SECONDARY SCHOOL MATHEMATICS TEACHER EDUCATION IN ZAMBIA

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INTRODUCTION

In Zambia, the Ministry of Education (MOE) has for a long time recognised an acute shortage of degree holding teachers of mathematics (Ministry of Education, 1992). Consequently, the MOE is continuously engaged in efforts to alleviate the shortage of graduate teachers of mathematics. In this context, several initiatives have been undertaken (Ministry of Education, 1996), including the continued awarding of bursaries to secondary school mathematics student teachers to train at the University of Zambia (UNZA), and the engagement of UNZA to train graduate teachers of mathematics through what is called a „fast track‟ arrangement. The latter is a distance education setup where practicing teachers who already hold a secondary school teachers‟ diploma in mathematics are being trained with a view of upgrading to a degree level status. It is hoped that that in so doing, the deficiencies in the teaching of secondary school mathematics will be addressed, and consequently the problem of poor pupil performance in Grade 12 mathematics national examinations will have been solved (Ministry of Education, 2013b). Apart from valuing the critical role that the UNZA was expected to play in teacher training in the post-independence era (Ministry of Education, 1977), the MOE has been involved in projects to improve mathematics education in the country. A typical example is a project called the Zambia Mathematics and Science Teacher Education Project (ZAMSTEP), which was undertaken by the MOE and the European Economic Commission (EEC) (Haambokoma, 2002). This project was established due to the shortage of graduate mathematics teachers who could teach senior secondary school mathematics in Zambia. The main aim of ZAMSTEP was to upgrade the content knowledge and teaching skills of diploma holding secondary school mathematics teachers. It was envisaged that the teachers whose content knowledge and teaching skills would be upgraded would be in a position to effectively teach senior secondary school mathematics. Likewise, the Ministry of Education undertook another project between 1994 and the year 2000, Action to Improve English, Mathematics and Science (AIEMS), partly aimed at improving mathematics education in Zambia. In this regard, Teacher Resource Centres were established around the country with a view to facilitating decentralised in-service education of teachers.
The idea was to promote a realisation among teachers that they needed to take a lead in their own Continuing Professional Development (CPD) in their subject areas (British Council, 1997). Regardless of the successes that were achieved through these projects, it is argued that they had setbacks such as a loss of momentum when the donors‟ funding ended (Haambokoma, 2002). Unfortunately, instead of the teachers themselves identifying the professional development activities that need to be implemented, it was the Government agencies that identified these for the teachers (Haambokoma, 2002). This contributed to the exploration of alternative ways of enhancing sustainable teachers‟ CPD within secondary school mathematics and science. The intention was to involve mathematics and science subject associations in the country to promote teachers‟ CPD (Haambokoma, 2002). Notwithstanding, this approach focused on the practising teachers and did not directly include consideration of how thoroughly mathematics student teachers understand secondary school mathematics by the end of their training. Currently, mathematics is one of the core subjects in the Zambian secondary school curriculum. Learners have continued to perform poorly in the Grade 12 national examinations in this subject (Ministry of Education, 2013b). The MOE (2013b) reports that “cumulatively, one-third of boys, and two-thirds of girls, have registered complete fail in mathematics since 2005, while only half of the boys and one-fifth of the girls have managed to obtain a pass or better” (p. 4). This failure rate could be attributed to several factors that may include teachers‟ lack of comprehensive understanding of the mathematics subject matter taught at secondary school level. Although there is no direct relationship between teachers‟ qualifications and effective teaching (Watson & Harel, 2013), research has shown that teachers‟ mathematical content knowledge has an influence on the teaching of mathematics and student achievement (Ball, 1990; Ball, Thames, & Phelps, 2008; Campbell, Nishio, Smith, Clark, Conant, Rust & Choi, 2014; Hill, Rowan, & Ball, 2005; Ogbonnaya & Mogari, 2014). At the same time, a study involving primary school teachers showed that the majority of these lacked in-depth understanding of the mathematics intended for the levels that they taught (Venkat & Spaull, 2015).
Another study indicated that mathematics educators who likely possessed metacognitive skills could not satisfactorily implement these skills in their classrooms (van der Walt & Maree, 2007). These two studies seem to be in line with the views that teacher knowledge is complex and that subject matter knowledge is not a sufficient requirement for effective teaching (Fennema, 1992). However, teachers require a thorough understanding of the subject matter for them to assist learners to acquire an understanding of the subject matter (Even, 1990; Shulman, 1986). Thus, the effective teaching of mathematics requires that teachers should acquire an in-depth understanding of the subject matter that they are supposed to teach (Ball, 1990; Ball et al., 2008; Nyikahadzoyi, 2013; Steele, Hillen, & Smith, 2013). This is consistent with ideas advanced by Bennett (1993), who argues that teachers ought to have “enough understanding of the subject to know which ideas are central, which are peripheral, how different ideas relate to one another, and how these ideas can be represented to the uninitiated” (p. 10).
According to the MOE (1996), the Zambian national policy on education attaches significance to teacher training and states that “the essential competencies required in every teacher are mastery of the material that is to be taught” (p. 108). By implication, the MOE recognises the necessity of secondary school mathematics teachers having sufficient understanding of the mathematics topics that they teach in schools. This is consistent with the aspiration that is enshrined in the Zambia Education Curriculum Framework (ZECF), which suggests that Teacher Education (TE) programmes should produce teachers who are competent in the subject matter that is taught (Ministry of Education, 2013b), for example, teacher educators can engage in research that investigates and describes how well impending graduate mathematics teachers know secondary school mathematics. In this regard, the present study assessed and explored UNZA‟s mathematics student teachers‟ content knowledge (herein also referred to as subject matter knowledge) of two secondary school mathematics topics, namely: functions and trigonometry. The reason for selecting these two topics will later be discussed in Section 1.2. The following section presents a discussion of the rationale and background to the study.

