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## Contents

**Table of Contents**

**LIST OF ABBREVIATIONS AND ACRONYMS**

**DEFINITIONS OF TERMS**

**CHAPTER ONE**

**INTRODUCTION**

**1.1 Background information**

**1.2 Research aim**

**1.3 Main objective**

**1.4 Specific objectives**

**1.5 Significance of the study**

**1.6 Problem statement**

**CHAPTER TWO**

**LITERATURE REVIEW**

**2.1 Introduction**

**2.2 Teaching Mathematics at Secondary School**

**2.3 Some teaching methods used in Mathematics**

**2.3.1 Lecture Method**

**2.3.2 Inductive Method**

**2.3.3 Deductive Method**

**2.3.4 Heuristic Method**

**2.3.5 Analytic Method**

**2.3.6 Problem Solving Method**

**2.3.7 Laboratory Method**

**2.4 Discourse in the Classroom**

**2.4.1 Mathematical Communication**

**2.4.2 Mathematical Language**

**2.4.3 Tools and Representations**

**2.5 Conclusion**

**CHAPTER 3**

**METHODOLOGY**

**3.1 Introduction**

**3.2 Research Design**

**3.3 Places of study**

**3.4 Study population**

**3.5 Determination of the sample size**

**3.6 Sampling techniques and procedure**

**3.7 Data Collection Methods**

**3.7.1 Questionnaire surveys**

**3.7.2 Interview**

**3.8 Data collection instruments**

**3.8.1 Questionnaires**

**3.8.2 Interview schedule**

**3.9 Data Analysis**

**3.10 Ethical considerations**

**3.11 Limitations of the Study**

**References**.

## LIST OF ABBREVIATIONS AND ACRONYMS

Abbildung in dieser Leseprobe nicht enthalten

## DEFINITIONS OF TERMS

Abbildung in dieser Leseprobe nicht enthalten

## CHAPTER ONE

## INTRODUCTION

### 1.1 Background information

Mathematics has always been given special attention in school as the nature of the subject is related to many other fields and disciplines. Moreover, students' mathematics achievement has often been the focus and is seen as a critical global issue in many countries. Besides being perceived as a tough subject, problems in mathematics learning have also been related to the lack of regulation skills among students in learning mathematics. Self-regulation is a broad construct which covers before, during and after phases learning (Wolters, 2010). The rapid changes ofthe education system and delivery methods give a huge impact to students. This situation requires students to learn effectively and in a more self-directed manner (Winters, Greene & Costich, 2008). To achieve this, teachers are encouraged to use a variety of teaching methods when teaching mathematics. This leads to student motivation which is a very important element in the learning process as it is an inducer and propeller for one to do a task successfully. Therefore, motivation is essential for an individual to successfully face challenges in academic setting. Moreover, motivation will be used by students as the attribution or determinant to their behaviour in learning and performance. Behaviours that are related to academic motivation such as the desire to do difficult tasks and stay longer in difficult situations will be the determinant for students' ability in facing daily school life challenges (Masaali, 2007). It has been observed that there is still poor performance in mathematics despite the use of a variety of methods by teachers. This research intends to investigate the effects of using a variety of teaching methods in teaching and learning of secondary school mathematics.

### 1.2 Research aim

This paper aims at finding out the effects of using a variety of teaching methods in teaching and learning of Mathematics in Malawian secondary schools.

### 1.3 Main objective

The main objective of the research paper will be to investigate the effects of using a variety of teaching methods in the teaching and learning of secondary school Mathematics in Malawi.

### 1.4 Specific objectives

Specifically, the research is designed to:

- to identify the various teaching methods that are used in the teaching and learning of secondary school Mathematics

- to examine the effects of using various teaching methods in teaching and learning of secondary school Mathematics

- to establish teaching methods that are more effective in the teaching and learning of secondary school Mathematics

### 1.5 Significance of the study

The results of the study would be of great help to the field of Mathematics at secondary school level because it may promote the use of more effective methods in teaching and learning of Mathematics. Above all, the study will suggest better ways of addressing the effects of using a variety of teaching methods. Since many students regard the subject as complex in the sense that it does not necessarily deal with practical life situations, addressing the said effects would bring life to the Mathematics classroom as it would encourage methods that connect mathematics to the real world. Mathematics teachers stand to benefit from the analysis of the effects associated with the use of a variety of methods because in the end the paper will suggest better strategies of making sure various methods are used to the advantage of the learner.

