ORIGINAL RESEARCH article
Front. Educ.
Sec. Teacher Education
Volume 10 - 2025 | doi: 10.3389/feduc.2025.1611159
This article is part of the Research TopicMathematics teachers' construction and enactment of disciplinary knowledgeView all 5 articles
Ways of thinking about teaching an idea in mathematics: How teachers' mathematical meanings for teaching ideas impact their instructional practices
Provisionally accepted
- 1Rational Reasoning LLC, Gilbert, United States
- 2Arizona State University, Tempe, Arizona, United States
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Despite decades of reform efforts, many mathematics teachers continue to struggle with implementing instruction that supports deep mathematical understanding and meaningful student engagement. This case study demonstrates how professional development targeting teachers' mathematical meanings for teaching can transform instructional practice in K-12 algebra. Tracy, an Algebra II teacher, participated in professional development focused on quantitative reasoning while implementing research-based curriculum materials. Through classroom observations, interviews, and artifact analysis, the study shows how quantitative reasoning functioned as (1) a productive framework for analyzing teachers' mathematical meanings for teaching algebraic concepts, (2) an effective target for professional development that supports teachers in constructing pedagogically powerful mathematical understandings, (3) a vehicle enabling teacher decentering, and (4) a foundation for classroom instruction emphasizing meaningful quantitative relationships. Data were analyzed through the frameworks of mathematical meanings for teaching (Thompson, 2013, 2016) and ways of thinking about teaching an idea (Carlson et al., 2024a). Findings suggest that professional development addressing teachers' mathematical meanings, combined with curriculum supporting student reasoning and ongoing classroom support, can produce significant changes in instructional practice that create high-quality learning opportunities for students.
Keywords: Mathematical knowledge for teaching, mathematics education, Mathematical meanings for teaching, Quantitative reasoning, Curricular innovation, Professional Development
Received: 13 Apr 2025; Accepted: 08 Oct 2025.
Copyright: © 2025 O'Bryan. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Alan E. O'Bryan, obryan.alan44@gmail.com
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