This is a tall order, but since this site is for everything mathematical, here goes:
What are some nice games/puzzles/problems/problem-like activities that would be appropriate for a three-five year old?
I ask this because I'm not particularly interested in trying to accelerate "number literacy" or prepare for "school mathematics". One may assume the three year old can count to 20, say, but the games don't necessarily need to involve number. I would like some activities that would introduce the surprise and delight of the problematic.
An example:
An article by a Russian mathematician (I can't remember the reference…) pointed out that if you let a young child count three objects and then separate the objects, the child will think that the number of objects has increased. When prompted to actually count the separated objects, the child was surprised and amazed to see that the number was the same.
The goal is to bring a bit of the joy of mathematical thought to a very young child. Any ideas?
Best Answer
My limited experience with three-year-olds who can count to 20 suggests that the counting is simply a recitation. Can your particular three-year-old reliably count the number of matches (10-20) in a matchbox? That would be a rare talent, and one worth encouraging.
Edited to add: An article in today's New Scientist agrees with this assessment: