centering strategy

[Mike South]

I am a programmer by trade, and the language that I use is called Perl.  The Perl motto is TIMTOWTDI (which I pronounce "timtowdy", but I don't know if I've ever heard anyone else do that.  TIMTOWDI stands for "there is more than one way to do it".  This phrase comes from people asking "how do I do X with Perl", and, with this language in particular, the answer is often "there is more than one way to do it".  Perl is a remarkably expressive language that tries hard not to put you into a box and make you code in a particular way.

In thinking about the incident I am about to describe, it occurred to me that math is possibly the ultimate TIMTOWDI tool, because it so often presents us with multiple ways of solving the same problem.

Last night I was working with my son to warp his rigid heddle loom (google for 'Kromski Harp' to see the loom we were working with).  In order to make the tension even across the warp, it's best to center the warp.  We were working with a 9 inch wide project, and the warp is 31 inches across.  I have been thinking about how to explain the idea of dividing the size of the heddle in two, then dividing the size of the project (a scarf) in two and measuring half the length of the project away from the halfway point of the heddle.  A simple concept for me, but I didn't want to just have it be some mysterious magical formula for him.

Before we started we measured the length of the heddle and marked the halfway point on it.  I also marked off every inch along the heddle (both of these were suggestions in the materials that came with the loom).  Then I told him that we needed to figure out where to start so that our nine inch project was centered.

Here is what he did:

Putting his right hand on one side of the heddle, he said "one" and moved his right hand one inch forward from the center.  Then he said "two" and moved his left hand one inch back from the center.  Then he said "three" and moved his right hand forward again.  On that way to nine, at which point his hands were indicating points nine inches apart and (almost, because of the half inch) centered on the heddle.

I was blown away.  I don't know if I would ever have come up with that way of doing it.

Math: There is more than one way to do it.

TIMTOWDI,

mike

[Maria Droujkova]

This is a pretty reliable way of doing things! I googled the loom, and I could just picture the whole thing happening. Maybe you can send some pictures of working the loom with kids, though :-) Great story, Mike.

I actually have a name for that - Round-Robin Algorithms. There is a Wikipedia article about them: http://en.wikipedia.org/wiki/Round-robin_scheduling But first I read about them in studies of pirates, of all things. That's how pirates did their division problems :-) Last I saw kids using Round-Robin was to find a median of a data set.

I want to follow up on your TIMTOWTDI point with a long division algorithm I just found, which, Katherine says, follows the one she (and, apparently, many other kids) made up. It's called "partial quotients" and is much more explicit than the traditional one. Here is a blog post describing it: http://curriculalessons.suite101.com/article.cfm/teaching_division_part_ii

Adding TIMTOWTDI to the next Math Behavior Parent Bingo sheet here: http://naturalmath.wikispaces.com/bingo
Wikipedia advises your pronunciation, btw: http://en.wikipedia.org/wiki/There%27s_more_than_one_way_to_do_it


Cheers,
Maria Droujkova
http://www.naturalmath.com

Make math your own, to make your own math.

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[Bill Marsh]

Mike,
How old is your son? His method strongly resembles an inverse of what follows.

Remembering that computers use binary arithmetic, with just the “bits”
zero and one, you can learn how computers represent real numbers right
now.

To interpret something like .1010… in binary on a number line (which
we think of as going from left to right), start with your hands, palms
inward, about two feet apart and imagine that your left hand is at
zero on the number line and your right hand at one. Every time you
hear or see a zero, move your right hand to what was the midpoint
between your two hands. When you see or hear a one, move your left
hand to the midpoint. You can increase the sense of zeroing in on a
point, if you want to, by imagining moving forward a little each time
you move one of your hands.

Bill

[Mike South]

On Fri, Feb 5, 2010 at 12:02 PM, Bill Marsh <billma...@gmail.com> wrote:

Mike,
How old is your son?  His method strongly resembles an inverse of what follows.

10, just turned.

 

Remembering that computers use binary arithmetic, with just the “bits”
zero and one, you can learn how computers represent real numbers right
now.

To interpret something like .1010… in binary on a number line (which
we think of as going from left to right), start with your hands, palms
inward, about two feet apart and imagine that your left hand is at
zero on the number line and your right hand at one.  Every time you
hear or see a zero, move your right hand to what was the midpoint
between your two hands.  When you see or hear a one, move your left
hand to the midpoint.  You can increase the sense of zeroing in on a
point, if you want to, by imagining moving forward a little each time
you move one of your hands.

Utterly awesome.  I would argue that it's...wait for it...an order of magnitude more complex!  Bwahaha!

Ok but seriously, that really is beautiful.   

Bill