Chapter one Introduction Background to the study Accomplished teachers use multiple paths to knowledge to help students learn and facilitate understanding. Such teachers know that students learn in different ways and use different modalities to take in information and demonstrate knowledge. In order to meet these needs, accomplished teachers use a variety of strategies and methods to ensure that all students have equal opportunities to learn (Clarke, 1989). Teaching in the twenty -first century faces many challenges.A proficient teacher should have a broad grounding and knowledge of the subject(s) to be taught. He should also know the skills to be developed, and the curricular arrangements and materials that organize and embody that content: knowledge of general and subject-specific methods for teaching and for evaluating student learning; knowledge of student and human development, skills in effectively teaching students from diverse backgrounds, and the skills, capacities and dispositions to employ such knowledge wisely in the interest of students (Allwright, 1990).Teachers are these days challenged to know and communicate their subject matter, design curriculum and instruction, and be knowledgeable about diverse student populations and effective uses of data and technology to conduct action research to improve their own practice and to implement existing research.
Gaining confidence in teaching and, for that matter, the teaching of mathematics takes time and requires goal -setting, reflection, dialogue and collaboration with students and colleagues. The two biggest challenges facing teachers are adequate planning and classroom management.Certainly, new teachers benefit from the wisdom of their experienced colleagues who are better able to integrate and draw connections between current, past and future learning and relate their content to other curricular areas.
They tend to be able to better use such classroom management skills as voice, gesture, improvisation, reading, student facial expressions, body language and proximity. They can use the picture in planning, anticipate problems and need for alternative plans. The teaching of mathematics in Ghanaian Senior Secondary Schools (SSS) seems to be a problem.This stems from the fact that either the children find it difficult to grasp some mathematical concepts or the teachers find it a problem getting the children to understand these basic concepts.
The problems that these students face may start from the Primary and the Junior Secondary Schools (JSS) where these concepts are sometimes not properly taught or made clear to the children. The problem may also be that some of the teachers who handle these students at those levels are untrained teachers who lack the right methodologies and, therefore, cannot get the children to understand what they teach most of the time.Another possible cause may be that although the teachers may be professionally trained, they do not expose the children to classroom situations that may help to facilitate the understanding of these concepts (for example, making the students handle improvised objects and finding other Teaching and Learning Materials (TLMS) to help bring out the real meaning of these concepts to them). Other factors like class organization, teacher’s relationship with students, the tradition and the academic tone of the school also affect teaching of mathematics either positively or negatively.The teaching and learning process has this time become student or learner-centred. The process should be such that the child is the focus and that everything that goes on during a lesson should centre on the child.
Modern methods of teaching and learning have created a conducive atmosphere in classroom situations where many opportunities have been placed at the disposal of the child to enhance his or her ability to understand the concepts.The onerous task now lies on the teacher who should explore every possible means to diversify his teaching and make it learner-centered by allowing the student to work with the relevant teaching and learning materials which will help make the lesson appear real to the student. This needs serious lesson preparation and the teacher has to make conscious efforts to prepare and use the relevant teaching and learning materials that will make the child understand the concepts to enable him or her to apply the principles with ease.The teaching of mathematics in the Senior Secondary Schools (SSS) notwithstanding the inherent problems can still be taught in a way which will make students understand the concepts and meaningfully apply the principles involved. The way out is how the teacher approaches his lessons, organizes his class, and his interaction with the pupils during the lesson. However, in spite of this and many roles mathematics play in the development of the country’s human resource, it is sad to note that, majority of students have not developed interest in the subject.A close study of the chief examiner’s report by the West African Examinations Council over the years has revealed that the general performance of students in mathematics is very poor. Unfortunately, in spite of the numerous benefits that made the learner-centered method as the best approach to the teaching and learning of the subject, many at times, teachers find nothing wrong with students behaving as passive listeners during mathematics lessons instead of being active participant.
Undoubtedly this has not only affected students but has also undermined the aims of the subject.Evidence of the Problem It was noted from the following that students’ participation in lessons involving the area of a trapezium was actually discouraging and their performance was not good. • Interview: When some students were interviewed on why the poor participation of students during mathematics lessons, they confirmed this observation. On their part, they did not have interest in the subject because they saw it to be very difficult.
• Observation: The researcher observed that during area of trapezium lessons, the students were very passive in the teaching and learning process. Class Exercises: In most of the class exercises involving the area of trapezium, students were scoring low marks (i. e.
1/10, 2/10, 3/10). • Assignments: Students performance was not different from class exercises and most at times they copy from each other. • Terminal Examinations: Students’ were scoring very low marks. Causes of the Problem: The researcher found out that low participation level of students during area of trapeziums lessons were as a result of the following: • The teacher was not using relevant improvised teaching and learning materials (TLMS) to enhance students understanding.
Students did not show any interest in the subject due to it being very abstract. • There was lack of interest in mathematics on the part of the students, due to a misconception that mathematics is a difficult subject reserved for brilliant students. The need for this action research came about as a result of the inability of some SSS 1 students of the Sunyani Secondary School to solve mathematical problems involving the area of trapeziums because they could not apply the concepts that they had already learnt.This was because the topic was taught without the use of relevant teaching and learning materials (TLMS), therefore, making it very abstract for students to understand. Statement of the Problem Understanding some basic concepts involving the area of trapeziums seem to be a problem to students at the Senior Secondary School (SSS) .
