Authors: Mitchell J. Nathan and Kristen N. Bieda

March 2006, 13 pp.

Abstract: This study investigates middle school mathematics students’ views and interpretations of graphical representations as they use graphs to answer algebraic questions — specifically, questions that require them to extrapolate information from graphs. Using data from videotaped interviews, we analyzed students’ verbal responses and any gestures they used during the solution and answer phases. From the analysis of both response modalities, the constructs of bounded and unbounded views of graphs developed. The effects of these constructs and students’ metaphors for the graphs were tested against the students’ performance on far prediction tasks. Gestures provided a particularly useful window into students’ views and predicted student performance on complex tasks more effectively than speech.

Keywords: algebraic reasoning, representation, student perception and cognition, embodied cognition

Read the full working paper: What Gesture and Speech Reveal About Students’ Interpretations of Cartesian Graphs: Perceptions Can Bound Thinking (PDF)