I'm going to quote Bill Thurston from his interview for [More Mathematical People](https://books.google.sk/books?id=Nu_uAAAAMAAJ): 

> Thurston: ... One thing that is very important is the education of children... In the elementary schools in Princeton that my kids have attended, there is an annual event called Science Day. They bring in scientists from the community, and we spend a day going around from class to class talking about things. I have enjoyed doing that quite a bit. 

> MMP: What have you talked about? 

> Thurston: I have done different things every year for ten years or so; for example, topology, symmetry, binary counting on fingers... I find that kids are really ready to pick up mathematics in the way that I myself think about it. Of course, it's toned down. 

> MMP: Can you be a little bit more specific about the way you think about mathematics? 

> Thurston: That's a tough question. It might be nice to give an example. At one time I went into a class of kids and made lots of equilateral triangles. We made a tetrahedron by putting three triangles at each vertex. Then I asked what happens if you put four triangles, and they constructed an octahedron. Then with five triangles at each vertex they constructed an icosahedron. But with six triangles they found that the construction just lays flat. And then I asked about seven triangles at each vertex. They pieced it together and they got these hyperbolic tesselations in four-space. They loved that. The kids did. But the teacher really felt ill at ease. She didn't know what was happening.