Prospective Zimbabwean "A" Level mathematics teachers' knowledge of the concept of a function
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Date
2006
Authors
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Publisher
University of the Western Cape
Abstract
The purpose of the study was to investigate prospective 'A' level mathematics teachers' knowledge of the concept of a function. The study was a case study of six prospective Zimbabwean teachers who were majoring in mathematics with the intention of completing a
programme leading to certification as secondary mathematics teachers. At the time of the study the six prospective teachers were in their final year of study. Prospective teachers' knowledge of the concept of a function was assessed through task-based interviews and
reflective interviews. These interviews, which were done over a period of three months, were structured to capture the prospective teachers' subject matter knowledge and pedagogical content knowledge for teaching the concept of a function. The interviews were also meant to
capture the prospective teachers' underlining pedagogical reasons for their choices of the examples, representations and teaching approaches when planning to teach the concept. As part of the study a theoretical framework for understanding prospective teachers'
knowledge of the concept of a function was developed. The framework, which was developed, was used as an analytical tool in analyzing prospective teachers knowledge of the concept of a function. The results of the study indicated that the prospective teachers had a process conception of a function although some of them had given a set-theoretic definition of a function in which a function is perceived as a mathematical object. They also confined the notion of a function to sets of real numbers. Functions defined on other mathematical objects (for example, the differential operator and the determinant function) were not considered as functions by five of the six prospective teachers.
Description
Philosophiae Doctor - PhD
Keywords
Ministry of Education, Mathematics National Panel, Zimbabwe Schools Examination Council (ZIMSEC), Curriculum Development Unit, American Mathematical Association of Two-Year Colleges (AMATYC), National Council of Teachers of Mathematics (NCTM), Professional Teaching Standards of the National Council of Teachers of Mathematics