From: dal3@cbnewsg.cb.att.com (dale.e.parson)
Newsgroups: sci.math,misc.education,sci.edu,misc.kids
Subject: Young kids, math, & physical modeling (was Re: Is Math Hard?)
Date: 23 Nov 92 16:25:38 GMT
Organization: AT&T

In article <13670@ecs.soton.ac.uk> ekg90@ecs.soton.ac.uk (E K Gottesman) writes:
>Advice needed.
>--------------
>
>   I've got a bright four-and-a-half year old who is due to start
>school after Christmas. I've done my homework and found what I think
>is the best state primary school in the area and got him into it.
>However, I'm not convinced about the school's teaching of maths and
>science and I'd like to back it up with  some work at home. I don't
>want to force-feed my son, but I do want him to realise that maths is
>fun (I'm a maths undergrad, so I personally think it's pretty yummy).
>He's already playing at weighing and measuring things (without any
>prompting) and has a fair idea of number up to about 20 (and is
>interested in the concept of numbers bigger than 20). How do I keep
>alive his natural curiosity and use it to expand his world-view? 
>nb the British school-system is notorious for dampening a child's
>enthusiasm.

I recommend LOTS of physical models that embody mathematical processes.
We're homeschooling our 6 & 3 year olds, & besides some conventional
arithmetic fare we:

Make up games that include use of double-9 dominoes instead of dice.
All single-digits pairs from 0-0, 0-1, 0-2, ..., 9-9 are there.
They're good for practicing single-digit addition & subtraction,
using the two halves of a domino as argments, giving the kids something
to count off on their way up to a sum or down to a difference.
The first game our 5 year old invented was grouping them into 'families'
based on identical sum, which wound up giving us a bell-shaped pile
of dominoes. For younger kids we've use dominoes with colored animal
pictures for matching games.

Cuisenaire rods are good for a bunch of things. They're colored rods
of length 1 cm (white), 2 cm (red), ... cm units up through 10 cm (orange).
There are also 100 cm squares that you can compose into 1000 cm cubes
when you get that far. You can explore length, measurement, addition,
subtraction, 2-place addition & subtraction, & a bunch of other stuff.
Like dominoes they're great toys. The current address in US is (they
originated in Belgium, so you can find them closer to home):

Cuisenaire Co. of America, Inc.
P.O.Box 5026
White Plains, NY 10602-5026

We even done little physics experiments involving force to mass, with the
kids blowing different size rods across the table using straws, alo
weighing & balancing. There's a book of geometric puzzles from above
for ages 10+, but I've found our 6 year old likes to do them:

"Spatial Problem Solving with Cuisenaire Rods"
by Patricia Davidson & Robert Willcott

We also model other things like magnetic domains with them when discussing
magnets. We modeled the solar system with balls & pebbles across
a mile radius the other week.

My favorite intro. to geometric concepts is to take the kids orienteering,
using a map & compass to find checkpoints at organized meets. I've found
that, with practice, the map reading for the 6 year old proceeds at about
the same rate as regular reading, which is impressive considering that it's
a fundamentally geometric activity. I don't know what the local UK
O club would be, but you could contact the US Orienteering Federation to
find out if you like (although O is more popular over there, so maybe
it's even in the phone book). Our daughter started at 5 and could handle the
physical part of a beginner's course right away, can almost navigate one
on her own now (at 6 1/2). 

USOF
PO Box 1444
Forest Park, GA 30051

Our personal answer to "How do I keep alive his natural curiosity and use
it to expand his world-view?" has been to be curious, inventive
home schoolers. I don't know anything else to tell you about schools.

Good luck.

Dale Parson, Bell Labs, dale@mhcnet.att.com

 ---------------------------------------------------------------------- 
|    "These words are too solid, they don't move fast enough           |
|     to catch the blur in the brain that flies by, and is gone..."    |
 ----------------------------------------------------------------------
|     Suzanne Vega                                                     |
 ----------------------------------------------------------------------