The Serious Truth About Silly Mistakes

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In math, silliness happens. Slips of the pen, or the tongue, or the LaTeX-typing-fingers. We all make foolish mistakes now and again.

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But I have on occasion noticed among students (and their parents) a peculiar tendency to attribute all mistakes to silliness.

“Look at his test!” a parent might say. “He lost all his points on silly errors. He knows how to do it.” Then we’d go through the test together, and in each question where he’d lost points, I’d see topics to address, room to grow. Not just hiccups and typos.

Why the divergent views?

To some, mathematics feels like the successful performance of prescribed steps. In that case, the whole subject is mechanical and straightforward. All mistakes, in this light, are “silly” misfires. Multiplied when I should have added? Hey, just silliness! Obviously I know how to add! I just happened to zig when I should have zagged!

I take a different view of math. Some aspects – say, employing rich mental models for key concepts – may be hard to assess, but are crucial. Multiplied when you should have added? It’s possible your mental models of “addition” and “multiplication” (or “area” and “perimeter,” etc.) are leading you astray, or could use further development.

It’s comforting, of course, to view all one’s mistake’s as “silly.” Easier to admit occasional clumsiness than real confusion. But it’s the deep mistakes that signal the greatest opportunities to learn.

Missing out on those chances – that’s the really silly mistake.

6 thoughts on “The Serious Truth About Silly Mistakes

  1. There was a stretch of time in my first Algebra class where on every quiz or test 2 * 3 = 5 and 2 + 3 = 6. It was only those two numbers. When I got older, I pondered (briefly) the long term ramifications of such a number theoretic change. Thankfully, I grew out of both phases.

  2. I spent my entire mathematical academic experience being chided for “silly mistakes” until my calculus teacher explained it to me (and my parents) thusly: you *understand* the topic really well, you just have a very hard time getting it to go right on paper.

    As an adult, I would eventually be diagnosed with a learning disability, NLD, which is characterized by a discrepancy between verbal and visual language skills. No amount of “checking my work” was ever going to fix those “silly mistakes”

    I was fortunate I had a natural interest in logic and logic puzzles that kept me engaged with the topic despite the feedback I got. Otherwise, I never would have purservered though to calculus and met the teacher who finally understood my confused relationship with math.

    Please, keep being that teacher. Students like me need you!

  3. This reminds me of when I have to explain to students and parents why I weight the students’ work more heavily than the answer on tests and quizzes. Yes, there needs to be an accountability factor in the final answer, working through an entire problem and finding a solution but there are skills we are assessing, techniques to be learned, and if I cannot follow their thinking or they get a final solution that is somehow correct but nothing that leads up to it is mathematically sound the answer means less than what the key says should be circled or in the blank.

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