The growing national attention to students’ learning trajectories (LTs) renews the opportunity to explore the ways that teachers may use students’ thinking in their instruction. In this article, we examine teachers’ learning of two frameworks, one for students’ thinking in a particular domain and one for broad student-centered instructional practices, in the context of an elementary grades mathematics professional development setting. As a part of a retrospective analysis of a design experiment, we analyzed 19 lessons of teachers who participated in 60 hr of professional development designed to support their learning of one LT and one framework about student-centered instructional practices. Our findings describe the ways in which teachers brought together these frameworks to enact instructional practices that elicit and use students’ mathematical thinking in classroom instruction. We conclude by arguing that LTs can serve as a referent for student-centered instructional practices, bridging guidelines for student-centered instruction with domain-specific understandings of students’ thinking for teachers.

Mathematics teacher educators play a critical role in translating research findings into frameworks that are useful for mathematics teachers in their daily practice. In this article, we describe the development of a representation that brings together four research-based learning trajectories on number and operations. We detail our design process, present the ways in which we shared this representation with teachers during a professional development project, and provide evidence of the ways teachers used this translation of research into a pedagogical tool to make sense of students' mathematics. We conclude with revisions to the representation based on our analysis and discuss the role of mathematics teacher educators in translating research findings into useful tools for teachers.

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This study examines teachers' discussions in a professional development setting to understand the ways in which learning a mathematics learning trajectory may change aspects of their discourse about students as learners. Using mixed methods, we bring together two theoretical frames that use a Vygotskian perspective on learning to analyze professional discussions among 22 elementary-grade teachers participating in a yearlong, 60-hour mathematics professional development program. Results indicate that over time, some discursive patterns for explaining students' academic performance P. HOLT WILSON is an associate professor of mathematics education at

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