intended for the levels that they taught (Venkat & Spaull, 2015). Another study indicated that

mathematics educators who likely possessed metacognitive skills could not satisfactorily implement these skills in their classrooms (van der Walt & Maree, 2007). These two studies seem to be in line with the views that teacher knowledge is complex and that subject matter knowledge is not a sufficient requirement for effective teaching (Fennema, 1992). However, teachers require a thorough understanding of the subject matter for them to assist learners to acquire an understanding of the subject matter (Even, 1990; Shulman, 1986). Thus, the effective teaching of mathematics requires that teachers should acquire an in-depth understanding of the subject matter that they are supposed to teach (Ball, 1990; Ball et al., 2008; Nyikahadzoyi, 2013; Steele, Hillen, & Smith, 2013). This is consistent with ideas advanced by Bennett (1993), who argues that teachers ought to have “enough understanding of the subject to know which ideas are central, which are peripheral, how different ideas relate to one another, and how these ideas can be represented to the uninitiated” (p. 10). According to the MOE (1996), the Zambian national policy on education attaches significance to teacher training and states that “the essential competencies required in every teacher are mastery of the material that is to be taught” (p. 108). By implication, the MOE recognises the necessity of secondary school mathematics teachers having sufficient understanding of the mathematics topics that they teach in schools. This is consistent with the aspiration that is enshrined in the Zambia Education Curriculum Framework (ZECF), which suggests that Teacher Education (TE) programmes should produce teachers who are competent in the subject matter that is taught (Ministry of Education, 2013b), for example, teacher educators can engage in research that investigates and describes how well impending graduate mathematics teachers know secondary school mathematics.
In this regard, the present study assessed and explored UNZA‟s mathematics student teachers‟ content knowledge (herein also referred to as subject matter knowledge) of two secondary school mathematics topics, namely: functions and trigonometry. The reason for selecting these two topics will later be discussed in Section 1.2. The following section presents a discussion of the rationale and background to the study. Copper belt, one of the ten provinces of Zambia (Maliwatu, 2011). Although mathematics student teachers formed part of the sample of Nalube‟s (2014) study; its focus was not on the exploration of the student teachers‟ content knowledge of functions and trigonometry at secondary school level. Similarly, Maliwatu‟s (2011) research was premised on a comparison of classroom practices and not an exploration of the student teachers‟ content knowledge. The findings of the research indicate that degree holding mathematics teachers had more competency in content knowledge than their counterparts who held secondary teachers‟ diplomas.
Moreover, Maliwatu‟s study involved mathematics teachers and not mathematics student teachers. The situation highlighted above encouraged the researcher to make a contribution towards the growth of mathematics education literature in Zambia. Another reason why UNZA student teachers were selected for this study is that the Government of the Republic of Zambia views the University of Zambia as a vitally important institution. Government contends that the knowledge that student teachers acquire during training at this institution would enable them to implement the school curriculum effectively (Ministry of Education, 2013b). This view motivated the researcher to investigate what student teachers trained at that university knew and how well they understood secondary school mathematics. The researcher wanted to find out whether, by the end of their training in mathematics, student teachers actually acquired a thorough understanding of functions and trigonometry, which they are supposed to teach upon graduation. In Section 1.2.3, the justifications for selecting functions and trigonometry for secondary schools as the topic under study are presented.

