DOI: 10.14686/buefad.1905992 ISSN: 1308-7177

How Can We Visualize Mathematical Concepts Outside the Box? Tracing the Journey from Formal Definitions to Inventive “Pictures of Mathematical Concepts”

İlknur Gülşen Turgut, Ahmet Arıkan
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Purpose: Visualization offers the opportunity to represent the features of mathematical concepts and the relationships between mathematical concepts in various forms. This study aimed to examine the visualization process of mathematical concepts of preservice mathematics teachers (PMTs). Method: The study employed a qualitative method. All participants were given formal definitions of mathematical concepts and asked to draw pictures of them. They attempted to visualize the features and relationships of concepts with the help of drawing and painting. Discussions were carried out in the classroom about whether the pictures were appropriate in terms of representing the concepts visually. Following these discussions, interviews were conducted with the groups whose pictures were deemed suitable by the class to represent the concept visually. The pictures and views of the PMTs regarding the visualization process of the concepts were analyzed through the techniques of the grounded theory method. Findings: It was determined that the PMTs did not randomly draw pictures of the concept; instead, they drew their pictures from the ideas they associated with the concepts. It was also determined that PMTs tend to produce pictures that illustrate more than one concept in one representation, and they think it is more useful this way. It was observed that there were some differences between the pictures of the concepts drawn by the PMTs and their explanations of the concepts, and that PMTs sometimes depicted more or fewer aspects of the concepts than they had thought. Conclusion: Through their pictures of concepts, the PMTs discovered relationships among concepts, or between concepts and pictures, and made some generalizations.

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