It's interesting to hear you both talk about teaching math.

I work on math with my three year old, not intensively but I try to make it creative and fun. She counts into the twenties well but she losses focus beyond that and I'm not being a drill sargent.

I do things like put out a pile of M&M's and we count them. Then she has to make two piles with the same number of M&M's in them and count them. I did even numbered piles the first few times we played this game and then I started introducing piles with odd numbers. "There is one left over! What is going on here!" Talk a bit about even and odd number piles, hope to move to piles of three with the same number of objects soon. No idea if this is a very good game for teaching but we have a good time.

Puzzles seem great for young kids and spacial relations. We have some picture puzzles with boarders some that are in the shape of the object being puzzled (stuff like fruits) and another free form geometric shape puzzle where you can try and copy form or just do what you want.

We talk about how triangles can look different and still be triangles but also that it's strange that rectangles, rhombuses and squares are called different thing but are so much alike.

Reading what you guys wrote I'm realizing that it's time to go three dimensional, I see a construction project in our future this week. Cones, cylinders and spheres will be interesting.