Career choice and mathematics achievem – Project topics materials

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INTRODUCTION AND BACKGROUND

A thorough understanding of mathematics is an asset if not essential for applicants interested in obtaining employment in South Africa. According to Steen (1989:19) mathematics does not only empower people with the capacity to con trol their lives but also provides science a firm foundation for effective theories, and also guarantees society a vigorous economy. At its most basic level mathematics is a requirement for science, computer technology and engineering courses. Seen from a social perspective, mathematical competence is an essential component in preparing numerate citizens for employment and it is needed to ensure the continued production of highly skilled persons required by industry, science and technology. Throughout the world a major difference between the advanced and the underdeveloped count ries of today has been noted in their level of development in modern science and technology. There is thus a compelling need for South Africa as a developing country to keep up with new and emerging technologies. However, literature on the academic achievements and success of historically disadvantaged learners in mathematics is mostly about their academic failure. Since mathematics is a requirement for science, computer technology and engineering courses as well as for advanced mathematics courses, a low level of mathematics has become a barrier preventing many learners from pursuing careers related to these areas at tertiary institutions (universities or universities of technology).

THE MAIN RESEARCH PROBLEM

Mouton (1996) believes that research begins with reflection, which includes unstructured thoughts, assumptions and questioning. This r eflection can be seen as a run-up to the development of a research problem. The central research question to be addressed in the study is: What factors facilitate achievement in Grade 12 mathematics in traditionally disadvantaged schools, particularly in Limpopo Province?

FORMULATION OF THE RESEARCH QUESTIONS

In any scientific study the research problem has focus, direction and an element of planning. Relevant questions focus the researcher’s attention on the aspects that should be cientifically described. This will provide a direction factor for the study (McMillan &Schumacher, 2001).

EXPECTED OUTCOMES OF THE STUDY

Factors that contribute to better achievement in mathematics of learners in traditionally disadvantaged schools will be identified and studied. The methods that will be used to achieve this aim are focus group interviews, classroom observations and individual interviews with the selected students and teachers. In order to start any realistic attempt to trace factors that facilitate achievement in mathematics in traditionally disadvantaged secondary schools, a thorough investigation will first be conducted to detect the possible causes of what is perceived to be a very poor situation. Moreover, in an attempt to gather more information concerning the research problem, this study will seek to find answers to the fol lowing questions:
RESEARCH QUESTION 1
What are the attitudes and competencies of mathematics teachers in high-performing and under-performing schools?
RESEARCH QUESTION 2
What are the learners’ attitudes towards mathematics and their perceptions of their successes and/or failures in mathematics?
RESEARCH QUESTION 3
What factors facilitate successful classroom practices in mathematics in Grade 12 schools?

