Affordances for graphical shape thinking through vivid informal classroom talk

The shape of a graph arising from the covariation of variables is a crucial idea in reasoning about functions and graphs. Students’ perspectives on graph shape may foreground visual features and consider the shape to be a fixed property of the function (static graphical shape thinking). In contrast, students can perceive the graph as a trace of covarying quantities, through which its shape arises (emergent graphical shape thinking). It is of interest to understand how these perspectives are supported and promoted by teachers in classroom discourse. We present findings from a study of classroom discourse in which we used systemic functional linguistics (SFL) to identify features of how teachers and students described graphs. We identified informal but vivid descriptions of graphs that may have affordances for, and even foreground, emergent graphical shape thinking.