Author ORCID Identifier


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Publication Title

Frontiers in Education


Mathematics education research has long focused on students’ conceptual understanding, including highlighting conceptions viewed as problematic and looking for ways to develop more desirable conceptions. Nevertheless, limited research has examined how mathematicians characterize understanding of concepts and definitions or promote activities beneficial for students. Based on interviews with 13 mathematicians, we present thematic characterizations of what it means to understand a concept and definition, highlight activities mathematicians believe assist students’ learning, and examine their reasons for promoting these activities.

Results include mathematically grounded descriptions of what it means to understand a concept but general descriptions of approaching and supporting learning. Implications include a need for attending to intended meanings for “understanding” in context and how this impacts appropriate activities for developing understanding, as well as a careful examination of the extant research literature’s claims about seemingly unified notions of conceptual understanding.


Publication Date


Original Citation

Rupnow, R., & Fukawa-Connelly, T. (2024). How mathematicians characterize and attempt to develop understanding of concepts and definitions in proof-based courses. Frontiers in Education, 8, 1284666.


Center for the Interdisciplinary Study of Language and Literature| Department of Mathematical Sciences


The author(s) declare financial support was received for the research, authorship, and/or publication of this article. Funding for publication was generously provided by Northern Illinois University’s Division of Research and Innovation Partnerships (RIPS) and the University Library.



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