, 1. Emphasis on learning Geometry 2. Conceptualization of Learning Geometry 3. Way of Teaching

Teaching is about the emphasis on learning geometry, he claims that the curricular objectives are insufficient to address the two aspects of the changing context. Firstly, the curricula do not have a focus on communication. Secondly, the curricula also lack on emphasis on spatial reasoning. He also suggests that communication in necessary to increase students reading, writing, discussing,

7 representing and modeling mathematics. In addition, spatial reasoning helps to develop the understating of every day application (e.g. reading maps, understanding 2D, 3D objects)

Next, thinking about the contextualization, he suggests contexts and relating instruction to the real life situation. In addition, in the third way of teaching, he claims that most of the Nepalese schools students have fewer chances to interact with their peer and teachers. They have to listen to the teacher’s idea. Furthermore, he claims that crowed classrooms are one of the major problems of implementing interactive teaching and learning situation.

Supporting this idea, Bhusal (2000, pg.6) states, “Most of Nepalese classrooms are characterized bye recitation, full hour lecture and passive participation by students and rote memorization and cramming for examination without any emphasis on other outcomes of education. ‘Teaching mathematics in Nepal is still characterized as the memorization of facts conveyed to students by the teachers. Teaching of geometry is not free from this rituality mode of instruction.

About the modern mathematics classrooms , Bhatic & Bhatia (1987) said that the teacher’s tools have long consisted of chalk, blackboard red pen and the text book. However, the today is to use demonstration models of various shapes and sized, slide ruler, overhead projector, drawing instrument, graph stencils measuring instruments, and many pictures, pamphlets, books and mathematics magazines. Films, slides, manipulative kits, teaching machines and computers are being used in teaching mathematics in modern classroom.

However, teaching and learning in Nepalese schools is totally based on textbooks since the students have been writing in formal nepali language it is difficult for those students who have other language speaking background than Napali. On the other hand, the teachers use the textbook as an ultimate means

8 of teaching that does not provide the opportunity of relating their learning with local context. Because of financial problems, Nepalese cannot procure and afford money to spend in materials and equipments. Some schools do not even have enough classrooms. A large number of students are packed in a small classroom. Thus, the crowed classroom is one of the major problems of implementing interactive teaching and learning situation. Classroom is not well-lighted and well-ventilated, physical facilities such as teachers salary, teaching materials, mathematical lab, computers and collection of low cost and no cost materials that are essential for teaching and learning activities are not organized properly by concerned agencies. A teacher is being faced such type of problems.

Statement of Problem The study will be concerned with the study of problems faced by secondary school mathematics teachers in teaching geometry. This study is focused on answering the following research questions.  What are the current problems in teaching geometry?

Significance of the Study

Mathematics is taught as an essential and important component of school curriculum. It has been taught as the compulsory subject at any level of school education program. Although mathematics has given an important place in curriculum of all levels of school education most of the students are found to be weak in mathematics. However it is felt that the most of the students dislike mathematics and afraid of it. The result of recent years of SLC examination has shown the most of failure are in math. There are some factors hindering student’s progress in this subject. On of the major factors may be the teacher’s problems in teaching geometry.

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Thus, the purpose of this study is to identify the levels and extents of problems faced by the teachers in teaching geometry. This study will contribute a lot of identify the problems and this help the teachers in teaching geometry. This study will contribute a lot to identify the problems and thus help the teacher to know their actual problem in teaching Geometry. This study may provide some logical and valuable information to the concerned to reform and improve the contents of mathematics subjects of secondary level.

Objectives of the study Main objectives of the study will be:  To identify the problems faced by the teachers while teaching geometry

Delimitation of the Study a) This study was concerned with only the problems faced by the secondary schools mathematics teachers in teaching geometry. b) The study was carried out only in private and public schools of Pokhara Municipality of Kaski District. c) For the study, one teacher was chosen from a school d) Data was generated through questionnaire.

Definition of terms

 Public School Public schools are those, which receive regular government logistic and financial support.  Private Schools

Private Schools are those schools, which are established by the individual or by the community, which does not receive government logistic and financial support.

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 Secondary School Mathematics Teachers

It refers to the teachers, who are teaching mathematics at the grade 9 and 10.

 Trained Teachers

The teachers who have bachelor’s degree in mathematics provided by MOE or NCED of authorized institution.

 Untrained Teachers

The teachers who have bachelors in any faculty of mathematics except education faculty or haven’t got ten-months special training provided by MOE or NCED or any authorized institution are defined as untrained teachers.

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Chapter-II REVIEW OF RELATED LITERATURE

Empirical Review The researcher tried to find out the literature on the topic that related to problems faced by mathematics teachers in teaching Geometry. Number of books, research reports, paper and other booklets can be found concerning with curriculum teaching materials, methods and so on. The researcher has reviewed some related literature as follows.

Butler and Wren (1965) believed that one of the major problems that confront the teacher of demonstration geometry is to teach the pupil to reason without reference to unestablished circumstantial evidence. Similarly, VSG (2005) writes many high schools teachers can attest to difficulties that they have in teaching geometry of the dedication nature. Further, he writes despite the best efforts of teachers, learners continue to have difficulty with deduction and proof.

Luitel (2005) mentioned that the crowded classroom is one of the major problems of implementing interactive teaching and learning situation in Nepalese schools. About the classroom situation of Nepalese Schools he writes the classroom was appropriate for thirty students, but there were more than fifty students thus it was difficult to listen to teachers from all sides of class.

According to Glaesser (1986), many failure in mathematics are due to inability to read and understanding the statements of the problem, furthermore Butler & Wren (1965) states the following problems in studying Geometry.

 Inability to read well and understand the meaning of theorems or problems clearly.  Inability to restate theorems or problems.

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 Failing to have background of geometrical information in well organized manner so that it could aid to facilate the search for theorems or postulates which might be helpful in given situations.  Not knowing how to get started.  Failing to justify each step in proofs.  Trying to memorize proofs, sometimes without understanding them.  Poor drawing or sketching of geometrical figures.  Drawing conclusions merely from the appearance of figures and diagrams.

Amatya (1978) did a comparative study on effectiveness of teaching mathematics with and without the use of instructional materials. He concluded that the achievement of students taught by using instructional materials is sufficiently higher than the achievement of the students taught without the instructional materials.

Maskey (1975) conducted a comparative study on “mathematics achievement of primary schools students under different class sizes. He has concluded that the students studying in small class size has higher achievement than the students do in large class size.

Bhusal (2000) did a research on “A study on the effectiveness of geometry using discovery module and expository module of teaching in secondary level”. He has concluded that discovery module of teaching was better than the expository module of teaching in Geometry.

In a study on “The problems faced by the Teachers in Kathmandu District in the Implementation of Mathematics Curriculum for Lower Secondary Schools”, Pathak (1986) concluded that most of the teachers of Kathmandu District have not been facing problems in selection and use of the instructional materials but they were facing problems in selecting proper evaluation devices.

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In the similar Study, Baral (2000) concluded that the objectives of curriculum seem to be idealistic; hence, they couldn’t be fulfilled in present context of mathematics teaching learning situations. He did find the textbook for this level as inadequate. He concluded that only paper pencil test was in use.

Lamichhane (2001) did a survey type research on “A Study of problems faces by Secondary Level Mathematics Teachers in Teaching Mathematics” in Kaski District. He concluded that several problems propped up in the eye of teachers such as inadequacies of text books and teachers guide book, lack of instructional materials, irrelevancy of teachers training, lack of supervisory help, lack of physical facilities etc. further, he concluded that the motivation to learn mathematics is poor in students.

In a similar study on ‘Teaching problems faced by mathematics teachers in existing curriculum of grade eight’ in Jhapa District, Basnet (2003) concluded that the teachers and students are facing many problems due to the lack of training, orientation, opportunity for the mathematics teachers in existing curriculum, inadequacy of textbooks, lack of teachers guide and reference books, lack o f large class, defective evaluation system and so on.

In the article “Improving Geometry Teaching, Dhulikhel Experience”, Luitel (2005) has indicated the three issues of geometry learning and teaching in Nepalese schools are; emphasis of geometry learning, contextualization of learning and change from traditional one-way classroom to two way interactive classrooms. Furthermore, he has discussed on four teaching strategies in order to improve geometry teaching and learning situations in Nepalese school such as group investment, writing in geometry, problem solving and use of locally available materials.