The situation whereby teachers teach some topics over and over again in the classroom but still do not get their children to understand has been a source of worry to teachers of mathematics and their students.It is a matter of fact that area plays important role in our daily lives and in mathematics learning too. Mereku (2004) revealed that 45. 5% of the teachers he interviewed were found to be teaching without Teaching Learning Materials. He further said that because of the infrequent use of Teaching Learning Materials and practical activities, pupils have little chance of asking questions. He found just about 17% of the teachers to have provided meaningful answers to pupils’ questions mainly because many of the teachers hardly engage pupils in activities, which will urge them to ask questions.
Surprisingly, most teachers in Sunyani Secondary school hardly make use of teaching learning materials when teaching. This had contributed immensely to students’ inability to find area of a trapezium Therefore, the researcher wants to try the use of relevant improvised teaching and learning materials (TLMS) in the teaching of mathematics in the school. The problem however is that the extent to which the use of relevant teaching and learning material can solve the problem identified is known yet. Purpose of the StudyMany students in Ghanaian Senior Secondary Schools (SSS) seem not to like mathematics as a subject which is on their curriculum. Much of students’ abysmal performance in both internal and external examinations may be linked to this dislike or fear of the subject. 1. The researcher intends to find ways that will improve teaching and learning of area of trapezium in the school.
2. It is envisaged that the study would enable the researcher to find the effects of using relevant improvised teaching and learning materials (TLMS) on the performance of students in mathematics. . The research is designed to enable teachers to focus on problems students encounter in the learning of area of trapezium and to solve the problem. It is also designed to help the students find the area of a trapezium through the use of Geoboard. Research Questions The pertinent questions that can direct this action research include the following: 1. To what extent does the use of relevant improvised teaching and learning materials (TLMS) help to improve students’ performance in finding the area of a trapezium? 2.How effective is the use of relevant teaching and learning materials (TLMS) in the learning of area of a trapezium? Significance of the Study The study, it is believed, will assist teachers of mathematics in the Senior Secondary Schools (SSS) to effectively teach mathematics to their students.
Having indepth knowledge in the use of relevant improvised teaching and learning materials (TLMS) in the teaching of mathematics in the Senior Secondary Schools (SSS) will help students to easily understand some basic concepts in mathematics and also help to improve on the performance of students in the subject.CHAPTER TWO REVIEW OF RELATED LITERATURE This chapter concerns itself with a review of related literature. The purpose of the review is to look at observations made by researchers and writers on the subject, varied teaching methodologies and improved teaching and learning materials (TLMS), especially in the teaching of mathematics. It also looks at the relevance of literature to this study and specific direction it can give to the researcher as regards the methodology, collection and analysis of data and final findings and recommendations of the study. The literature review concentrates on the following areas: . The essence of using Teaching and Learning Materials (TLMS). 2.
Characteristics and sources of TLMS 3. The role of Teaching and Learning Materials (TLMS) in relation to other elements. 4. Conclusion The Essence of Using Teaching and Learning Materials (TLMS) Mathematics instruction has five important components, namely; students, a teacher, materials, teaching methods and evaluation (Kitao, 1982). Farrant (1982) urged that net of these solids needed to be drawn in order to make understanding easier to students and make the lesson taught a bit practical.Devine, Olson and Olson (1991) suggested that introducing the concept of area, examples should be provided that include covering regions with squares and other units of area and filling of containers with cubes and units of volume.
They said that students should not be expected to learn these from books but they should develop procedures and formulas to determine area and by partitioning and rearranging figures. Mitchelmore and Raynor (1967) used diagrams to explain the concept of area.They drew a Trapezium and divided it into smaller squares. The squares were counted and the area of the trapezium was equal to the total number of the squares. Allwright (1990) argues that teaching and learning materials should teach students to learn, that they should be resource books for ideas and activities for instruction /learning and that they should give teachers rationales for what to do. From Allwright’s point of view, textbooks are also too flexible to be used directly as instructional material.O’Neil (1990) in contrast argues that materials may be suitable for students’ needs even if they are not designed specifically for them, that textbooks make it possible for students to review and prepare for their lessons.
According to him, textbooks are efficient in terms of time and money, and that they (i. e. textbooks) can and should allow for adaptation and improvisation. Allwright (1990) emphasizes that improvised teaching and learning materials control teaching and learning.O’Neil (1990) on his part says that improvised teaching and learning materials help in teaching and learning.
It is true that in many cases, teachers and students of mathematics rely heavily on text books, and textbooks determine the components and methods of learning. That is to say, they control the content, methods and procedures of learning. Students who learn mathematics according to O’Neil learn what is presented in textbooks and the way the textbook presents material is the way students learn it.The educational philosophy of the textbook will influence the class and the learning process. Therefore, in many cases, teaching and learning materials are the centre of instruction and one of the most important influences on what goes on in the classroom. According to Allwright (1990), theoretically, experienced teachers can teach mathematics without a textbook.
