Using Error Analysis to Boost Engagement and Student Talk in Math

While math class may not always feel like the most engaging and motivating space for students, especially if they feel they are not “mathematicians” or experience math anxiety, teachers can shift this narrative and create more meaningful opportunities for students. Through error analysis, teachers can create learning opportunities in which students work together, communicate using mathematical language, and feel truly engaged in the work before them.

CREATE A CULTURE WHERE MISTAKES ARE VALUED

In math classrooms, mistakes provide a valuable learning opportunity for students, but only if teachers create a positive culture around mistakes. Rather than students feeling anxious or overwhelmed by making a mistake, teachers can help them realize the reality that everyone makes mistakes and it is part of how we learn. To build this kind of culture, teachers can model and share their own feelings about mistakes. Additionally, it can be helpful to tell students that just as we reread in reading and revise in writing, we fix problems in math and seek more efficient strategies.

In my own classroom, I’ve worked to model mistake making by sharing out my own math mistakes with the class when they happen. For example, when setting up a bulletin board in my classroom, I initially mis-measured the lengths and thought they seemed off, so I double-checked and found my error, saving me time and paper. I shared this experience with my students as just a quick story to help bring attention to mistakes as a common and valuable part of life.

Additionally, teachers can celebrate students when they make a mistake and solve it by drawing attention to the perseverance the student showed.

DIG INTO A COMMON MISTAKE FROM A PREVIOUS LESSON

To start using error analysis as a way to build engagement and deep understanding, teachers can open a lesson with a common error from the previous day’s learning—many teachers call this “My Favorite Mistake” and frame it as an opportunity for rich learning.

To get started, teachers should post a worked example that includes a mistake; teachers should ask student permission to show their work or rewrite what a student did on a new sheet of paper. Give students two minutes to think on their own—they may work independently to solve the problem. Then provide two minutes for them to turn and talk with a partner about what the mistake is, why they think the person made it, and how they can avoid the same mistake in the future.

As students are discussing, it can be helpful to remind them to use mathematical language and offer them opportunities to use unit-specific terms. For example, when we’re analyzing a mistake problem about geometry, I remind students to refer to the anchor charts we have co-constructed during the unit with terms such as trapezoid, square, and circle.

After students have finished their partner discussions, invite a few students to share their ideas with the class. It is helpful to have multiple students share, as there may be many ways to fix the mistake or avoid it in the future, all of which can help students deepen their understanding of the content. Encourage students to share using language that incorporates their partner’s thinking: “My partner and I saw this error and fixed it by ____.” Debrief with the whole class by reflecting on the strategies that were learned as a result of unpacking a mistake.

This strategy is best used when students have an opportunity to solve a similar problem right after they engage in the error analysis. They can apply all that they just learned and see the importance of thinking through mistakes and solving strategies. I love this strategy because I don’t have to go searching for ideas—it is based on what the students in front of me found challenging in the previous lesson.

STOP MID-LESSON TO ADDRESS A MISTAKE

Another way to introduce a math mistake is to pause within a lesson when a pattern of mistakes emerges. This allows you to intervene in real time based on what you’re seeing in the classroom. How this usually works in my classroom is that during independent practice, I circulate the room and look for any common misconceptions. Once I notice something, I quickly re-create the mistake on my own paper and then call the class back together to take a look. I post the mistake work, and then give students time to discuss it with their partners.

I encourage students to focus not only on what the mistake is, but also on why someone might have made that mistake and how they would explain why it is not the correct solving strategy. Once students have had the opportunity to discuss with partners, I invite students to share their ideas. From there, I encourage students to turn back to their independent work and look to ensure that they don’t have any of the same mistake on their papers, and to fix it if they find it.

ADDITIONAL RESOURCES FOR ERROR ANALYSIS PROBLEMS

Aside from using a mistake from the previous day or a mid-lesson mistake, teachers can use pre-created mistake problems as a jumping-off point for discussions. This saves teachers the time of writing out a problem with a mistake in it.

When looking for examples of certain types of mistakes or common mistakes in math, NCTM can provide ideas. I did a Google search on “find the mistake math problems nctm,” which generated types of common mistakes and where to go for example problems. I can also drill down to a standard by searching, “examples of ​​common mistakes—fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.” One example I’ve found online and used in my own classroom came from a web search on counting dollar bills.

By providing opportunities for students to examine mistakes, teachers can increase both student engagement and understanding of content. Moreover, teachers can help students understand the value of mistakes and how to address mistakes to solve a problem with confidence.