Intuition and Visualization in Mathematical Problem Solving
In this article, I will discuss the relationship between mathematical intuition and mathematical visualization. I will argue that in order to investigate this relationship, it is necessary to consider mathematical activity as a complex phenomenon, which involves many different cognitive resources. I will focus on two kinds of danger in recurring to visualization and I will show that they are not a good reason to conclude that visualization is not reliable, if we consider its use in mathematical practice. Then, I will give an example of mathematical reasoning with a figure, and show that both visualization and intuition are involved. I claim that mathematical intuition depends on background knowledge and expertise, and that it allows to see the generality of the conclusions obtained by means of visualization.
KeywordsMathematical intuition Mathematical visualization Diagrammatic reasoning Problem-solving
I thank Roberto Casati, Davide Crippa, Leon Horsten, John Mumma, and Mario Piazza for their useful suggestions on a first draft of the article. The research was supported by the European Community’s Seventh Framework Program ([FP7/2007-2013] under a Marie Curie Intra-European Fellowship for Career Development, contract number no. 220686—DBR (Diagram-based Reasoning).
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