However, he stresses that it is not easy to do it all the time, though teachers may do it sometimes.Many teachers, he opines, do not have enough time to make supplementary materials and so they just follow the textbook. Characteristics and Sources of Teaching and Learning Materials (TLMS) Littlejohn and Windeatt (1989) argue that materials have a hidden curriculum that includes attitudes towards knowledge, attitudes toward teaching and learning, attitudes towards the role and relationship of the teacher and student, and the values and attitudes related to gender, society and others.Teaching and learning materials, according to them have an underlying instructional philosophy, approach, method and content whilst choices made in writing textbooks are based on the knowledge and experience writers have about mathematics and how it should be taught.
Clarke (1989) argues that communicative methodology is based on authenticity, realism, context and a focus on the learner. He however, argues that what constitutes these characteristics is not clearly defined, and that there are many aspects to each. He questions the extent to which these are reflected in textbooks that are intended to be communicative.In addition to publishers, there are many possible sources of teaching and learning materials. There are a lot on the internet. The library is also another good source.
Many mathematics teachers these days prepare improvised teaching and learning materials by using odd materials and rejected materials like empty milk and milo cans, cardboards and similar materials for such purpose. Television and radio are good sources. They provide a variety of materials. The information is current but the content has to be chosen carefully. Teachers can also take photos and make video tapes (Clarke, 1989).He concludes that both students and teachers of mathematics can browse the World Wide Web and search for useful materials for classes since there are lots of sources of materials and photos on the World Wide Web.
The Role of Materials in Relation to other Elements Since the end of 1970s, there has been a movement to make the learner rather than the teacher the centre of learning mathematics (Kitao, 1982). According to him, in this approach to teaching, the learners are more important than the teachers, materials, curriculum, methods or evaluation.As a matter of fact, the curriculum, teaching and learning materials, teaching methods and evaluation should be designed for learners and their needs. It is the teacher’s responsibility to check to see whether all of the elements of the learning process are working well for learners to adapt them if they are not. In other words, learners should be the centre of instruction and learning etc.
The role of teachers is to help learners to learn. Teachers have to follow the curriculum and also monitor the progress and needs of the students and finally evaluate students.Materials in this content include textbooks, video tapes, computer software and visual aids. They influence the content and procedures of learning. The choice of deductive versus inductive learning, the role of memorization, the use of creativity and problem-solving, and the order in which materials are presented are all influenced by materials.
Conclusion Writers like Allwright (1990) and O’Neil (1990) think that teaching and learning materials (TLMS) should teach students to learn. They believe that materials may be suitable for students’ needs even if they are not designed specifically for them.According to these writers, it is important that every teacher as part of his or her preparation should get enough teaching and learning materials which he will use to make learning easy.
The roles that varied teaching methods and the use of improvised teaching and learning materials play in the teaching and learning process have been highlighted in this review and their effects on teaching and learning should not be underestimated. It is the belief of these scholars that if these elements are used effectively, teaching and learning will undoubtedly be improved.From what have been discussed so far, one can also come out that it is more appropriate to use concrete materials to involve students in practical activities when introducing the concept of area to them. CHAPTER THREE METHODOLOGY This chapter is concerned with the description of the research method used for the study. It describes the various processes and procedures that were used to collect data and the method of analysis employed. The main areas considered comprise the research design, intervention, population, the sample and sampling techniques, research instrument, data collection procedure and method of data analysis used.
Research Design The design for the study employed is the Action Research. The Action Research was carried out at Sunyani Secondary School in the Sunyani Municipality of the Brong Ahafo Region. Action Research is done to solve an immediate problem in a specific situation.
Action Research results are situation- specific. Accordingly, all activities during the pre-intervention stage of the research were confined to Sunyani Secondary School. The post-intervention or evaluation stage was also carried out in the same school with the same instrument. Pre-InterventionResponses to the pre-intervention questionnaire revealing the use of improvised teaching and learning materials(TLMS) were received from the selected sample and analyzed, the views expressed were compared with; • The researchers own observation in the school and the results of the interview he had with Assistant Headmaster in charge of academic affairs of the school. • The three tests at the pre-intervention period conducted by the researcher to know the ability of the students. The relevant corrective measures deduced there from were implemented in the intervention period.Intervention During the intervention stage, information obtained from the pre-intervention findings was implemented. The objective was to improve students’ performance in finding the area of a trapezium through the use of relevant improvised teaching and learning materials (TLMS).
The following were some of the interventions: 1. The researcher taught the sampled classes using the guided discovery approach. The researcher employed this technique because studies have shown that students learn best when they are active rather than passive learners (Spikell, 1993).
The theory of multiple intelligence also addresses the different learning styles. Lessons are presented for visual, musical, logical interpersonal, intrapersonal and verbal and that everyone is capable of learning but may learn in different ways. 2.