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Bhattan T. (2005) conducted the research on “A Study on Problems faced by the Mathematics students in Existing Curriculum”. He concluded that learning mathematics in Secondary level is distributed by so many factors such as lack of teachers involvement in curriculum planning, lack of referential and instructional facilities and aids, students weak background in subject matter, students defective promotion policy, no opportunity given to upgrade their knowledge and huge number of personnel problems of students and teachers are the main obstacles.

Pundit (1999) did the thesis on “A Study of attitude towards geometry”. He concluded that a positive attitude of secondary school students was found that teachers had negative attitude towards geometry

Sidhu (2002) has mentioned defects in the present day of teaching of mathematics as in the major heading like, teachers qualification, Teachers Burden, Teachers Salary, Teachers Attitude, lack of equipment, Method of Teaching, Rigor in Study, large class, Practical Aspect, mathematical language, syllabus, Text Books, The students, child-centre, Approach, Libraries and laboratories, Ban on Shortcut methods, Examinations etc.

After studying overall literature, researcher has found that no research has been done on the problems faced by secondary level matchematcis teachers in teaching geometry in Kaski district. So, an attempt to find out problems faced by the mathematics teachers in teaching geometry has been carried out.

Theoretical Framework

In this survey study, Likert scale has been applied to collect and analyze data for the questionnaire.

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Likert Scale

Many kinds of rating scales have been developed to measure attitudes directly (i.e. the person knows their attitude is being studied). The most widely used is the Likert Scale.

Likert (1932) developed the principle of measuring attitudes by asking people to respond to a series of statements about a topic, in terms of the extent to which they agree with them, and so tapping into the cognitive and affective components of attitudes.

Likert-type or frequency scales use fixed choice response formats and are designed to measure attitudes or opinions (Bowling 1997, Burns & Grove 1997). These ordinal scales measure levels of agreement/disagreement.

A Likert-type scale assumes that the strength/intensity of experience is linear, i.e. on a continuum from strongly agree to strongly disagree, and makes the assumption that attitudes can be measured. Respondents may be offered a choice of five to seven or even nine pre-coded responses with the neutral point being neither agree nor disagree.

In it final form, the Likert Scale is a five (or seven) point scale which is used to allow the individual to express how much they agree or disagree with a particular statement.

For example: I believe that ecological questions are the most important issues facing human beings today.

Strongly agree / agree / do not know / disagree / strongly disagree Each of the five (or seven) responses would have a numerical value, which would be used to measure the attitude under investigation. Likert Scales have the advantage that they do not expect a simple yes / no answer from the

16 respondent, but rather allow for degrees of opinion, and even no opinion at all. Therefore, quantitative data is obtained, which means that the data can be analyzed with relative ease. However, like all suveys, the validity of Likert Scale attitude measurement can be compromised due the social desirability. This means that individuals may lie to put themselves in a positive light. For example, if a likert scale was measuring discrimination, who would admit to being racist?

Offering anonymity on self-administered questionnaires should further reduce social pressure, and thus may likewise reduce social desirability bias. Paulhus (1984) found that more desirable personality characteristics were reported when people were asked to write their names, addresses and telephone numbers on their questionnaire than when they told not to put identifying information on the questionnaire. Examples of Likert Scales.

Agreement Frequency

 Strongly Agree  Very Frequently

 Agree  Frequently

 Undecided  Occasionally

 Disagree  Rarely

 Strongly Disagree  Never

Importance Likelihood

 Very Important  Almost Always True

 Important  Usually True

 Moderately Important  Occasionally True

 Of Little Importance  Usually Not True

 Unimportant  Almost Never True

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Analyzing data from a Likert Scale •Summarize using a median or a mode, the mode is probably the most suitable for easy interpretation. • Display the distribution of observations in a bar chart (it cannot be a histogram, because the data is not continuous).

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Chapter – III METHODAS AND PROCEDURES

Research methodology presents the logistics of study because it determines how the research becomes complete and systematic. The research design is survey, analytic, descriptive and comparative in nature. The study will be concerned with the study of problems faced by secondary level mathematics teachers in teaching Geometry. The major procedures that was followed in this study are,  Research Design  Population of the study  Sample of the study  Instrument  Validation of the study  Data collection procedure  Scoring procedure  Data analysis procedure

Research Design The ‘Descriptive Survey Method’ was adopted to conduct the study for the convenience. Using this method, more items can be asked and more flexible but factual information can be gathered

Population of the Study All the mathematics teachers who were teaching compulsory mathematics at Secondary Level of Kaski District were the population of the study. There were 251 secondary schools in the Kaski District, but for the convenience, researcher conducted the thesis in the city area (Pokhara Sub-metropolitan) of Kaski District. There were 90 secondary schools and among them 75 were private schools and 15 were public schools in Pokhara sub-metropolitan city

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Sample of the study

For the study, sixteen secondary mathematics teachers were selected from private and public schools. The sample of teachers were selected equally form public and private secondary schools i.e. 8 from public schools and 8 from private schools. Stratified random sampling method was adopted but at most two teachers were selected from a school and study has included schools situated in city areas of Pokhara municipality. Table: 1 describes the profile of teachers such as gender, academic qualification, types of schools, teacher’s training status, educational background and teaching experience etc.

Table: 1 describes the profile of teachers such as gender, academic qualification, types of schools, teacher’s training status, educational background and teaching experience etc. Table: 1 Detailed Sample Characteristics S.N. Sample Characteristics Numbers 1. Teacher’s Gender Male Teacher 16 Female Teacher 0 2. Types of School Private Schools 8 Public Schools 8 3. Academic Qualification Graduate 8 Master 8 4. Academic Background B Ed/M Ed 6 B Sc /M Sc 6 B A/MA 6 5. Academic Experience 1 to10 years 8 11 to 20 years 4 21 to30 years 4

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Instruments

Questionnaire will be the main tool of the study. The researcher developed the questionnaire with the help of supervisor. The questionnaire was constructed after the detail study of related geometry literatures, curriculum, documents, thesis etc. Before developing the questionnaire, the researcher consulted with supervisor, mathematics experts and experienced teachers. The questions of questionnaire were constructed in such a manner that they could find out the problems of teachers while teaching geometry. The questionnaire concluded various items related to the problems faced by the secondary level mathematics teachers in teaching geometry. The areas of problems related to students background characteristics, instructional problems, materials and methods, curriculum, textbook. Teacher’s professional development, problems related to school administration and student evaluation system are also included.

Reliability of questionnaire

Before finalizing the questionnaire, the items were piloted on some math teachers. The pilot test was done on five teachers. After piloting, correlation coefficient of each statement was calculated. Those answers of questions whose correlation coefficient was in between the range of 0.3 to 0.8 were termed as reliable. And those which were not in the range of 0.3 to 0.8 was rejected or modified.

The following statistical formula was adopted to calculate correlation coefficient. xy r    x 2  y 2 Where x=X- 푋 and y=Y-푌. The rank score 5, 4, 3, 2, 1 were indicated by X and teachers response was indicated by Y.

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Validation of questionnaire

The supervisor ensured the validation of questionnaire. Finally, questionnaire was prepared for the data collection.

Data Collection Procedure

Questionnaire was distributed to the secondary mathematics teachers to fill it. Ten days was provided to fill questionnaire. After ten days, researcher went to each teacher to collect properly filled questionnaire.

Scoring Procedure

For the analysis of items likert five point scale was adopted .respondent were requested to fill the questionnaire. Scores of 5,4,3,2,1 was `assigned to statements and which was for the words ‘Always’, ‘often’, ‘Sometimes’, ‘seldom (or rarely) and Never respectively. Similarly, weightage of 5,4,3,2,1 was assigned to the statement and which was for the words ‘strongly agree’, ‘agree’, ‘undecided’, ‘Disagree’, and ‘strongly Disagree’, respectively. For the statements opposing to this point of view, the items are scored in the opposite order. Mean weightage was calculated. Total score of five point Likert scale was 15, thus its average score is three. If the calculated mean is greater than three than it is concluded that the statement indicates the problem and if the mean is less than or equal to three, then it doesn’t indicate any problem. (Source: http://en.wikipedia.org/wiki/Likert_scale)

Data Analysis Procedure

The obtained data were analyzed and interpreted with the help of following statistical techniques. The mean weightage was used to locate the central position of the response to the statement of teachers as a whole in the rating scale. The formula for the mean weightage is:

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Total rank score of statement Mean Weightage = number of teacher′s response

The questionnaire consists of 62 items to the various problems as faced by the secondary school mathematics teachers in teaching geometry. The areas of problems studied were related to various student’s background characteristics, instruction in geometry due to poor student’s geometrical concepts, teaching geometry theorems, teaching aids, techniques, materials, and methods, geometry curriculum and textbooks, school’s administration, professional development of teachers and student’s evaluation techniques. Specially, the questionnaire was divided into ten sections. The first section of the questionnaire consisted of the items related to the personal bio-data such as name, age, gender, academic qualification, and school’s name, trained or untrained, length of teaching experience etc. of the teachers.

