Technology and Versatile Thinking in Mathematics.

Today’s technology gives us a great opportunity to complement the subtlety of human thought with the power and accuracy of modern computers. In this presentation I consider fundamental modes of human thinking to see how enactive, visual and symbolic methods can be used in a versatile way with the support of welldesigned software. My analysis focuses on the use of symbols to think about mathematics and to do mathematical procedures and how visual enactive software can be used to enhance our conceptual thinking processes. In particular, I consider a theoretical cognitive development in arithmetic, algebra and the calculus and reflect on empirical research to show how the computer can be used both well and badly in supporting mathematical learning.

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