### 1.6 Problem statement

Experience has shown that in Malawi learners' performance in Mathematics is worrisome. As noted from the Malawi National Examinations Board (MANEB) website, in 2018 alone over two thousand (2000) candidates got zero marks in Mathematics during national examinations. According to MANEB this figure surpassed zero marks that students got in all other subjects. One would attribute this poor performance to many factors that come into play in the process of teaching/learning Mathematics, teaching methods being among them. There are a number methods that teachers use in Mathematics lessons, that may be grouped as teacher-centred and learner centred, but still for years the performance in Mathematics has not been any better.

There is an observation that lately there has been much advocacy on the use of a variety of teaching methods in the teaching and learning of many subjects, Mathematics inclusive. Despite all this effort, however, not much has been achieved in Mathematics in terms of grades during national examinations. Students still find the subject difficult and as such they do not score better grades. It is in view of this that the researcher would like to fmd out the effects that are associated with the use of various methods that could lead to students' poor performance in Mathematics.

## CHAPTER TWO LITERATURE REVIEW

### 2.1 Introduction

Mathematics is "the branch of human enquiry involving the study of numbers, quantities, data, shape and space and their relationships, especially their generalizations and abstractions and their application to situations in the real world" (Clapham & Nicholson, 2009, p. 505). Mathematicians generalise new formulas or methods based on similar patterns for different branches of mathematics (Devlin, 2004). Before teaching mathematics, every teacher should be informed well about the educational values of this subject. Proper teaching method should also be adopted according to the situation, learning environment and educational background of the students. It is very important to keep the motivational level of students high otherwise they lose interest in mathematics (Butler & Wren, 1965). Students can be motivated by highlighting the importance of this subject, for example, mathematics is quite essential to learn other science related subjects. Moreover, students can avail good employment opportunities in their future life because of diverse applicability of mathematics in many fields (Rani, 2007).

### 2.2 Teaching Mathematics at Secondary School

Curriculum of mathematics at secondary in Malawi is developed and updated by the Ministry of Education, Science and Technology (MoEST). National curriculum for mathematics at secondary level has been divided into different small units in which the benchmarks are clearly mentioned. These units are designed for different branches of mathematics like number and operations, algebra, geometry, information handling and trigonometry etc. Malawi is a developing country where educational situation is not very much encouraging. Lack of resources and funds are the biggest hurdles in educational reforms. Situation in private schools is relatively good but their fee structure is very much high and not affordable by everyone. Majority of the students are studying in the public schools which are in very poor condition. Properly trained teachers are not available everywhere. Strength of students is very much high in most of the schools so that teachers cannot give attention to each student in a proper way.

### 2.3 Some teaching methods used in Mathematics

Pedagogy of mathematics includes application of different teaching methods like lecture, inductive, deductive, heuristic or discovery, analytic, synthetic, problem solving, laboratory and project methods. Instructional methodology of every teacher should be adaptive according to each unit of syllabus, available resources and strength of the students.

#### 2.3.1 Lecture Method

In this method, knowledge is delivered through a speech. This is the oldest and most important teaching method because it has always remained a part of all other instructional methodologies. In this method, a teacher takes part as an active participant and students are at the receiving end most of the time. That is why; it is a teacher centred approach. This is also referred to as direct instruction, training model (Joyce, Weil, & Shower, 1992), active teaching (Good, Grouws, & Ebmeier, 1983) and explicit instruction (Rosenshine & Stevens, 1986). Lecture method is not only used for teaching theoretical concepts but it is also helpful for giving training of complex skills and procedures.

#### 2.3.2 Inductive Method

This method is also called scientific method in which we proceed from known to unknown, from specific to general and from example to rule or formula. In this method based on induction, students are presented with some similar examples or problems related to one particular domain. Then students try to establish a formula, rule, law or principal by observing them. If a generalised result is true for those similar examples or problems then it would also be true for all other such kind of examples (Sidhu, 1995).

#### 2.3.3 Deductive Method

This method is totally different from inductive method. In this method, we proceed from general to specific and from a rule to an example. Already constructed formulas, rules, methods or principles are taught to the students and they apply them to solve the problems (Sidhu, 1995). In this teaching approach, we can also prove a theorem with the help of undefined terms, defined terms, axioms and postulates. Then with the help of that theorem along with different rules and principles, we can derive other theorems as well (Singh, 2007).

