Mathematics

This conceptual paper presents a framework for supporting multilingual students’ mathematical discourse through teacher professional development grounded in design-based research (DBR). Drawing on sociocultural learning theory, the Integrated Language and Mathematics Project (ILMP) was co-developed with elementary educators to promote integrated instruction that simultaneously advances students’ mathematical understanding, language development, and cultural identity. The ILMP framework centers around three instructional pillars: attention to language, attention to mathematical thinking, and cultural responsiveness. Through collaborative inquiry cycles, educators engaged as learners, contributors, and designers of practice, iteratively enacting and reflecting on instructional strategies rooted in students’ linguistic and cultural assets.

Prior research has explored innovative ways to introduce data science to young learners, emphasizing not only the development of data skills but also the connection of data science to students’ authentic inquiries and critical actions. Building on this foundation, this study aims to achieve two complementary goals: integrating Knowledge Building, a well-established pedagogical approach, into K-12 data science education, and enhancing students’ epistemic agency through data practices in knowledge building.

Fostering student engagement with mathematical reasoning and proving requires a special kind of teacher knowledge – Mathematical Knowledge for Teaching Proof (MKT-P). One important component of MKT-P is Knowledge of Content and Teaching specific to Proof (KCT-P), which is knowledge of pedagogical practices for supporting student learning of proof. Providing effective feedback on students' mathematical arguments is one of the key aspects of KCT-P. This study examined the qualitative differences in written feedback of secondary teachers, undergraduate mathematics and computer science majors, and pre-service teachers participating in a capstone course focused on mathematical reasoning and proving.

Grounded in a vision of teaching that is responsive to children’s mathematical thinking, we investigated connections between teachers’ expertise in noticing children’s thinking and their centering of children’s thinking in whole-class discussions. This study provides insight into the importance of expertise in teacher noticing for whole-class discussions while also illustrating the mathematical and pedagogical richness of the details of children’s mathematical thinking.

We present findings from an analysis of tests of teacher mathematical knowledge identified over a 20-year period of mathematics education literature, and report on how these tests are discussed in the literature, with a focus on validity arguments and evidence.

In this mixed-methods study, we introduce an activity-based perspective on mathematical authority that considers who leads mathematical activities in a classroom. Our framework for mathematical authority extends existing research that focuses primarily on Authoring mathematical ideas to include the activities of Visualizing and Speaking.