Response to "Editors’ Introduction: What Is Mathematical Visualization?" by Zimmermann and Cunningham

After reading this introduction, I am not sure that I fully understand what is meant by visualization in mathematics education. The definition and interpretation of the term "visualization" depends on who is describing this term. First, mathematics educators interpret visualization to describe "the process of producing or using geometrical or graphical representations of mathematical concepts, principles or problems, whether hand drawn or computer generated." Second, for scientists, the process of visualization enhances "scientific discovery and fosters profound and unexpected insights." Last, for psychologists, this term merely represents an individual's "ability to form and manipulate mental images."

Psychologists' narrow definition of visualization has major impacts on mathematics education. Psychologists often test their subjects' capacity to "form mental images" through answering a series of questions. These test results are then analysed, repeated, and observed in order to provide their insights to the process of visualization. However, in terms of mathematical visualization, the editors, suggest that manipulating mental images without the use of paper-and-pencil or computers to be an artificial experience. When curriculum policies are based on the so-called objective findings of psychological studies, psychologists’ interpretations and recommendations may be implemented. What may not be taken into account when curriculum decisions are made is the fact that the objectives of the psychologists' and mathematics educators' research interests. In terms of mathematical visualization, the objective is to be able to generate "an appropriate diagram to represent a mathematical concept or problem and to use the diagram to achieve understanding." This implies that visualization in mathematics education can be thought of as a tool for forming mental images (not an end) and for "mathematical discovery and understanding."

Zimmermann, Walter, Cunningham, Steve. Editors’ introduction: What is mathematical visualization 1991