Do you ever use error analysis during math instruction? Have you ever had students catch your mistakes while teaching? You know the whole “I did that on purpose to see if you would catch it?” joke? This might be something you can laugh about with your students, but having students find mistakes can be a powerful tool.
In fact, I love using error analysis during math instruction with my students. Of course, I prefer that it isn’t based on my own honest mistakes (although what a good time to model growth mindset ideas and how to bounce back from and learn from mistakes).
What is Error Analysis?
Error analysis requires students to look at work examples with errors. Students examine the work to find and fix any mistakes. This deeper-level thinking activity requires students to work backward, evaluating an answer instead of completing a question to find an answer.
Error analysis during math instruction also pulls on some of the mathematical practices. Students have to make sense of the different problems and persevere in solving them, attend to precision and critique the reasoning of others. By including error analysis during math instruction, students are getting additional practice with these important mathematical skills.
Why I Love Error Analysis
1. Error analysis is engaging for students
I love collecting different engaging ideas to try with my students. Error analysis always seems to be a hit because my students love the opportunity to “be the teacher” and “grade” work. Students are highly motivated by searching for the mistake. One of my favorite ways for students to practice error analysis during math instruction is by showing students a math question with 2 possible answers, one that is correct and one that is incorrect. Students have to decide which answer is correct and then decide what mistake was made to get the the incorrect answer.
2. Error analysis helps students think about the material in a new way and encourages deep thinking
When students are searching for a mistake, they need to think more deeply about the material. It isn’t just about figuring out what the correct answer is, but also finding out the reason why someone else might be confused. This means thinking about the material in a way that someone else might think about it. Taking it a step further, students have to think about helping the person who made the mistake. What would that person need to understand? Can your student find where the other person’s math work went astray?
One of the things I like students to look at is if mistakes are computation or conceptual errors. For example, if students are looking at a subtraction problem, they need to determine if the incorrect answer was from a miscalculation making it computational, or if there is a conceptual mistake like regrouping when it wasn’t necessary. It helps to show students examples of these types of mistakes.
To take it further, I encourage students to imagine themselves as the teacher. If they find a conceptual understanding, what would they say to the student who made the mistake? How would they help the student understand the correct way to regroup from the subtraction example?
3. Teachers can assess students’ understanding and find student misconceptions with error analysis
As students are explaining mistake they find, the teacher is able to see some of their students’ thoughts and understandings of a topic. If the students don’t see the mistakes themselves, it could be highlighting their own misconceptions as well.
If students can fully explain mistakes, it shows that the student has a good grasp on the material. We know that as teachers, we need to understand material at a deep level to teach and explain it.
Sometimes error analysis can help teachers find where their students only have surface-level understanding. Through additional practice and discussion, students can better understand content when working on error analysis.
4. Error analysis promotes growth mindset ideas
We all know that we can learn from our mistakes, however, this is not an easy lesson to learn. Most people don’t like to make mistakes. With error analysis, students can see how errors can help someone learn and grow their understanding. It is much less scary to talk about someone else’s (and often a fictional someone else’s mistake) than one’s own.
This discussion and practice can the applied to students’ own work. Once when they can see the importance of mistakes, they can also see how their mistakes can help them learn. Mistakes become a natural part of learning, not something to be ashamed or embarrassed by.
5. Students can start checking their own work with the same error analysis critical lens.
We want our students to be able to check their own work. This idea of “double checking” work is often lost on our students. However, with lots of error analysis practice and experience, students can start to look at their own work in the same way. It helps if teachers help guide these conversations by encouraging students to find their own mistakes.
In fact, this can be a powerful tool for assignment or test corrections. On a math test, I can mark what questions students solved incorrectly. However, instead of providing the correct answer, I can have students go back and analyze their own work. With a second look, can they correct their own mistake? Was their error computational or conceptual? Do they still have questions to deepen their own understanding?
Error analysis during math instruction has become a go-to of mine. In fact, having error analysis as part of the routine makes planning easy. I can easily put error analysis practice into a math center, for a guided math group, or as a whole class warm-up or close of a lesson. I know that the activity will engage my students and help them strengthen their own mathematical understanding.
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