Identifying Graphical Forms Used by Students in Creating and Interpreting Graphs

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 activated and used to interpret and construct graphs. In this study, we expand on the current knowledge base related to the specific graphical forms used by students. Based on data involving pairs of students interpreting and constructing graphs we present a list of empirically documented graphical forms and organize them according to similarity. We end with implications regarding graphical forms' utility in understanding how students construct graphical meanings and how instructors can support students in graphical reasoning. [For the complete proceedings, see ED630060.]