Ways of thinking about teaching an idea in mathematics: how teachers’ mathematical meanings for teaching ideas impact their instructional practices

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 and ways of thinking about teaching an idea. 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.