The researcher during his teachings employed the use of teaching and learning materials (TLMS). The teaching and learning materials used were: • The Geoboard • Cut out shapes of solids • A cardboard and rubber band DESCRIPTION OF TEACHING AND LEARNING MATERIALS (TLMS) USEDThe Geoboard was used as a teaching and learning material (TLM) for teaching the area of a trapezium. According to Mereku et al (1994), the Geoboard provided a wealth of activities for learning about the area of trapezium. The Geoboard consisted of a square array of nails around which rubber bands were stretched to form various polygons.
It closely resembles the use of a dot paper or square paper but it was more concrete since the board was made of woods as shown in figure 1 below. 3. The learner-centered classroom which focused primarily on the individual student was used.The researcher’s (i.
e. teacher’s) role was to facilitate learning by utilizing the interests and unique needs of students as a guide for meaningful instructions. LESSON 1: Drawing of Solid Figures Using the Geoboard The researcher reviewed students’ knowledge on the area of a triangle. Students were grouped, with each group having at most four members. Each group was given the geoboard and the elastic band. Students were given enough time to explore the materials by drawing so many solid figures using the geoboard and the elastic band and then counting the number of squares in each figure.
The researcher went round and guided students to draw meaningful shapes. He led students to name the figures they drew through discussion and also through asking leading questions. Some of the students were called to draw some of the shapes on the chalkboard. Through the researcher’s discussion with students, the students became aware of the characteristics of a trapezium as a quadrilateral with only one pair of sides parallel. That is the base length and the top length.
By guiding the students they were able to identify trapezium from the shapes they drew and other cut-out shapes that were shown to them.The researcher enabled the students to become aware that the geoboard was an effective material for teaching the area of a trapezium. Through demonstrations, the students imitated how to use the Geoboard and the rubber bands to draw the shape of a trapezium.
They were guided by the researcher to draw trapezium using their Geoboard and rubber bands as shown in figure 2 below. FIGURE 2 The researcher then supervised and directed students’ activities. Students were guided to draw a diagonal from one end of the trapezium to the other so that the trapezium was seen as two triangles put together as shown in figure 3 below.FIGURE 3 The researcher then guided the students to draw the shape into their notebooks. LESSON 2: Finding the Area of Trapezium through Guided Discovery. Students were asked to join their various groups. Each group was given a cardboard paper and a pair of scissors. They were asked to look into their note books and draw similar shapes of the trapezium they drew during the last lesson on the cardboard paper given to them.
The researcher guided the students to cut out the shape drawn on the cardboard paper and labeled it as shown in figure 4 below. FIGURE 4The students were asked to cut out the trapezium through the diagonal into two parts so that two triangles were depicted as shown in figure 5 and 6. FIGURE 5 FIGURE 6 The activities were repeated for several times. The researcher guided the students to discover that the area of triangle ACD = [pic] and that of triangle ABC =[pic]. The researcher led the students to discover that the two triangles formed the trapezium and hence the area of the trapezium would just be adding the area of the triangles.The students were then guided to add the area of the two triangles as shown below.
Area of Trapezium = area of triangle ACD + area of triangle ABC. = [pic] = [pic] = [pic] Hence the concept was justified by telling the students that Area of Trapezium = [pic]height[pic]sum of lengths of parallel lines. Post- Intervention At the post-intervention stage, three tests were administered to evaluate the impact of the intervention introduced into the system of teaching and learning of the area of trapezium. Population for the StudyThe research was carried out at Sunyani Secondary School in the Sunyani Municipality of the Brong Ahafo Region of Ghana. The population for the study was made up of 5 classes out of the 10 SSS 1 classes of the Sunyani Secondary School, all mathematics teachers from these sampled classes, and the Assistant Headmaster in charge of academic affairs. The sampled classes had a population of 294 students. Out of the total population of 294, 187 were males and 107 were females as at the 2006/2007 academic year. The breakdown was as follows: Table 1 Breakdown of Student Population of Sampled Classes.
| | | | |CLASS |MALE |FEMALE |TOTAL | | | | | | |1 ARTS 1 |31 |24 |55 | | | | | | |1 ARTS 2 |34 |30 |64 | | | | | | |1 BUS. 1 |37 |21 |58 | | | | | | |1 BUS. |47 |15 |62 | | | | | | |1 AGRIC 1 |38 |17 |55 | | | | | | |TOTAL |187 |107 |294 | All the 4 teachers (all males), formed part of the teacher population.
The study is therefore, limited to the Sunyani Secondary School. The purposive sampling techniques were used in all the categories of the respondents.All the mathematics teachers who handled the students were selected because they were all subject teachers. Since the Assistant Headmaster in charge of academic affairs was also the person responsible for the students’ academic performance in all the subjects including mathematics, he was also selected for the vital role that he plays in the academic affairs of the school. Development of Instrument A structured interview comprising seven items was used. This sought to find out from the Assistant Headmaster in charge of academic affairs, the performance of the students in mathematics during internal and external examinations.
