🚀 go-pugleaf

In article <17meeoINNc0f@agate.berkeley.edu> bh@anarres.CS.Berkeley.EDU (Brian Harvey) writes:
>chuck@ksr.com (Chuck Shavit) writes:
>>Why would you want to teach Logo to very young children?  As I understand
>>it, Logo is a tool for developing math and programming skills.  But at the
>>level described above, it seems to me that there is very little educational
>>(math and programming) value to a session in which the very young kid press
>>some buttons on the keyboard and watch the effect on a graphics display.
>
>Certainly I wouldn't want a kid (or anyone!) to play with Logo *instead of*
>having lots of other experiences, both with and without a computer.
>
>Caveat #2:  My teaching experience is all high school and above, so I'm now
>talking about my understanding of other people's ideas, not my own work.

I want to see suggestions that I can try with my kids, so I'll chip in
my two cents.

>
>I think that the idea of Logo for young kids is partly to get across the idea
>of algorithms -- that a repeatable set of instructions causes something repeatable
>to happen on the screen -- and also partly to begin developing the ideas of
>distance and angle.  The kid who uses an INSTANT program isn't working with
>numbers, but is doing a sort of pre-number exploration in which pushing the
>button once causes a little change and pushing the button a bunch causes a
>bigger change.

INSTANT Logo wasn't a failure with my daughter--at age 4 she was even capable
of typing fd with a number to see how far the turtle would go, and got a
charge out of turning it slightly and wrapping it around the screen a bunch of
times. I think Logo will be great now that she has become more comfortable
with numbers and reading/writing, but getting comfortable with symbol
manipulation was largely through means other than Logo. Occasional Logo
use did contribute its piece, and I'm not detracting from it in any way,
but some direct PHYSICAL manipulatives seemed to work better both at 
keeping her interest for longer periods of time, and at exposing her to
mathematics while using a minimum of symbol crunching.

As an example, my 6 yr. daughter & I have recently begun to work with
a book of geometric puzzles using Cuisenaire rods. For the uninitiated,
these are colored rods in lengths 1 cm (white), 2 cm (red), 3 cm (lt. green),
4 cm (purple), 5 cm (yellow), 6 cm (dk. green), 7 cm (black), 8 cm
(brown), 9 cm (blue) and 10 cm (orange). Lengths that share prime factors
share loose color associations. You can explore arithmetic operations
and assorted mathematical laws and relationships by arranging the rods in
various ways.

The puzzles are superimposed on centimeter graph paper (I can post Cuisenaire
Co.'s address if anybody wants it). The recommended ages are ages 9-17,
although at age 6 she's having no trouble knocking out the beginner puzzles.
The puzzle gives you an outline to fill on the graph paper, which I transcribe
onto plain graph paper to keep the book for our son, and a list of rods
to use in that puzzle. More advanced puzzles constrain the rods without
telling you exactly what to use (e.g., 20 rods of exactly 2 colors).

The first puzzle was VERY easy, there were many solutions (i.e., it was the
BAIT), so when the 2nd didn't yield to immediate solution, she was ready to
pack it in. I told her I found that puzzle interesting so I would solve
it (as she was leaving the room), so I began enunciating my strategy:
"I'm taking the biggest rod, and putting it into the tightest fitting spot.
I'm taking the biggest remaining rod & putting it into the tightest
fitting spot." After hearing me say this twice she walked back into the room,
sat down at the puzzle, and completed the remaining 8 placements in about a
minute. She now has an algorithm

For all blocks
	Select biggest remaining block
	For all available spaces
		Try block in space, place block in space
			with least remaining space after placement

The algorithm is good for about the first 8 puzzles, before we hit backtracking
(which right now would be too much I think, but perhaps not by the time we
get there). We also have another heuristic for getting different solutions
to previously solved puzzles: find two pieces lying end-to-end, and swap
their positions. This is the commutative property of addition, and easier than
the first strategy.

Thus she's collecting algorithms & heuristics, and while some verbalization
occurs, the algorithm is in a big way sensory and direct, A lot of finding
the solution is thinking with the rods--putting them down, turning them,
exchanging them, etc. This quality was what I meant in a previous post about
predominance of 'sense crunching' over 'symbol crunching'. At the end of
an exercise she can abstract out some more mathematics, but input to the
system is largely sensorimotor. My experience suggests the contents of my
previous post, that at ages 3-6 the computer is more interesting if the
kid can manipulate it as a physical thing rather than a symbol crunching
thing. That's why the mouse-to-screen interface is great, because it's a
physical association, not a symbolic one.

I haven't tried doing a Cuisenaire analog on the computer, but I don't
think a direct implementation of Cuisenaire rods would be very interesting.
The are fun to pick up & play with, very colorful, and my daughter enjoys
coloring the solution on the graph paper after completing the puzzle (part of
what drew me to the puzzle book was the opportunity for coloring, which she
loves). A lot of what makes them fun is holding and playing with them.
Yesterday she and her brother invented a game of blowing them across the
kitchen table with straws, and a little information about mass-to-force
came out as they tried blowing rods of different sizes.

Simple drawing programs that manipulate geometric entities based
on their key parameters HAVE kept the kids' interest, and are largely
pre-symbolic. I think a nice segue into Logo would be a mouse-driven front end
that lets kids capture templates of Logo procedures. A simple version
would simply capture explicit lines into turtle movement procedures, along
with color changes and the like. More interesting enhancements would
include the ability to put constraints on properties (e.g., these
angles are equal, this is twice that), and allow the user to point out
(as in point-and-click) graphical features that share some intended
commonality; such features become procedure parameters. If anybody has
a student interested in doing a Logo graphical CASE tool, I'd certainly be
interested in testing, debugging, & critiquing. Winter may bring more
indoor time for me to actually design something. Whereas traditional Logo
turtle programming is symbol-in-graphics-out iteration, Logo CASE would
bind graphical manipulation to the input of Logo interpretation as well.
It could be a pretty fancy capability.

>
>Much of this sort of thing has been done by researchers whose interest was to
>see just how young a child can be and still understand mathematical things.
>(Did you see the article in the news yesterday about some study that seems
>to show tiny preverbal kids understanding 1+1=2?)  I'm not terribly interested
>in accelerating kids, but it *is* interesting to know what's possible.

Our son used to love counting toothpicks at age 2. He had an Australian
aborigine's concept of counting: 1, 2, 3, many. His interest was aroused
by listening to his sister count during games of hide-and-seek. A sister
can be a very interesting computer for a 2 year old.

Our daughter invented hypothetical syllogism at age 3, although she didn't
call it that. I don't think it's anything that requires acceleration:
it's already in them, wanting to come out. I'm simply on the lookout for
interesting media that give it ways to come out. At ages 3-6, I think these
media can certainly be geometric, but are mostly pre-symbolic.


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

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|    "These words are too solid, they don't move fast enough           |
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|     Suzanne Vega                                                     |
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