Abstract
M.Ed. (Mathematics Education)
This dissertation was on mathematical proficiencies that learners displayed in their response to final examination questions on sequences and series, differential calculus, analytical geometry and trigonometry. The main focus was on four mathematical proficiencies, procedural fluency, conceptual understanding, strategic competence and adaptive reasoning. The initial goal was to review examination questions to identify mathematical proficiencies that the examination questions demanded and then an analysis of learners’ scripts to identify the mathematical proficiencies that the learners displayed in their response to examination questions.
Review of literature first focused on the theoretical framework of the study, constructivism, its guiding principles and how it contributes towards mathematics learning. The framework for mathematical proficiency was shown with an aim of viewing other underlying issues on mathematical proficiency. The four mathematical proficiencies; conceptual understanding and procedural fluency constitute mathematical knowledge and strategic competence and adaptive reasoning are mathematical skills. Mathematical tasks are reviewed as properties of well-structured mathematical tasks in which examination questions were also mathematical tasks. The taxonomy of learning was discussed with an aim of finding properties of the taxonomy that inform the structure of the examination questions. Examination questions on sequences and series, differential calculus, analytical geometry and trigonometry were reviewed, to find mathematical proficiencies that the examination questions demanded and those that learners display in their responses.