Developing Mathematical Understanding through Multiple Representations

Abstract

What purpose is served by studying multiple representations of a mathematical idea? Let me begin by recounting a story. Once upon a time, five people who had never seen an elephant were blindfolded and led to an elephant and asked to describe what they thought the creature looked like. The people were allowed to touch the animal. They approached it from different directions. One felt the tail, the second found its leg, the third reached for the trunk, another felt its ear, and the fifth person touched the great stomach of the animal. Each one then described his or her version of the animal and each was, in turn, completely surprised at the contrasting view offered by the others in the group. Finally, the blindfolds were removed, and the five looked at the animal that each had described. Each person realized that not only was his or her perspective valid, albeit in a limited way, but also that this applied equally to every member of the group. Only after opening their eyes (literally and metaphorically) and seeing the animal from a variety of angles could they appreciate the complete picture.