Role of Visualization in Mathematical Abstraction: the Case of Congruence Concept

Abstract

Mathematical abstraction is an important process in mathematical thinking. Also, visualization is a strong tool for searching mathematical problems, giving meaning to mathematical concepts and the relationships between them. In this paper, we aim to investigate the role of visualizations in mathematical abstraction through a case study on five pre-service secondary mathematics teachers. To do this, we formulated instructions that are appropriate for abstracting the concept of congruent figures or objects, and then determined the visualizations used by the participants, how they established these and what kind of visual images they had. The data were collected through class observations and semi-structured interviews. Data analysis showed that visualizations were used frequently by the participants and differently while engaged in abstraction. They used isomorphic and homeomorphic visualizations and these were mostly in coordination and internalization processes. The participants also produced different visual images which were commonly concrete and dynamic ones. The visualizations that were used in the abstraction processes significantly aided the understanding of the concept of congruent figures and strengthened the visual images of the participants.