Pictures are Valuable in Math Learning, but They’re Often Overvalued

Pictures can help build mathematical intuition, but sometimes learners think they should fully visualize every single problem they solve, which actually handicaps their thinking. Math involves generalizing patterns in logically consistent ways, and the generalizations eventually go beyond what you can fully picture in your head.

Want to get notified about new posts? Join the mailing list and follow on X/Twitter.

Pictures are definitely helpful for building mathematical intuition, but sometimes math learners think that they should be fully visualizing every single problem that they solve, which actually handicaps their thinking.

For instance, it’s great to visualize fractions as “cutting a cake” at the beginning. But eventually you want to get to a point where you don’t need to imagine a picture of a cake. In the long run, what you’re aiming for is

1. an intuitive gut feel about how various processes behave, and
2. a level of procedural automaticity where you can quickly and effortlessly arrive at an exact result.

At its core, math is all about generalizing simple patterns in logically consistent ways – and the generalizations eventually go beyond what you can picture in full resolution in your head.

Pictures are ultimately scaffolding towards generalization – use them to guide your thinking, but don’t let them confine your thinking.

Want to get notified about new posts? Join the mailing list and follow on X/Twitter.