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

[yhlee]

If unhappy associations are likely to be a problem, I recommend looking at something like discrete math. I used to have a textbook around here on loan but darned if I know where it is.

Are you looking to learn to do the math or to learn about the math?

For a general overview of what-it-is-that-mathematicians-do that's aimed toward the layperson, Philip J. Davis & Reuben Hersh's The Mathematical Experience is pretty good, if dated. A couple other pop math things that don't teach you how to do the math: Ivars Peterson's The Mathematical Tourist is exactly that (with lots of pictures), along with its sequel, Islands of Truth. James Gleick's Chaos is about the birth of chaos theory and is very fun in its own right. The Diagram Group's Images of Infinity is a very cool children's book about transfinite numbers.

For learning-to-do-math, you may have some luck with books on problem-solving--you can do a lot of interesting math without having a deep background. I have not finished reading either of these books because my attention span sucks like whoa, but Ian Stewart's Concepts of Modern Mathematics is fairly user-friendly, and it's a Dover paperback for $13, which sort of recommends it to me all by itself. You might also enjoy Thinking Mathematically (focus on problem-solving) by John Mason with Leone Burton & Kaye Stacey, which...actually, I now feel like working through this and making comments as I go, if that would at all be helpful to you. (Although I might do it anyway.)

I will point to this post because I do know some people mathier than I am who might have things to say. :-)

[coraa]

I think at this point I have enough distance from my junior high frustration that I don't think unhappy associations will kill it for me, but discrete math still sounds like a good idea.

And I'm interested in both learning about the math and learning to do the math, although I will probably start with learning-about-the-math because that will give me an idea of why learning-to-do-the-math is cool, hopefully!

Thank you for the recs; they look very good (and the library has several of them, hurrah!). And I would love to see you work through Thinking Mathematically; it'd be fun to work through it myself and then see what your comments were as well.

And thank you for the signal boost. :)

[jazzfish]

Ditto on The Mathematical Tourist.

You also may be interested in (warning: pdf) A Mathematician's Lament, on the deplorable state of math class. The part that really struck me, that made me think "i /like/ math!", was from the bottom of page 3 ("For example, if I’m in the mood to think about shapes") through the top of page 5. That's exactly the sort of pattern-matching and -finding that I adore, and that got squashed out of math for me ages ago.

reposted to cut the personal details...

[cathexys]

I concur on the discrete math. That was my first thought as well. You might actually try formal logic, which gives you a nice intro into the beauty of math aspects but is often taught in philosophy departments, so... :)

[viridian]

I have no suggestions, but I wandered over here from someone on my flist and will be stealing recs from people because your math experience sounds exactly like mine.

I've often wondered if I have discalculia, and they just hadn't really discovered it when I was in grade school/early jr. high & having the most difficulty. I was also at the top of my class in every other subject, my grades only really suffering slightly when I had to work with mathy concepts, like in chemistry and physics. The result is that I'm kind of phobic about math. It makes me anxious and I literally had the same problem as you, where I would understand the concept as it was being taught, think that I understood it well enough to take a test, and then get wrong answers and have no real idea why. I could often do the same problem twice without getting the same answer, and then have to try a third time to figure out which one was correct. It sucked.

[telophase]

I had problems with math, and as my mom was a math teacher, it was more annoying. than usual. :) I think my big problem was that I don't learn well unless I have a thing I want to do with this knowledge: I never thought I was a programming-type person until I had a pressing need to create a database-driven dynamic website, and then it turned out that I'm a perfectly fine programming person. So learning math was hard because I never saw the point of doing this thing, and the vague "but you'll need it later!" never really fit, because even though I could conceptualize needing math as an astronomer (or one of the other things I wanted to be as a kid), I couldn't grok the reality of it.

