Too many students view mistakes as a bad thing to be avoided. The truth is that mistakes are inevitable. We need to start treating these moments as opportunities to learn instead of something to be ashamed of. In this post, Sarah Dunn, a high school math teacher, shares the strategy she uses to get students thinking critically about mathematical mistakes.
In mathematics, there is so much room for error. Record the numbers for the answer backward. Use the exponent inappropriately. Forget to distribute the negative. These mistakes are common and easy to make. I think it’s powerful for students to practice recognizing errors.
Making mistakes is how students learn. In fact, I tell my students not to erase their errors. Instead, I have them circle their mistakes and explain what they did wrong. The practice of allowing students to identify errors and think critically about what led to those errors can help them to avoid making those same mistakes in the future. It also normalizes mistakes. They are not something to be ashamed of. They are something to learn from.
It also normalizes mistakes. They are not something to be ashamed of. They are something to learn from.
In a previous post, I wrote about how to design kinesthetic math stations. I encouraged teachers to design activities that would help students to physically engage with mathematical concepts. But, let’s be honest – a lot of learning still needs to happen in the classroom. In the past, I would have made my offline station a practice worksheet. The students would get the necessary practice for the unit, and I would provide them with an answer key on Schoology. However, during a station rotation lesson, my offline error analysis station typically follows my kinesthetic station. My students love the kinesthetic station, so I wanted to follow that station with an activity that would maintain their interest. How could I maintain this high level of engagement in other stations? Working in pairs on a worksheet simply would not yield the level of engagement I was craving. So, I challenged myself to design a more dynamic offline station.
Rather than give them a practice worksheet about circles, right triangles or volume, I challenge the students to really think critically. I create seven or eight problems and each problem contains an error or multiple errors. The students are responsible for identifying and describing the errors, then they make the necessary corrections. The errors range from calculation based mistakes to using the wrong formula. In some cases, I just make up the math. In every case, I do my best to make all my answers believable.
For this station, the desks are set up to resemble speed dating. With the speed dating set up, the students can bounce questions off of one another and engage in discussion. The students collaborate with their partners to determine where the errors are in the problems and discuss the best strategy for fixing them. Mistakes help drive conversations about mathematical concepts and allows the students to help each other.
How do I determine what kind of errors to present to the students? Generally, I use common errors I have seen my students make in the past. Additionally, I think about the misconceptions students have about the mathematics in question. When I first started with this station, the students were not looking at the problems with a critical eye. For example, I had given the students an arc length problem and then done all the correct work for a sector area problem.
I have also noticed that students do not read the full question. As a result, they struggle to find the error. But, not reading the questions carefully is a common mistake made in mathematics. The habit of taking time to ‘read the full question’ is not only important in our math class, but also on the SAT. My students learn the value of reading the entire question as they engage in this error analysis station, which helps them when they sit down to take the SAT in spring.
I am still working to perfect this station. In fact, a learning support coach suggested bringing back topics from other units, or even previous courses. So, as I progress through the course, I spiral back to problems from previous units to keep those mathematical concepts fresh for the students. There are so many topics covered on the final exam and creating a space for students to revisit the concepts we have previously covered is important.
The students need time to practice applying specific concepts. But, they also need to be assessed on their understanding of those concepts. The error analysis station ties the application and assessment together. If there are ideas the students do not understand as they work through the error analysis tasks, this station allows them to engage in a productive conversation with a peer about the content. In math, cultivating a productive conversation is not always an easy task. But, getting students to explain math to one another in their own words…that’s the whole point!
Sarah Dunn is a high school math teacher and digital teacher leader in a vocational-technical school district in Wilmington, Delaware. She has flipped the instruction of the content to incorporate more hands-on and blended learning activities. In her free time, she enjoys being outdoors and spending time with her husband and two daughters.