Each statement was studied in terms of whether the teacher’s problems are up to the index or not. If the calculated mean weightage is greater than three then it is assumed that the statement indicates the problems and it is strongly favorable to it. If the mean weightage is less or equal to three, than it doesn’t indicate the problem which is less favorable to the problem.

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Chapter-IV ANALYSIS AND INTERPRETATION

The data were collected for the study from sixteen school teachers working in the school of Pokhara municipality. The collected data were tabulated and analyzed according to the objectives of the study. The data obtained (See Appendix B) were statistically analyzed and interpreted by using statistical tool ‘mean weightage’. These data were calculated item wise and then area wise in the various problems faced by teachers related to students characteristics background ,instructional problems, teaching facilities, aids, materials, teachers professional development, curricular and text problems, school administration, and student evaluation system. The collected data were analyzed under the following headings, which correspond to the objectives of the study:

 Problems faced by teachers because of variation in student’s background  Problems related to instruction in geometry due to poor students geometrical concept  Problems while teaching geometrical theorems  Problems related to teaching aids, techniques, materials, and methods.  Problems related to geometry curriculum and text.  Problems related to school’s administration.  Problems related to professional development of the teachers.  Problems related to student’s evaluation techniques.

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Analysis and Interpretation of Teacher’s Response on Problems related to student Various Background Characteristics

Table: 2

Teacher’s Problems due to Students’ Various Background Characteristics 1. What problems have you faced while teaching Secondary Level Geometry regarding student’s classroom activities?

S.N. Response Number MW remarks Statements Always Often Seldom Rarely Never 1 Difficulties in Classroom 3 10 1 2 0 3.87 favorable management because of student’s individual differences, different intellectual abilities and age. 2 Difficulty on teaching geometry 2 7 5 1 1 3.5 favorable because of difference in social, cultural , and family environment of students 3 Difficulty to involve both male and 0 3 7 5 1 2.75 Unfavorable female students equally in teaching learning activities.

4 Problems in understanding 5 6 3 2 0 4.25 favorable geometrical words translated in English and Nepali language to students whose mother tongues are other than Napali. 5 Problems in teaching geometry due to 5 8 2 1 0 3.56 favorable poor geometrical background of students at primary and lower secondary level. 6 Difficulty in managing classroom 4 2 4 4 2 3.12 favorable teaching learning activities due to large size of class 7 Difficulty in motivating students due 4 9 0 3 0 3.87 favorable to passiveness on reasoning & creative thinking. Total 3.56 favorable Note MW= Mean Weightage Favorable = there is problem of teachers on the respective statement Unfavorable= there is no problem of teachers on the respective statement

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Problems related to student’s various background characteristics have been categorized into seven different items to identify the response of teachers. For the convenience of analysis towards the response, mean weightage for each item has been calculated. The mean weightage of the statement, ‘teaching learning management due to variables of age, individual differences, and intelligence of students is 3.87 that indicates problem. Variation in socio- cultural and family environment of student has been a problem for teachers. Mean weightage value of this statement is 3.5, which clearly indicates the problem. The mean weightage of the statement ‘problems in understanding geometrical words translated in English and Nepali language to students whose mother tongues are other than Napali’ is 4.25, which clearly indicates the problem. During the research, majority of teachers claimed about the students poor background on the Geometrical concept at primary and lower secondary level. Mean of this statement is 4.35, which strongly shows the problem on the statement. Similarly, for the statement of large class size classrooms and passiveness of students of students on reasoning and creative thinking in geometry class have become challenging problems on implementing interactive teaching and learning. Mean values on these categories 3.125 and 3.875 respectively show the problem. However, mean weightage response 2.75 for gender difference has indicated the less significance over the problem. Table:1 summarizes the overall problems of teachers due to student’s various background characteristics and the total mean of all seven items is 3.56 which indicates that the teachers are facing problems on students various background characteristics.

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Analysis and Interpretation of Teacher’s response on the Problems of Instruction

Table:3 Problems of Instruction while Teaching Geometry at Secondary Level

What are the problems related to students learning in teaching geometry?

S.N Statements Always Often Seldom Rarely Never MW remarks 1 Problem in understanding 4 6 4 2 0 3.87 Favorable while teaching new concepts, facts, relations or skills to students 2 Problems on assimilation in 1 9 3 3 0 3.5 Favorable teaching new concepts, facts, relations or skills to students 3 Difficulty in teaching for 4 1 10 0 1 3.43 favorable transfer of knowledge, skills, concepts and relations learnt once by students. 4 Problems in teaching for 5 7 1 3 0 3.875 Favorable Permanence of geometrical knowledge skills, relations, facts and concepts learnt by students Total 3.67 Favorable

Teacher’s problem on instruction is divided in to four items. Above table shows that most of the teachers were facing significant problems on understanding in teaching new concepts, facts, relations or skills. Mean weightage response on this statement is 3.75, which indicates the problem. Similarly, mean score of second statement ‘problems on assimilating new concepts, relations or skills to the students’ is 3.5 which shows the problem. The mean weightage of third statement ‘transfer of knowledge’, and fourth statement ‘teaching for permanence’ has the average values 3.43 and 3.87 respectively indicates the problem. Table: 3 presents the four basic problems of instructions and teachers responses over these problems while teaching

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Secondary Level Geometry. The total mean of all four items of this table is 3.67, which indicates that teachers are facing problems in instruction.

Analysis and Interpretation of Teachers Response on Problems While Teaching Geometrical Theorem

Table: 4 Problems due to Student’s Learning Trouble in Proving Geometrical Theorem 2. What are the problems you have faced because of students in teaching geometry theorem at secondary school? S.N Statements Always Often Seldom Rarely Never MW Remarks 1 Inability of students 3 7 2 4 0 3.56 Favorable to read well and to understand clearly about the new geometrical terms, concept and vocabulary 2 Failing to understand 2 6 4 4 0 3.37 Favorable terms and definitions of Geometrical shapes completely 3 Students failing reuse 3 10 3 0 0 4.0 Favorable geometrical terms, definitions, axioms, postulates and already proved statements that are needed to prove 4 Students failing to 0 7 6 3 0 3.25 Favorable arrange and to justify each step in a proof 5 Inability of students 5 6 4 0 1 3.81 Favorable to identify the given part and prove part from statement of the theorem Total 3.59 Favorable

The teacher’s problems while teaching geometrical theorem is divided into five sections. The mean weightage of the statement ‘Inability of students to read

28 well and to understand clearly about the new geometrical terms, concept and vocabulary’ is 3.56 which indicates the problem. Similarly, mean value 3.37 refers that students are even failing to understand the definition of geometrical terms and shapes. The mean score of the statement ‘Students failing reuse geometrical terms, definitions, axioms, postulates and already proved statements that are needed to prove’ is 4.0 which is little higher and clearly shows the problem of that statement. Likewise, the mean weightage value 3.25 indicates the problem on student’s inability to arrange and to justify each step in the proof. According to mean value 3.18, students are unable to identify the given and poof part of the theorem or problem. Table:4 illustrates the teachers response on problems due to student’s learning difficulties in teaching of Geometry Theorem. The total mean weightage of all items is 3.59, which indicates that teachers are facing problems in teaching of geometrical theorems.