CHAPTER 1: INTRODUCTION
1.1 Introduction and background
1.2 The main research problem
1.3 Formulation of the research questions
1.4 Expected outcomes of the study
1.5 Significance of the proposed study
1.6 Motivation of the study
1.7 Motivation for selection of grade 12 classes
1.8 Research design overview
1.8.1 Data collection and analysis strategies
1.8.2 Triangulation
1.8.3 Sampling strategy
1.8.4 Participants/ respondents in the study
1.9 Ethical considerations
1.9.1 Permission
1.9.2 Appointments
1.9.3 Confidentiality
1.9.4 Post-research relationships
1.10 Definition of key concepts
1.10.1 Disadvantaged learner
1.10.2 Factor
1.10.3 Effective learning
1.10.4 Learner
1.10.5 Achievement
1.10.6 Secondary school mathematics
1.11 The role of the researcher
1.12 Limitations and assumptions of the research design
1.13Summary and chapter divisions
CHAPTER 2: LITERATURE REVIEW
2.1 Introduction
2.2 School -related variables
2.2.1 Learning environment
2.2.2 Curriculum
2.2.3 School and class size
2.2.4 Culture
2.2.5 Effectiveness of schools
2.3 Learner-related variables
2.3.1 Attitudes and beliefs
2.3.1.1 Career choice and mathematics achievem
2.3.1.2 Enjoyment and ability
2.3.1.3 Peer pressure
2.3.1.4 Peer support
2.3.2 Effort and recognition
2.3.2.1 Self-esteem and mathematics anxiety
2.3.2.2 Interest
2.3.3 Language
2.3.4 Learner motivation
2.3.5 Learners’ academic involvement
2.3.5.1 Homework
2.3.5.2 Time on task
2.3.6 Learning approaches
2.3.7 Learners’ poor achievement in mathematics
2.4 Teacher-related variables
2.4.1 Attitudes and beliefs
2.4.1.1 Attitudes towards mathematics
2.4.1.2 Attitudes towards learners in mathematics
2.4.2 Teacher quality
2.4.2.1 Teachers’ role
2.4.2.2 Pedagogical content knowledge
2.4.2.3 Teacher experience and in-service training
2.4.2.4 Competence
2.4.3 Mathematics lesson structure
2.4.4 Teaching methods and strategies
2.4.5 Indicators for effective classroom teaching
2.4.6 Co-operative learning
2.4.7 Problem-solving
2.5 Epistemological considerations
2.5.1 Behaviourism
2.5.2 Gestalt learning theory
2.5.3 Information processing
2.5.4 Cognitive learning theories
2.5.5 Constructivism
2.5.6 Constructivism and epistemology
2.5.7 Constructivism and mathematics learning
2.6 Summary
2.7 Conclusion
CHAPTER 3: RESEARCH DESIGN AND METHODOLOGY
3.1 Introduction
3.2 Research design
3.3 Research questions and statement of hypothesis
3.4 Sampling of schools
3.5 Defining the sample
3.6 Organisation of the study
3.6.1 Qualitative research methodology
3.6.1.1 Phase 1
3.6.1.1.1 Part 1: Classroom observation
3.6.1.1.2 Part 2: Interviews with teachers
3.6.1.2 Phase 2: Focus group interviews
3.6.1.3 Data analysis of qualitative research
3.6.1.3.1 Steps in data analysis
3.6.1.3.2 Tesch’s approach
3.6.1.3.3 Strauss and Corbin’s approach
3.6.1.3.4 Data coding and categorisation of interviews
3.6.1.3.5 Processing interview data
3.6.2 Quantitative research
3.6.2.1 Phase 3
3.6.2.1.1 Questionnaire for learners
3.6.2.1.2 Questionnaire for teachers
3.6.2.2 Data analysis of quantitative research
3.7 Triangulation (quality assurance)
3.8 Issues to consider when using triangulation procedures
3.9 Quality assurance: reliability of the study
3.10 Quality assurance: validity of the study
3.11 Bias of the study
3.12 Ethical considerations
3.12.1 Permission
3.12.2 Appointments
3.12.3 Confidentiality
3.12.4 Consent
3.12.5 Data anonymity
3.12.6 Post-research relationships
3.13 Summary
CHAPTER 4: RESULTS OF QUALITATIVE INVESTIGATION
4.1 Introduction
4.2 Phase 1: Classroom observations and teacher interviews
4.2.1 Results from school A: High-performing school
4.2.2 Results from school B: High-performing school
4.2.3 Results from school C: Low-performing school
4.2.4 Results from school D: Low-performing school
4.2.5 Summary of results obtained from Phase 1
4.3 Phase 2: Focus group interviews
4.3.1 Focus group interviews: High-achieving learners
4.3.2 Focus group interviews: Middle-achieving learners
4.3.3 Focus group interviews: Low-achieving learners
4.3.4 Comparison of all focus group interviews
4.3.5 Summary of results obtained from Phase 2
4.4 Conclusion
CHAPTER 5: ANALYSIS AND INTERPRETATION OF QUANTITATIVE DATA: RESPONSES FROM LEARNERS
5.1 Introduction
5.2 Category A: Parental education and involvement
5.3 Category B: Commitment
5.3.1 Items with a significant difference
5.3.2 Items with a difference that was not significant
5.3.3 Précis of findings
5.4 Category C: Attitudes and self-concept
5.4.1 Items with a significant difference
5.4.2 Item for which the difference was almost significant
5.4.3 Items for which the difference was not significant
5.4.4 Précis of findings
5.5 Category D: Perceptions of and interaction with peers
5.5.1 Items with a significant difference
5.5.2 Item for which the difference was almost significant
5.5.3 Précis of findings
5.6 Category E: Perceptions of teachers
5.6.1 Item with a significant difference
5.6.2 Items for which the difference was not significant
5.6.3 Précis of findings
5.7 Category F: Perceived causes for poor performance in mathematics
5.7.1 Items with a significant difference
5.7.2 Items for which the difference was almost significant
5.7.3 Items for which the difference was not significant
5.7.4 Précis of findings
5.7.5 Learners’ most important cause for poor performance
5.8 Summary on chapter findings
CHAPTER 6: ANALYSIS AND INTERPRETATION OF QUANTITATIVE DATA: RESPONSES FROM TEACHERS
6.1 Introduction
6.2 Teachers’ responses to the questionnaire
6.2.1 Category A: Teacher commitment
6.2.2 Category B: Teacher attitude and self-concept
6.2.3 Category C: Teacher perceptions of learners and interaction with learners
6.2.4 Category D: Teachers’ instructional methods
6.2.5 Category E: Perceived causes of poor performance in mathematics
6.3 Teachers’ responses to open ended questions
6.3.1 Summary of responses to factors contributing to good achievement in mathematics
6.3.2 Summary of responses to factors contributing to poor achievement in mathematics
6.3.3 Summary of responses on how teachers motivate learners in mathematics
6.3.4 The principal’s contribution to learners’ achievement in mathematics.
6.4 Summary on chapter findings
CHAPTER 7: CONCLUSIONS AND RECOMMENDATIONS
7.1 Introduction
7.2 Overview of the study
7.3 Addressing the research questions
7.3.1 The first research question
7.3.2 The second research question
7.3.3 The third research question
7.4 Conclusion
7.5 Recommendations
7.5.1 Recommendation 1: Influence of learners’ career prospects
7.5.2 Recommendation 2: Increasing learners mathematics attitudes and self-concept
7.5.3 Recommendation 3: Improving mathematics study and learning methods
7.5.4 Recommendation 4: Improving order and disciplin mathematics classrooms
7.5.5 Recommendation 5: Encourage ongoing teacher development in mathematics
7.6 Constraints and limitations of the study
7.6.1 Limitations regarding participants to the study
7.6.2 Limitations related to the method used for collecting data
7.7 Suggestion for further study
8. Bibliography