#### 2.3.4 Heuristic Method

Sometimes a teacher only focuses on delivering lectures through speech in which students do not actively participate and get bored most of the time. But in the heuristic method, students are encouraged to reach the solution by constructing the knowledge themselves. Teacher only facilitates them by raising relevant questions. That is why it is also called inquiry method (Suchman, 1962). As students discover the solution under the guidance of a teacher so it is also known as guided discovery method or programmed instruction. So many researches (Ashton, 1962; Wills, 1967; Wilson, 1967) have proved that heuristic or discovery method is more effective in teaching mathematics than expository approach.

#### 2.3.5 Analytic Method

In this method, we analyse the problem first by breaking up the problem into small segments and then move towards solution. It is also called descriptive method. It leads us from the unknown part of the problem to something already known or given in the problem statement. This method emphasises on why we are applying different kinds of operations and what is the relationship between the required solution and other portions of the problem (Rani, 2007; Singh, 2007).

#### 2.3.6 Problem Solving Method

Every child has the curiosity to explore the things and this psychology of the children can be utilised in a better way through problem solving method. It is the most important instructional methodology for mathematics (Collier & Lerch, 1969). Bruner, Oliver, Greenfield (1966) and Gagne (1970), the most famous psychologists, also gave the top priority to this method. In this method, students are given such problems which cannot be solved easily or their solutions are not obvious. A student tries to reach the goals or solutions through the set of events or procedures. Gagne (1970) calls these events or procedures as lower order capabilities in which formulas, rules and concepts are used from which a student is already familiar.

#### 2.3.7 Laboratory Method

Mathematics is different from the subjects involving readings thus practical work is its major part. Laboratory method has the capacity to deal with practical work in mathematics. It is a method of "learning by doing". That is why, different kinds of tools and equipment are used in it to perform practical work which includes drawing of different shapes, taking measurements of geometrical figures and making of charts and graphs. Students go through different experiments in laboratory or classroom and learn by observing and calculating themselves. During this process, they get opportunity to draw conclusions and generalise different laws and formulas.

### 2.4 Discourse in the Classroom

#### 2.4.1 Mathematical Communication

Teaching ways of communicating mathematically demands skilful work on the teacher's part (Walshaw & Anthony, 2008). Students need to be taught how to articulate sound mathematical explanations and how to justify their solutions. Encouraging the use of oral, written and concrete representations, effective teachers model the process of explaining and justifying, guiding students into mathematical conventions. They use explicit strategies, such as telling students how they are expected to communicate (Hunter, 2005).

Teachers can also use the technique ofre-voicing (Forman & Ansell, 2001), repeating, rephrasing, or expanding on student talk. Teachers use re-voicing in many ways: (i) to highlight ideas that have come directly from students, (ii) to help the development of students' understandings implicit in those ideas, (iii) to negotiate meaning with their students, and (iv) to add new ideas, or move discussion in another direction. When guiding students into ways of mathematical argumentation, it is important that the classroom learning community allows for disagreements and enables conflicts to be resolved (Chapin & O'Connor, 2007). Teacher's support should involve prompts for students to work more effectively together, to give reasons for their views and to offer their ideas and opinions. Students and teacher both need to listen to other's ideas and to use debate to establish common understandings.

#### 2.4.2 Mathematical Language

If students are to make sense of mathematical ideas they need an understanding of the mathematical language used in the classroom. A key task for the teacher is to foster the use, as well as the understanding, of appropriate mathematical terms and expressions. Conventional mathematical language needs to be modelled and used so that, over time, it can migrate from the teacher to the students (Runesson, 2005). Explicit language instruction and modelling takes into account students' informal understandings of the mathematical language in use. For example, words such as -less than, -more, -maybe, and -half can have quite different meanings within a family setting. Students can also be helped in grasping the underlying meaning through the use of words or symbols with the same mathematical meaning.