TABLE OF CONTENTS :

• DECLARATION
• ETHICS CLEARANCE CERTIFICATE
• ETHICS STATEMENT
• ABSTRACT
• List of tables
• List of figures
• List of abbreviations
• CHAPTER 1 INTRODUCTION
  • 1.1 INTRODUCTION
  • 1.2 RATIONALE AND BACKGROUND TO THE STUDY
    • 1.2.1 Personal interest in the study
    • 1.2.2 Why conduct a content knowledge study involving UNZA’s student teachers?
    • 1.2.3 Justifying the selection of the topics functions and trigonometry
  • 1.3 PROBLEM STATEMENT
  • 1.4 AIMS AND OBJECTIVES OF THE STUDY
  • 1.5 SIGNIFICANCE OF THE STUDY
  • 1.6 RESEARCH QUESTIONS
  • 1.7 METHODOLOGICAL AND DATA ANALYSIS CONCERNS
  • 1.8 DEFINITIONS OF TERMS
• 1.9 SUMMARY OF THE CHAPTER AND STRUCTURE OF THE STUDY
• CHAPTER 2 CONTEXT OF THE STUDY AND LITERATURE REVIEW
  • 2.1 INTRODUCTION
  • 2.2 SECONDARY SCHOOL MATHEMATICS TEACHER EDUCATION IN ZAMBIA
  • 2.2.1 Secondary school mathematics teacher training at the University of Zambia
  • 2.3 TEACHING AND LEARNING OUTCOMES: FUNCTIONS AND TRIGONOMETRY
  • 2.4 RELEVANT FRAMEWORKS OF TEACHER KNOWLEDGE
    • 2.4.1 Teacher content knowledge
    • 2.4.2 Summary of relevant teacher knowledge frameworks
  • 2.5 STUDENTS’ CONTENT KNOWLEDGE OF FUNCTIONS AND TRIGONOMETRY
    • 2.5.1 Overview of students’ content knowledge of functions
    • 2.5.2 Overview of students’ content knowledge of trigonometry
    • 2.5.3 Student teachers’ content knowledge of functions and trigonometry: The Zambian context
    • 2.5.4 Summary of students’ content knowledge of functions and trigonometry
  • 2.6 INVESTIGATING STUDENT TEACHERS’ CONTENT KNOWLEDGE
  • 2.7 CONCEPTUAL FRAMEWORK
    • 2.7.1 General explanation of the conceptual framework
    • 2.7.2 Common Content Knowledge
    • 2.7.3 Specialised Content Knowledge
  • 2.8 SUMMARY OF CHAPTER
• CHAPTER 3 RESEARCH DESIGN AND METHODOLOGY
  • 3.1 INTRODUCTION
  • 3.2 PHILOSOPHICAL ORIENTATION TO THE STUDY
  • 3.3 RESEARCH APPROACH AND DESIGN
  • 3.4 DATA COLLECTION
    • 3.4.1 Introduction
    • 3.4.2 Research site and sampling
    • 3.4.3 Data collection instruments
  • 3.5 METHODS USED TO ANALYSE THE DATA
    • 3.5.1 Data analysis methods for Phase
    • 3.5.2 Data analysis procedures for the interview data
  • 3.6 TRUSTWORTHINESS
  • 3.7 ETHICAL CONSIDERATIONS
  • 3.8 ADMINISTRATION OF THE DATA COLLECTION INSTRUMENTS
  • 3.8.1 Administration of the test
  • 3.8.2 Administration of the interviews
  • 3.9 SUMMARY OF CHAPTER
• CHAPTER 4 ANALYSIS OF THE DATA ON FUNCTIONS
  • 4.1 INTRODUCTION
  • 4.2 RESULTS AND ANALYSIS OF STUDENT TEACHERS’ PERFORMANCE IN THE TEST
    • 4.2.1 Proficiency of student teachers in the CCK of functions
    • 4.2.2 Student teachers’ ability to explain and justify reasoning in functions
    • 4.2.3 Ability of the student teachers to use different representations in functions
