|August 22nd, 2011, 10:33 PM||#1|
Joined: Aug 2011
Thoughts on math education - From a young college student.
I am a second year student of engineering at a Canadian university and am very interested in mathematics and education. I feel like the methods of teaching math in high school and early university (I have no experience with senior university classes) are not only an inefficient use of the teachers knowledge but are also boring, stifling, and doesn’t do justice to the subject.
If we look at English classes, students are required to be familiar with certain material before attending class. ie) reading a chapter of the book being covered. And, the majority of class time is spent discussing said material. The teacher guides the students to think about what they have read and encourages everyone to collaborate and answer some kind of question. It is essentially an exploration of the work. Personally, I find this to be a very rewarding method of learning, and only someone with extensive knowledge of the topic would be capable of guiding such a discussion.
Now if we look at math class, the teacher dictates results to students (often skipping proofs, the mathematicians motivation, and the general concept) who copy the notes and try to essentially memorize how to apply a theorem. (This is of course somewhat of an over simplification, but that is the core of math classes in my experience). This is very boring for the student, and probably for the professor as well. Moreover, I could copy notes onto a blackboard as well. Professors with advanced degrees are essentially turned into middle-men between the text book and the student. A clearly inefficient use of the profs expertise.
Why not model math education after English education? In my math class: students would be required to familiarize themselves with a chapter in the textbook and then come to class to discuss the material with their peers and the professor. The professor could talk to the students about the motivation for researching such a topic, explain the proof behind it, and enthusiastically answer any of the students’ curious/clarifying questions. Again – it is essentially an “exploration” of the material. Finally, I think that the most rewarding part of modeling a math class in such a manner is that the class could take part in a discussion to try to solve a very difficult problem, just like in an English class.
I feel like this type of approach would be a much more effective way of teaching math. In my grade 12 trig class i had a seriously terrible teacher. Because of this i started to try to teach myself from the text book. And, the more i teach my self (as apposed to taking notes in class) the better i have done in class, and the greater my understanding. I recently got 99% in integral calculus, and 96% in vector calculus. I attended ~1/4 of my classes. I am not trying to brag, and i do not think i am gifted either. But i do think that i took a superior approach to the subject.
I would greatly appreciate peoples thoughts on the matter.
|August 23rd, 2011, 02:01 PM||#2|
Joined: Apr 2011
Re: Thoughts on math education - From a young college studen
You really don't want to get me started on math education. I work at the college level so I see the results of our math education, and when I find people who can't do what I'd consider elementary school math and who cannot think for themselves on everyday things, then I know there's a problem going on.
But despite that, I disagree with quite a bit of what you're saying, because you're approaching it from the point of view of someone who wants to learn very specific things that are not being taught to you, and assuming that's what everyone wants or needs to learn.
Let's use your literally class as example. You seem to be assuming people are bored in math because it isn't approached like your literally class. Well, I'd be bored stiff in your literature class, despite the approach. I am not bored discussing a piece of literature, assuming I like it to start with. I love to read, but am generally not interested in the typical things done in literally classes. (I suppose we'd have to define "literature" - most of what I read would probably not be designated as such.) We were required to read stuff before coming to class and would discuss it... I was bored. Out of the typically required stuff we had in high school, 1984 was the only one I was interested in discussing.
If you talked about the motivation for researching some specific math topic, that isn't going to interest someone who isn't interested in it. I also find that having students try to familiarize themselves with a chapter first doesn't really do much if they don't understand it. Of course, a lot of math books suck to begin with. So actually, yes I do see an instructor as the gateway between the book and understanding. In fact, I very much see that as the instructor's job because a great many people won't get it out of the book.
You're talking to "the math crowd" here so there may be much agreement with your statements cause most of these people take a great interest in math. I'm not like most of the others here - I like math fine, I loved algebra, I liked stats fairly well, I hated trig and I hated my introduction to calculus. (I grant you I had a terrible teacher for trig & calculus, but not for the reasons you're stating, but had the same teacher for analytic geometry and liked it despite this teacher. I re-took trig in college and it was easier for me, but I didn't "like it" any better.) I'm a business person and am more geared towards that type of math. But do keep in mind that even though I'm rather "the odd man (gal) out" at this site, there's a whole world of people taking math classes who don't hang around here, and you have to consider them as well. So I'm giving you the perspective of someone who's coming from a different place.
I'm seeing a problem coming from the beginnings, and not just classes where you can discuss motivations and proofs. I do agree that there's just too much memorization and then trying to apply it with memorization, rather than the teaching of underlying concepts, the teaching of thinking, and then finding ways to apply to different things by thinking about it. Things are normally taught as: we do this equation to solve this problem, and that equation to solve that problem, but it's never taught that we can do this equation for this TYPE of thing, what it means, and therefore what it can be used for. (Just as a silly example, if a kid learns how to add apples but is never taught what addition really is meaning, then they don't later know how to add marbles. Although I'm really not exaggerating by much.)
So these kids are completely lost on everything before they ever get to algebra or trig or anything beyond. You can't force someone to like a subject they don't like, so there will be people never interested in talking about proofs, but if they had a better foundation, they could at least handle these classes a bit better and probably get more out of it on their own, regardless of the text or teacher. And... apply it to other things they are interested in.
I work with people in things requiring basic arithmetic, a fair amount of business math, some basic algebra... and that's about it. And lots of people can't even do this stuff. So there's an issue right there in elementary school that I think is much more important to solve... partly cause a lot of that is used in everyday life, and also because it will set them up better for later more advanced classes. (I've worked with people I thought should have someone with power of attorney over their money cause they couldn't comprehend the most basic things. That's real life.)
And it's not just math. I have to assume it's everything, going back to elementary school. And because elementary school is so terrible, I'd rather concentrate on that problem first, and the schools in general, before worrying about calculus. I think there's some lousy teachers who don't comprehend that this stale memorizing isn't working. But I'm sure there's also plenty of good teachers who have their hands tied by the system. And I do agree that interest and enthusiasm on the teacher's part would help. But I would say it's a rare gift when a teacher comes along and actually can get everyone to like a subject, when generally it's a simple fact that everyone doesn't like everything. (I can think of few who were like that, and that was back in a day when teachers were just generally better overall.)
I did say you didn't want to get me started on this. Everyone here is probably sick of my rants by now.
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