Inverses and rambling.

[go_team]

So help me, I cannot remember figuring out the concept of mathematical inverses (multiplicative and additive), let alone when they were first introduced to me. I guess at the time I didn't even think it was cool, probably because it was only explained to me in terms of how to solve simple algebra problems, and not in terms of "ok, so this is one of those basic recurring concepts that'll keep turning up to interconnect all the math you know". Which is a shame. I'm trying to explain to my pre-algebra student about addition and subtraction are kind of the same, only opposite, and multiplication and division are the same, only opposite, and I don't know if I'm getting through at all. I'm trying to put it in terms of turning math problems inside out so they look prettier and easier to solve, but I don't know if that's the right thing to do. Part of the problem, I think, is that he's still struggling with complicated multiplication and division. Part of me wants to stop and work on those, but mostly I want to give him a calculator for the arithmetic and work on the concepts, since they're ever so much cooler. What I remember most about pre-algebra is Mr. Gelfand, who taught it: I swear, the man had a different suit for every day of the month, but he seemed particularly fond of a burgundy-red number that he wore with a yellow shirt. Also he apparently had a really bad toupee, but I never noticed. I'm kind of unobservant about that kind of thing; hairpieces have to be really, blatantly fake (like a different color from the rest of the person's hair), or else on someone I know to be bald, for me to pick up on them. But I digress. I digress so much, in fact, that I just took time out to write one of the few people I knew in middle school who might remember Mr. Gelfand and/or even be able to tell me when we learned inverses. I'm dork-tacular.

In other news, I still need a haircut, and Mother Kali's Books is probably going out of business, which means it's time for me to buy a copy of all the Alix Olson CDs they have in stock, because ack! Nowhere else has them in stock! I might complete my Dar Williams collection and finally get me some Toshi Reagon, while I'm at it. Did I mention waaaah? I knew Mother Kali's hadn't been doing well for some time, and that they'd gone through a horrific traumatic reorganization last fall, but wah!

Um, what else? Contact improv tonight (yay hippie dance!) and I should probably go get myself some binders and stuff to better organize my tutoring course materials and suchforth (plus, any excuse to go play in office-supplies land! Woo!) Maybe a trip to the library as well. Also food. Yes. Food would be good.

Comments

[cabanasloth.livejournal.com]

Hmm. Yeah, I don't know how I'd teach inverses either. My immediate response was to jump into abstract algebra, but I'm almost certain that's not the right answer. ;)

I'd be interested in hearing more about this... I mean, how *do* you get across something like an inverse to somebody who hasn't even seen algebra yet? Even something like "6 times the inverse of 6 equals 1" is, well, algebra.... If you do figure out a good way to get that across, I'd like to know what it is.

[coldtortuga.livejournal.com]

Inverses are the mathematician's Ctrl-Z.

(Or C-/ for disciples of at least one of the One True Editors.)

[pmb.livejournal.com]

I am sure you mean the universe's u key.

[coldtortuga.livejournal.com]

Ahhhh, the One True Editors... where else can you download an emulator package for your neighbor's religion?

[kweerious.livejournal.com]

toshi is funny live, and she lies. she did this improv song which we got on tape and she rerecorded it for later. i wonder if it will make it into something later?

[goteam.livejournal.com]

I saw Toshi open for Dar way back in the day (like, 5 years ago at Central Park Summerstage, and now I'm feeling really old) and she was great. She essentially told the entire audience, "Good Lord people, you so white!" Then she explained to us about feeling the funk, so we could sing along better. I've been meaning to buy some of her music ever since, but that whole college student with no money and recent grad with no job thing got in the way for awhile there.

[leech.livejournal.com]

In a way, inverses in the context of normal numbers are almost too obvious for students to understand. The fact that multiplying by 1/5 is the same as dividing by 5 is easily taken for granted. I think that's not a bad way of explaining it, though.

However, I'm pretty anti-calculator for arithmetic. I don't think one can develop any intuition for multiplication without actually doing a bunch of problems. (This is not to say that the way arithmetic is taught in public schools is good, of course.)

[goteam.livejournal.com]

I'm thinking of doing a whole crapload of exercises where my student and I convert expressions from subtraction into addition of negative numbers and division into multiplication of fractions and back. It'll give him a lot of practice with arithmetic, too. Eventually I'll impose the "no more subtraction or division" rule (I'm pretty sure I actually had this in one of my algebra classes) and hope the concept's sunk in a little. Also we'll do a lot of simplifying fractions. I seem to recall that multiplying fractions and simplifying them out was a really big deal for me when I finally figured that out.