Favorite Theorems 11 and 12

Happy MLK day everyone!

An exchange with jd2718 has forged an unexpected connection between my last two posts, reminding me to add two biggies to my list of favorite theorems:

XI. The multiplication algorithm.
XII. The division algorithm.

“Ben, those are algorithms, not theorems.”

Nah, yo, EVERY ALGORITHM FOR A COMMON TASK is (signals the presence of, necessitates) a theorem. Namely, that the algorithm accomplishes the task.

In this case both theorems rest on the distributive property and the nature of place value. When we teach the algorithms, let’s treat them with due respect as theorems – i.e. worthy of being excited about, honored, and justified.

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How do you all seem to keep abreast of everyone so effectively in addition to writing? I spent like 7 hours on Friday writing my last post and probably another 6 yesterday just reading a handful of blogs, and following links they sent me to. Does Google Reader contain a magic sauce?

*jd2718 links to what looks to be a very thought-provoking issue of American Educator. Just browsed it myself so far – I was trying to avoid having the internet eat me.

*WCYDWT strikes again.

*Sam Shah implements a kick-*ss homework accountability structure that doubles as basic training in staying organized. I’ve done something similar (though somewhat less ambitious) with good results too.

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In honor of MLK day: a shout-out to the continuing awesome work of The Algebra Project.

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I managed to write a short post!

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One thought on “Favorite Theorems 11 and 12

  1. Um…fear, surprise, and ruthless efficiency? No, that’s how I run detention. Damn.

    I’ve never spent 7 hours working on a post. I think of something, write it up, and hit “Save Draft.” Then I read it a few times over the next day, make edits, and publish. Luckily nobody expects awesomely tight writing on a blog.

    I do a lot of skimming in my Reader. Don’t feel obligated to read everything thoroughly for understanding. I can tell in a few seconds if something is going to interest me enough to read it read it.

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