My favorite toy when I was a child was the Soma Cube. Ostensibly the puzzle is to take the seven pieces and form a cube, but my Soma came with a booklet that displayed dozens of other 3d shapes to make, and I spent many hours trying to solve them all.
Puzzles like the Soma (or books like these or games like these) had a greater influence on me then any school math class. With the holiday gift giving approaching, I surveyed some of my MC2 friends to see what other toys or games they remembered from their childhoods.
Julienne Au was full of suggestions. Like me, she loves spirographs. This wikipedia entry gives the mathematical underpinnings of spirographs; I’m reminded of the pre-Copernican model of the motion of the planets, as described in Kuhn’s “Copernican Revolution,” which I highly recommend!
Ms. Au’s favorite puzzle is Izzi, another classic like the Soma Cube. She also likes 24, Chocolate Fix (which we played at our Julia Robinson Math Festival in June), and modular origami–here, you fold several pieces of paper each into a ‘unit’, and then combine the units into a larger model. When I first started teaching I was introduced to this technique through the work of Tomoko Fuse–check out this tutorial based on Fuse’s work. Used copies of Fuse’s “Unit Origami: Multidimensional Transformations” can be picked up cheap!
Matt Moran went with a classic–Connect 4. This game has been solved, although with 4,531,985,219,092 game positions I doubt this will influence your own game play. And finally, PJ Karafiol suggested Meta-Forms–like Chocolate Fix or the ever popular Traffic Jam puzzle, Meta-Forms start out easy but get progressively harder.
We at MC2 are looking forward to seeing you in January. In the mean time, play with some mathematical toys, games, and books, and give the gift of math!