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Geometry Class


Date: 9/2/96 at 21:42:55
From: Kathy Miller
Subject: Geometry class

How can I survive my first year of high school geometry?  I am very 
confused.  Even the first week's lectures about points and planes have 
me lost.  Please help!


Date: 9/3/96 at 18:27:24
From: Doctor Tom
Subject: Re: Geometry class

Hi Kathy,

Well, there's no guaranteed answer to your problem, but I can
make a few suggestions.

First off, geometry is often tough for people because it is pretty 
different from any math you've ever done before - the emphasis is 
usually not on numbers and measurement (although there is some), but 
on thinking about simple geometric shapes (points, lines, triangles, 
etc.).

The teacher may be trying to be more precise than you like at the 
beginning.  For example, if you think of points as dots on a paper, 
and lines as the pencil lines that connect them, you'll do fine.  Of 
course, a "dot" should be really small, and a "mathematical dot" is 
really, really, really tiny, so what you really need to imagine is a 
perfect pencil, and so on.

Actually, geometry is a funny subject in that a lot of people who were 
"good at" math before geometry have trouble in geometry class and 
those who had trouble suddenly find themselves doing better.  The 
reason is that geometry represents a different kind of thinking - 
instead of thinking about symbols and calculations and stuff like 
that, you need to think about shapes and be able to think about how 
shapes interact.

For example, here's a question. Try to work it in your head, not with 
a pencil. 

   Imagine drawing 2 triangles on a piece of paper.  What's the 
   maximum number of times you can get the lines to cross?  

You'll find yourself thinking about sliding around triangles over each 
other in your mind's eye, and you'll probably notice some sloppiness 
in my question - what if the triangles lie exactly on top of each 
other, or share edges, or whatever?  Eventually, you'll probably 
decide that if they can't share edges, 6 crossings (arranged like a 
Star of David) is about the best you can do.

But you didn't do this with calculations like in algebra class, did 
you? Your "calculations" were more like moving shapes around in your 
mind. Of course, you can use pencils too, and that's a great help, 
and you MUST draw pictures of what the text says.

Get together with your friends and try to make sense of it. This can 
work really well. Or find somebody who took the class last year to 
work on it with you. Or maybe your parents can help.  Or you can ask
specific questions here, of 'Doctor Math'. Or look in other geometry 
books - sometimes a different book will explain things in another way 
that makes more sense to you.

I hope this helps a little.

-Doctor Tom,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Euclidean/Plane Geometry
High School Geometry

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