In this article, we propose a theoretical connection between research on learning and research on teaching through recent research on students’ learning trajectories (LTs). We define learning trajectory based instruction (LTBI) as teaching that uses students’ LTs as the basis for instructional decisions. We use mathematics as the context for our argument, first examining current research on LTs and then examining emerging research on how mathematics teachers use LTs to support their teaching. We consider how LTs provide specificity to four highly used frameworks for examining mathematics teaching, namely mathematical knowledge for teaching, task analysis, discourse facilitation practices, and formative assessment. We contend that by unifying various teaching frameworks around the science of LTs, LTBI begins to define a theory of teaching organized around and grounded in research on student learning. Thus, moving from the accumulation of various frameworks into a reorganization of the frameworks, LTBI provides an integrated explanatory framework for teaching.

We describe the process and outcomes of a project aimed at bringing together a set of diverse experts to generate a set of design recommendations for what should be considered when creating, sustaining, and assessing professional development systems to support the Common Core State Standards in mathematics. Although the recommendations were generated in mathematics, the underlying guiding principles for professional development are generalizable to other disciplines. As such, we discuss implications for professional development more broadly.

This Research Commentary addresses the need for standards for describing mathematics professional development in mathematics education research reports. Considering that mathematics professional development is an emerging research field, it is timely to set expectations for what constitutes high-quality reporting in this field. Through an examination of the research reports on the topic published in the Journal for Research in Mathematics Education during the past decade, I offer a framework and a set of features to be used in initiating discussions about pros and cons of having reporting standards. I contend that when researchers have standards for describing the mathematics professional development they are studying, better quality will be attained in the new research field.

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.