In this paper, we trace the development of our theorizing about students' mathematical understanding, showing how the adoption of an enactivist perspective has transformed our gaze in terms of the objects of our studies and occasioned for us new methods of data analysis. Drawing on elements of Pirie-Kieren (P-K) Theory for the Dynamical Growth of…

"Setting the Stage with Geometry" is a new math program aligned with the National Council of Teachers of Mathematics (NCTM) standards that is designed to help students in grades 6-8 build and reinforce basic geometry skills for measuring 2D and 3D shapes. Developed by The Actuarial Foundation, this program seeks to provide skill-building math…

Over the years the technology behind displaying the image of the unit circle has changed, but the defining features remain constant. The key question for the author as a teacher is this: are the relationships embodied in the image simple, memorable and rich enough to be grasped by any KS3 student at his school? It needs to be simple enough to…