Connecting Research to Teaching: When Visualization Is a Barrier to Mathematical Understanding

Abstract

AS MATHEMATICS TEACHERS, OUR INTUITION TELLS us that students benefit from being able to understand a variety of representations for mathematical concepts and being able to select and apply a representation that is suited to a particular mathematical task. Students develop mathematical power as they learn to operate on mathematical objects and to translate from one mathematical representation to another when necessary. For example, graphic representations convey mathematical information visually, whereas expressions represented symbolically may be easier to manipulate, analyze, or transform. The National Council of Teachers of Mathematics (NCTM) reinforces our intuition: “Different representations support different ways of thinking about and manipulating mathematical objects. An object can be better understood when viewed through multiple lenses” (NCTM 2000, p. 360). Notwithstanding our intuition and experience with students' representations, we teachers tend to think that students' graphic and visual abilities are always an advantage in mathematics learning. Indeed, we accept on pedagogical faith that students' conceptual understandings are enhanced whenever they use visualization.