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A growth-oriented route to the reification of function. (English)
Owens, D.T. et al., 17. annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA XVII). Proceedings. Vol. 1. ,. 284-290 (1995).
This paper presents an alternate perspective for utilizing the action/process/object framework when discussing student conceptions of function. This perspective extends previously used frameworks by incorporating student conceptions that deal with functional properties and situational contexts, but differs in the analysis of the nature of the functional properties that are considered. The hypothesis is that students not only use notions of set-based correspondences and transformations to think of functions as mathematical objects, but functions are also conceived as mathematical objects that possess (or fail to possess) growth properties of specific functions. These properties include symmetry, linearity, continuity, etc. It is argued that all students who develop a structural view utilize functional properties, but a focus on different kinds of properties produce different conceptions of function. Empirical evidence is used to support the theory. (orig.)
Classification: I20
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