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Teacher conceptual knowledge exercise in statistics
The conceptual knowledge exercise was adopted to collect data in this study. The National Curriculum Statement for Mathematics for the Senior Phase of the Further Education Training (FET) bands for Grades 10–12 and the prescribed textbooks were reviewed and analysed. The aim was to ascertain the targeted knowledge, competence and skills for developing the test items based on the mathematics assessment taxonomy. A large number of multiple-choice test items were initially formulated by the researcher from sources such as public examinations, locally prepared past examinations and tests, selection tests, achievement tests and textbooks in mathematics. The items were designed in line with Bloom’s Taxonomy and the South African Mathematics Assessment Taxonomy, as indicated in the examination guidelines of the NCS (DoE, 2008) and Table 3.2. The competencies tested according to Bloom’s Taxonomy included knowledge, comprehension, analysis, synthesis, application and evaluation (DoE, 2010). The levels of the mathematics assessment taxonomy are knowledge (level 1); applying routine procedures in familiar contexts (level 2); applying multi-step procedures in a variety of contexts (level 3); and reasoning and reflecting (level 4) (DoE, 2010). Comprehension and application of Bloom’s Taxonomy were used to design the conceptual knowledge exercise, in line with the mathematics assessment taxonomy. The mark allocation was the total mark allocated to all items that were developed according to levels. For instance, all marks allocated to level 1 questions that test knowledge in any mathematics test or examination must not exceed 20 out of the total mark of 100 for the examination or test.
Teacher written reports
The teachers’ structured written reports (ref Appendix XXVII), in which they recorded what made the lessons easy or difficult, were used to assess instructional strategies and learners’ learning difficulties after a four-week period of teaching statistics. The purpose of the teachers’ written reports was to determine what (for the teacher) made the lessons easy or difficult, and to triangulate other data related to how the teachers developed their PCK over time. The written reports were compiled from teachers’ and learners’ portfolios, as well as learners’ workbooks. For instance, the participating teachers were asked, ‘How did learners respond to classroom activities as well as homework or assignments?’
The teachers’ portfolios contained information such as a formal programme of assessment in mathematics for Grade 11, mathematics assessment tasks (standardised tests, assignments, investigations or projects and examination papers), tools for assessments (memoranda, checklists, rubrics, etc), and model answers for all assessment tasks. The learners’ portfolios contained continuous moderation reports, a summary of marks, tests, examinations, and assessments (DoE, 2010).
Document analysis
In this study the documents analysed in terms of teachers’ compliance with curricular recommendations for teaching and learning school statistics were the learners’ class workbooks, learners’ and teachers’ portfolios, and the NCS for mathematics. The purpose of the analysis was to triangulate the data, using the teacher interviews, questionnaires, lesson observation and written reports on how teachers developed their PCK in statistics teaching.
At the end of the four weeks’ teaching, these documents were made available to the researcher.
The learners’ workbooks contained completed, written classwork, homework, and remedial work. Teachers’ portfolios for example included work samples and reflective commentary by the teachers as to what had made the lesson easy or difficult, and intervention strategies adopted to address learners’ learning difficulties, if any (ref Appendix XXI).
The NCS policy documents gave an indication of whether the teachers were adhering to policy recommendations for teaching and learning, such as the work schedule to be used for teaching statistics according to grade, resources, and assessment plans. It is assumed that a teacher with adequate knowledge of the curriculum would be able to design good teaching strategies in line with the curricular goals. In practice, this requirement meant checking for consistency in the implementation of lesson plans according to the NCS.
CHAPTER 1
Introduction
1.1 Background to the study
1.2 The research problem
1.3 Aims of the Study
1.4 Statement of the problem
1.5 Research questions
1.6 Significance of the study
1.7 Theoretical framework
1.8 Scope of the study
1.9 Criteria for selecting the topic
1.10 Definition of terms
1.11 The chapter structure of the thesis
1.12 Summary of the chapter
CHAPTER 2
2.0 LITERATURE REVIEW
2.1 Introduction
2.2 National Curriculum Statement for mathematics and statistics
2.3 Research on teaching of statistics in school mathematics
2.4 Assessing Teachers’ PCK
2.6 Summary of the chapter
CHAPTER 3
3.0 RESEARCH METHODOLOGY AND PROCEDURE
3.1 Introduction
3.2 Assumption of PCK development during classroom practice
3.3 Research design and methods used in this study
3.4 Population and sample description
3.5 Research instruments used for collecting data
3.6 Validation of the research instrument
3.7 The Pilot study
3.8 The Main study
3.9 Data analysis and results of the Main study
3.10 Ethical issues
3.11 Summary of the chapter
CHAPTER 4
4.0 DATA ANALYSIS AND DISCUSSION
4.1 Introduction
4.2 Conceptual knowledge exercise
4.3 Teacher demographic profile
4.4 Concept mapping
4.5 Classroom practice (Lesson observation)
4.6 Video Recording of the lesson observation of the four teachers
4.7 Teacher development of PCK
4.8 Summary of the chapter
CHAPTER 5
5.0 Discussion of results
5.1 Introduction
5.2 Teacher development of PCK
5.3 Evaluation of theoretical framework
5.4 Summary of chapter
CHAPTER 6
6.0 Summary and recommendations of the study
6.1 Introduction
6.2. Focus of the study
6.3 Summary of the results according to the theoretical framework
6.4 Concluding remarks
6.5 Educational implication of the study
6.6 Suggestions for further study
6.7 Limitations of the Study
6.8 The role of the researcher in the non-participatory lesson observation
6.9 Summary of the chapter
BIBLOGRAPHY
