Making Math Interesting

Date: 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/