RUME 28
2026
Alexandria, Virginia
Mathematicians’ Views on Intuitive Concepts in Abstract Algebra
Page: 1305
We explore mathematicians’ views on intuitive knowledge specific to the teaching and learning of abstract algebra. More specifically, we narrow in on the views of seven mathematicians as they discussed what the word intuitive means, what abstract algebra concepts they find intuitive or not intuitive for themselves and learners, and how those concepts became intuitive for them. Our findings highlight (a) the criteria mathematicians used to determine if a concept was intuitive or not, and (b) the varied approaches that they took to develop an intuitive feel for some of the most difficult abstract algebra concepts. These findings contribute to the fields’ understanding of intuitive knowledge as we compile defining criteria for “intuitive” and undocumented methods used to develop an intuitive feel for abstract algebra concepts. We also provide future directions for research.