Reports on a research project designed to implement an adapted Lesson Study cycle whereby pre-service mathematics teachers co-create a lesson with an experienced expert instructor and observe the instructor teach the lesson. Results show development in the pre-service teachers' attention to elements of planning such as anticipation and pedagogical…

We examined the suggestions mathematics coaches provided to teachers as part of one-on-one coaching cycles. The purpose was to understand the object (content) of the suggestions, the lesson phase in which the suggestion would occur, and the clarity of the suggestion (how actionable the suggestion would be if the teacher followed the suggestion).…

By highlighting the curriculum modifications that lead to maintaining, or enhancing, the mathematical quality of an algebra lesson introducing the substitution method for solving systems of equations from an algebra textbook, we present an analysis of how a teacher and her students impact how the mathematical ideas unfold across the lesson and how…

Mathematics teachers make numerous decisions that form lessons that in turn greatly influence what students learn. In making these decisions, teachers rely on their curricular reasoning (CR) to decide on what mathematics to teach, how to structure their lesson, and what problems or tasks to use to achieve their lesson goals. However, teachers…

In this paper, we offer a novel framework for analyzing the Opportunities for Reasoning-and-Proving (ORP) in mathematical tasks. By drawing upon some tenets of the commognitive framework, we conceptualize learning and teaching mathematics via reasoning and proving both as enacting reasoning processes (e.g., conjecturing, justifying) in the…

Positioning theory has been used in research to understand how elementary student teachers are positioned while working with their mentor teacher. While this research has identified four general positions, there remains a lack of clarity about these positions, particularly in how they differ. This study explores three contrasting student…

Teachers hold complex goals when making decisions about their curriculum. In particular, the proliferation of supplemental resources means teachers negotiate both how to use the adopted curriculum and how to supplement it with additional resources. Through a study of the language teachers use, the decision-making of three elementary classrooms is…

This study investigated how 155 pre-service teachers solved three pattern generalization problems in a two-part written test and sequenced them for teaching purposes to demonstrate their curricular noticing. Participants' solutions were analyzed using inductive content analysis, which showed that only 8.4% of PSTs produced correct answers to all…

This study investigated Queer high school students' participation in the teaching of mathematics for social justice. The goal of this research was to introduce the TMSJ to Queer students and understand their experiences with this type of teaching. This study is centered on the transformative paradigm using a poststructuralist approach. Therefore,…

The fields of quantitative and covariational reasoning boast a wide range of powerful theoretical tools, which are described carefully in the literature. Less frequent and explicit attention, however, has been paid to writing down detailed, practical guidance for operationalizing these theoretical constructs. Some guidance is provided by…

We examined changes in how mathematics coaches facilitated debriefing conversations after learning about a debrief conversational structure we created based on the principles of our content-focused coaching model. We compared participant coaches' first debriefing conversation, which occurred prior to learning about the debrief conversational…

Secondary mathematics preservice teachers enrolled in a methods class at a large Midwestern University were supported to develop their TPACK knowledge. Instructional tasks included engaging with explorations using technology to support reasoning and sense making, creating entries for a technology portfolio, studying theoretical constructs about…

Describing and measuring instructional quality of mathematics lessons is a common goal amongst mathematics education researchers. Such work takes several forms such as classifying and coding instructional moves and student activity or providing high-level rubric-based scores in relation to categories. In this work, we share an innovative mixed…

This study investigated the effect of teaching rehearsals on 22 preservice secondary mathematics teachers (PSMTs) who were in their first mathematics pedagogy course. The objective of the teaching rehearsal was to introduce PSMTs to student-centered teaching. PSMTs worked in groups to complete a learning cycle consisting of analyzing a mathematics…

This paper explores how a professional learning community (PLC) redesigns high school mathematics lessons towards a shared commitment. We describe the nature of a PLC's collective curricular vision to illuminate how teachers can come to new understandings as a group in order to shift the ways students experience mathematics. Using the curricular…