Later on in college, when a friend learned I was majoring in a field that didn't require me to take calculus, he was aghast at the concept that I wasn't taking it anyway. I said "When will I ever need it?" He said "Well, if you wanted to fill the fountain in front of the student center with Jell-O, then you'd need to be able to calculate how many boxes of Jell-O you'd need."

I stared at him for a while, then solemnly promised that if I ever wanted to fill the fountain with Jell-O, I'd pick up the phone and ask him how many boxes I should buy.

[djkittycat]

My wall in math came in statistics and calculus. I could do computation, but I could not do all the graphing shapes and such very well. I was bad at econ for the same reason. I could not for the life of me figure out how and when to move the graph of supply and demand. Maybe I wasn't meticulous enough, I don't know. But I can't do statistical analysis using a graph. It gives me a headache.

You can have a learning disability and also be gifted at the same time. They are not mutually exclusive categories. In fact, people with learning disabilities are also often gifted in some other way.

I am wondering what you do when you have to half or double a recipe. To me, cooking is about math. I guess you have a calculator in the kitchen, right? I have seen pastry chefs using calculators on tv.

Anyhow, for math books, I'd recommend Flatland. It's about geometry and largely philosophical.

[ursula]

William Byers' book How Mathematicians Think is interesting & readable. It talks about the role of ambiguity & paradox in creating mathematics. And sexy things like infinity.

[coraa]

Ooooooh yes. Thank you for the link. That's painfully accurate as to my experience of junior high/high school math.

Re: reposted to cut the personal details...

[coraa]

Thank you!

I actually had a formal logic class in junior high and loved it to pieces. I ought to pick that up again.....

[coraa]

Sorry, I was unclear: I was tested as gifted in mathematics, as well as in language. (That sounds like bragging, and I don't mean it that way [I may have technically been gifted but I still sucked], but I think it's important to note that this kind of difficulty with calculation and so on isn't just restricted to people with learning disabilities; it's possible to put someone with plenty of aptitude off math that way, too.) My problems were all skill-based, not aptitude-based.

EDIT: Although, now you mention it, while I did peachy on the math-and-logic problem-solving sections, my weakest part was always visual/spatial intelligence, which might be related. Dunno. I did always do okay in geometry despite that, but I think that was just because I got on well with proofs.

When baking, yeah, I use conversion tables and a calculator. When cooking, I eyeball most things anyway (I cook by ear, mostly), so the math of it doesn't matter.

And thank you for the rec!

[coraa]

Yay, thank you for the rec!

[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.

[coraa]

Haha, yes. I remember teachers being very indignant about the "when will I need this?" question, but the truth is, there's very little in my daily life that requires math beyond, say, calculating a tip. (I don't even need to balance my checking account: I have software for that.)

Which isn't to say that it's not worth studying. I mean, there's nothing in my daily life that requires knowledge of Charlemagne or familiarity with The Iliad, and I still am glad I studied them. But yeah, trigonometry, not much relevant to my life!

[telophase]

Not arguing there (*coughanthropologymajorcough*)! I do envy people who can see the beauty of doing math, but long ago figured out that unless I get a hankering to do something for which I need to know it, I'm better off reading books about people who do math instead of doing it myself.

[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]

Yeah, I understand that. It's how I feel about a lot of disciplines: I am glad other people love it, and I am happy to read about how much they love it, but my desire to learn it myself hovers around zero. (Chemistry is that way. One of my dear friends is a chemist and he loves it, and I'm glad he does it and loves it, but I'm... not interested, except for the vague sideways bits of chemistry I get from Alton Brown.)

[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.

[rho]

I'm not entirely sure who to suggest, and mainly wanted to comment to cheer you on. I think it's fantastic that you're willing to give maths another shot, and I really hope that you enjoy it as much as I do.

That said, I will offer a tentative recommendation for Ian Stewart's books, particularly Professor Stewart's Cabinet of Mathematical Curiosities. It certainly won't teach you how to do maths, and it won't even teach you a whole lot about maths, but it just may teach you how to embrace and appreciate maths.