Drawing on the conference theme of looking back and looking ahead, in this paper I first look at the placement of equity throughout PME-NA as a way to set the stage for where to go next. I then focus on aspects of my work on the affordances and tensions around out-of-school and in-school mathematics to discuss equity as opportunity to participate…

In this paper, we integrate a set of theoretical considerations that together serve as a model for investigating how high-leverage practices could be generative of teacher learning. We use the context of rehearsals to investigate how the use of a specified question sequence aimed at eliciting student mathematical thinking can afford opportunities…

Over the last couple of decades, there has been a growing call for teachers to become more responsive to the increasing cultural diversity of students as a means of improving students' experiences in school and their learning outcomes. Challenges exist in working with secondary mathematics teachers due to the common belief that math is…

We describe two metaphors that we hope can be used to better understand the contemporary mathematics curriculum context in U.S. middle schools, to see how this new context is both similar to and different from prior curriculum contexts. We explain the role and positioning of middle school mathematics curriculum materials over the last century or…

We report on the development and evaluation of MathVision, a mobile-application designed to develop Virtual Professional Learning Communities through asynchronous discussion about 2nd, 3rd, 4th, and 5th grade students' mathematical thinking. MathVision allows teachers to upload videos of problems solving sessions using Cognition Based Assessment…

In this study we examined two prospective secondary mathematics teachers' constructions of box plots and their understanding of the distribution they were representing. The participants constructed box plots with paper-and-pencil, graphic calculator and TinkerPlots during clinical interviews. The study indicated that prospective mathematics…

This study is part of a larger research program aimed at studying mental mathematics with objects other than numbers. It concerns operations on functions in a graphical environment with Grade-11 students. Grounded in the enactivist theory of cognition, particularly in problem-posing, the study aims to characterize students' mathematical activity…

This paper reports an instrumental case study of the strategies employed by Year 11 students engaged in solving a functions population task. The task was implemented as part of a study of students studying functions in a Technology-Rich Teaching and Learning Environment (TRTLE). Student strategies related to the perception and enactment of…

This paper addresses the role of learning progressions in informing many international standards documents, discussing the affordances and limitations of building standards and curricula from a learning progression model. An alternate model, the hypothetical learning trajectory, is introduced and contrasted with learning progressions. Using the…

This paper details a framework for evaluating the potential of particular forms of technology for supporting student engagement with mathematics. I propose that, focusing on the strength of affordances to engage in particular ways allows us to begin to build an analytic frame that serves two purposes: (1) to begin to document learning as an…

The theme of the 38th meeting of the International Group for the Psychology of Mathematics Education (PME 38) and the 36th meeting of the North American Chapter of the Psychology of Mathematics Education (PME-NA 36) was "Mathematics Education at the Edge." Academically, the theme provides opportunities to highlight and examine…