on mathematics
Jul. 9th, 2010 10:24 am![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
coraaI 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.)
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.)
no subject
Date: 2010-07-09 06:26 pm (UTC)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. :-)
no subject
Date: 2010-07-09 06:32 pm (UTC)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. :)