From: lady@uhunix.uhcc.Hawaii.Edu (Lee Lady)
Subject: Re: Is Math Hard?
Followup-To: sci.math,misc.education
Summary: Keep up the good work!
Organization: University of Hawaii (Mathematics Dept)
Date: Sun, 15 Nov 1992 20:48:04 GMT

In article <00721449615@elgamy.uucp.taronga.com> elg@elgamy.uucp.taronga.com (Eric Lee Green) writes:
>       ....
>So I'm back to second grade material: I'm going to have them do a scale
>map of the classroom. How about -- fractions, basic integers, base-12
>arithmetic, all in one, along with a fuller understanding of how maps
>represent reality?

Good.  But don't get too caught up in trying to teach a whole lot of
skills.  The objective is more to simply get them more comfortable with
numbers, to have them see numbers as something of real interest and
importance.  To move numbers from the realm of the abstract into the
concrete.  As far as fractions go, maybe you could teach them to use a
measuring cup.  


I was always interested in numbers.  In elementary school (before the days
of the new math), as soon as I got my arithmetic text at the beginning of
the school year I'd read through the whole thing and learn all the
techniques.  When I was lying in bed at night I would often decide to
work out some problem like "How many seconds are there in a year?"  (I
almost always got lost before I got the answer, though.)  

So where did this interest in numbers come from?  As you might expect, I
don't completely know.  I can remember when I was about four years old 
having a discussion with some other kids in a sandbox about what the
biggest number is.  As far as I knew, the biggest number was 15, but one
of my playmates thought that there were even bigger numbers than 15, 
which intrigued me.  

I wasn't too much older than that when I learned about 100.  My mother
told me that a dollar was the same as 100 pennies and that impressed me
because I'd been told that a dollar was a whole lot of money (that was a
long time ago!) and I knew that a penny could only buy a piece of candy
or a package of gum.  

I also learned about inches.  An inch was pretty small, even to somebody
my size.  And one day I started wondering about how long a hundred inches
would be.  I was fascinated by the idea of combining a number that large
with something so small.  

Older children can become fascinated with numbers much larger than a
hundred, of course.  Suppose you had a million millions, for instance,
how much would that be?  

It was in sixth grade, I think, when I finally learned that there is no
largest number.  We had a hot shot student teacher who explained to our
class that no matter how large a number is, you can always add one to it
and get a still larger number.  I remember walking home from school that
afternoon and being really bothered by this.  The logic of what he said
seemed unassailable but I just couldn't see how anything could just keep
going on forever and never have an end.  

Later on, I found Krassner and Neumann's book MATHEMATICS AND THE
IMAGINATION in the library.  They invented numbers like the googol, which
is a 1 with a hundred zeros after it (10 to the one hundredth power) and
the googolplex, which is 1 followed by a googol zeros.  And then in a
later chapter they talked about infinity and explained that some
infinities can be bigger than others.  (As I remember, they talk about
both infinite cardinals and ordinals.)  I could see that this was really
profound shit, but it was a bit over my head.  


>As for my success (or lack thereof): I'm glad SOMEBODY thinks I'm
>successful. I'm afraid that I go in everyday and just don't see where
>I'm doing these kids a whole lot of good. There's so much they don't know,
>that they should know. And I have to move so slow with these kids. Not

That sounds a lot like the way I feel about my calculus students :-)

--
It is a poor sort of skepticism which merely delights in challenging
those claims which conflict with one's own belief system.  
                                                          --Bogus quote 
lady@uhunix.uhcc.hawaii.edu         lady@uhunix.bitnet