Thursday, June 14, 2007
What's Really Going on With Multiplication in Everyday Math?
As promised elsewhere, I'm going to look carefully at what Everyday Math offers about multi-digit multiplication, how it advises teachers to teach this topic, and what I've seen in practice (and how I attempted to rectify problems with how it was being taught in some classrooms).
First, from p. 140 of the first volume of the EM 4th grade teacher's manual, the very first thing it says about multiplication. If you've never seen this before, it's no doubt because no one who attacks EM would dare quote it to you.
"The authors believe that most students should learn the basic facts for addition and multiplication to the point of instant recall. Mastery of the basic facts will give students surprising power in making quick estimates and operating with larger numbers."
I hope you were sitting down when you read that. Surprising, isn't it, if you've been getting your propaganda feed from various hate blogs or the Mathematically Correct/HOLD websites and those they link to?
Don't you wonder why the anti-reformers don't mention that quotation? It's not hidden somewhere deep in the unit. It's the very first paragraph teachers are expected to read.
Well, let's look a little further:
p. 144 "Calculators are used in this unit for games . . . In BEAT THE CALCULATOR, students quickly realize that their brains are much more efficient than their calculators when finding a product like 7 * 3. . . .
"However, the no-calculator icon (see margin) does appear on many journal pages, including those on solving number stories and Math Boxes pages in which the intention is to encourage practice with algorithms for adding and subtracting numbers. Alert students for the icon."
Hmm. Gosh, that doesn't sound much like the usual version of the EM philosophy I read about all over the internet. Sounds dramatically different, in fact. Could it be that the anti-reform bloggers and hate-mongers just overlooked those glaringly obvious examples that undermine their propaganda about EM? Are they all a little myopic? Yes, they're VERY myopic when it comes to having to see evidence that works against their fanatical dislike of programs like EM and INVESTIGATIONS.
Okay, I'm going to skip the rest of Unit 3, but you should not. If you have access to a copy of the 4th grade student book or the teachers' guide, do read over those parts of the unit that deal with multiplication facts (fact families, etc.) and how to think about and apply multiplication in context.
NEXT: A look at Lesson 5.5 in the unit entitled Big Numbers, Estimation, and Computation. Here we get the first formal algorithm for approaching multidigit multiplication, partial products.