We describe results of a long-term design experiment focused on promoting mathematics learning among multilingual ninth graders classified as English Learners. The intervention at a linguistically diverse public high school in the US focused on a unit introducing concepts related to linear rates of change. We analyze results from a…

This report proposes a framework for describing student analogical reasoning activities in abstract algebra that moves beyond the traditional literature-based treatment of analogical mapping. The Analogical Reasoning in Mathematics (ARM) framework captures the activities that students engage in when anticipating, creating, and reasoning from…

This study investigates the effects of a technology methods course containing a unique collaborative design experience on prospective elementary and secondary mathematics teachers' technological beliefs, computer algebra system (CAS) beliefs, and technological pedagogical content knowledge (TPACK). Overall gain scores on all three instruments were…

We describe how we supported middle-school students developing meanings for quadratic growth by bringing together three theoretical framings and designing a task sequence grounded in that framework. Specifically, this framework was assembled from the research on students' quantitative and covariational reasoning, Realistic Mathematics Education,…

In this paper we present the results of an investigation related to the developing of mathematical knowledge and skills by first semester university students when solving a Model Eliciting Activity [MEA] which involves quadratic function knowledge. This was a qualitative research. The theoretical framework was Models and Modeling Perspective…

Facilitating productive mathematical argumentation is challenging; it is critical to develop a specific guiding vision of practices to help teachers learn to teach argumentation. However, what counts as acceptable classroom-based mathematical argumentation remains an open question. In this study, building on Habermas' theory of communicative…

We report our findings and perspective to document the knowledge exhibited by three experienced high school teachers in their instructional decisions for lessons on the equation of an exponential function. We describe the nature of the mathematical ideas and connections teachers promoted in discourse and the decisions that supported the emergence…