Far too often, math is seen as a subject that is either right or wrong, and so you better get the answers right or you’ll fail the test. And while it is technically true that we want students to understand math concepts deeply and be able to correctly solve math problems, creating this kind of mindset can cause students to feel frustration and a sense of failure anytime a mistake is made. The reality, however, is that mistakes are a part of the learning process, and we should be teaching and encouraging kids (and ourselves!) to see mistakes as an opportunity for growth and deeper understanding.
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And while making mistakes is necessary, and deepens and challenges our thinking (this is true of any new skill or subject, not just math), students often would rather leave a math problem blank than to try, only to get it wrong.
But in contrast, brain research shows that deeper learning and greater neural connections form from making mistakes on difficult tasks, rather than simply having constant success on easy tasks.
So in math class, encourage this kind of view of mistakes, and help your kids learn that mistakes are opportunities for growth!
My kids and I have been reading Mistakes that Worked, by Charlotte Jones to inspire them to embrace their mistakes and encourage perseverance and hard work. It’s really a fantastic book for kids (and adults!) of all ages!
8 Reasons Why Making Mistakes in Math is a Good Thing:
- Making a mistake shows that you tried:
As a classroom teacher, nothing frustrated me more than students coming to class with empty homework assignments and the excuse, “But I didn’t know how to do it.” You will never learn until you try. Many of the world’s greatest leaders and inventors saw an unbelievable amount of failure before finding success. But their successes would never have happened if they simply sat back and said, “But I don’t know how!”
- It’s a workout for the brain:
The brain is like a muscle that needs to be used and exercised in order to be strengthened. Wrestling with challenging problems is good and important work for your brain!
- It gives ownership of learning:
Although many see the classroom teacher’s role as that of lecturer, the truth is students will learn and remember more if they take ownership of their learning and discover solutions for themselves. When students can recognize mistakes and then take time to understand why it’s wrong and how to fix it, they own the understanding and have not simply relied on the teacher to give them the answer.
- It shows what doesn’t work:
Understanding what doesn’t work is just as valuable in the learning process as knowing the correct method and solution. As Thomas Edison said,
Negative results are just what I want. They’re just as valuable to me as positive results. I can never find the thing that does the job best until I find the ones that don’t.”
- You might notice a concept or pattern that you wouldn’t have seen otherwise:
Sometimes trying an ineffective method to solve a problem leads to other important mathematical ideas and discussions that might never have been had otherwise. Just because you don’t find the correct answer to the current problem does not mean you can’t learn some other important math fact or concept.
- You understand and can talk about the problem a little bit better:
When you have spent time working out a challenging problem but have not yet found the solution, you can still explain what the question is asking and why what you’ve tried hasn’t worked. Maybe your solution is wrong because you didn’t rightly understand the question in the first place, but now you do. This is valuable math learning.
- Understanding WHY a method didn’t work can lead you to the correct solution:
This goes back to #1: You’ll never solve it if you never try. Maybe you get it wrong on the first (or tenth) try, but seeing why that’s wrong may point you in the right direction so that you are able to solve it eventually.
- Mistakes make the moment you finally solve it that much sweeter:
If all you ever do is solve math problems that are easy for you and you never get any wrong, it will not mean much or feel like much of an accomplishment. But what victory and pride you’ll feel when you’ve gotten ten wrong answers and then finally find the solution!
While mistakes are a good and healthy part of math learning, this is really true of mistakes in all facets of life. I have read a little of the book, Better By Mistake: The Unexpected Benefits of Being Wrong, by Alina Tugend, and have thoroughly enjoyed it so far. I look forward to learning more about brain research and how I can learn to stop being such a perfectionist and instead embrace my mistakes as a catalyst for learning!
Want to help kids see the value of mistakes and learn to analyze math errors? Grab my new Error Analysis Pack!
This includes blank templates to analyze mistakes plus teaching tips and classroom posters to help teach kids about types of mistakes and how we can learn from them.
What do you think? Do you tend to see mistakes as a sign of failure or as an opportunity to learn something? What kind of message do you want to send to your students?
Want to learn more about making mistakes in math? Check out this post which outlines the types of math mistakes and how to help kids learn from them and prevent them.
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