The purpose of this study is to examine the use of a Vending Machine applet as a cognitive root for the development of preservice teachers understanding of function. The applet was designed to purposefully problematize common misconceptions associated with the algebraic nature of typical function machines. Findings indicated affordances and…

In this mixed methods study, we use positioning theory to analyze teachers' professional discussions about students' mathematical work over the course of 60 hours of professional development focusing on a learning trajectory. After identifying a category of speech actions that suggested student learning is limited by their age or grade level, a…

This paper reports on a design experiment within a professional development context purposefully planned to teach teachers about students' mathematics thinking and learning. We examine the factors to which participating elementary teachers attributed student mathematics success or failure when engaging with the projects' professional learning…

In this paper, I examine the utility of a mathematics learning trajectory as a tool to support teachers' attention to students' mathematical thinking. I present findings from one second grade teacher's use of a learning trajectory as she planned a sequence of three mathematics lessons. Findings suggest learning trajectories support teachers in…

As learning trajectories gain traction in mathematics education, we seek to understand the ways in which teachers may use them in interactions with students. This paper reports on one group of elementary teachers' use of their emerging knowledge of a learning trajectory to examine key pedagogical practices. Findings suggest that a learning…