This interview was also conducted to find out the challenges that the students encountered in their learning of mathematics.Two categories of questionnaire consisting of 10 items each were also used to collect data from class teachers who taught mathematics and the students on the performance of students in mathematics, challenges the mathematics teachers faced in the teaching of the subject and ways to overcome those challenges. (A copy of the questionnaire is attached as appendices I, II and III) Administration of Instrument Most authors in research methods in education agree to circumstances that determine the choice of data collection instruments. Factors such as availability of time, cost, rate of recovery, purpose and type of research should be given the necessary consideration.The researcher had taught in the school for a period of three months. He had personal interviews with the Assistant Headmaster in charge of academic affairs whereas the class masters and students answered the questionnaire. The teachers were observed whilst they taught and separate tests were conducted to test students’ ability in selected topics in mathematics.
The researcher had two lessons with each class using relevant improvised teaching and learning materials (TLMS). Students were tested after every lesson and the exercises were marked to assess the performance of each of them. The results in every class test were recorded. All results were put together and analyzed.
With regard to the administration of the questionnaire, since the researcher was an intern at the selected school, he made prior arrangements with the Assistant Headmaster of the school and gave him the itinerary regarding the research and the type of data that he would be collecting on specific dates. Copies of the questionnaire were delivered to respondents (i. e. teachers and students) by hand and prior arrangements were made with the Assistant Headmaster in charge of academic before the researcher interviewed him.
Before the respondents answered the items, the researcher took his time to explain the essence of the research and the meaning of the items to them.This was to ensure that the teachers and students actually understood the individual questions. If the items were well understood, it would enhance reliability of responses. In order to ensure maximum return of copies of the questionnaire, the teachers and students were allowed time to respond as independently and frankly as possible to the items.
The copies of the questionnaire were collected after three days. This was to enable both teachers and students to have enough time to deliberate on the issues and bring out genuine opinions without unduly delaying the programme. In all, four copies of the questionnaire were given out to the teachers while the students had 294 copies.This meant that every student in the sampled class was given a copy each of the questionnaire. The students were also briefed. For example, they were informed that the researcher would be coming to conduct some mathematics lessons and assess them from time to time.
The researcher briefed the Headmaster, the Assistant Headmaster, teachers and students on the purpose of the study and also appealed to them for their cooperation. All this was done to ensure that the students, teachers and the headmaster understood the purpose of the research to enhance the reliability of the responses. In this way, the ethical implications of the research were satisfied.Method of Data Analysis In the first stage of data analysis, the data gathered from the questionnaire were edited. The completed questionnaire were serially numbered and considered one after the other. The major items were tabulated and frequency distribution tables were drawn from the various responses. The frequencies were then converted into percentages.
Percentages were used for the data analysis because they are simple to use and help in representing facts clearly. Since the study was an Action Research, during the second stage of the data analysis, the qualitative and quantitative analysis involving frequencies, percentages and means were used.The data for the pre-intervention period were compared to the data of the post-intervention period with regard to the use of improvised teaching and learning materials (TLMS) and the performance of the students in the selected topic. CHAPTER FOUR PRESENTATION, ANALYSIS AND DICUSSION OF DATA This chapter focuses on data presentation and analysis, the key findings and discussion of emerging issues. In general, the research aims at finding the effects of using relevant improvised teaching and learning materials (TLMS) in the teaching of the area of a trapezium to SSS 1 students of the Sunyani Secondary School (SUSEC).
It also aims at finding the challenges facing teachers and students in teaching and learning of mathematics as a subject at Sunyani Secondary School (SUSEC).Results of six tests that were conducted by the researcher during the pre-intervention and post-intervention periods were used. In all, three tests each were conducted at the pre-intervention and post intervention periods. Pre-Intervention Data Analysis of the Questionnaire. This deals with the analysis and interpretation of views and opinions of staff and students on the subject matter. The data under discussion were obtained from the staff and students’ responses to questionnaire administered during the pre-intervention stage of the research.
Male respondents outnumbered their female counterparts. Table 2 Categorization of Respondents by Gender |Male Female Total Number of | | |No. % No.
% Respondents | | | | |Staff |5 100 0 0 5 | | | | |Students |187 63. 6 107 36. 4 294 |Table 2 shows that the male respondents were 64. 2% and 35. 8% females for both staff and students respectively. Item 1 of the questionnaire for teachers tested the number of mathematics periods they have in a week.
Two of the teachers answered 25 periods and the other two answered 12periods a week. The two who answered 25 periods were permanent staff of the school while those who answered 12 periods were students on internship programme. (Please find the questionnaire for teachers as Appendix II) Item 2 was to find out whether the teachers taught with teaching and learning materials (TLMS), 3 of the teachers answered “No” and only one answered “Yes”.This result indicates that 75% of the SSS1 mathematics teachers did not use teaching and learning materials (TLMS) and that only 25% made use of them. Item 3, which was to find out when the teachers used the teaching and learning material was answered by the only teacher who answered yes to test item 2. He ticked “only at the beginning of the lesson” and this implies that he uses the teaching and learning materials (TLMS) only at the beginning of the lesson. Item 4 was on the number of exercises given to students by the teachers in a week and in this, one teacher answered 1-2 exercises, 2 answered 3-4 and one also answered 5-6.
