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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.
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.