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Analysis and Interpretation of Teachers Response on the Use of Devices and Techniques of Teaching Table:5 Problems on Devices and Techniques of Teaching 3. What are the educational techniques you use in teaching geometry described as follows? S.N Statement Always Often Seldom Rarely Never MW Remarks 1 Extensive 0 11 3 2 0 2.43 Unfavorable use of teaching materials 2 Make the 6 5 3 1 1 2.12 Unfavorable students do oral question answers. 3 To engage 1 13 2 0 0 2.06 Unfavorable students on their class work as well as homework. 4 Review of 0 4 10 1 1 2.93 Unfavorable important chapter or topics 5 Make the 1 5 7 2 1 2.81 Unfavorable students do group discussion and interaction in class Total 2.47 Unfavorable

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In the study of this topic, the items are divided into five sections and it has been found that the results doesn’t show the problems to each statement. Mean score 2.43 indicates that the teachers are using teaching materials sufficiently. The mean score of the statement ‘Make the students do oral question answers’ is 2.12 which doesn’t indicate the problem. Similarly, mean value 2.06 shows that teachers are able to engage the students on their homework as well as class work. The, mean value 2.93 showing the review of important chapters is satisfactory and in the case of group discussion and interaction in class, the mean value 2.81shows the satisfactory result. Summary on problems related to use of device and techniques of teaching is shown in above table:

Analysis and Interpretation of Teachers Response on the Problems in Instructional Materials

To make teaching learning process effective and fruitful, use of instructional materials are indispensable. There are so many instructional materials used in Geometry teaching which is mainly categorized in to three different kinds; lecture, audiovisual aids, and models and manipulative materials. These materials can be used in classroom to facilitate teaching learning situation. Instructional materials are strong weapon to motivate the class. Thus, to improve the geometry teaching, all sorts of instructional materials should be adopted. Different teaching tools and materials can be used to make the teaching effective. To generalize the text on material it can be further sub divided into two categories: Locally available and Modern-Ready made materials.

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Use of Locally Available Materials

Table:6 Problems on Using Teaching Materials 4. What are the local teaching materials you have constructed and used among following? S.N Questionnaire Always Often Seldom Rarely Never MW Remarks 1 Graph Board 0 4 9 1 2 3.06 favorable 2 Geo Board 0 2 9 3 2 3.31 favorable 3 Meter Scale 12 3 1 0 0 1.31 Unfavorable 4 Set Square 13 2 1 0 0 1.25 Unfavorable 5 Paper Folding 0 6 4 4 2 3.12 favorable 6 Mechno Strip (model made 0 1 1 7 6 4.18 favorable from wood, Bamboo which can rotate, fold or separate according to need) Total 2.70 Unfavorable

Form the table, it has been found that teachers are not using Graph board sufficiently which is indicated by the Mean weightage 3.06. Mostly used materials are meter scale, geo-board, paper folding, setsquare. The use of Graph board, Paper folding and Mechano Strip is very few. The mean scores on the use of Geo-board, meter scale, set square, and paper folding are 3.31, 1.31, 1.25 and 3.12 respectively which indicates the less use of paper folding and geo-board and excessive use of set square and meter scale . However considerable problems on the use of Machno strip, Geo-board, Graph board has been found. The mean weightage response of teachers on the use of Mechno- strip is 4.18, which is very high showing the problems on using such instrument. In general, it seems that there is no satisfactory result in the use of teaching materials. The mean score (in total) of all materials of this category is 2.70.

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Problems related to construct Locally Available Instructional Materials

Table: 7 Problems in Constructing Locally Available Materials 5. What problems have you faced while constructing and using local teaching materials? SN Statement Always Often Seldom Rarely Never MW Remarks 1 Lack of time to 5 4 7 0 0 3.87 Favorable construct 2 Problems to construct 0 10 4 2 0 3.62 Favorable and collect lesson wise appropriate materials. 3 It is difficult to 1 12 0 2 1 3.62 Favorable complete the whole course using teaching materials. 4 Raw materials aren’t 2 6 2 3 3 3.06 Favorable easily available 5 Difficulty and boring 9 2 4 0 1 4.12 Favorable to construct 6 Difficulty to control 0 7 4 2 3 3.06 Favorable classroom and management while using materials Total 3.55 favorable

Effective teaching needs instructional materials, and lesson planning. However, teachers cannot invest adequate time for these necessities. During the study, it has been found that most of teachers are unable to give more time to construct teaching materials. Mean weightage respondent for this statement is 3.87 that show the strong favor on the problem. Mean value 3.62 shows that most of the teachers have indicated the problem on appropriate material collection according to the need of lesson. On the other hand, if they go on preparing materials themselves along with the lesson, it takes more time for completing

33 the course. Mean weightage 3.62 of the respondent reveals this fact showing the favor on the problem. The mean score 3.06 for the statement ‘Raw materials aren’t easily available’ indicates the problem of the teachers for not getting raw materials easily. Similarly, according to their views, construction of such materials is much boring and difficult too. Mean score 4.12 clearly shows this fact. In addition, some teachers believe that there will be little difficulty in controlling the class with use of materials. Mean weightage 3.06 clearly indicates that most of the teachers find difficulty in controlling the class if they use materials while teaching. The average mean weightage of all items of this topic is 3.55 and from which it can be concluded that teachers are having problems in constructing Locally Available Instructional Materials.

Use of Modern and Readymade Instructional Materials Table: 8 Problem on Using Modern and Readymade Materials 6. How do you have used modern and readymade materials while teaching geometry among given? S.N Statements Always Often Seldom Rarely Never MW Remarks

1 Geometry Box 12 4 0 0 0 1.25 Unfavorable 2 Computer (Geodraw 0 0 0 16 5.0 favorable programme, Proof, Checker programme) 3 Overhead Projector 0 0 0 0 16 5.0 favorable 4 Charts, Graphs, 0 6 4 3 3 3.18 Unfavorable Maps, Posters etc. Total 3.60 favorable

Electronic technologies such as calculators, computers, and overhead projectors are essential tools for teaching, learning and doing mathematics. The concern of the study was to identify the availability and adequacy of materials such as geometry box, computer software program (e.g., Geo Draw, Proof checker), overhead projector, and mathematical literature in the school.

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From the above table: 8, it has been found that most of the teachers use geometry box. Mean weightage value 1.25 indicates that there is no problem in the use of geometry box in geometry teaching. Beside this, none of them had used computer software and overhead projector in teaching geometry. The mean weightage value 5.0 and 5.0 respectively shows that teachers have problem in using computers and overhead projectors in their class. Similarly, mean score 3.18 indicating that use of graphs, Maps, Charts, and Posters etc is not satisfactory. The mean weightage respondent as whole on these statement is 3.60 that reflects the less use of Modern and Readymade instructional materials. The fabove table:8 represents the overall situation on the use of modern and readymade teaching materials.

Problems in Using Modern Methods Table:9 Problem in using Modern Methods 8. What problems have you been facing on using modern methods in teaching geometry beside usually used lecture and demonstration methods? S.N statements Always Often Seldom Rarely Never MW Remarks 1 Lack of opportunity for 6 8 1 1 0 4.18 favorable training 2 Lack of time 2 9 4 0 1 3.687 favorable 3 Confusion on methods to 0 5 7 4 0 3.062 favorable be used due to different knowledge level of students, in different chapter 4 Lack of help from 3 2 3 10 0 3.25 favorable school administration Total 3.54 favorable

According to respondents comment on teaching methods it is found most of them are using only lecture and demonstration methods. It means that there is problem on using modern methods .From the above table: 9, the mean weightage for the statement ‘Lack of opportunity for training’ is 4.18 which

35 indicates that teacher’s problem of not getting opportunity for teacher’s training. The mean weightage for the statement ‘lack of time on adopting new methods’ is 3.68, which indicates the problem of teachers. Mean score 3.062 for the statement ‘problems on using new methods’ shows the clear problem in that statement. The mean weightage of lack of help from school administration is 3.25 that indicate the problem of not getting help from school administration. And total mean score is 3.54 which indicates the problem of teachers in using modern methods. Table: 9 summarizes the overall situation of this category.

Analysis and Interpretation of Teachers Response on Problems Related to Curriculum and Textbook Table: 10 Problems Related to Curriculum and Textbooks 9. What difficulties have you been faced while teaching secondary school geometry? S.N Statements Strongly Agree undecided disagree Strongly MW Remarks agree disagree 1 Geometry syllables 2 8 6 0 0 3.75 favorable is not practicable according to need of time 2 Geometry syllables 3 7 3 3 0 3.62 favorable don’t care about concern, interest, needs etc of learners. 3 Students are not 5 7 2 1 0 3.90 favorable able to implement the knowledge skill, concepts, and relations in practice. 4 Syllables don’t 0 5 8 3 0 3.31 favorable match according to age, standard, ability, interest, and needs of students. Total 3.645 Favorable

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In this topic, the items are divided into four sections. The mean weightage for the statement ‘Geometry syllables is not practicable according to need of time’ is 3.75 which indicates the problem on impracticability of geometry curriculum. Similarly, mean score 3.62 tells that they agree with the fact that geometry syllables do not care about concern, interest, needs of learners. According to the table many teachers have a view that students are not fully able to implement the knowledge, skills, concepts and relations they learnt in practice (see mean score 3.90). And most of them think syllables don’t even match according to age, standard, ability, interest and needs of students (see mean score3.31). The total mean weightage of all statements is 3.645 which indicates the problem of teachers in curriculum and textbook.

