Intuition and Visualization in Mathematical Problem Solving |
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Authors: | Valeria Giardino |
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Institution: | (1) Institut Jean Nicod, CNRS, Paris, France |
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Abstract: | 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. |
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Keywords: | |
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