Spike's Bitches 35: We Got a History
[NAFDA] Spike-centric discussion. Lusty, lewd (only occasionally crude), risque (and frisque), bawdy (Oh, lawdy!), flirty ('cuz we're purty), raunchy talk inside. Caveat lector.
The answers were right there in the ether and I wrote them down. So long as I had the right answer, I expected credit.
See, the thing is? He did write down a whole lot of stuff. And the stuff he wrote down does (sort of) show why he picked these numbers. It's just that his "why" doesn't answer the question that was being asked. (The question was, if you're building a box that's got to be 8 cubic feet in volume, and the base is a square, and the material for the top costs $5 per square foot, the material for the bottom costs $15 per square foot, and the material for the sides costs $10 per square foot, what are the dimensions of the box that will cost the least? He said that, since the box is 8 cubic feet, it will be 2 feet per side, and then he calculated what the cost would be of a box that's 2 feet per side. And it happens that 2 feet per side IS the dimensions that'll give the lowest cost, but he didn't give any justification for why he picked 2x2x2 rather than any other combination of sides that'll end up as 8 cubic feet.)
(As soon as I saw this problem, I knew this would happen. It's a pretty standard calculus word problem, and there are always several people who will just say that the box has to be a cube. And so, when the answer actually IS that it's a cube, it makes it really hard to explain to those people why they didn't get credit. It's like, if the prices of the materials had been different, the right answer would have been different, but his answer would have still been 2x2x2.)
(Sorry. I'm getting over-explainy.)
See the oppression of the creative mind! See how rigid expectations thwart the development of genius! See how we're supposed to shill for grades instead of revelation!
Hee. I've actually got a whole lot of issues with the "find the right answer the right way" philosophy of teaching math, and I always give full credit for an answer that uses a method that's unconventional but mathematically sound. But here, he's lacking the "mathematically sound" part of it.
One education book I was reading said something like, "When a child gives a wrong answer, he was probably answering a different question than the one you asked." And that's exactly what's going on here. He's got the right answer to what he THINKS the question was. But that's not what the question actually was.
(Sorry. I'm getting over-explainy.)
Not at all, you're explaining perfectly why I shouldn't have gone into form of mathematics where there are multiple ways of answering a question. I know you're supposed to work out equations and stuff for these sorts of things, but I always play with the patterns of things until the right answer, well, kind of pops up or I give up.
I am not the stuff of which math teachers are proud. But I rock at geometry.
The question was, if you're building a box that's got to be 8 cubic feet in volume, and the base is a square, and the material for the top costs $5 per square foot, the material for the bottom costs $15 per square foot, and the material for the sides costs $10 per square foot, what are the dimensions of the box that will cost the least?
42
But, yeah, I can see how he answered the wrong question.
but I'm pretty sure that's not what my teacher wanted me to learn.
Nor me. But I had the right answer. Sometimes I would try to reverse engineer so there would appear to be work shown.
Sometimes I would try to reverse engineer so there would appear to be work shown.
Which I think is why I did as well as I did on the math portion of the SATs. I mean, it's multiple choice, one of them's right, it's just a matter of plugging the number in and balancing the ends until they match.
I know you're supposed to work out equations and stuff for these sorts of things, but I always play with the patterns of things until the right answer, well, kind of pops up or I give up.
That's a perfectly fine way of doing math! That's what math is about! The equations and formulas are just ways of generalizing those patterns!
Seriously, I'd say that just about the only way to really learn math is to play with the patterns and stuff. Just about all of my research starts with playing around and trying to see if there's a pattern or a sort of logic to the way something works (most of my notes from early on working on something tend to be kind of blobby diagrams), and then, once I've figured it out that way, go back and work on the details of the equations.
The way John Holt explained it in one of his books (I've been kind of binging on Holt lately) is some students will look for the answer IN the problem. They see the problem as a description of a situation, with one piece of it missing, and they have to figure out what piece fits into that hole. Those students generally have a pretty good understanding of what they're doing. Other students see the problem as a bunch of numbers, and they've got to plug the numbers into some equations or formulas, and then that'll give them the answer. The answer isn't in the problem; the question is in the problem, and then all the "math" is a sort of bridge over to Answerland, where the answer lives. And if they're pretty good at remembering stuff, they'll get the right answer a lot of the time, but they won't understand the connections between things -- each problem is on its own little island, and they know how to get from there to the answer, but they don't understand how the equations work other than as a bridge to Answerland.
That's a perfectly fine way of doing math! That's what math is about! The equations and formulas are just ways of generalizing those patterns!
Dammit, why weren't you teaching math in Southwestern Pa 35 years ago! If I'd known my mind really was working on a mathy track, I'd be an engineer today.
the question wasn't 'what is the answer' but 'why is the answer the right answer'. To be very honest - the right answer is a start, however, the why part is often more important in both the theoretical areas of math, and in the practical real world areas of a job. So I understand why he doesn't get all the points.
happy birthday young Christopher!
More ma ~~~ sending out to all in need.
and extra karma points to Aimee.
xyz = 8
5(xy) + 15(xy) + 10(yz)
25xy + 10yz
25(8/z) + 10(8/x)
200/z + 80/x
Okay, I'm clearly doing this problem wrong.
Oh shit! There are four sides!
5(xy) + 15(xy) + 4 x 10(yz)
25xy + 40yz
25(8/z) + 40(8/x)
200/z + 320/x
320/x + 200/z
Okay, I'm still clearly doing this problem wrong.
Well, fuck, there's the part where I CAN'T ADD.
20xy + 40yz
20(8/z) + 40(8/x)
160/z + 320/x
320/x + 160/z
Well, shit, this has them all costing the same. I suck.
P-C, you missed the part that said that the base is a square.