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Analysis and Interpretation of Teachers Response on School Administration Problem

Table: 11 Problems Related To School Administration 10. What problems have you been faced from school, and administration while teaching geometry?

S.N Statements Strongly agree undecided Strongly MW Remarks agree disagree disagree 1 Compulsion to take more 2 5 4 5 0 3.25 favorable classes because of low number of mathematics teachers

2 Irresponsible administration 2 6 3 5 0 3.93 favorable to manage and construct necessary teaching materials.

3 Lack of refreshment to teach 2 9 2 3 0 3.62 favorable difficult and rigor topic

4 Lack of facilities and award 10 4 1 1 0 4.43 favorable for the good performance

5 Unavailability of curriculum 1 6 7 2 0 3.37 favorable and teachers guide on time

6 Lack of mathematics 7 8 1 0 0 4.37 favorable laboratory in school

7 Unavailability of 6 3 7 0 0 3.93 favorable mathematical journals, dissertation and new books

Total 3.84 favorable

School administration plays a vital role for the professional development of teachers and for collection and construction of necessary instructional

38 materials. Above table: 11 shows that mean weightage respondent for the statement ‘Compulsion to take more classes because of low number of mathematics teachers’ is 3.25 indicating the problem of teachers. Similarly, mean score 3.93 express that teachers are facing problem because of irresponsible administration to manage and construct necessary teaching materials. Refreshment training for difficult and rigor topics to foster a good education is a factor to improve the quality of education. But the mean score 3.62 for the statement shows that teachers are not getting such refreshment trainings. To encourage them, good facilities and awards for good performance on their respective subjects should be provided. However, according to their response for the statement ‘Lack of facilities and award for the good performance’, it seems they are not given such facilities. Mean score for this statement from the table is 4.43, which indicates the problem. The most interesting finding during the study none of the schools have mathematical laboratory. Mean weightage response for the statement ‘Lack of mathematics laboratory in school’ is 4.37, which shows this as a problem of geometry. Similarly, teachers indicated they were facing problems of unavailability of curriculum and teacher’s guide as well as mathematical journal, dissertation, new books and references. The mean score for these two statements are 3.37 and 3.93 respectively, which indicates the problems on those statements. The total mean weightage of all statements is 3.84, which indicates the problem of teachers concerned with school administration.

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Analysis and Interpretation of Teachers Response on Problems Related to Professional Development

Table: 12 Problem Related to professional Development of Teachers 11. What are the professional problems in teaching geometry beyond your access? SN Questionnaire Strongly agree undecided Strongly MW Remarks agree disagree disagree 1 Lack of training 0 13 2 0 0 3.75 favorable opportunity

2 Lack of 0 13 2 0 1 3.56 favorable information about the new instructional techniques and invention 3 Lack of time to 4 8 2 2 0 3.87 favorable study about related literature 4 Lack of 3 10 2 1 0 3.93 favorable opportunity to participate on interaction workshops related to subject matter 5 Lack of 5 4 4 2 1 3.62 favorable opportunity for higher study Total 3.74 favorable

Generally, professional development is regarded as teacher development. From the above table, it had been found that most of teachers were facing problem on professional development. Mean weightage response of the professional development of teachers is 3.747 that signify the problem. Teachers accepted on lacking training opportunities to update their knowledge and skills. Mean

40 weightage response 3.75 on this statement shows the problem of teachers. Nepal is a developing country, so it is difficult to develop and to innovate new instructive techniques itself. However, teachers are also far from access of new instructive techniques. On the statement ‘Lack of information about the new instructional techniques and invention’ asked by researcher, mean weightage response is 3.56, which indicates the problem. Sometimes teachers cannot manage the time to read related literature, so teachers do not have confident while teaching. The mean weightage response for the statement ‘Lack of time to study about related literature’ researcher is 3.87 which shows the problem of teachers of not getting time for the study of related literature. Likewise, teachers had accepted that they don’t have opportunity to participate on interactions, workshops etc to become skilled. The mean weightage 3.93 indicates the strong favor on the problem. Most of the Nepalese teachers are poor in their economical status. So, they are not getting opportunity for higher education to develop rooted knowledge on subject matter. Mean weightage response on this statement is 3.625 indicating the problem of teacher. The total mean weightage of all statements is 3.74 which indicates the problem of teachers related to their professional development.

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Analysis and Interpretation of Teachers Response on Problems Related to Students Evaluation. Table: 13 Problems Related to Students Evaluation 12. What problems have you been faced on students evaluation in teaching geometry? S.N Questionnaire Strongly agree undecided Strongly MW Remarks agree disagree disagree 1 Lack of 2 13 1 0 0 4.06 favorable interaction between guardians and subject teacher about the educational improvement of students 2 Interest not shown 0 12 4 0 0 3.75 favorable by school about interaction with guardians on the achievement of students 3 Lack of personal 1 8 6 1 0 3.56 favorable interest on student about the result of geometry with teachers. 4 Lack of approach 5 6 2 2 1 3.75 favorable about the difficulty level of questions asked in exams. Total 3.78 favorable

This topic is divided into four sections. Most of the teachers claimed that guardians are not willing to interact with the subject teachers about the mathematical achievement of their children. The mean weightage response on the statement ‘Lack of interaction between guardians and subject teacher about the educational improvement of students’ is 4.06, which shows the problem. Similarly, the mean score of the statement ‘Interest not shown by school about

42 interaction with guardians on the achievement of students’ is 3.75 that indicates the teachers are facing problems because of school not showing the interest for the interaction with the guardians. Equally, lack of willingness on students to discuss about the poor result has been found as a problem during the research. The mean weightage for the statement ‘Lack of personal interest on student about the result of geometry with teachers’ is 3.56, which indicates the problem faced by the teachers. It is found that concerned authorities are not sincere to analyze the difficulty level and modify the questions yet. The average response on the statement ’Lack of approach about the difficulty level of questions asked in exams’ is 3.75 and because of this teachers are facing problems in student’s evaluation. Table:13 summarizes the whole situation of problems on students evaluation. The overall Mean weightage response of teachers on students evaluation is 3.78. This indicates that teachers are facing problems in student’s evaluation.

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Chapter-V

SUMMARY, CONCLUSION AND RECOMMENDATION

This chapter deals with the summary, major findings, conclusion and recommendations.

Summary The purpose of the study was to identify of problems faced by mathematics teachers in teaching geometry at secondary level. The objectives of this study were to find out the problems faced by teachers due to various background characteristics of students, to identify the problems related to instruction in geometry in the process of teaching and learning, to identify the problems while teaching geometrical theorems, to identify problems related to teaching aids, techniques, materials and methods, to find out the problems concerned with curriculum and text book, to identify the problems related to professional development of teachers, to find out the problems related to students evaluation techniques.

For the convenience of the study, the problems were categorized into different eight areas viz. student’s various background characteristics, instructional, teaching aids, techniques, materials, methods, curriculum, school administration, teacher’s professional development and student’s evaluation techniques.

This study was entirely survey type. The researcher himself developed the questionnaire under the guidance of supervisor. Before collecting the data, the researcher conducted a pilot study on five mathematics teachers to test the reliability of the questionnaire. The collected data were quantified based on Likert-five point scales. After pilot study, correlation of each statement of the questionnaire was calculated, some questions were modified, and some

44 rejected. The questionnaire was the main tool of study. The data were collected from different secondary school mathematics teachers. The teachers were selected from the sample schools where sample schools were selected by using stratified sampling method. Open questionnaire were included in each category of problems and descriptive analysis of collected response were carried out. Statistical indicator the mean weightage was used for analysis of the problem.

After research, it was found that the teacher’s problems were mainly on student’s various background characteristics, teaching aids, techniques, materials, methods, mathematics curriculum and textbook, school administration, teacher’s professional development and student’s evaluation techniques.

Major Findings

From the field survey and statistical analysis of the collected data, it was found that teachers have been facing numerous problems during the course of teaching Geometry. On the basis of analysis and interpretation of data, the findings of this study are presented below.

Problems related to student’s Various Background Characteristics

The findings of the problems related to student’s various background characteristics are presented below.  Difficulties in Classroom management because of student’s individual differences, different intellectual abilities and age  Difficulty on teaching geometry because of difference in social, cultural , and family environment of students  Problems in understanding geometrical words translated in English and Nepali language to students whose mother tongues are other than Napali.

