Abstract
What is mathematics? The difficulty of having a precise, universal definition of mathematics has led prospective teachers to define the term in ways that make sense to them. This paper is part of a larger research project conducted in 2000 in an Ontarian university, Canada. The objectives were to identify and discuss conceptualizations of mathematics that prospective teachers brought to their preparation program and to explore the implications of such conceptualizations in terms of teaching and learning. It was believed that both the identification tools and understandings of prospective teachers’ conceptualizations of mathematics were significant for designing an effective pedagogy in accordance with mathematics reform-based perspectives. The research sample consisted of ten prospective teachers enrolled in a one-year bachelor of education program at an Ontarian university. The research used mathematics autobiographies of the respondents and semi-structured interviews of them as sources of data. Guided by the theory of personal construct for analysis of the data, the results showed that the respondents conceptualized mathematics in terms of metaphor, metonymy and combination of the two. The conclusion explores implications of such conceptualizations for mathematics teaching, learning and assessment.
Highlights
AND PURPOSE OF RESEARCHOver the years, mathematics educators, researchers and theorists have used different strategies to think about the nature of mathematics
Common themes running through the mathematics autobiographies and the semi-structured interview transcripts were grouped into metaphor, metonymy, and a combination of the two, using Kelly’s (1955) theory of personal construct as a guide
Metaphoric conception of mathematics has to do with defining mathematics in terms of something else, such as climbing steps or ladder, symbols or building a house
Summary
AND PURPOSE OF RESEARCHOver the years, mathematics educators, researchers and theorists have used different strategies to think about the nature of mathematics. Two dominant schools of thought can be associated with the nature of mathematics: Absolutism and fallibilism (Ernest, 1996). The absolutist orientation views mathematics as objective, absolute, and incorrigible body of knowledge that has been discovered and built on foundations of deductive logic. The fallibilist philosophy, on the other hand, views mathematics as a social construction, fallible and open to revision and interpretation in respect of its proofs and concepts. These philosophical orientations tend to influence mathematics teaching and learning; yet teacher educators in Ontarian universities hardly provide opportunities for prospective teachers to explore their conceptualizations of mathematics and their ramifications on teaching and learning of mathematics.
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