This shows that 25% of the teachers gave 1-2 exercises, 50% gave 3-4 exercises whilst 25% gave whilst 5-6 exercises a week.Whether or not exercises were marked and discussed was what item 5 sought to find out. One teacher answered “Yes” and the other three answered “No”. Their opinion was that exercises were marked but there was not enough time to discuss them. This means that 75% did not discuss marked exercises with students whereas 25% of the teachers marked and discussed exercises with their students.
When asked about the performance of their students which was under item 6, 2 answered that their students were “average” students whilst two answered that their students were “good” students. This implies that 50% of the teachers thought that their students were average. The other 50% considered their students to be good.Whether or not the teachers faced challenges in the teaching of mathematics, their response was “Yes”.
This means that 100% of them encountered problems and challenges in the teaching of mathematics. Item 8 which required the teachers to state at least two of the challenges had the following responses from the teachers: Teacher 1 1. Students do not have the basic knowledge in mathematics. 2. Some students fail to do their assignments and exercises. Teacher 2 1.
Students do not study or practise mathematics on their own after lessons. 2. Some students fail to understand certain basic concepts.
Teacher 3 1. Students seem to put in less effort in the learning of mathematics. 2.The school has failed to provide the teachers of mathematics with teaching and learning materials (TLMS). Teacher 4 1. The large class sizes do not give teachers of mathematics the opportunity to tackle individual problem/s. 2.
Lack of teaching and learning materials (TLMs) makes it difficult for students to understand certain topics. As to how the teaching of mathematics in the school can be improved which was item 9, these were the responses from the teachers: Teacher 1 1. Class size should be reduced drastically. 2. Teaching and learning materials (TLMS) should be made available to the teacher.
3. There should be proper supervision of teachers. Teacher 2 1. Teachers should use teaching and learning materials (TLMS) in their lessons. 2.
Teachers should vary their teaching/ instructional methods and make good use of teaching and learning materials (TLMS). Teacher 3 1. Teachers should be motivated so that they can give of their best. 2. The school should provide teachers with adequate teaching and learning materials (TLMS).
Teacher 4 1. Class sizes should be reduced to enable the individual student to be given the necessary attention. 2. Mathematics teachers should be provided with teaching and learning materials to help make teaching and learning of the subject easy and interesting. Item 10 on the teacher’s questionnaire was what students should do to improve the learning of mathematics at Sunyani Secondary School (SUSEC).
These were the responses from the teachers. Teacher 1 1.Students should develop a positive attitude towards the learning of the subject.
2. Students should do a lot of work on their own. Teacher 2 1. Students should develop interest in the subject. 2.
Students should solve a lot of problems on their own. Teacher 3 1. Students should be motivated to learn mathematics as a subject. 2. Students should try to learn on their own.
Teacher 4 1. Students should do a lot of practice on their own and solve more problems. 2. Students should be encouraged by their teachers to develop interest the subject. Item 1 of the questionnaire for students tested the number of mathematics periods they had in a week and they all answered 6 periods.This means 100% of respondents did 6 periods of mathematics a week.
(Please find the questionnaire for students as appendix III) The second item on the questionnaire was to find out whether their mathematics teachers reported for classes every time that they had mathematics to which all the students responded “Yes”. This meant that the teachers’ class attendance was 100%. Item 3 was to find out whether their teachers taught them using teaching and learning materials, 220 answered “No” and 74 answered “Yes”.
This means that 74. 8% of students were taught without teaching and learning materials (TLMS) and only 25. 2% of students were taught with teaching and learning Materials (TLMS).As to when the teacher used the teaching and learning materials (TLMS) only the 74 students who responded “Yes” to test item 3 answered that the teacher used teaching and learning materials (TLMS) only at the beginning of the lesson. The next item sought to find out the number of exercises that they did in a week, 130 students responded 1-2, 89 responded 3-4 and 75 responded 5-6. This shows that 44. 2% of students did 1-2 exercises a week, 30. 3% of students did 3-4 exercises a week and 25.
5% of students did 5-6 exercises a week. As to whether exercises were marked and discussed, 101 students responded “Yes” whilst 193 answered “No”. This shows that 34. 4% of the students had their exercises marked and discussed whilst 65. % either had their exercise marked but not discussed, or not marked and discussed at all. When students were questioned about their performance in assignments and exercises, their responses were as indicated in table 3.
Table 3 Performance of Students in Exercises and Assignments |Performance | No. of Students Percentage | | | | |Poor |11 3. % | | | | |Below Average |26 8. 8% | | | | |Average | | | |106 36. 1% | |Good | | | |102 34.
% | |Very Good | | | |49 16. 7% | Table 3 shows the responses given by student about their performance in exercises and assignments. 11 students responded that their performance was poor, 106 responded that they were average, 102 were good and 49 very good. This means that 3. 7% knew their performance was poor, 8. 8% below average, 36. 1%, 34.
7% good average and 16. 7% very good. Item 8, was to find out the performance of their mathematics teachers. The responses they gave are shown in the table below. Table 4 Performance of Teachers as Indicated by Students |Performance | No. f Students Percentage | | | | |Poor |0 0% | | | | |Below Average | | | |0 0% | |Average | | | |16 5. 4% | |Good | | | |153 52.