#### 2.4.3 Tools and Representations

Effective teachers draw on a range of representations and tools to support learners' mathematical development. Tools to support and extend mathematical reasoning and sense-making come in many forms including the number system itself, algebraic symbolism, graphs, diagrams, models, equations, notations, images, analogies, metaphors, stories, textbooks, and technology. Teachers have a critical role to play in ensuring that tools are used effectively to support students to organize their mathematical reasoning and support their sense-making (Blanton & Kaput, 2005). Providing students access to multiple representations helps them to develop conceptual and computational flexibility. Using an appropriate model, learners can think through a problem, or test ideas. Care is needed, however, particularly when using pre-designed concrete materials (e.g., number lines, tens-frames), to ensure that all students are able to make sense of the materials in the mathematically intended way.

Tools are helpful in communicating ideas that are otherwise difficult to talk about or write about. Teachers and students can use representations, such as stories, pictures, symbols, concrete objects, and virtual manipulative, to assist in communicating their thinking to others. As well as ready made tools, effective teachers acknowledge the value of students generating and using their own representations, but it an invented notation, or a graphical, pictorial, tabular, or geometric representation. For example, young children frequently create their own pictorial representations to tell stories before using the more formal graphical tools that are fundamental to the statistics curriculum (Chick, Pfannkuch, & Watson, 2005). An increasing array of new technological tools is available for use in the mathematics classroom. In addition to calculator and computer applications, new technologies include presentation technologies (e.g., the interactive whiteboard (Zevenbergen & Lerman, 2008), digital and mobile technologies, and the Internet. These dynamic graphical, numerical, and visual technological applications provide new opportunities for teachers and students to interact, represent, and explore mathematical concepts.

### 2.5 Conclusion

The list of teaching methods in mathematics and classroom practices could go on and on but the general idea as presented in many literature is that a teacher should be familiar with all of these teaching methods because he or she can get better results by applying an appropriate method according to the nature of a problem, available resources and number of students in a class. However, with the knowledge of all the tools, methods and practices used in Mathematics teaching, teachers are still unable to get the best out of their students in Malawian secondary schools as regards to Mathematics grades during national examinations. At the same time, most of the discussions that the researcher has gone through do not necessarily present the effects of using a variety of methods and classroom practices in the teaching of secondary school Mathematics. Due to the worrisome Mathematics grades that secondary school students come up with it is imperative, as per the overall object of this study, to investigate the effects of using a variety of teaching methods in the teaching and learning of Mathematics.

## CHAPTER3

## METHODOLOGY

### 3.1 Introduction

This chapter describes the procedures that will be followed in conducting the study. The chapter involves; research design, study population, determination of the sample size, sampling techniques and procedure, data collection methods and instruments. It will also describe the procedure of data collection and data analysis.

### 3.2 Research Design

This research will follow a mixed research approach. Mixed methods research, according to Mugenda and Mugenda (2003), is the type of research in which a researcher or team of researchers combines elements of qualitative and quantitative research approaches (e. g., use of qualitative and quantitative viewpoints, data collection, analysis, inference techniques) for the broad purposes of breadth and depth of understanding and corroboration. A mixed methods design as a product has several primary characteristics that should be considered during the design process. The overall goal of mixed methods research, of combining qualitative and quantitative research components, is to expand and strengthen a study's conclusions and, therefore, contribute to the published literature.

In the study we will use quantitative methods to present data in form of tables, pie charts and graphs. This will be used to analyse data collected by use of questionnaires, more especially data collected through close-ended questions. For open-ended questions and interview, the researcher will use qualitative methods to analyse the data.

### 3.3 Places of study

The study will be conducted in three secondary schools, Mkwero Community Day Secondary School (CDSS), Msalura CDSS and Salima Secondary School in Salima District. Three sites have been chosen in order to have a representative sample size in the study. Two school have their students operate from their homes on daily basis while one is a boarding school. This distinction would help in collecting data from students subjected to diverse learning conditions.

### 3.4 Study population

Mugenda and Mugenda (2003) describe study/target population as the population to which a researcher wants to generalize the results of a study and should be defined according to the study. The researcher will use cross sectional survey of the population that will include: Mathematics teachers in the three selected schools and students who take Mathematics. The schools will include: Mkwero CDSS, Msalura CDSS and Salima Secondary School.

### 3.5 Determination of the sample size

In order to avoid unguided generalization, a sample will be used as suggested by Amin (2005) that sampling is vital in selecting elements from a population in such a way that the sample elements selected represent the population. The respondents for this study will be drawn from three secondary schools in Salima district. The sample size will be selected from Mathematics teachers and students. The sample will be guided by: Understanding Power and Rules of Thumb for Determining Sample by Carmen and Betsy (2007).