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 Problems in teaching geometry due to poor geometrical background of students at primary and lower secondary level.  Difficulty in the process of motivation due to passiveness on reasoning and creative thinking at primary and lower secondary level of students  Difficulty in managing classroom teaching learning activities due to large size of class

Problems Related to Geometry Instruction in the Class

The findings of the problems related to geometry instruction to geometry instruction in class are presented below in hierchacial order:  Problems on understanding in teaching new concepts, facts, relations or skills to the students  Problems on assimilation in teaching new concepts, facts, relations or skills to students  Difficulty in transfer of knowledge, skills, concepts and relations learnt once by students  Problems in permanence of geometrical knowledge, skills, relations, and concepts learnt by students

Problems Related to teaching Geometry Theorem

The findings of the problems related to teaching geometry theorem are presented below in hierchacial order:  Inability of students to read well and to understand clearly about the new geometrical term, concept and vocabulary  Students failing to understand terms and definition of Geometrical shapes completely  Students failing to reprocess geometrical terms, definitions, axioms, postulates, and already proved statements that are needed to prove

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 Students failing to arrange and to justify each step in a proof  Inability of students to identify the given and prove part from statement of the theorem.

Problems Related to Constructing and Using Locally Available Teaching Materials The findings of the problems related to construction and using locally available materials are presented below in hierchacial order:

Unavailability of time to construct  Problems on appropriate material construction and collection needed according to text  Necessary raw materials are not being available easily  Difficulty in completion of whole course if taught using teaching materials  Difficulty and boring to construct  Difficulty to control the classroom in order to teach geometry by using teaching materials.

Problems Related in Using Modern and Readymade Instructional Materials

The findings of the problems related to using modern and readymade instructional materials are presented below in hierchacial order:  Teachers are not using any modern and readymade instructional materials except geometry box, graphs and charts  Most of the teachers are unknown about modern instructional materials like computer, overhead projector etc.

Thus, it is concluded that there are problems in using such modern and readymade instructional materials.

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Problems related to Using Modern Methods and Techniques

From the research, it was found that most of the teachers are using only lecture and demonstration methods (chalks and talks method). The main reasons behind this were:  Lack of opportunity for trainings for the teachers  Lack of time for the implantation of new methods and techniques of teaching  Lack of help from the school administration in implementation of such modern methods of teaching

Problems Related to Curriculum and Texts The major findings on problems related to curriculum and text are:

 Syllables not matching according to age, standard, ability, interest, and needs of students.  Students are not able to implement the knowledge skill, concepts, and relations in practice.  Geometry syllables not caring about concern, interest, needs etc of learners.  Geometry syllables is not practicable according to need of time

Problems Related to School’s Administration

The major findings on problems related to school’s administration are  Compulsion to take more classes because of low number of mathematics teachers  Irresponsible administration to manage and construct necessary teaching materials  Lack of refreshment to teach difficult and rigor topic  Lack of facilities and award for the good performance

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 Unavailability of curriculum and teachers guide on time  No mathematics laboratory in school  Unavailability of mathematical journals, dissertation and new books

Problems Related to Teacher’s Professional Development

The findings of the problems related to teacher’s professional development are presented below in hierchacial order:  Lack of opportunity to participate on interactions, workshops related to subject matter  Lack of information about the new instructional techniques and invention  Lack of training opportunity  Lack of time to study about related literature  Lack of opportunity for higher study

Problems Related to Student’s Evaluation Techniques

The findings of the problems related to student’s evaluation techniques are presented below in hierchacial order:  Lack of interaction between guardians and subject teacher about the Geometrical achievement  Lack of approach to analyze difficulty level of Geometrical question asked in exams  School not showing interest about interaction with guardians on the achievement of students  Lack of personal interest on student about the result of geometry with teachers

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Conclusion

Findings of this study that geometry teaching and learning is not satisfactory in Kaski district. Among the eight different categories described above, it is found that teachers don’t have significant problems on applying educational techniques and using locally available materials. Among the remaining categories, most of teachers have faced problems in various way. The problems are presented in order: ● Problem related to student’s evaluation techniques ● Problems related to Geometry Instruction ● Problems related to teacher’s professional development ● Problems related to Constructing and using instructional materials ● Problems related to school’s administration ● Problems related to student’s various background characteristics ● Problems related to curriculum and texts

It was found that both trained and untrained teachers have been facing more or less similar problems. On the same way, Public as well as private school teachers are facing almost similar kinds of problems.

Moreover, problems have arisen due to student’s poor Geometrical background. Geometry being abstract subject, thus students has less interest in it. Teachers don’t have access to modern teaching techniques, methods, and materials. Geometry teaching seems to be exam centered rather than practical oriented. Conceptually negative attitude towards the geometry has become a major psychological problem. Most of students think that they can pass math easily only preparing algebra and arithmetic. Geometry itself is comparatively difficult subject and it demands more practice and devotion from the learners. Crowed classrooms, student’s negative attitude to memorize theorems and proofs, hurried and carelessness and untidy written works and rote memorization are the major student centered problems. Similarly, crowed

50 classroom has become a problem for both teachers and students while implementing interactive teaching and learning situation.

Recommendations

On the basis of findings, the researcher concludes that the following measures would help to improve the teaching learning situation of geometry.  Time to time modern and refreshment trainings and orientation should be provided to teachers.  School administration should gather students, teachers and guardians for open interaction so that problems can be identified easily.  The curriculum designer, teachers and authors must consider the new techniques of geometry teaching like methodologies advocated by the Van Hiele’s model while designing the geometry course especially in the phase of learning.  The contents and methods of work should be influenced by some practical motives.  A lot of feedback should be provided for students as they learn to construct proof.  Evaluation system should be more precise and scientific.  Geometry teaching should be based on psychological, theoretical, and practical consideration.  The aim of teaching theoretical geometry should be centered to give idea of logical proofs of accuracy and clear reasoning.

Recommendations for Further study From the study, it has been concluded that there are various problems faced by the teachers in teaching geometry at secondary level, so same study can be made in lower secondary and primary level. Similar studies are essential in Algebra, Arithmetic and other subjects to modify the curriculum of secondary school. Similar studies can be carried out in regional or national level.

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REFERENCES

A Vision for school Geometry (2005), www.google.com Albert, E & Meder, J. (1958).’Whats Wrong with Euclid?’ Mathematics Teachers,51 Amatya, B.P. (1978).‘An Effectiveness of Teaching Mathematics with and without the use of Instructional Materials’. Master’s thesis, Department Of Mathematics Education, TU. Bhatia,B.D. &K.Bhatia(1987), ‘The Principle and Methods of Teaching’, New Delhi, Doba House, Book sellers and Publishers. Basnet, D.B. (2003), ‘A Study Of Problems Faced By the Mathematics Teachers in Existing Curriculum of Grade Eight’, Master’s thesis, Department Of Mathematics Education Bechan Mahato (2006),’ Analysis of Compulsory Mathematics Textbook of Secondary Level’, Master’s thesis, Department Of Mathematics Education, T.U. Bhattarai, T. (2005), ‘A Study of Problems Faced By the Secondary Level Mathematics Students in Exiting Curriculum’, Master’s thesis, Department Of Mathematics Education Bhusal, I.P. (2000), ‘A Study of Effectiveness of Teaching Geometry using Discovery Module and Expository Model ’, Master’s thesis, Department of Mathematics Education,T.U. Budathoki, T.B. (2004), ‘Effectiveness of Cooperative Learning Method in Teaching. Mathematics Education (Geometry in School)’, Volume 5, edited by Robert Moris Butler,C. H. , Wern, F.C. &Banks, J. h. (1970) ‘The Teaching of Secondary School Mathematics’New York; McGrawl-Hill. CDC (1999), ‘Secondary School Curriculum’, Kathmandu: HMG/Nepal, Ministry of Education

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Chaulagain, Raj Kumar, ‘A Study of Problem Faced by Secondary School Mathematics Teachers in Teaching Geometry’, Master’s thesis, Department of Mathematics Education T.U Gautam, D. (2005), ‘Effectiveness of Instructional Materials in Teaching Menstruation at Secondary Level’, Master’s thesis, Department of Mathematics Education, T.U. Hornby, A.S. (2005), Oxford Advanced Learner’s Dictionary Of Current English, (Seventh Edition) Oxford University Press. Likert scale- Wikipedia, the free encyclopedia: http://en.wikipedia.org/wiki/Likert_scale Koirala H.P., ‘Identification of Geometrical Concepts Needed for Perspective Secondary School Teachers’, an Master’s thesis, Department of Mathematics Education T.U Koman, ‘Some Problems Concering Teaching Geometry to Pupils Age to 10- 14’, Studies in Mathematic Education (Geometry in School), Volume 5, edited by Robert Moris Lamichhane, H. (2001), ‘A study of problems faced by the secondary level mathematics teachers in teaching mathematics’, Master’s thesis, Department of Mathematics Education T.U Luitel , B. C. (2005) Improving Geometry Teaching Dulikhel Experience. Retrieved on June, 2005 from proquest database. Malkevitch , J. (1998),Finding Room In The Curriculum For Recent Geometry, Mammana C & Villain, V. (Eds), ‘Perspectives on the Teaching of Geometry for the 21st Centaury’, 18-24 Dordrecht Kluwer Meserve, B.E & Mesaeve, D.T (1986), ‘Teacher Education and the Teaching of Geometry Studies in Mathematics Education (Geometry in School)’, Volume 5, Edited by Roberts Moris. NCTM, (2000), ‘Teaching Mathematics’. Upadhaya, H.P (2004). Kathmandu Ratna Pustak Bhandar.

