Apprehending Mathematical Structure: A Case Study of Coming to Understand a Commutative Ring |
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| Authors: | Adrian Simpson Nada Stehlíková |
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| Institution: | (1) School of Education, Durham University, Leazes Road, Durham, DH1 1TA, UK;(2) Department of Mathematics and Mathematical Education Faculty of Education, Charles University, M.D. Rettigove 4 116 39, Praha 1, Czech Republic |
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| Abstract: | Abstract algebra courses tend to take one of two pedagogical routes: from examples of mathematics structures through definitions
to general theorems, or directly from definitions to general theorems. The former route seems to be based on the implicit
pedagogical intention that students will use their understanding of particular examples of an algebraic structure to get a
sense of those properties which form the basis of the fundamental definitions. We will explain the transition from examples
to abstract algebra as a series of shifts of attention and in this paper we will use a case study to examine the initial shift,
which we will call apprehending a structure, and examine how one student came to apprehend the structure of the commutative ring Z99. |
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