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Math is about more than just finding the correct answer. It’s about applying the concepts of math to problems and thinking them through to come to those correct answers. Educators acknowledge this every time we ask students to show their work and award them partial credit for wrong answers that demonstrate correct problem solving.

But learning to work through problems can be its own challenge, and students need practice thinking through the process. They need to develop the persistence to keep trying when they don’t get it right away and the confidence that they can solve a problem. For students to become persistent, confident, world-class problem solvers, educators need to create math-rich environments that cultivate those skills.

The power of failure

Failure is a powerful tool for learning that takes advantage of the perception-action cycle—a process that  takes place in all humans’ brains. Our brains create a model of the world based on past experiences and then make predictions based on that model. In math, our prediction would be the answer. If that answer is correct, our model is reinforced and the neural pathways underpinning it are reinforced.

But if our answer is incorrect, the perception-action cycle says, “Aha! It’s time to learn something.” The neural pathways of our existing model become a little weaker, and we’re able to adjust that model and begin carving new pathways in our brains.

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