What Can Math Do for Me?Date: 11/24/2005 at 23:52:58 From: Todd Subject: What can math do for me How can math help me in the future? I feel some of the problems we are doing in my grade 11 math class seem to be quite ridiculous. Although I understand them I cannot possibly paint a picture in my mind of how I could use it in my lifestyle. The only way I feel I could use it is if I became a scientist or something where math is a huge factor, or of course if I became a mathematician. Date: 11/25/2005 at 10:08:17 From: Doctor Ian Subject: Re: What can math do for me Hi Todd, >How can math help me in the future? That depends on what you think your future is going to be like. Unless you can predict the future, it's hard to know ahead of time how math might help you. About the only thing you can say for sure is that the less math you know, the harder you're going to have to work, Math is Power? http://mathforum.org/library/drmath/view/62716.html What is Mathematical Modeling? http://mathforum.org/library/drmath/view/61551.html and the easier it will be for other people to take advantage of you, Understanding Graphs http://mathforum.org/library/drmath/view/61632.html Is Algebra Useful in the Real World? http://mathforum.org/library/drmath/view/61611.html >I feel some of the problems we are doing in my grade 11 math class >seem to be quite ridiculous. Although I understand them, I cannot >possibly paint a picture in my mind of how I could use it in my >lifestyle. The only way I feel I could use it is if I became a >scientist or something where math is a huge factor, or of course if >I became a mathematician. An analogy I like to use is this: When you were very young, you probably spent a lot of time stacking up blocks and knocking them down. You might ask yourself: When was the last time you did that? Probably a long time ago. When do you see yourself doing it again? Probably never. Does that mean it was a waste of time? Not at all, because you were using a very specific and somewhat useless skill (stacking things) as a way of developing a very general capability (hand-eye coordination). And that very general capability is something you _do_ use, every day of your life. Math is pretty much the same way. You're using a very specific skill that is useless to most people (setting up and solving equations) as a way of developing a very general capability. What capability is that? You're learning to use abstraction to turn the problem in front of you into some version of a problem you already know how to solve. That is, math is providing a _context_ for learning about something else--in sort of the same way that in Japan, learning about archery or tea ceremonies or flower arranging provides a context for learning about Zen Buddhism, which is the real goal. (In that tradition, there is a metaphor for this kind of learning, which is that you use a boat to get you across a river, but once you're across, you don't take the boat with you. Once you've realized the essence of Zen, you can arrange flowers or not arrange them. It was just a boat to get you there. Similarly, once you've realized the essence of mathematics, you can leave the techniques behind.) What makes math a good context for learning about problem-solving? There are at least two things, I think. One is that the amount of complexity can be very precisely controlled. That is, you can take a math problem, and introduce one new wrinkle, and it becomes a slightly harder math problem. Most "real world" problems aren't like this at all. In fact, any truly realistic problem introduces all kinds of complexities that can easily overwhelm any regularity that we might be trying to exploit. A second thing that makes math good for learning about problem-solving is that it is formal, in the sense that when creating mathematical systems, we aren't bound by what happens in the "real world". By altering our axioms, we can create new systems in which our intuitions don't always work, which can force us to move beyond common sense and into more sophisticated and systematic kinds of reasoning. Let me know if this helps. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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