Engaging in the construction and interpretation of graphs is a complex process involving concerted activation of context-specific cognitive resources. As students engage in this process, they apply fine-grained, intuitive ideas to graphical patterns: graphical forms. Using data involving pairs of students constructing and interpreting graphs, we…

This review of the introductory instructional substance of functions and graphs analyzes research on the interpretation and construction tasks associated with functions and some of their representations (algebraic, tabular, and graphical). The nature of learning is analyzed in terms of intuitions and misconceptions. (TJH)