Group Theory Students' Perceptions of Binary Operation

Authors

Kathleen Mary Melhuish, Texas State University - San Marcos
Brittney Marie Ellis, Portland State UniversityFollow
Michael D. Hicks, Texas State University - San Marcos

Published In

Educational Studies in Mathematics

Document Type

Citation

Publication Date

1-1-2020

Abstract

Binary operations are one of the fundamental structures underlying our number and algebraic systems. Yet, researchers have often left their role implicit as they model student understanding of abstract structures. In this paper, we directly analyze students’ perceptions of the general binary operation via a two-phase study consisting of task-based surveys and interviews. We document what attributes of binary operation group theory students perceive as critical and what types of metaphors students use to convey these attributes. We found that many students treat superficial features as critical (such as element-operator-element formatting) and do not always perceive critical features as essential (such as the binary attribute). Further, these attributes were communicated across three metaphor categories: arithmetic-related, function-related, and organization-related.

Description

© 2020 Springer Nature Switzerland AG. Part of Springer Nature.

Locate the Document

http://doi.org/10.1007/s10649-019-09925-3

DOI

10.1007/s10649-019-09925-3

Persistent Identifier

https://archives.pdx.edu/ds/psu/32604

Citation Details

Melhuish, K., Ellis, B. & Hicks, M.D. Group theory students’ perceptions of binary operation. Educ Stud Math 103, 63–81 (2020). https://doi.org/10.1007/s10649-019-09925-3