% | |Very Good | | | |125 42. 5% | Table 4 shows none of the students saw their teachers performance to be either poor or below average. 16 students saw their teacher’s performance to be average, 153 assessed their teacher’s performance to be good whilst 125 considered their performance to be very good. The percentage of their performance as indicated by the students were 0%, 0%, 5. 4%, 52. 1% and 42. 5% respectively. As to how the teaching of mathematics can be improved in Sunyani secondary School, most of the students gave these responses.
1. Teachers should use relevant teaching and learning materials (TLMS) and adequately too. 2.Teachers should vary their teaching methods to make lessons lively. 3. Teachers should mark and discuss exercises and assignments with students. 4. Teachers should not discourage students by passing unpleasant comments.
They should rather motivate students to give of their best. What should students do to improve upon their performance in Mathematics was the last item on the questionnaire for students and these were some of the responses that were given. 1. Students should spend some time to solve more examples on their own after classes. 2. The six periods on the Time Table should either be increased or teachers be asked to organize extra classes for their students. 3.Students should contribute in class during discussions and must take active part in whatever is going on.
4. Students must develop interest in the subject. 5. Students who have understood the topic should help their fellow students who may face difficulties. Question 1 of the interview for the Assistant Headmaster in charge of Academics (appendix I) was to find out how long he has served in that position. His answer was 3-4 years. When he was asked how he assesses the teaching of mathematics in Sunyani Secondary school he said that it was good.
When asked if the school had adequate and qualified teachers to handle mathematics in the school, his answer was “Yes”When he was asked about the general performance of students’ in mathematics in both external and internal examinations he answered averagely. To question 5 which sought to find out whether teachers in the school faced challenges regarding the teaching of mathematics, he said “Yes”. He enumerated some of the challenges as follows: 1. The large number of students per class does not give teachers the chance to give more exercises and mark. 2. Insufficient teaching and learning materials (TLMS) makes it difficult for teachers to teach certain topics.
3. Some students have developed negative attitudes towards the subject from the Junior Secondary School (JSS) and this makes it difficult for them to learn the subject.When asked to suggest ways of improving teaching and learning of mathematics in the school, he said: 1. Teachers should do their best to use improvised teaching and learning materials (TLMS). 2. They should vary their instructional methods to suit the individual student. 3.
The learning and teaching method used should be student-centered. As part of the study, the researcher at the pre-intervention period conducted three different tests in all the five sampled classes to assess the students’ ability. Tables 5-10 show the scores of the students. Average marks for each class were calculated. The modal mark for each class was also found. Apart from these, the general average mark or mean mark for the five classes was also calculated. Table 5Results of Three Tests during Pre-Intervention periods for 1 Arts 1 | | TEST 1 TEST 2 TEST 3 | | | | |TOTAL SCORES |219 214 2O8 | | | | |AVERAGES |4.
0 3. 3. 8 | | | | |MODAL MARKS |5 3 4 | | | | |GENERAL AVERAGE |3. 9 | Table 5 captures the results of the three pre-intervention tests for Form 1Arts 1.Table 5 shows that the total scores for the 55 students of 1Arts 1 in the three tests were 219, 214 and 208 respectively. The average marks for the same class in the three tests were 4.
0, 3. 9 and 3. 8 respectively. The modal marks were 5, 3 and 4 in that order. The general average score for the students in the three tests was 3. 9.
This shows that the general average score for the class was 39%. Table 6 Results of Three Tests during Pre-Intervention periods for 1 Arts 2 | | TEST 1 TEST 2 TEST 3 | | | |TOTAL SCORES |242 245 232 | | | | |AVERAGES |3. 7 3. 8 3. 6 | | | | |MODAL MARKS |3 3 3 | | | | |GENERAL AVERAGE |3.
| Table 6 shows the results of the three tests conducted for Form 1 Arts 2 during the period under review. Table 6 reveals that the total scores for the 64 students of 1 Arts 2 in the three tests were 242, 245 and 232 respectively. The average marks for the same class in the three tests were 3. 7, 3. 8 and 3. 6.
The modal marks were 3, 3, and 3. From the scores, the class general average in the three tests was 3. 7. This implies that the percentage score for the class was 37%.
Table 7 Results of Three Tests during Pre-Intervention periods for 1 Business 1 | TEST 1 TEST 2 TEST 3 | | | | |TOTAL SCORES |227 210 227 | | | | |AVERAGES |3. 8 3. 6 3. 8 | | | | |MODAL MARKS |3 3 4 | | | | |GENERAL AVERAGE |3. | Table 7 shows the results of the three tests conducted for Form 1 Business 1 during the period under review. Table 7 reveals that the total scores for the 58 students of 1 Business 1 in the three tests were 227, 210 and 227 respectively. The average marks for the same class in the three tests were 3.
8, 3. 6 and 3. 8. The modal marks were 3, 3, and 4. From the scores, the class general average in the three tests was 3. 7. This implies that the percentage score for the class was 37%. Table 8 Results of Three Tests during Pre-Intervention periods for 1 Business 2 | TEST 1 TEST 2 TEST 3 | | | | |TOTAL SCORES |246 232 236 | | | | |AVERAGES |3.
