Making Math InterestingDate: 08/15/2000 at 12:15:35 From: Laura Subject: Math Tips Hi, My name is Laura and I am going into 7th grade. This summer, I have been studying and trying to practice pre-algebra almost every day. I read people's questions and write down the math tips you give them. I hear math starts to get really hard around 7th and 8th grade, so do you have any tips for how I can stay focused in math this coming year, and succeed? Thanks. Laura Date: 08/16/2000 at 09:43:34 From: Doctor Ian Subject: Re: Math Tips Hi Laura, Actually, math starts to get _fun_ in 7th and 8th grade. You stop dealing with particular numbers, and start dealing with patterns, which are much more powerful, and therefore much more interesting. I don't believe that anyone can stay focused for long on a subject that she doesn't like, so my advice would be to learn to enjoy math, instead of looking at it as something that you're 'supposed' to learn. 'Easier said than done', you're thinking? Well, it's not as difficult as you may think. One way to get interested in anything is to read books (or listen to lectures) by people who really love the subject, because that kind of love can be contagious. If you want to learn physics, you can't do better than to listen to Richard Feynman lecture about it. If you want to learn how the mind works, the best places to start (in my opinion) are with Doug Hofstadter's book _Godel, Escher, Bach_ (but just read the dialogs between the chapters to start) and Marvin Minsky's book _The Society of Mind_. And if you want to learn about math... well, there are so many good books that I hesitate to recommend just one or two. Go to the math section of a good bookstore and start browsing. Pick up a book that looks interesting, open it to somewhere in the middle, and read a few pages. See if the author seems to be on your wavelength. When he or she explains things to you, do they seem clear, or do you have to struggle to understand what he or she is saying? If it isn't connecting with you, put the book down and look at another one. The good news is, I can guarantee you that there are a number of books out there that, once you've found them, will seem to have been written especially for you. The bad news is, you may have to kiss a lot of frogs to find a prince. So kiss them quickly, and keep looking. I also find that biographies are an excellent way to keep a subject interesting. I discovered in college that whenever I wanted to learn about a new subject, I should start by reading a biography of the person who came up with it. Sometimes that would be a whole book. Sometimes it would be an encyclopedia article. And that method may not work for you as well as it did for me, but I would suggest that you give it a try. (A good biography will do two things for you: first, it will place whatever the subject did in context, letting you know why other people thought it was important - why it let them do something they had previously been prevented from doing. Second, it will expose you to what more often than not turns out to be the clearest explanation of the relevant concept - that is, the one that the innovator used to explain it to himself.) In any case, I guess I would ask you to keep two things in mind: (1) Mathematicians don't do mathematics because they get paid to do it, or because they think it will somehow be useful. In almost every case, they are motivated by one of two things: fun or beauty. I know that can be hard to believe, given the way math classes are normally taught in schools, but it's true, and just what makes mathematics fun and beautiful is the kind of thing that you can learn by reading biographies. (2) Technical subjects (like math or chemistry) are often taught backward, and I wish I could give you a good reason for that, but I can't. Everyone I knew growing up hated high-school chemistry, and so did I, because we seemed to spend endless hours doing things like converting grams to pounds and ounces to liters, and learning to determine how much of reagents X and Y you'd need to make some particular amount of reagent Z. None of which has anything to do with what's really going on in chemistry! They don't help you understand why different substances have different colors, why some are transparent while others are opaque, why some are hard and brittle while others are soft and pliable, why water gets larger when it freezes while most other things get smaller, why fish smell so bad if they aren't frozen immediately, how two things as different as diamonds and graphite can be made by arranging the same kinds of atoms in different configurations... and so on. It's an enormous, endlessly fascinating subject - and it almost seems at times as if there is a conspiracy among high school chemistry teachers to keep all the good stuff a secret. It wasn't until I got to college, where they started dealing with the components of molecules (atoms and electrons) that chemistry started making sense. That's where they should have started, and there is no telling how many kids had their interest in the subject killed by starting at the other end. Similarly, mathematics is, by and large, taught backward. You are drilled on little skills, which turn out to be important, but without ever really being shown the bigger picture, which would help you understand _why_ they are important. Can you imagine trying to teach someone to play chess by having them practice moving the individual pieces, without ever letting them know that there was such a thing as a chess 'game', or even letting them see a board with more than one piece on it? Who would bother to learn it? That's something like the way we currently go about teaching math. Is it any wonder that so many students lose interest so early? I hope this helps. If you'd like to write back and tell me more about what you have and haven't liked about the math that you've learned so far, I may be able to point you towards the resources that would be most suitable for you. Or maybe I can help you see the larger picture, which will help make the skills you'll be asked to learn seem valuable, rather than arbitrary. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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