Date: Jan 6, 2013 7:56 PM
Author: Michael Paul Goldenberg
Subject: Re: 'At Right Angles' - a journal from India

Odd. I just searched "teaching fractions with paper folding" using quotation marks and got exactly one (1) hit.

Then, I searched "teaching fractions using paper folding" and got exactly zero (0) hits.

Searching "teaching fractions paper folding" with quotations got me 'no results' followed, actually by one page of results.

Google must work differently in the People's Republic of Brooklyn.

Of course, removing the quotation marks gets a lot more responses, but how many are actually relevant? Who can really know?

My old hats are not feeling the slightest sense of abuse. But they ARE curious about your use of language. You say, "To say that teaching fractions with folding paper is old hat is to be unkind to old hats."

Now, who said that teaching fractions with folding paper is "old hat" or anything of the kind? Surely not GS. Seems like you're the one who made that claim, though apparently you meant something different. Because you want to claim that it's been around forever, more or less, for sufficiently large values of 25 years.

But the existence of a 25 year-old lesson plan using ANY approach to ANY topic hardly demonstrates that it is in wide practice. It wasn't in 1992, just slightly over 20 years ago, when it was used as part of a study with sixth grade math teachers in the Willow Run School District in Ypsilanti, MI. No one there had previously heard of it. And when I worked with upper-grade elementary school teachers in Pontiac, MI schools in 2004-2006, none of them were familiar with that representation. So maybe in the ensuing 6-8 years, it's caught fire nationally, if not globally.

Or maybe ideas in mathematics teaching spread a LOT more slowly than they would if there were actually an educational mafia, or even just a ministry of education similar to the one in Japan.

Then again, let's not feel constrained to limit our thinking to the rapidity with which ideas spread to math classrooms. Rumor has it that old ideas reappear after unpredictable periods of dormancy in the business world, enjoying new vogues for reasons that aren't always simple to understand or explain. Perhaps this phenomenon is less an indictment of public education and evil, all-knowing, all-powerful (but, sadly, irredeemably corrupt) godfathers and capos, but rather a combination of the ease with which things fade ofter one or two generations and the general fickleness of the human species, even with all the high-powered equipment moving us down the ever-widening, ever faster-paced information super highway.

Heck, it might even turn out that we get some things wrong in our initial rejection of them, for any number of reasons. Like, say, the very non-monolithic set of projects mistakenly lumped together and conveniently dismissed as "The New Math."

Maybe we should google it. And whatever we turn up on the Internet will have to be the truth, the whole truth, and nothing but the truth.