Mistakes Are More Fun

A young man sits at his desk.  Furrowed brow, furious scratchings on paper, shoulders hunched, one hand gripping the desk. He struggles with the concept, working and reworking the ideas. Realization begins to creep across his face.  He follows the path.  He looks up.  Our eyes meet, and his hand shoots into the air.  We share a knowing smile. I nod, playing casual. The class waits, ready with either admiration or disgust, depending on where they are in the food chain.

He speaks, carefully explaining his logic, and the processes he went through to get to his answer. He has gone deep with the question, trying not only to use the rules and procedures, but to think conceptually and understand for meaning. He’s used manipulatives. He’s made connections to other concepts and thought about the context of the problem. He states the answer, sits back, and lays his pencil down on the page, satisfied with a job well done.

He is wrong.

Not entirely wrong.  There were big pieces that were correct. Strings of reasoning that were absolutely solid. But, in the end –  still wrong.

But as I was listening to him talk, I realized that I was coming to understand something about that particular kind of question that had eluded me until now.  Typically, I had reacted with frustration: “But I taught them this!” “We covered that!” Surely I had taught them the rules. We had even come at it from a variety of ways, but there was an underlying fault in the structure that I had tried to build that I had not addressed. Cory helped me understand what it was.

“You are SO wrong. But thank you for making that mistake!”

I was triumphant, delirious with the new knowledge, excited by what had been revealed to me. Now, I could finally help these kids. Cory didn’t quite know what to do with my excitement. He knew he’d done good, but he hadn’t got the right answer. Oh well. He shrugged his shoulders and played along with me to see what new game I was up to. As a class, we explored where he had gone wrong in his thinking. I finished with the promise that next day I would come back with an activity that would help them bridge the gaps in their thinking.

This moment entirely changed the culture of my class, and my teaching practice for the rest of my career. The sharing of mistakes became a badge of honour and courage, nevermind entertaining. Students started to compete with each other to explain their thinking so that I could diagnose where they had gone wrong. I was reading their minds, and it felt a little like a party trick, but I rolled with it.

The change for me was in the way I listened to students talk about their work. Normally I would listen for a particular, correct way of doing things, and filter out the stuff that was not correct. With my new listening superpower, I started to approach the student response more like I was looking at one of those Magic Eye pictures, waiting for the misconception to emerge three-dimensionally from the background. It fascinated me, and it very often taught me stuff about how to do math that I would never have figured out for myself.

Later in my career I would start to say that everything good I ever learned about teaching math, I learned from my students. I still say it.

For more discussion about listening to students as an important part of formative assessment practices, check out: Even, R. & Wallach, T. (2004). Between student observation and student assessment: A critical reflection. Canadian Journal of Science, Mathematics and Technology Education, 4 (4), 483-495.

  1. I agree, across the board. There is no such thing as life without mistakes, learning without mistakes, and growth without the same. I think we focus far too much on getting things ‘right’ that we’re creating a culture of wimpy, fearful learners — really, they’re not learners: they are recipients, seeking the party line from the sage so that they can regurgitate it, unaltered, on command.

    Children don’t do that: they engage life head on, run into things, break stuff, and figure so much out on their own (if only intrusive parents lay off long enough). I think we need to encourage that natural form of learning, where sometimes it’s entirely possible to master a process while failing to reach, initially, the end it seeks to reach. I tell my students, when their valid reasoning leads them down a dead end that they’ve just made their search a little easier by determining that ‘that’ route is not going to work. Great! Now you’ve whittled down the list of possibilities by one…that’s called progress!

    And yet, through the lens of the bean-counter, the politician, and the uninformed public that implicitly trusts standardized test scores & school labels in newspapers, ‘wrong’ is bad…very bad, indeed, and is to be avoided.

    Back to my first assertions: how, then, are our students supposed to learn if mistakes are not only tolerated, but welcomed?

  2. What a powerful post! In today’s world, kids are afraid to make mistakes and oftentimes their parents (end even teachers) do everything they can to ‘save’ students before they make them. It is a wonderful situation to establish a classroom culture where mistakes are celebrated and explored — it is a phenomenal situation to establish a school-wide culture where this takes place!

  3. So much learning can result from making and analyzing our mistakes. At what point did we learn to try to avoid mistakes at all costs? I believe it begins at a young age. It pains me to see students who are afraid of volunteering answers in class or participating in discussions for the fear of giving an “incorrect” answer. I agree the use of formative assessment is key, and the more students are direct that process, the better! Enjoyed reading your thoughts!

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