PROCEEDINGS OF THE 21ST ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2018
San Diego, California
Shape Thinking and the Transfer of Graphical Calculus Images
Page: 834
Shape thinking has previously detailed how students may view function graphs. Students using static shape thinking view a function graph as if it were a wire where learned rules, formulas and quantities appear as a consequence of the perceived shape. This study presents a case study that demonstrates how static shape thinking can be extended to other graphs seen within calculus. Results demonstrate how one first-semester calculus student perceived a “triangular” shape within a function graph. Quantities appeared as a consequence of this perceived shape and his reasoning on multiple related tasks was influenced by his transfer of this perceived shape onto subsequent graphs. Even the the student’s reasoning led to inaccurate responses to interview tasks, his reasoning was accurate and consistent within his perception