on mathematics

[coraa]

I have a lot of people on my friendslist who like math and appreciate the beauty of mathematics. I would like to appreciate the beauty of math too! This is a gradual change for me, because through high school I haaaaaaaaaated math, and I was positively gleeful when I got to college because my major and minor of choice required no math classes whatsoever. (I could fulfill that part of my general education requirements with either math or science GEs, and so I went with biology, mostly. Biology and paleontology.)

Anyway.

Here's my background in math, in case it helps. (I get long-winded.) The reason I haaaaaaaated math was that I was no good at arithmetic. (I can hear you all saying, as has been said to me before, 'but arithmetic isn't all there is to math!' I know. Bear with me.) This started all the way back in, like, first grade, and it started because while I have an excellent memory, I am bad at memorization. (They're not the same skill at all, in my opinion.) I remember, distinctly, being tested to find out what math group I should be in toward the beginning of first grade, and being asked 2+3, and then being penalized for counting on my fingers, because I should have had it memorized. I remember, a year later, being so bad at timed multiplication tests that they actually tested me to find out if I had a learning disability. (I didn't; I turned out to be gifted, with no learning disability in math and in fact a very good grasp of the theory behind multiplication and etc. I was just not good at memorizing multiplication tables.) That sort of set the tone for everything: I wasn't much good at memorizing multiplication tables, and I wasn't meticulous enough, and so even though I had no problem with the concepts, I struggled a lot with the arithmetic.

The problem is that if you're not so good at arithmetic, you'll have trouble in pre-algebra; if you're not so good at pre-algebra, you'll have trouble in algebra; and if you're not so good in algebra, you'll have trouble with... everything. By the time we were allowed to use calculators in Algebra II, it was too late: my association with math classes was that they were the classes in which I could totally understand the material and study for the test and still get not-so-good grades because I made arithmetical errors. And that's probably fair, because you actually do need to be able to calculate as well as understand the material, but it put me off the whole topic.

I actually got As in math in high school, partly because yay for graphic calculators, and I did trigonometry (I actually rather liked geometry and trig) and calculus, but I didn't enjoy it: because I had associations that math was the classes where I'd get poor grades without knowing why or how to fix it, they were the classes I liked the least and feared the most, even though by this point I did reliably well at them, and I was relieved to be done with the whole topic when I got to college.

However.

Reading the posts of mathy people on my flist, and having mathy friends in my discipline (being a technical writer means I spend time around lots of mathy types), makes it clear to me that I Missed Something in my desperate attempt to flee arithmetic and its descendants.

So. If you were to recommend a course of math study to an adult who still loathes arithmetic but wants to learn more about the rest of mathematics, what would you recommend? Any particular books? Where would you start?

I would love to learn more.

(Feel free to link your mathy friends to this post, if you think they might have ideas. although not if you think they will mock my lack of arithmetical prowess, because then I will a) ask how their medieval Welsh is these days, and b) bite their faces. ahem.)

Comments

[coraa]

Yeah, I think a lot of my trouble in high school was math anxiety: by that point, with the help of a calculator, I could do the work, but the anxiety of 'I may get this wrong and not know why' made me hate the subject.

I also remember doing the same problem several times, in that 'if I get the same answer twice, that's probably the right one' way.

[viridian]

I wasn't helped much by calculators, only because I never did quite trust that I was using them right. And because we usually still had to show our work. :/

Now I wonder if I didn't actually have an issue at all beyond anxiety and inattention. I still have trouble with mathy concepts, like geometry & telling directions, though that could be due to being afraid of them as much as anything. It'll be interesting to see if reading some books with no pressure attached to them makes me want to deal with math more.

[coraa]

Oh, huh. You know, I have no sense of direction, and very little ability to visualize things, and I wonder if that's related. (Visual/spatial was always my weakest part of any standardize test.)

I got along okay in geometry despite that, but I think it was partly because I loved proofs.

[tedeisenstein]

But geometry has little to do with visualizing; it has everything to do with logic (is this argument/proof internally consistent).

[yhlee]

I don't think this is entirely true--I am under the impression that for a lot of people, visuals/diagrams are where people get the intuition that gives them the motivation behind a given proof. It's hard to prove something when you don't believe it. I loved the proof aspect of geometry, but I can't visualize, and for that part I always had to resort to paper and pencil. :-]

[coraa]

Yeah, I always had to draw a little thumbnail sketch to get the problem straight in my head, even if I didn't actually use the sketch for anything in the process that followed.

I think another part of my problem is that I can't hold very many steps in my head at once; I have to write them down. Which is fine, technically speaking! But there was a real sense somewhere along the line, possibly as far back as grade school, that 'math people' could do math in their heads, and so I mentally slotted myself as, well, not one, because I couldn't.

[yhlee]

They actually teach mental math in Korea (or did when my parents were in school). I am actually strongly under the impression that it is, or can be, a learned skill. I only had one or two teachers who dealt with it at all, and as a result, because I never put in the time, I tend not to be very good at it. At this point it's easier just to use the computer as a calculator, although I do play the game of "how much change will I get?" when I buy things. But my parents are very fast and very accurate at mental math, and I honestly think it's a schooling thing.

I have the same problem with proofs: there are some of them where you need to be able to hold several pieces of the structure in your head all at once, and I have trouble with that, so I end up doing it...in stages? Which is kind of fallible, and is probably one of the reasons I am pretty slow at proving things. On the other hand, I don't have to take timed tests anymore and I am doing fine.

[coraa]

Oh, interesting! I could easily believe it's a learnable/teachable skill, just not one I've ever been taught. (Actually I understand that there's a well-regarded professor at the university the boy went to who taught all kinds of mental math 'tricks,' which I assume is a showy subset of the same thing.)

Part of the reason that I'm willing to try math again is that nobody's going to expect me to get a set of problems done in an hour. Much lower anxiety that way, and I actually have time to check my work.

[yhlee]

Yeah, I've seen mental math tricks. I do not have brainspace for them, but they can be pretty impressive! And handy.

I totally hear you on the timed thing. I am ordinarily pretty fast with computations if I know the material, but once we started having proofs on exams, the timer became my enemy.

[tedeisenstein]

I don't think it's entirely false, either. When I took geometry, for example, there was no way I could ever visualize any of the in-between parts between the starting point and the QED; my proofs were not at all visual, entirely "hmmm, let's see if this plays out logically - ooops, no, let's backtrack and try method b..." And I never drew pictures; it was verbal almost all the way (visual at the beginning, yeah, but that was about it.)

'Course, I have a lousy time converting words into pictures anyway. Give me a games rulebook and I can't play the game. Show me what goes on with a deck of cards in hand, and only _then_ can I follow the printed rules.

Visual? I am. Verbal? I am. Verbal -> visual? No way.