Visualization in Mathematics Learning

Exploring the role of visualization in mathematics learning

Abstract

The role of visualization in mathematics learning has been the subject of much research (e.g. Arcavi, 2003 Bishop, 1989 Eisenberg Dreyfus, 1986 Presmeg, 1992 Stylianou Silver, 2004). In accordance to Zimmermann and Cunningham (1991) as well as Hershkowitz et. al. (1989), Arcavi (2003) defines visualization as followsVisualization is the ability, the process and the product of creation, interpretation, use of and reflection upon pictures, images, diagrams, in our minds, on paper or with technological tools, with the purpose of depicting and communicating information, thinking about and developing previously unknown ideas and advancing understandings.This definition emphasizes that, in mathematics learning, visualization can be a powerful tool to explore mathematical problems and to give meaning to mathematical concepts and the relationship between them. Visualization allows for reducing complexity when dealing with a multitude of information. However, the limitations and difficulties around visualization and even the reluctance to visualize have also been discussed (Arcavi, 2003 Eisenberg, 1994 Stylianou Silver, 2004). Visual techniques which rely on “not always procedurally ‘safe’ routines” (Arcavi, 2003) are considered to be cognitively more demanding than analytical techniques. In a different context, visualization is discussed as an important part of so- called “concept images” (Tall Vinner, 1981). The concept image includes visual images, properties and experiences concerning a particular mathematical concept. To understand a formal mathematical concept often the learner is required to generate a concept image for it.Nevertheless, Vinner (1997) points out that “in some cases the intuitive mode of thinking just misleads us.” The chapters focus largely on the visual aspects of the concept image.