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Saturday, May 1, 2010

Negative Numbers are Hard

Go read, especially if you teach math in grades 6-9, but really, go read it anyway. Ben Blum-Smith is performing a public service, reporting on primary sources you should read but are too-hard-a-slog and when-do-you-have-the-time and teasing out recommendations you can use in any classroom. The post is lengthy but well worth your time if you've ever watched a student struggle with negative numbers, and who hasn't.

I won't give away the punchline because Ben lays it out much more elegantly than I can summarize, but here's as good an analogy for a typical clumsy, contrived introduction of algebra as any:
The way I learned it was the opposite of “natural” or “meaningful.” Very cool, but only in an after-the-fact sort of a way. Like you came to the show at the very end and only saw the climactic scene, and everybody in the audience gasped and shrieked, except you because you didn’t care about any of the people in the show because you just walked in one second ago. And then after it was over your friend explained to you what had been going on and you understood why the other audience members cared, and were kind of mad you hadn’t gotten to watch the rest of the play first.


  1. THANK YOU for posting this! As a HS teacher going down to ms I am learning how to teach what I feel like I have always know. This is HARD. Much harder than I thought it would be. I think the material is so easy. This makes me stop and remember that it is NOT easy at first. I need to slow down my planning train...

  2. Thanks for highlighting this cool article.

    1) I love the idea of letting negative numbers flow naturally from answers to meaningful questions. I did that with my 6 year-old son and it worked naturally and without me trying to force anything. He's no prodigy, but once I described how they fit on the number line, negative numbers made sense as answers (e.g., "what is 40 minus 70?") to him.

    2) Using math history to find ways of teaching key concepts has always been quite appealing. When you follow the path along which math concepts were developed, you can find great pedagogical nuggets along the way. We math teachers don't follow this approach often enough.


    K12 blog


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