Apprehending Mathematical Structure: A Case Study of Coming to Understand a Commutative Ring

Simpson, A.; Stehlikova, N.

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.

Citation

Simpson, A., & Stehlikova, N. (2006). Apprehending Mathematical Structure: A Case Study of Coming to Understand a Commutative Ring. Educational Studies in Mathematics, 61(3), 347-371. https://doi.org/10.1007/s10649-006-1300-y

• Journal Article Type: Article
• Publication Date: 2006-03
• Deposit Date: Mar 21, 2007
• Journal: Educational Studies in Mathematics
• Print ISSN: 0013-1954
• Electronic ISSN: 1573-0816
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 61
• Issue: 3
• Pages: 347-371
• DOI: https://doi.org/10.1007/s10649-006-1300-y
• Keywords: Abstract algebra, Advanced mathematical thinking, Representational redescription, Structural thinking, Apprehending structure.
• Public URL: https://durham-repository.worktribe.com/output/1579512