  • 4.3 RESULTS AND ANALYSIS OF THE INTERVIEWS ABOUT FUNCTIONS
  • 4.3.1 Analysis of the student teachers’ ability to explain and justify their reasoning regarding functions
  • 4.3.2 Analysis of the student teachers’ ability to use different representations in functions
  • 4.4 SUMMARY OF CHAPTER
• CHAPTER 5 ANALYSIS OF THE DATA ON TRIGONOMETRY
  • 5.1 INTRODUCTION
  • 5.2 ANALYSIS OF THE TEST DATA ON TRIGONOMETRY
    • 5.2.1 Proficiency of student teachers in the CCK of trigonometry
    • 5.2.2 The student teachers’ ability to use different representations in trigonometry
  • 5.3 RESULTS AND ANALYSIS OF THE INTERVIEWS ON TRIGONOMETRY
    • 5.3.1 Analysis of the student teachers’ ability to explain and justify their reasoning in trigonometry
  • 5.4 SUMMARY OF CHAPTER
• CHAPTER 6 FINDINGS AND DISCUSSION
  • 6.1 INTRODUCTION
  • 6.2 DISCUSSION OF THE FINDINGS ON FUNCTIONS
  • 6.2.1 How proficient are the student teachers in the CCK of functions at secondary school level?
  • 6.2.2 What SCK of functions at secondary school level is held by the student teachers?
  • 6.3 DISCUSSION OF THE FINDINGS ON TRIGONOMETRY
  • 6.3.1 How proficient are the student teachers in the CCK of trigonometry at secondary school level?
  • 6.3.2 What SCK of trigonometry at secondary school level is held by the student teachers?
  • 6.4 SUMMARY OF CHAPTER
• CHAPTER 7 CONCLUSIONS
  • 7.1 HOW PROFICIENT ARE THE STUDENT TEACHERS IN CCK?
    • 7.1.1 How proficient are the student teachers in CCK of functions for secondary schools?
  • 7.1.2 How proficient are the student teachers in the CCK of trigonometry at secondary school level?
  • 7.2 WHAT SCK IS HELD BY THE STUDENT TEACHERS?
    • 7.2.1 What SCK of functions at secondary school level is held by the student teachers?
    • 7.2.2 What SCK of trigonometry at secondary school level is held by the student teachers?
  • 7.3 DESCRIBING UNZA’S MATHEMATICS STUDENT TEACHERS’ CONTENT KNOWLEDGE OF FUNCTIONS AND TRIGONOMETRY AT SECONDARY SCHOOL LEVEL
  • 7.4 REFLECTIONS
    • 7.4.1 Reflection on the conceptual framework
    • 7.4.2 Reflection on the methodology
  • 7.5 CONCLUSIONS
    • 7.5.1 Contribution and general result of the study
    • 7.5.2 Specific conclusions about the student teachers’ CCK of functions
    • 7.5.3 Conclusions about the student teachers’ SCK of functions
    • 7.5.4 Conclusions about the student teachers’ CCK of trigonometry
    • 7.5.5 Conclusions about the student teachers’ SCK of trigonometry
    • 7.5.6 Specific findings of the study in relation to previous research
    • 7.5.7 Student teachers’ misconceptions
  • 7.6 LIMITATIONS OF THE STUDY
  • 7.7 RECOMMENDATIONS FOR PRACTICE AND RESEARCH

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