Five Math Procedures To Help Students Learn From Their Mistakes

In math classrooms, students often interpret a wrong answer as a dead end, making it hard for them to recognize that mistakes can be one of the most powerful ways to learn. “Just as we reread in reading, and revise in writing, we fix problems in math and seek more efficient strategies,” says Kathy Collier, an elementary school instructional coach.

Mistakes push the brain to reconcile contradictory information and build more accurate, durable solutions—research also suggests they catalyze a chain reaction of productive brain activity. Before a learner is even aware of a mistake, “error” neurons fire; milliseconds later, “conflict” neurons respond, signaling the need to resolve competing ideas. In this state, the brain is especially well positioned to encode new information deeply.

In math, learning from mistakes can help students solidify a formula, drive home a complicated concept, or prepare them for future assessments. But this will only happen if students learn to value mistakes. “When teachers create a classroom culture that normalizes error-making and encourages students to analyze, discuss, and understand their missteps, mistakes can be powerful tools,” writes Wendy Amato, chief academic officer at K12 Coalition, in a recent EdWeek article.

Drawing on Amato’s strategies and other classroom-tested procedures, we’ve curated a list of five concrete ways to encourage and celebrate mathematical mistakes. From solo and collaborative projects to formative assessments, these activities help students embrace and reflect on their errors.

Highlight Your “Favorite No”

Making a mistake doesn’t have to be something that students feel they need to hide. In an activity she calls “Favorite No,” Amato uses errors as a starting point for classwide learning. 

Students are directed to independently and anonymously solve a math problem on separate pieces of paper, such as index cards, sticky notes, or pages from their notebook that they can rip out. After they finish, their work is collected and sorted by right (“Yes”) and wrong (“No”) answers. The teacher then picks out a “Favorite No”—an incorrect answer that demonstrates a common error—to kickstart a conversation about the problem. 

As the teacher presents their “Favorite No”, Amato encourages instructors to say things like, “Let’s look at this answer—what can we learn from it?” or “Why do you think this mistake happened, and how can we fix it?”

“This approach transforms mistakes into illustrations and helps students understand processes, not just answers,” said Amato.

Start With Errors, Not Scores 

When students make a mistake on a traditional math quiz or test, points are usually deducted without the opportunity for students to review and learn from what they got wrong. 

Amato recommends an alternative assessment: test students with already-solved quizzes that are riddled with intentional errors. This challenges students to analyze problems critically, recognize mistakes, and use their knowledge to correct them. 

“This shift transforms assessments away from penalizing and instead promotes understanding and boosts confidence,” explains Amato. 

Turn Error Analysis Into a Team Sport

Instead of asking students to grapple with mistakes alone, group-based error analysis invites them to slow down and compare their thinking with peers.

In an activity called the “carousel” seventh-grade algebra teacher Connell Cloyd posts four incorrectly solved math problems around the room and separates his students into groups. Groups circulate between each problem, writing out what error they think was made on a paper under the problem. Once they’re done writing their “claim”, the group rotates to the next problem and the second group reads the previous claim and chooses to either support or refute it with evidence. In the final round, students come up with the correct solutions. Cloyd says he is less interested in students getting questions right, and more so in their “discourse” about the problems and the errors made: “It’s about slowing down the mathematical thinking,” he said. 

The “place mat strategy” also gets students into groups to analyze a problem riddled with errors. First, they identify mistakes independently before sharing their errors with the rest of their group and debating which errors they agree on and using their analysis to solve the problem.

In the end, one member of each group—chosen at random—shares the group’s process, findings, and solution—a key part of the strategy. “By randomly selecting the presenting student, the whole group must take ownership for their work together and be prepared to speak about it,” says Stefan Singh, a high school assistant principal in New York City.

Turn Mistakes into Learning Tools 

Math teacher Emma Chiappetta uses a three-round exercise to help students not only recognize their errors, but also generate their own. In the procedure, she randomly separates students into groups of three and gives them a board to work on their problems. 

Round one: Each group is prompted to create a problem related to the current unit of study. They write the problem and intentionally perform a common error without noting where the error occurs in the solution.

Round two: The groups rotate to the next board, so that they are looking at a different problem and an incorrect solution created by the previous group. Using a different color marker, they must identify the error in the solution and solve the problem correctly.

Round three: The groups rotate again, so they are now looking at a problem, an incorrect solution, and a correct solution. The current group verbally explains to the rest of the class the mistake made by the first group and the correct solution generated by the second group.

“Generating an example of a common misconception requires a great deal of metacognition,” said Chiappetta. Throughout the exercise, students exercise critical thinking skills, problem-solve collaboratively, and finally, complete the activity with a lesson in constructing arguments. “Thinking about the same content from all of these perspectives and modalities encourages a much deeper understanding of the material.”

An Iterative Reflection Process

Helping students learn from their own math errors is almost like teaching them how to reflect on their past behavior, writes mathematics educator, writer, and consultant, Joseph Manfre. It requires them to take ownership of their mistakes and correct their actions to approach future problems. To set up this process, Manfre provides the following step-by-step prompts for students when they’re correcting their own work: 

1. What choice––or series of choices––led to your mistake?
2. What should you have done?
3. Redo the part of the problem where the mistake occurred (not the entire problem).
4. Create and solve your own example of this part.

This framework progressively deepens students’ mathematical understanding, Manfre says, and helps them develop the habits of reflection they can apply to future problems. “As educators, we need to create conditions that allow students to make and document their mistakes, and that provide the time for them to reflect on and value learning from such mistakes.” 

If there are other classroom activities that you use to celebrate math mistakes, please share them in the comments.