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Saturday, March 8th, 2008 12:33 am
mathematics - it's called inducement. blackmail, even
So started section 1.1 of THE HUGE PRECAL BOOK OF DOOM, mostly because I have a suspicion that maybe eight years since my last advanced math? Needs a refresher. I kidnapped Child, his wipeboard, a spiral, pencils, and the first half season of Fullmetal Alchemist. Holding it in front of Child's head, I explained carefully that his ability to watch this show, Dr. Who, Torchwood, or anything sci-fi was directly proportional to how much he fought me.
So, section 1.1 - Algebra review. It feels pretty obvious--the types of properties, negation, rational/irrational, whole, natural, et al, but--shockingly--reading the text was actually educational and a lot easier than when I did it the first time. No, not that I remembered any of it specifically, but that most if it was fairly obvious. The part that was interesting, of course, is explaining to Child, because every property I made a new example for him and he took careful notes. It wasn't hard so much as--hmm.
The thing is, in elementary school, I was taught the shortcuts, which totally fucked forever my ability to prove anything, and in fact, made me unable to conceptualize proofing at all. I got away with it through Calculus, but not in a good way, mostly in a desperate way. Getting the answer was always fairly easy for him; outlining each step to illustrate the why was hard. I don't do it that way; I look and write the answer. For him, it was worse: it was his introduction to parentheses as deciding precedence *and* multiplication, and the dot for multiplication. I really need a bigger whiteboard for this.
a(b + c) = ab + ac -- distributive property really did a number on him. Not because it was hard, per se, but because he didn't see the point.
3(8 + 2) = 3(8) + 3(2) -- he just wanted to solve the plus inside, which yes, according to precedence would work, but I explained in this case, we were doing it this way. I couldn't explain later, it would actually be:
x(3 + y) = (y + 7)/(y + 2) or variations thereof because he would run away. And I need my study partner.
He went with it, but I get the feeling he's not going to understand until he sees it. Same with irrational numbers; he nods at the theory, but I'm guessing it won't sink in until the problem sets.
It's fun, though, in that way I know it will be so much less fun later. His big incentive, apparently, is to be ahead of every other kid in school. And you know, Fullmetal Alchemist, season one second half.
So, section 1.1 - Algebra review. It feels pretty obvious--the types of properties, negation, rational/irrational, whole, natural, et al, but--shockingly--reading the text was actually educational and a lot easier than when I did it the first time. No, not that I remembered any of it specifically, but that most if it was fairly obvious. The part that was interesting, of course, is explaining to Child, because every property I made a new example for him and he took careful notes. It wasn't hard so much as--hmm.
The thing is, in elementary school, I was taught the shortcuts, which totally fucked forever my ability to prove anything, and in fact, made me unable to conceptualize proofing at all. I got away with it through Calculus, but not in a good way, mostly in a desperate way. Getting the answer was always fairly easy for him; outlining each step to illustrate the why was hard. I don't do it that way; I look and write the answer. For him, it was worse: it was his introduction to parentheses as deciding precedence *and* multiplication, and the dot for multiplication. I really need a bigger whiteboard for this.
a(b + c) = ab + ac -- distributive property really did a number on him. Not because it was hard, per se, but because he didn't see the point.
3(8 + 2) = 3(8) + 3(2) -- he just wanted to solve the plus inside, which yes, according to precedence would work, but I explained in this case, we were doing it this way. I couldn't explain later, it would actually be:
x(3 + y) = (y + 7)/(y + 2) or variations thereof because he would run away. And I need my study partner.
He went with it, but I get the feeling he's not going to understand until he sees it. Same with irrational numbers; he nods at the theory, but I'm guessing it won't sink in until the problem sets.
It's fun, though, in that way I know it will be so much less fun later. His big incentive, apparently, is to be ahead of every other kid in school. And you know, Fullmetal Alchemist, season one second half.
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From:*stares at you* Okay, I'm confused at that example. Why pick something that works either way? Bad textbook, no cookies.Okay, I get it now. It all seems to work fine. regardless of order, it still works. (Yeah, we can tell that BODMAS -- Brackets Over Division, Multiplication, Addition, Subtraction -- got well and truly drilled into my head as a kid.)
Does it still work on higher numbers? Like 10(13 + 18) = 130 + 180 = 310 as opposed to 10 x 31 = 310. Oh, that's so weird. I was sure that if you did things in the wrong order the answer became different.
I don't know. I mean, I got into algebra with our teacher saying, "Imagine the a is an apple and you're trying to find the price of that one apple." So, yeah, within the first lesson we were using it to solve stuff, like 10(a + 8) = 120, then you have to stretch it out to get the answer for a:
10a + 10(8) = 120
10a + 80 = 120
10a = 120 - 80
10a = 40
a = 40/10
a = 4
It was a very practical-based approach to algebra that worked for me. Maybe it'll help Child grasp *why* we expand it that way, because it's the only way to solve for one unknown. (and then approach the idea of solving for two unknowns a little later.)
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From:... there were shortcuts? See, I just never grasped proofing at all. I could never get from one end to the other without help. I'm still amazed I passed geometry, and I never went anywhere near calculus.
And then I was somehow able to test out of math entirely for college and never took another math course again. So looking at the above makes my head hurt.
But just from the way you're describing things, I can tell you're way better at helping Child than my father was when he tried to help me with 9th Grade Algebra. Because whenever Dad tried to explain anything to me, he always went the long way around, and not the short way. He'd always get to the same answer eventually but it was 3x as frustrating and not even close to the way my teacher was doing it.
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From:I believe you mean inversely proportional, unless the more he fights you, the more you're going to allow him to watch.
*adores algebra*
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From:Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
This mnemonic helps us remember which order to complete mathematical operations. The order in which a problem is solved is crucial. Without having a set order, we would arrive at different results.
2 + 3 x 6
Is the answer 30? 2 + 3 = 5 5 x 6 = 30??
Wrongo!!!
This is why we need to learn the mnemonic Please Excuse My Dear Aunt Sally. If not, we would not know the correct answer to the above is 20!
The answer is 20. Our mnemonic tells us which order to solve the problem. We do not just read left to right as if it were an English sentence. Multiplication comes before addition in the mnemonic (My comes before Aunt), therefore, we must multiply before we add.
If we do that, then the answer is 20! 3 x 6 = 18. 18 + 2 = 20.
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From:That is the coolest and most evil parental motivating factor I've heard since my parents used to punish me by not allowing me to read. *awed*
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From:No, really, having your kid as your study partner sounds like a lot of fun!
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You inspire me!
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