Nancy Anderson, EdD

Q: How do mistakes help students learn?

A: It is not possible to learn without making mistakes. When teachers spend class time talking about errors, we let students know that trying out ideas, making mistakes, and revising one’s thinking are the ways that learners develop deep understanding.

Attending to errors is associated with a growth mindset. Thanks to the research of Carol Dweck and Jo Boaler, we know now that students’ beliefs about their learning affect how well they learn. Specifically, students with a growth mindset – an attitude that focuses on learning and improvement (instead of ability) – attend very closely to their errors as they work toward a solution (Boaler, 2016; Moser et al, 2011). This relationship suggests that classroom teachers may be able to help students develop a growth mindset by promoting mistakes as a source of learning.

Talking about errors helps students eliminate faulty misconceptions. It’s a common belief that we help students learn by talking about correct solution strategies and sound ideas. But focusing learners’ attention on what is correct does not eliminate misconceptions. If misconceptions are not addressed directly, students build new ideas on top of prior misconceptions (Bransford, Brown, Cocking, 2000). Talking about mistakes in math class puts a spotlight on faulty ideas so that they can be addressed and dismantled.

Errors that are “solutions in progress” can lead to correct solution strategies (Tugend, 2011). Posting a flawed solution strategy to a problem and talking about why the strategy is flawed illuminates the concepts that are required to formulate a correct approach. Students can learn to view their mistakes as clues that lead to sound approaches. When a mistake occurs in the midst of a solution strategy, students should not think, “I have to start all over.” Instead, if they can reflect on the mistake and why it is wrong, they can use it to help them move toward the correct solution.

NOTE: The text above is adapted from Anderson, N. (2017). *What's Right About Wrong Answers: Learning from Math Mistakes*. Portland, ME: Stenhouse Publishers.

Mathematics Teacher ~ Author ~ Consultant