Sameness in Mathematics: A Unifying and Dividing Concept

While many aspects of the teaching and learning of specific advanced mathematics courses have been studied, limited work has examined mathematical themes like sameness or its instantiations across disciplines. In this paper, we explore algebraists' collective example space for mathematical same...

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Bibliographic Details
Published in:International Journal of Research in Undergraduate Mathematics Education 2023-08, Vol.9 (2), p.398-425
Main Authors: Rupnow, Rachel, Randazzo, Brooke, Johnson, Eric, Sassman, Peter
Format: Article
Language:English
Subjects:
Advanced Courses
Algebra
Learning Theories
Mathematical analysis
Mathematical Concepts
Mathematics
Mathematics Education
Qualitative analysis
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Summary:While many aspects of the teaching and learning of specific advanced mathematics courses have been studied, limited work has examined mathematical themes like sameness or its instantiations across disciplines. In this paper, we explore algebraists' collective example space for mathematical sameness. We used qualitative methods to analyze survey responses from 197 algebraists in order to identify specific mathematical concepts that the algebraists associated with sameness and relevant factors to consider when determining sameness of objects. Using variation theory, we introduce the notion of a community example space for algebraists to highlight specific dimensions of variation in sameness as well as the range of variation for each dimension through specific instantiations given by multiple participants. Dimensions of sameness included contexts, concepts, objects, properties, and qualities. These results suggest potential for building connections across levels and branches of mathematics by highlighting how different choices for each dimension of sameness can produce different instantiations of sameness.
ISSN:2198-9745
2198-9753
DOI:10.1007/s40753-022-00178-9