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Trouble with math

gregbo asked me to write more on the following comment I made in an earlier post:

"I used to have trouble with math insofar as I need it to be taught in a certain way or I don't get it ..."

To talk about it I have to tell a fairly long story about my history with math education, which I will cut-tag.

My problems with math began in 3d grade. My family had moved and sent me to a new school, and the school was on the "experimental" side. In 3d grade I had a teacher whose teaching style was very informal. He encouraged us to pursue our own interests, and getting formal instruction from him was optional. When he taught multiplication, I didn't really get it, and so I stopped paying attention and went and did something else.

I guess we were tested at the end of the grade. I think I got a report that said I needed work on my math skills, and I was put into a 4th grade class with a teacher who was reputed to be very good at teaching math.

Which she may have been. But she was also emotionally volatile. Sometimes she would decide someone wasn't paying attention to something she was teaching, and she would angrily send them into another room to "think about it." One day she decided (incorrectly) that I wasn't paying attention to her lecture on Eskimos, so she sent me into the other room to write an essay about Eskimos.

I knew from seeing what happened to other kids who got sent into the room that I didn't dare come out until she came to get me. So I sat in there for a while after finishing my essay, and I could vaguely hear her beginning to teach division in the classroom. But I didn't dare come out.

Because I missed that first division lesson, I didn't get the subsequent lessons, so I didn't learn division properly either.

The family moved again before I went into 5th grade. I was tested to get into the new school I was going to start in. Naturally the tests came back that I needed work on math. So over the summer my father tutored me in math. He was one of the best math teachers I've ever had. I learned multiplication and division and a skill I've always felt really fortunate that he taught well, which was never taught to me in school as far as I remember - how to estimate.

I guess I did OK in math for a while. Then the problems started again in 7th or 8th grade. I was put into an advanced math group. We sat in a separate room from the regular class and I guess we were given problems to learn on our own. But that didn't work for me, and so I got behind again.

Throughout the rest of grade school and high school, math worked this way for me: If I had a teacher who taught how to do the problems first and then taught the theory behind the problems, I did OK. If I had a teacher who taught the theory first, and expected us to work out how to solve the problems by using the theory, or if I was in a group that was expected to do some kind of independent work, I didn't learn it.

I managed to do OK (low B's, which were lower than my grades in other subjects) until I got to calculus, which I took junior and senior years of high school. The teacher was very much into the method of "teaching the theory first and letting us figure out how to do the problems." I got hopelessly confused, and at one point I even took the very rare for me step of going to the teacher after class and saying that I needed to be taught in this other way. He refused. So I got C's in calculus.

Because most of the kids in school weren't taking calculus at all, the science classes never had any problems involving calculus. That was too bad, because learning calculus in an applied manner as part of science problems would have been ideal for me.

The final straw was that after my second year of calculus, where I had barely begun to get some grasp on the second year materials, we were given an advanced placement test for college credit. There were two tests, one for people who'd had one year of calculus and one for people who'd had one year. Without my knowledge, the teacher ordered the one-year test for me because I wasn't doing so well. But I knew the second-year material better than the first-year material. So I didn't have a chance of passing the test.

The university I went to was pretty loose as far as required courses were concerned, so I never took any math courses at all, except that when I got to my senior year I took some beginning programming courses, which didn't involve calculus.

I've noticed that I have a particular way of approaching the learning of certain kinds of new material. One way to describe it is that I have to rewire a portion of my brain to store the material - otherwise the information just won't stay stored. I start by reading a few things about it, and then trying some things. Then I go back and read the same things over again, only now they make a bit more sense because of the things I tried. So I read a bit more, and try some new stuff, then I go back and read again. Sometimes I add in writing about the stuff, as in helping people at an earlier stage by describing what I have learned. It's kind of like a spiral. I need both the reading and the trying, and in some cases the teaching, in order to store the material in my brain, and each time I read or try something, a little more of the construction work is done.

This learning style is especially necessary for me when it comes to things that involve working with my hands, learning new languages, and math and programming. It's much less true of writing, editing, and conceptual stuff in disciplines such as psychology and English literature and religion and philosophy. My brain seems pretty well constructed to do that stuff already. It's not especially true of graphic design and music type stuff (although the way my memory handles musical content is weird enough to warrant an entirely separate post, should anyone be interested).

I hope this addresses gregbo's question and I hope he explains why the topic was of interest to him.


( 11 comments — Leave a comment )
Dec. 26th, 2004 10:10 pm (UTC)
Thanks for sharing this. I thought it was fascinating, and I'd love to read the musical part as well, if you feel like writing about it.
Dec. 27th, 2004 04:33 pm (UTC)
Magn0lia: I talked about my own experiences with similar issues during the period where I had you on my friends list -- did you see it?

Oh, and Stef, I'm afraid to say that a lot of this sounds familiar. It sounds milder than what I deal with, but very much along the same lines. If you ever felt so inclined, you might find learning disability testing illuminating.

Dec. 27th, 2004 04:36 pm (UTC)
What have you gained from disability testing?
Dec. 27th, 2004 04:39 pm (UTC)
More knowledge about the specific areas I'm cognitively weak and strong in, and some strategies for coping better with them. A particular name to pin on problems I've lived with my whole life, and a better way of explaining those problems to other people who at first might not understand. Recommendations for further reading.

Dec. 27th, 2004 04:56 pm (UTC)
Dec. 26th, 2004 10:25 pm (UTC)
Me same way - example, then theory. Also, geometry, not algebra. Matrix formulation of quantum mechanics, not integral: discrete, not continuous, even if it amounts to the exact same thing. Math seems to be something where different minds are definitely wired for learning different ways, and different teaching/learning options should be mandatory. Blah random etc.
Dec. 26th, 2004 11:32 pm (UTC)
Fortunately, I included some of the problems (and some solutions) I had with math in my memories under the heading "problem solving."

Also, in the event that finding work in the computer industry doesn't pan out, or I decide I no longer want to pursue such work, I might try to become a high school math teacher. I'd like to understand different learning styles so I can hopefully be a better teacher.

I'd also like to know more about the way your mind handles musical content. From what I recall of your drumming and percussion, you didn't seem to have any problems.

Dec. 27th, 2004 03:59 pm (UTC)
Thanks for sharing your posts. They were really interesting. And I think you'd make a really good high school math teacher.
Jan. 28th, 2005 11:52 pm (UTC)
We'll see. I'm been reviewing some things, but I'm not anywhere near where I was when I was learning it in high school and college. Like last night, for example, I had to look up some trig formulas. Fortunately, there are a lot of online resources.
Dec. 27th, 2004 02:53 am (UTC)
Re: Trouble with math
very interesting; thanks for writing it!

some of that sounds a lot like me for similar domains. when it comes to doing things with my hands, i like to read some about the theory, watch how it's done, try a little by myself, read and watch more, try more...

if i just watch complex motions without knowing some of the theory it's all a visual swirl and doesn't get anywhere. if i read too much theory without watching, it doesn't connect to the physicality of it in my mind.

which explains why i am currently not learning how to spin -- i've never actually consciously watched somebody who's good at it do it; i only have books -- i've got enough theory to know what should happen, but all the nice still photography in the world is not doing it for me. i need to find at couple of videos, or a spinning group locally.
Jan. 3rd, 2005 11:27 pm (UTC)
You know, your math learning style sounds like the exact opposite of my sister's. She has to have the theory first, or she won't believe the rest!

I think I'm somewhat in-between. I need the problems for the overview to orient and motivate myself, but then I need the theory or I'll forget everything.

I'm glad your dad helped out with your math education.
( 11 comments — Leave a comment )

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