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Pandit, E.R. (1999), ‘A Study of Problems Faced by The Mathematics Teachers Towards Geometry’. Master’s thesis, Department of Mathematics Education T.U. Pandit R.P. (2001), ’A Study Of Problems Faced By The Mathematics Teachers Educators In The Implementation of Three Years B.Ed. Level Mathematics Curriculum In Nepal .An Education and Development CERID. Pandit, R.P (2002),’Geometry for Teachers’, Kathmandu: Rananta Prakashan Nepal Sachacht, J.F. et al. (1962), ‘Contemporary Geometry’, New York: Holt Rinechart and Winston INC. Sidhu, K.S. (2000), ‘The Teaching Mathematics’ New Delhi: Sterling Publishers Pvt. Ltd Fourth Edition. Smith, C.R. (1997), 'what do we want from school geometry?’ presentation at the MALATV/EMSSEP Geometry think shop, University Of Stellenbosch Thapa (2005), ‘Problems Faced by the Teachers in Teaching Mathematic at Primary Level ’, Master’s thesis, Department of Mathematics Education T.U Upadahya, H.P (2004),’Teaching Mathematics’, Kathmandu: Ratna Pustak Bhandar, Nepal www.helpingforever.com/secschool.html www.deokaski.gov.np/files_e/page.php

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Appendix A (I)

Detailed description of name of schools and teachers

Name of the Public Schools Location 1.Bhadrakali Higher Secondary Kundhar-13, Pokhara School 2.Kalika Higher Secondary School Rambazar-10, Pokhara 3.Balmandir Secondary School Nadipur-3 Pokhara 4.Nabin Higher Secondary School Gairapatan Pokhara 5.Amarsingh Higher Secondary Ramghat, Pokhara School 6.Shree Rameshowary Secondary Majheripatan, POkhra School 7.Janapriya Higher Secondary School Simal Chaur 8.Rastriya Higher Secondary School Tundikhel, Pokhara

Name of Private Schools Location 1.Pragati Higher Secondary School Batulechaur,Pokhara 2.Gandaki Boarding School Lamchaur, Pokhara 3.Pashchimanchal Higher Secondary Gairapatan, Pokhara School 4.Tarakung Secondary School Patan Besi, Pokhara 5.Prativa Secondary School Nadipur, Pokhara 6.Jyotikung Secondary Boarding Rambazar, Pokhara School 7.San Francisco Channedada, Pokhara 8. National Inventive Pardi, Pokhara

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Appendix A (II)

Name of Qualification Sex Teaching Status of Public School Experience Training Teachers 1.Ghanashyam M Sc Male 21 years Trained Rijal 2.Laxmi Kanta BA Male 21 years Trained Adhikari 3.Bishnu Mani I Sc, B Ed Male 17 years Trained Lamichhane 4.Narayan M Ed Male 7 years Trained Kumar Shrestha 5.Buddhi Man M Ed Male 22 years Trained Giri 6.Krishna B Ed Male 14 years Trained Acharya 7.Indra Thapa MA, B Sc, B Male 20 years Trained Ed 8.Bed Psd Osti M Ed Male 21 years Trained

Name of Qualification Sex Teaching Status of Private School Experience Training Teachers 1. Dhaneshwor M Sc Male 3 years Untrained Bhandari 2. Shree Ram M Sc Male 16 years Trained Adhikari 3.Basnet BA Male 4 years Untrained 4.Nawaraj B Sc Male 3 years Untrained Dhakal 5. Pravat K.C. B.A. Male 3 Years Untrained 6.Sunil B Sc Male 5 years Untrained Neupane 7.Pravat K.C. B.A. Male 2 years Untrained 8.Jagadis M.A. Male 5 years Untrained Pageni

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Appendix B

Dear Teachers,

I am going to conduct a thesis research entitled on ‘A Study of Problems faced by Secondary School Mathematics Teachers Geometry’ for the partial fulfillment of Master Degree of Education in Mathematics. Teaching-Learning activity could not be effective without addressing the real and factual problems of teachers related to teaching activities. Therefore, to complete this thesis I have prepared some questionnaires which are presented to you. Researcher is very much thankful for your valuable help, and would like to express gratitude to you all. Thanking you.

Researcher Saroj Thapa M.Ed. Department of Mathematics Education

I request to fill this questionnaire as follow:  Please read well and responses as you feel and tick(√) in the box for your answer.  For open questionnaire, please write your opinion.  Please don’t leave blank for any questions.  In this study, the teachers who have bachelor’s degree in mathematics education or have a ten months special training provided by MOE or NCED or authorized institution, are defined as trained teachers  Public schools are those which receive regular government logistic and financial support.  Private schools are established by the individual or by the community, which do not receive regular government logistic and financial support.

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Questionnaire for the pilot study Teacher’s Bio-Data Form Name: Sex: Age: Name of the school: Public ( ) Private: ( ) Academic Qualification: Academic of Teaching Experience: Trained ( ) Untrained ( ) Questionnaire on the Problems Faced by Secondary Level Teachers While Teaching Geometry. 1. What problems have you faced while teaching Secondary Level Geometry regarding student’s classroom activities? S.N Statements Correlation Remarks coefficient 1 Difficulty in Classroom management because of student’s 0.68 individual differences, different intellectual abilities and age. 2 Difficulty on teaching geometry because of difference in 0.65 social, cultural , and family environment of students

3 Difficulty to involve both male and female students 0.68 equally in teaching learning activities.

4 Difficulty to participate lower social class students groups 0.23 Rejected in teaching activities

5 Problems in understanding geometrical words translated in 0.47 English and Nepali language to students whose mother tongues are other than Napali.

6 Problems in teaching geometry due to poor geometrical 0.32 background of students at primary and lower secondary level. 7 Difficulty in managing classroom teaching learning 0.63 activities due to large size of class

8 Difficulty in motivating students due to passiveness on 0.67 reasoning & creative thinking.

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2. What are the problems related to students learning in teaching geometry S.N Questionnaire Correlation remarks coefficient 1 Problems in teaching geometrical new concepts, relations, 0.60 skills and understanding to students. 2 Problems in making students able to assimilate new 0.64 geometrical concepts, facts, relations or skills by understanding themselves. 3 Difficulty in transfer of knowledge, skills, concepts and 0.75 relations learnt by students. 4 Problems in permanence of geometrical knowledge skills, 0.67 relations, and concepts learnt by students.

3. What are the educational techniques you use in teaching geometry described as follows? S.N Questionnaire Correlation Remarks coefficient 1 Extensive use of teaching materials 0.53 2 Make the students do oral question answers. 0.49 3 To engage students on their class work as well as 0.67 homework. 4 Review of important chapter or topics 0.78 5 Make the students do group discussion and interaction 0.63 in class

2. What are the problems you have faced because of students in teaching geometry theorem at secondary school? S.N Questionnaire Correlation remarks coefficient 1 Students inability to understand new vocabulary and terms 0.61

2 Student’s inability to understand definition of geometrical 0.62 shapes and terms completely. 3 Student’s inability to reuse geometrical terms, postulates, and 0.65 already proved statements.