9 3. 7 3. 8 | | | | |MODAL MARKS |3 4 3 | | | | |GENERAL AVERAGE |3. | | | | Table 8 shows the results of the three tests conducted for Form 1 Business 2 during the period under review. Table 8 shows that the total scores for the 62 students of 1 Business 2 in the three tests were 246, 232 and 236 respectively.
The average marks for the same in the three tests were 3. 9, 3. 7 and 3.
8 respectively. The modal marks were 3, 4 and 3 in that order. The average score for the students in the three tests was 3.
8. This shows that the average score for the class was 38%. Table 9Results of Three Tests during Pre-Intervention periods for 1 Agric 1 | | TEST 1 TEST 2 TEST 3 | | | | |TOTAL SCORES |217 228 204 | | | | |AVERAGES |3.
9 4. 1 3. | | | | |MODAL MARKS |4 3 3 | | | | |GENERAL AVERAGE |3. 9 | Table 9 shows the results of the three tests conducted for Form 1 Business 1 during the period under review Table 9 shows that the total scores for the 55 students of 1Agric 1 in the three tests were 217, 228 and 204 respectively.
The average marks for the same in the three tests were 3. 9, 4. 1 and 3. 7 respectively.The modal marks were 4, 3 and 3 in that order. The general average score for the students in the three tests was 3. 9. This shows that the average score for the class was 39%.
Post-Intervention Period After the intervention, the researcher again conducted three different tests in all the five sampled classes to assess the students’ performance. Tables 10-14 show the total scores of the students. Average marks for each class were calculated. The modal mark for each class was also found.
Apart from these, the general average mark or mean mark for the five classes was also calculated. Table 10 Results of Three Tests during Post-Intervention periods for 1 Arts 1 | TEST 1 TEST 2 TEST 3 | | | | |TOTAL SCORES |291 297 341 | | | | |AVERAGES |5. 3 5. 4 6. 2 | | | | |MODAL MARKS |5 5 6 | | | | |GENERAL AVERAGE |5. 6 |Table 10 shows the results of the three tests conducted for Form 1 Arts 1 during the period under review. Table 10 shows that the total scores for the 55 students of 1 Arts 1 in the three tests were 291, 5.
4 and 6. 2 respectively. The average marks for the same in the three tests were 6. 9, 7. 3 and 7. 4 respectively. The modal marks were 5, 5 and 6 in that order.
The general average score for the students in the three tests was 5. 6. A marked improvement had been recorded in the extent of students’ performance. Table 10 indicates this improvement quite clearly.
An average mark of 56% confirms that students’ performance had improved in a “great extent”. Table 11 Results of Three Tests during Post-Intervention periods for 1 Arts 2 | TEST 1 TEST 2 TEST 3 | | | | |TOTAL SCORES |352 390 371 | | | | |AVERAGES |5. 5 6. 1 5. 8 | | | | |MODAL MARKS |5 6 5 | | | | |GENERAL AVERAGE |5.
8 |Table 11 shows the results of the three tests conducted for Form 1 Arts 2 during the period under review. Table 11 shows that the total scores for the 64 students of 1 Arts 2 in the three tests were 352, 390 and 371 respectively. The average marks for the same in the three tests were 5. 5, 6. 1 and 5. 8 respectively. The modal marks were 5, 6 and 5 in that order. The general average score for the students in the three tests was 5.
8. A marked improvement had been recorded in the extent of students’ performance. Table 11 indicates this improvement quite clearly.
An average mark of 58% confirms that students’ performance had improved in a “great extent”. Table 12Results of Three Tests during Post-Intervention periods for 1 Business 1 | | TEST 1 TEST 2 TEST 3 | | | | |TOTAL SCORES |295 301 313 | | | | |AVERAGES |5. 1 5. 2 5. | | | | |MODAL MARKS |5 5 5 | | | | |GENERAL AVERAGE |5. 2 | Table 12 shows the results of the three tests conducted for Form 1 Business 1 during the period under review. Table 12 shows that the total scores for the 58 students of 1 Business 1 in the three tests were 295, 301 and 313 respectively. The average marks for the same in the three tests were 5.
1, 5. 2 and 5. 4 respectively. The modal marks were 5, 5 and 5 in that order. The general average score for the students in the three tests was 5. 2. A marked improvement had been recorded in the extent of students’ performance.Table 12 indicates this improvement quite clearly. An average mark of 52% confirms that students’ performance had improved in a “great extent”. Table 13 Results of Three Tests during Post-Intervention periods for 1 Business 2 | | TEST 1 TEST 2 TEST 3 | | | | |TOTAL SCORES |316 359 334 | | | |AVERAGES |5. 1 5. 8 5. 4 | | | | |MODAL MARKS |5 5 5 | | | | |GENERAL AVERAGE |5. 4 |Table 13 shows the results of the three tests conducted for Form 1 Business 2 during the period under review. Table 13 shows that the total scores for the 62 students of 1 Business 2 in the three tests were 316, 359 and 334 respectively. The average marks for the same in the three tests were 5. 1, 5. 8 and 5. 4 respectively. The modal marks were 5, 5 and 5 in that order. The general average score for the students in