Among all the experiences we've had, the one that I think stands out is the idea of understanding the origins of mathematics as part of understanding mathematics.
Bernard's plenary reminded us of the human origins of mathematics, that mathematics was brought into existence to solve problems people had at specific historical junctures.
Our working group reminded me that mathematics is also called into being through the interaction between our human senses and tendency to notice patterns and abstract them, and the regularities of the world around us. Trees are not perpendicular cylinders, but they allow us to perceive perpendicular cylinders. Seeds in pine cones and nautilus shells do not trace logarithmic spirals, but they allow us to perceive logarithmic spirals. Experiencing this could help students understand themselves better, and perhaps to feel mathematics as something more a part of them and less alien.
I have mentioned two simple abstractions, but a more important one is the idea of a complex system. I would like to explore further how experiences of the complex world of a forest can help students to abstract the idea of a complex system, and to understand how simple starting points can give rise to unpredictable complexity, and how such complex systems behave when perturbed.
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