Leveraging Math Mistakes for Deeper Learning

October 16, 2024

What comes to mind when you think about making a mistake? Maybe it's embarrassment or you feel like giving up. What if, instead, making a mistake made you feel like you were learning something new, like you were on the path towards new understanding? I know I would rather let my mistakes empower me rather than defeat me, and I have a feeling your students might feel the same. When it comes to your classroom, it's inevitable that students are going to make mistakes. How you address those mistakes, and the classroom culture you create around the learning process can deeply impact your students' attitudes and their academic achievement.

 

Creating Space for Mistakes

For many students, the math classroom isn’t always an inviting or exciting place to be. Math anxiety impacts students across school communities and can make it hard for students to feel confident taking academic risks. The idea of making a mistake in math class can heighten these feelings of anxiety even further. That’s where the importance of classroom culture comes in. You have the opportunity to create the learning environment you want for your students, and that should be one that holds space for mistakes. By creating a classroom culture that not only allows, but encourages mistakes as part of the learning process, you can alleviate some of the anxiety your students feel, and ensure that they are able to engage in the deep learning necessary for academic success. 

There are many different ways you could work to create your classroom culture, but we want to highlight two key strategies that specifically show students that there is space for mistake making.

 

1. Modeling Mistakes

One of the simplest ways to help students recognize that it is perfectly ok to make mistakes while learning, is to actually make some yourself! And, maybe more importantly, model how to respond to a mistake you’ve made. 

You can either strategically plan a mistake into your lesson while intellectually preparing, or you can be ready to respond to a real, unexpected mistake you make in front of students. Either way, you want to, first, call attention to the mistake you’ve made in a non-demeaning way. This might sound like, “Uh oh, I just noticed I forgot to do an important step! Let’s go back.” This language demonstrates that, yes, a mistake has happened, and it isn’t too big of a deal. 

From there, you can simply go back and address the mistake. We will explore how to leverage this moment into a learning opportunity in the next section. 

 

2. Celebrating Academic Risks

A second strategy you can use to create a classroom environment that prioritizes the process of learning, is to celebrate academic risk taking. When a student puts themselves on the spot in class by offering up an answer, it can be a bit overwhelming. Now, add in the emotions around publicly making a mistake if they are wrong? This student may not want to try and answer another question in the future! 

You can step in to quickly and easily diffuse any negative emotions a student might feel about making a public mistake by acknowledging the academic risk a student has taken, and emphasizing the importance of bringing up a particular mistake. This might sound like, “I thought the same thing the first time I tried this problem! But I realized there was something missing. Let’s take another look and see if we can figure this one out together.”

By validating the student, you encourage them to keep participating in the future. And, by creating space to go back and try again, you remind all students that mistakes are just a part of the process.

 

Using Mistakes to Deepen Understanding

There are tons of options for utilizing mistakes in your math classroom to promote deeper learning, but we are sharing two of our favorite instructional strategies that you can easily implement during class as soon as today.

 

1. Where Did I Go Wrong?

This strategy is a great way to get students thinking critically about the steps in a problem-solving process. It can also be a helpful strategy to show students the importance of checking their work for all the small details—units, complete sentences, models, etc. 

Once you’ve modeled a mistake during the lesson, you can turn the mistake over to your students and ask them to figure out where you went wrong. You may ask students to identify your mistake right when you make it, or wait until a problem is complete to increase the rigor of the error analysis. 

As students become more comfortable with this process of recognizing a mistake has been made and then diagnosing it, you can encourage students to try it with their own work or that of their peers. It is important to ensure the proper classroom culture has been established before encouraging students to look at one another’s work with this critical lens, but, with the right attitudes and procedures in place, it can be incredibly effective. 

 

2. What Should I Try Next Time?

This next strategy ties into the first as an opportunity to push students’ thinking beyond the problem at hand. Once students have diagnosed the problem, you ask them how to avoid it in the future. By asking students what you should try next time, you task them with not only coming up with ways to avoid the same mistake, but also ways to avoid similar mistakes. 

Students can brainstorm strategies with partners or in small groups before sharing ideas with the entire class. These discussions remind students that everyone can benefit from looking at a mistake and working through it. The more you encourage students to work with mistakes and give them strategies to work through them, the more likely they are to feel comfortable making mistakes and learning from them.

 

It isn’t always going to be easy for your students to take academic risks and face the possibility of making a mistake, but, by creating space for mistakes and actively showing how those mistakes deepen everyone’s understanding, you can make it that much easier.

 

Looking for more tips and instructional best practices to bring to your classroom this school year? Subscribe to the Fishtank Blog for tons of teacher-trusted strategies to engage, challenge, and inspire all students. You can also unlock thousands of free K-12 ELA and Math lesson plans with a Fishtank Learning account.

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