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4 Student’s inability to arrange facts and reasons in order while 0.72 doing theorem. 5 Student’s inability to identify the given part and prove part from 0.63 statement of problem. 4. What are the local teaching materials you have constructed and used among following? S.N Questionnaire Correlation Remarks coefficient 1 Flatten board 0.25 modified 2 Geo Board 0.47 3 Meter Scale 0.67 4 Set Square 0.69 5 Paper Folding 0.63 6 Mechno Strip (model made from wood, Bamboo which can 0.62 rotate, fold or separate according to need)

5. What problems have you faced while constructing and using local teaching materials? S.N Questionnaire Correlation Remarks coefficient 1 Lack of time to construct materials. 0.67

2 Problems to construct and collect lesson wise appropriate 0.61 materials.

3 It is difficult to complete the whole course using teaching 0.65 materials.

4 Raw materials aren’t easily available 0.49

5 Difficulty and boring to construct 0.54

6 Difficulty to control classroom and management while using 0.57 materials

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6. How do you have used modern and readymade materials while teaching geometry among given? S.N Questionnaire Correlation Remark coefficient 1 Geometry Box 0.75

2 Computer (Geodraw programme, Proof, Checker 0.69 programme)

3 Overhead Projector 0.62

4 Charts, Graphs, Maps, Posters etc. 0.57

7. What problems have you been faced on using modern methods in teaching geometry beside usually used lecture and demonstration methods? S.N Questionnaire Correlation Remarks coefficient 1 Lack of opportunity for training 0.47 2 Lack of time 0.56 3 Confusion on methods to be used due to different knowledge 0.68 level of students, in different chapter 4 Lack of help from school administration 0.62

8. What difficulties have you been faced while teaching secondary school geometry? S.N. Questionnaire Correlation Remarks coefficient 1 Geometry syllables is not practicable according to need 0.75 of time 2 Geometry syllables do not care about concern, interest, 0.62 needs etc of learners. 3 Students are not able to implement the knowledge skill, 0.61 concepts, and relations in practice. 4 Syllables don’t match according to age, standard, 0.60 ability, interest, and needs of students.

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9. What problems have you been faced from school, and administration while teaching geometry? S.N Questionnaire Correlation Remarks coefficient 1 Compulsion to take more classes because of low 0.67 number of mathematics teachers 2 Irresponsible administration to manage and construct 0.45 necessary teaching materials. 3 Lack of refreshment to teach difficult and rigor topic 0.69 4 Lack of facilities and award for the good performance 0.64 5 Unavailability of curriculum and teachers guide on 0.71 time 6 no mathematicis laboratory in school 0.76 7 Unavailability of mathematical journals, dissertation 0.73 and new books

10. What are the professional problems in teaching geometry beyond your access? S.N Questionnaire Correlation Remarks coefficient 1 Lack of training opportunity 0.75 2 Lack of information about the new instructional 0.56 techniques and invention 3 Lack of time to study about related literature 0.74 4 Lack of opportunity to participate on interaction 0.45 workshops related to subject matter 5 Lack of opportunity for higher study 0.62

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11. What problems have you been faced on students evaluation in teaching geometry? S.N Questionnaire Correlation Remarks coefficient 1 Lack of interaction between guardians and subject 0.43 teacher about the educational improvement of students 2 Interest not shown by school about interaction with 0.46 guardians on the achievement of students 3 Lack of personal interest on student about the result of 0.56 geometry with teachers 4 Lack of opportunity to teachers for interaction with 0.27 rejected guardians and students about the achievement of geometry 5 Lack of approach about the difficulty level of questions 0.63 asked in exams

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Appendix C

Final Questionnaire

1. What problems have you faced while teaching Secondary Level Geometry regarding student’s classroom activities? S.N Questionnaire Always Often Seldom Rarely Never 1 Difficulty in Classroom management because of student’s individual differences, different intellectual abilities and age. 2 Difficulty on teaching geometry because of difference in social, cultural , and family environment of students 3 Difficulty to involve both male and female students equally in teaching learning activities. 4 Problems in understanding geometrical words translated in English and Nepali language to students whose mother tongues are other than Nepali. 5 Problems in teaching geometry due to poor geometrical background of students at primary and lower secondary level. 6 Difficulty in managing classroom teaching learning activities due to large size of class 7 Difficulty in motivating students due to passiveness on reasoning & creative thinking.

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2. What are the problems related to students learning in teaching geometry? S.N Questionnaire Always Often Seldom Rarely Never 1 Problems in teaching geometrical new concepts, relations, skills and understanding to students. 2 Problems in making students able to assimilate new geometrical concepts, facts, relations or skills by understanding themselves. 3 Difficulty in transfer of knowledge, skills, concepts and relations learnt by students. 4 Problems in permanence of geometrical knowledge skills, relations, and concepts learnt by students.

3. What are the educational techniques you use in teaching geometry described as follows? S.N Questionnaire Always Often Seldom Rarely Never 1 Extensive use of teaching materials 2 Make the students do oral question answers. 3 To engage students on their class work as well as homework. 4 Review of important chapter or topics 5 Make the students do group discussion and interaction in class

4. What are the problems you have faced because of students in teaching geometry theorem at secondary school? S.N Questionnaire Always Often Seldom Rarely Never 1 Students inability to understand new

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vocabulary and terms 2 Student’s inability to understand definition of geometrical shapes and terms completely. 3 Student’s inability to reuse geometrical terms, postulates, and already proved statements. 4 Student’s inability to arrange facts and reasons in order while doing theorem. 5 Student’s inability to identify the given part and prove part from statement of problem.

12. What are the local teaching materials you have constructed and used among following? S.N Questionnaire Always Often Seldom Rarely Never 1 Graph board 2 Geo Board 3 Meter Scale 4 Set Square 5 Paper Folding 6 Mechno Strip (model made from wood, Bamboo which can rotate, fold or separate according to need)

13. What problems have you faced while constructing and using local teaching materials? S.N Questionnaire Always Often Seldom Rarely Never 1 Lack of time to construct materials. 2 Problems to construct and collect lesson wise appropriate materials. 3 It is difficult to complete the whole course using teaching materials. 4 Raw materials aren’t easily available 5 Difficulty and boring to construct

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6 Difficulty to control classroom and management while using materials

14. How do you have used modern and readymade materials while teaching geometry among given? S.N Questionnaire Always Often Seldom Rarely Never 1 Geometry Box 2 Computer (Geodraw programme, Proof, Checker programme) 3 Overhead Projector 4 Charts, Graphs, Maps, Posters etc.

15. What problems have you been faced on using modern methods in teaching geometry beside usually used lecture and demonstration methods?

S.N Questionnaire Always Often Seldom Rarely Never 1 Lack of opportunity for training 2 Lack of time 3 Confusion on methods to be used due to different knowledge level of students, in different chapter 4 Lack of help from school administration 16. What difficulties have you been faced while teaching secondary school geometry?

S.N. Questionnaire Strongly agree undecided Strongly agree disagree disagree 1 Geometry syllables is not practicable according to need of time 2 Geometry syllables don’t care about concern, interest, needs etc of learners. 3 Students are not able to implement the knowledge skill, concepts, and relations in practice.

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4 Syllables don’t match according to age, standard, ability, interest, and needs of students.

17. What problems have you been faced from school, and administration while teaching geometry? S.N Questionnaire Strongly agree undecided Strongly agree disagree disagree 1 Compulsion to take more classes because of low number of mathematics teachers 2 Irresponsible administration to manage and construct necessary teaching materials. 3 Lack of refreshment to teach difficult and rigor topic 4 Lack of facilities and award for the good performance 5 Unavailability of curriculum and teachers guide on time 6 no mathematics laboratory in school 7 Unavailability of mathematical journals, dissertation and new books

18. What are the professional problems in teaching geometry beyond your access?

S.N Questionnaire Strongly agree undecided Strongly agree disagree disagree 1 Lack of training opportunity 2 Lack of information about the new instructional techniques and invention 3 Lack of time to study about related literature 4 Lack of opportunity to participate on interaction workshops related to subject matter 5 Lack of opportunity for higher study

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19. What problems have you been faced on students evaluation in teaching geometry? S.N Questionnaire Strongly agree undecided Strongly agree disagree disagree 1 Lack of interaction between guardians and subject teacher about the educational improvement of students 2 Interest not shown by school about interaction with guardians on the achievement of students 3 Lack of personal interest on student about the result of geometry with teachers 4 Lack of opportunity to teachers for interaction with guardians and students about the achievement of geometry 5 Lack of approach about the difficulty level of questions asked in exams

20. How geometry teaching can be made effective in your opinion? Mention views on priority basis ...... …………………………………………………………………………… …………………………………………………………………

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APPENDIX D

Statistical formula

 xy Correlation coefficient ( )   x 2  y 2

where, x =X- 푋 and y=Y-푌.

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