Table 3.1 below shows the summary of the sample size which will be considered in the study

Abbildung in dieser Leseprobe nicht enthalten

### 3.6 Sampling techniques and procedure

Sampling is the act, process or techniques of selecting a suitable sample for the purposes of determining the characteristics of the whole population. Koul (1990) stated that the simplest and most common system of allocating of sample units among strata is in proportion of size of the strata. Kombo and Tromp (2006) stated that stratified random sampling involves dividing your population into homogenous sub groups and taking a simple random sample in each sub group. The researcher intends to use the simple random sampling and purposive sampling. The sample random sampling refers to a process of selecting in such a way that all individuals in the defined population have an equal and independent chance of being selected. The purposive sampling will be used to select the 3 Mathematics teachers from each school. This technique, according to Gay (1996) though may not necessarily be a representative sample; but enables the research to acquire an in-depth understanding of the problem.

### 3.7 Data Collection Methods

The researcher intends to employ the data collection methods below:

#### 3.7.1 Questionnaire surveys

These will involve preparing open and close ended questions which will be sent to Mathematics teachers. The researcher will design both open and close ended; open ended questions will give the respondents the opportunity to provide their own answers to the questions while close ended, the answers will be provided for the respondents to choose from.

This tool will be used because its coverage is wide and many respondents can be reached at the same. It will allow the respondents to give their own answers to the study especially when the open ended questionnaire is used.

#### 3.7.2 Interview

This will involve face-to-face interactions between the researcher and the respondents through question and answer.It will involve the researcher preparing interview schedule and use it to orally ask respondents questions. This has been chosen because the responses are on spot during interviews. This is also based on the fact that the technique of face to face treats the interview as a pipeline for extracting and transmitting information from the interviewee to the interviewer and are also very necessary in strengthening the clause of confidentiality {DeVos, 2001). Students will be interviewed in groups and this will lead to the researcher using Focus Group Discussions {FGDs).

### 3.8 Data collection instruments

The following data collection instruments will be used during the study:

### 3.8.1Questionnaires

The researcher intends to develop the questionnaire in line with the study objectives and the respondents are expected to answer the questions as per the guidelines given. The questionnaires for the teachers will consist of three sections. Section one on the demographic information including gender, professional and teaching experience. Sections two and three will focus on the classroom practices.

#### 3.8.2 Interview schedule

The researcher intends to develop an interview schedule that will consist of a set of questions that will be administered during the study to interview students. The researcher will use it to ask questions and the answers will be recorded on spot.

### 3.9 Data Analysis

Analysis of the data collected will be based on the purpose and the objective of the research study. The researcher will use both qualitative and quantitative methods to answer the research of the study. Quantitatively data obtained from closed and open ended questions derived from the questionnaires will be analysed using Microsoft Excel. Tables, pie charts and bar graphs will be used to present data. Qualitative data generated from open ended questions in the research instruments will be organized in themes and patterns, categorized through content analysis and then tabular forms accompanied with narratives.

### 3.10 Ethical considerations

To make sure that autonomy and confidentiality are fully exercised throughout the study, both written and oral informed consent will be obtained from the participants prior to participation. In addition, the participants will be informed about the purpose of the study. A coding system will be used to conceal the identity of the participants thus addressing the issue of confidentiality. Participants will not be required to give their names. Instead each participant will be given an identity number, thus maintaining anonymity of participants' information. Also the benefit of this study will be explained to them and that no harm will result from participation, like dismissal or punishment. Additionally, an explanation will be offered that no payment will be given to them. Participation will be entirely voluntary and no participant will be compelled to provide information manyway.

### 3.11 Limitations of the Study

The researcher is expected to encounter various challenges during the research process. These may include insufficient funds for stationery, transport and buying other important materials. Also, there should be shortage of time because the researcher will conduct the study in selected secondary schools situated far apart from each other, at the same time performing other duties.

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- Quote paper
- Thom Phiri (Author), 2019, Investigating the Effects of Using a Variety of Teaching Methods in Teaching and Learning of Secondary School Mathematics, Munich, GRIN Verlag, https://www.grin.com/document/468270

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