According to this **article **by Jo Boaler — professor of mathematics education at Stanford and co-founder of www.youcubed.org — *math memorizers scored poorly *on the international PISA test, and the U.S. has more memorizers than most other countries in the world. The highest achieving students internationally were those who thought of math as a set of connected, big ideas.

Here’s what we see:

## 1. A visual approach to fractions gives students better number sense, and better access to word problems.

When we require drawing, *every problem becomes a word* problem. In the problem below, all students recognized that 1/2 is 6 out of 12, visually. This is a “12-peak Toblerone”, so a total of 17 twelfths (by simply counting!) . Then this student imagined moving one 12th from the top row to make the 2nd row equal to one, leaving 5/12 on top. This shows *number sense! * Our students can do fraction addition and subtraction mentally. More importantly, visualization helps facilitate the transfer to word problems, as below.