In this paper, we describe a framework for characterizing students' graphical reasoning, focusing on providing an empirically-based list of students' graphical resources. The graphical forms framework builds on the knowledge-in-pieces perspective of cognitive structure to describe the intuitive ideas, called "graphical forms", that are…

In this paper, we introduce and discuss a construct called "graphical forms," an extension of Sherin's symbolic forms. In its original conceptualization, symbolic forms characterize the ideas students associate with patterns in a mathematical expression. To expand symbolic forms beyond only characterizing mathematical equations, we use…

This work is part of a larger project that seeks to understand how students blend (integrate) chemistry and mathematics as they work through chemical kinetics problems. Here we focus on four students from our larger sample: two students that demonstrated more instances of blending chemistry and mathematics in their interviews ("high-frequency…