John S. Macnab

Visualization in mathematics, reading and science education

OVERVIEW.- PART I: AN INTRODUCTION TO VISUALIZATION.- 1. A Commonsense View and Its Problems.- 2. A History of Visualization in Psychology and Science.- 3. The Concept of Visualization.- 4. Cognitive Theory.- PART II: CURRENT EDUCATIONAL RESEARCH.- 5. Visualizations and Mathematics.- 6. Visualizations and Reading.- 7. Visualizations and Science.- PART III: CAUTIONS AND RECOMMENDATIONS.- 8. Research and Guidelines on Computer-Generated Visualizations.- 9. Concluding Comments, Recommendations and Further Considerations.- REFERENCES.- AUTHOR INDEX.- SUBJECT INDEX.

Visualizations and Science

By way of contrast to the situation in mathematics education, there has been a general consensus among researchers during the past 20 years that visualization object s assist in explaining, developing, and learning concepts in the field of science.

Visualizations and Visualization in Mathematics Education

There is no shortage of interest in visualization in mathematics education. Mathematics textbooks are filled with pictures, diagrams, and graphs. There are video lessons available for countless topics. Graphing calculators have become commonplace in secondary school classrooms. Dedicated computer programs such as Geometer’s Sketchpad, Mathematica, Maple, and the open-source programs that are intended to replicate many of their functions are now in use in secondary and postsecondary mathematics classrooms. Data visualization programs are becoming common in statistics classes. And there are countless applets available on line. Given the sheer volume of visualization materials available for mathematics education, it is surprising how little empirical support there is for their use. In addition, there are no robust educational theories of how to use best visualization in mathematics education. There are two powerful but conflicting cognitive theories of visualization, and both point to some practical application of visualization in spite of their mutual inconsistency.

Visualizations and Mathematics

The question of whether visualizations help develop mathematical concepts has an ambiguous, and oftentimes contradicting, response. We reviewed over 40 articles focusing on visualizations in mathematics classrooms, with the majority focused on general mathematics, followed by geometry (see Fig. 5.1).

Concluding Comments, Recommendations, and Further Considerations

We opened this book with the question: Is there a single defensible theoretical model of visualization? The short answer is that there is not, at least not at this time. The current state of research does not point to a single model of visualization but, rather, to partial models. We expect that in the short run educators and researchers should use the available results in contexts similar to those in which they were found, because we do not have theories adequate to the task of determining their generalizability to other situations. First, in this chapter, we review three important distinctions that we have made.

A Commonsense View and Its Problems

We introduce some commonsense notions of visualization for two reasons. First, we establish some basic ideas and vocabulary by looking at everyday examples of visualization in learning. Second, we establish a baseline for the sort of activities and objects that are the main focus of this book. Let us begin by conceiving of a visualization object as any object that a student observes to assist in the learning or understanding of some topic of educational importance. A visualization object could be a picture , a schematic diagram, a computer simulation, or a video. The student who uses the visualization object we will say is visualizing. The student who uses visual imagery in the absence of visualization object s we will say is introspectively visualizing. These terms will undergo refinement as the book proceeds, but these general notions will be sufficient to introduce our main themes.

A History of Visualization in Psychology and Science

Visualization as a psychological phenomenon has been studied for little more than a century. Nineteenth century studies opened the important and interesting question of whether visual thinking involves a reproduction of the object of the visualization or whether it is something else altogether. Despite considerable progress in psychological understanding of the mechanisms of visual perception and visual thinking, that question and others are still open. In what follows, we try to show where the main issues lie.

Research and Guidelines on Computer-Generated Visualizations

Throughout the literature, the themes of technology and computer development recur. We found 40 articles dealing with computer software and animations in general, as well as many other articles that emphasized computer -based visualization in the context of the specific subjects of mathematics , reading , and science . The impact that technology is having on educational visualization is already significant and is showing signs of growth. We further note that a peer-reviewed journal dedicated to computer issues in visualization has emerged, the IEEE Transactions on Visualization and Computer Graphics.

Visualizations and Reading

The research reviewed in this chapter supports the conclusion that there are few unqualified generalizations about the efficacy of visualization object s in reading . We begin with an examination of the important motivational role of visualization object s. Second, we examine the effect of visualizations on reading comprehension, taken to be the main aim of reading .

The Concept of Visualization

Perhaps the most defining feature of the current state of empirical research on visualization is the lack of consensus about the most elemental issues that surround it, including