In reading this blog post from Musings of a Mathematical Mom, I found out about an awesome series of math workbooks (or maybe I should call them playbooks?) called MouseMatics for young children (ages 4 - 7) by Jane Kats. She also has a book of math games called Math for Dessert, and a Christmas Coloring Book.

These books aim to break the standard conventions:

They know that a picture with dots drawn in the corners of a square is called “four”, and an identical picture with an extra dot in the middle is called “five”. But can they recognize the same number five if it looks different?Always representing the number of five with the same configuration of dots allows students to memorize the picture instead of counting. This book makes sure to not let that happen:

In some problems, we have two correct solutions (a pair of friends can split a chocolate bar in different ways); some problems lack an answer (an odd number of objects cannot be divided in two). After all, in mathematics no solution is also a solution. A matching pair of shapes can be found in the same column. We build geometric figures using not only the usual squares, but also diamonds, trapezoids, and triangles. When the child is asked to find a number value, we use a variety of shapes in addition to dots: diamonds, crosses, anything. Also, their arrangements in the boxes are random, unlike the standard dice configurations.However, the thing I like most about these books is this:

The main purpose of the Mousematics series is not to teach preschoolers to count (this is something every child will inevitably learn sooner or later), but to spark the children's interest, to invite them along on an exciting journey into the world of logics and mathematics.