I decided to share my experience on teaching (if it can be called teaching 
) math. Here I translated an old entry from my blog.
Circus is a board game where each participant has one figure and all the participants have one dice. how many points you throw up, so steps can go ahead. in many places you have to go up or down. wins the first who goes to finish. kids like this game because adults are not favored because of their wisdom.
it looks like this http://www.freko.lv/trade/product/images/1278/
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MM and the board game circus
she began to play circus only from 4.5 years. earlier she did not understand how to play.
At the beginning, I had to show with my finger where to stand and where to go. although she can count from 1 year of age, however, she was quite regardless of whether a digit is omitted. with circus, she quickly was motivated to count fast and accurate. soon I no longer had to show where to go.
then somehow we started to play with two or three dice together. MM rolls three dice, counts the points, goes. so she learns addition.
than we started to play with cheating. a small cheating - a goat (top-down stairs) has a holiday. with more cheating - all top-down figures have holidays. recently we cheat pretty boring - we can go wherever we want. for example, MM wants to get a lion (upward stairs). until the lion is 8 points. MM puts three dice so that the sum is 8.
so a long time every evening MM in half an hour dealt with the excitement of mathematics. Interestingly, the circus induced her to the counting. by then she knew how to count with understanding to the 15. After some circus she started to count further and further. she already counted to 49 when for three weeks we stopped the circus play. and she stopped counting. than we started to play circus again and she quickly counted up to 99. and 140. I did not ask or urge her to count; in circus we count only up to 6, rare up to 12 or 18.
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Now she is five (and two weeks). We do not play circus because it is boring. I do not press her to anything concerning math. but it seems that she herself continues to think about math. sometimes at the breakfast time she says something like “if I have 10 sweet sticks and I take 4 away than I have 6 sweet sticks” (in this region we do not have sweet sticks; we see them only in movies). she can add and subtract up to 15 and do some multiplying. she understands written numbers up to 120 (or more; I do not test).
I can not teach her directly. she does not allow it. so I do not teach, I just encourage