School of Mathematical & Statistical Sciences Faculty Publications and Presentations

Teachers’ Perceptions of Coherence and Relevance of Advanced Mathematics for Teaching Secondary Mathematics

Document Type

Article

Publication Date

9-5-2025

Abstract

Secondary in-service and pre-service teachers often perceive a lack of coherence and relevance of advanced mathematics for their teaching, so they need opportunities in their coursework to reason about the connections between advanced and secondary mathematics and apply their advanced mathematical knowledge and practices in teaching scenarios. We designed a master’s-level mathematics for teachers course that focused on connections between secondary mathematics and abstract algebra, real analysis, and advanced probability. This course used approximations of practice (Grossman et al., 2009a) as teaching simulations in which the teachers could apply their advanced mathematical knowledge. After the course, we analyzed the teachers’ perceptions of the coherence of advanced and secondary mathematics and the relevance of advanced mathematics for teaching secondary mathematics. The coherence connections teachers perceived were related to perceiving knowledge of advanced mathematics as helpful for teachers to better understand the concepts, procedures, and mathematical practices in secondary mathematics. We identified types of ways in which teachers perceived advanced mathematics as relevant for teaching secondary mathematics: using their knowledge of advanced mathematics to (1) elicit and notice student thinking, (2) engage in mathematical practices and habits of mind while teaching, (3) explain concepts to students to make them understandable, and (4) facilitate class discourse. We then identified aspects of the course that the teachers considered beneficial for helping them perceive those connections. These included the course’s focus on specific content connections and the course’s use of approximations of practice.

Publication Title

International Journal of Research in Undergraduate Mathematics Education

DOI

10.1007/s40753-025-00274-6

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