Hi everyone,

My name is Bryan Penfound. Awhile back I was asked if I would be interested in helping out at MathMistakes and I said yes not knowing how challenging this term would be for me. Now that I have settled in a little bit, I thought I was a bit overdue for a post, so here goes!

Recently while volunteering at a local high school in a grade 9 classroom, I had to opportunity to observe students’ answers to the following question: “Create a trinomial in the variable t that has degree 3 and a constant term of -4.”

Here are five of my favourite responses:


I would love to get some discussion going. Choose one of the polynomials above and try to deconstruct what the student knows and what the student still has misconceptions about. What follow-up questions might you ask to learn more information about how the student is thinking? What follow-up questions might you ask to help with any current misconceptions?

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I think the temptation I have is to call this a “careless” mistake and urge more practice. Let’s probe deeper.

1. What does this kid know and understand about exponents?

2. What’s the fastest way to help?

3. What makes this mistake so tempting?

Thanks to Sadie Estrella for the awesome addition to our ever-mounting pile of exponents mistakes.

Here are 7 mistakes. There represent all of the variety of mistakes from a selection of 36 students. The first two mistakes were repeated by several students, but the last 5 were unique in the sample.


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Which of these mistakes would you predict? Which ones surprise you? Can you make sense of them all?

Here are two classic mistakes:

Whenever I see a mistake that recurs at all different levels, and with all different students, I wonder: what makes this mistake so attractive? What’s the misconception? And what can we do about it?

Say something smart in the comments, and then go check out this post from Fawn Nguyen.