Helping Students Fail Productively
By Nathan Warnberg, Associate Professor, University of Wisconsin-La Crosse
Credit: Geoffrey Roberts
When I first started teaching I unwittingly used the power that I had over the classroom to reinforce perfectionism. This was most obvious when I would make mistakes in front of the classroom. I would get defensive. I would feel my face flushing. I would worry that my students were no longer going to respect me because I did not know how to answer every question. I would worry that my colleagues would not respect me because I did not understand every detail of the Calculus textbook. Fortunately, I have matured on this front and now accept the mistake, thank the student for pointing it out, and use the opportunity to normalize mistake making. To help students mature with their mistake making reactions I use an error analysis assignment.
The error analysis assignment I use is mostly standard: identify a mathematical error, fix the mathematical error, create and complete a similar problem to reinforce what you learned. However, a non-standard part of this assignment is to answer the question:
How did you feel/react when you realized your mistake and was that feeling/reaction supportive or unsupportive of the learning process? Below is an emotion wheel to help you with this question.
The motivation to add this question was from a ‘hallway’ discussion with a colleague in Fall 2020 when the COVID pandemic was still new. My intuition was that my students would have a harder time than normal in my classroom due to the trauma of the pandemic. My colleague reinforced my intuition by pointing me to the book Emotions, Learning and the Brain: Exploring the Educational Implications of Affective Neuroscience, by Mary Helen Immordino-Yang, which quickly establishes the fundamental connection between emotional reasoning/intelligence and logical reasoning/intelligence. Essentially, learning/reasoning without emotional context makes transferring the learning to a non-classroom setting very challenging. Educators ignoring the fundamental role that emotions play in the classroom may be ignoring why students learn anything at all.
I was not sure what to expect but here are some typical responses (from College Algebra, PreCalculus, Calculus I and Calculus II): dumb and ashamed; frustrated then optimistic; unfocused and dumb; stressed; disheartened and frustrated; perplexed; humiliated and appalled; guilty; annoyed and foolish; embarrassed and angry. I did not know what to do with all of this information but my go-to is to normalize and share. Thus, around week 3 of each semester I compile the responses (anonymously) and have a discussion.
THE DISCUSSION
These discussions were challenging at first but positive feedback from students encouraged me to continue having them. Some important things that I have learned are:
be mindful about the language I use and push back against categorizing emotions as ‘good’ and ‘bad;’
normalize anger, frustration and disappointment when things do not go our way (and make sure to talk about myself having these responses as well);
discuss how the inability to regulate these emotions can literally cut the learning process short; for example:
When I had realized I had made the mistake I was quite angry with myself. I am very hard on myself when it comes to doing things the right way. Especially when it was a simple subtraction mistake because I was going too fast. Reacting the way I did was very unproductive for myself, I wasn't in the right mindset to continue working on math for the rest of that day;
offer up some basic strategies to work through the anger and frustration if they find themselves getting too worked up.
To deepen our discussion and to reinforce that having a reaction that does not support the learning process is not something to be ashamed about, we also talk about (toxic) perfectionism as defined by Jones and Okun in White-Supremacy Culture. In particular, I have students identify and write about what part of (toxic) perfectionism they see in themselves. Every single semester (five semesters running) the most common response is:
making a mistake is confused with being a mistake, doing wrong with being wrong.
Connecting (toxic) perfectionism culture with their reactions to making mistakes in a mathematical setting is powerful and helps students understand that they may have some work to do.
I also try and wrap the discussion up with a response that supports the learning process. There is always at least one student who stands out for how healthily and maturely they respond to their mistakes:
When I got the answer wrong, I felt disappointed and embarrassed because I definitely thought we did the problem correctly. I stopped myself from being too hard on myself because I remembered, "This is an opportunity to learn." Keeping this in mind, it reminded me that I'm going to make mistakes, especially in math, and that's okay. How I approach my failure is far more important than how it makes me feel or the failure itself. So, in a way it was productive in reminding myself that it's okay and now I have learned how to do the problem correctly.
Finally, I would encourage you to ask a question like this of your students. Maybe you could embed it into an exam wrapper. Or, you might be able to incorporate it into a beginning of the semester ‘getting to know your students’ type of assignment. Or, you could add an error analysis assignment to your course. One last student quote when asked for their thoughts about ‘the feelings/reaction question:’
My thoughts are, "Man, this is making me face my doubts and combat them so they will inevitably not crush me in the future. This teacher must be insane! This will never work!" Whelp I was wrong. For the first time since junior year in high school, I have a good grade in a math class and I couldn't be more confident in my future and my goals I have set.
Nathan Warnberg is a father, husband, friend and DIY expert. He is also an Associate Professor of Mathematics at the University of Wisconsin-La Crosse where he spends much time and effort helping students transition from high school to college and investigating Anti-Ramsey type problems.