It’s a math thing…

Posted on March 8, 2012

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   Today’s success that I need to take notes about and remember: a woman was *completely* overwhelmed by (a + b)(c+d).  

    First we did three *pages* of the distributive property of the a(b + c) flavor.   This was absolutely necessary, and may be necessary again, because while she was fine with “b + c is as simple as you can get,” 3b + 5c should be 8bc.   We should add these things together. Showing her that it didn’t work by substituting numbers in was a complete failure. That concept isn’t solid, either.   (News flash, algebra teachers — they can do that skill in isolation and get all kinds of right answers, but not apply it, because the old stuff gets in the way.)

   Being a hands-on learner (clues:  lots of gestures, lots of pointing… and even if it’s not your main mode, motor memory can be your friend in math), I showed her the “draw little arrows to the things you’re multiplying by,” *and* I showed her what 3 (a + b) looked like as repeated addition.  (I made a movie about it… but I don’t really like it.  The visuals just aren’t that clear.)   That made the light go on… so she did 20 of those problems and then went home.

    Next day I wasn’t there when she came, and she didn’t ask for the next practice that I’d printed out … but today, I was here, so she did it, acedit… and I showed her

    a (b + c)   

              + d (f + g)

and walked through doing the distribution thing with every letter… (to my surprise, I did not have to review the repeated addition visuals — but when she’s confident, she’s smart).

and then I told her that mathematicians being the efficient creatures they are decided that since both of the guys were being multiplied by the same stuff in the parentheses, that we could save some space adn write it as (a + b) (c + d).

Then she did another page of review.  

Tmoorrow we’ll do anotehr page of review, then walk through the same explanation and see what she remembers, and *then* try a few foily problems.

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