YET MORE ALGEBRA….I just can’t get enough, can I? However, having uncovered one error in Diane Ravitch’s op-ed about math instruction in the Wall Street Journal, I’ve now learned of two others:
Attempts to solve problems without basic skills caused some critics, especially professional mathematicians, to deride the “new, new math” as “rainforest algebra.”
This is woefully misleading. The person who coined the term “rainforest algebra” was Marianne Jennings. She isn’t a professional mathematician, she’s a business professor at Arizona State University and a well known conservative columnist.
A new textbook, “Rethinking Mathematics: Teaching Social Justice by the Numbers,” shows how problem solving, ethnomathematics and political action can be merged.
“Rethinking Mathematics” is not a textbook. It’s a collection of articles that provide suggestions for math projects to be used at various grade levels.
This isn’t a pedantic distinction. “Textbook” implies a primary text used to teach mathematics to children, and suggests that it’s meant to be the sole text used. A resource book, conversely, is meant for occasional use by teachers who are constructing math units. There’s nothing insidious about a math resource book that focuses on social justice, just as there’s nothing insidious about a resource book aimed at Christian schools that focuses on math problems taken from the Bible. I Kings 7:23 might make a good geometry unit, for example.
That’s three factual errors in the first four paragraphs of Ravitch’s op-ed. This is not a good track record.
On a broader note, over the past few days I’ve accidentally become pretty familiar with the “math wars,” a staple of 90s education criticism. The basic outline is pretty simple: reformers, led by the National Council of Teachers of Mathematics (NCTM), wanted to put more emphasis on “discovering” math and real-world problem solving , while traditionalists wanted to keep the emphasis squarely on computation skills and “basics.”
I’m temperamentally sympathetic to the benefits of teaching basic skills, but at the same time I’m sure we all remember from our own primary and high school math classes that “story problems” were always harder than basic skills. Way harder. Learning computation is important, but surely everyone understands that knowing how to apply math to actual situations is far more important?
Here’s an example ? ironically from a “back to basics” supporter. It was written for the Washington Post in 1998 by Frank Wang. Let’s call this Problem A:
I am worried that…only 23 percent of American eighth-graders could solve the following simple proportionality problem on the 1994-95 Third International Mathematics and Science Survey test: “Peter bought 70 items, and Sue bought 90 items. Each item cost the same and the items cost $800 altogether. How much did Sue pay?”
Now let’s rephrase this into Problem B:
What is 70 + 90? (A: 160)
What is $800 ? 160? (A: $5)
What is $5 * 90? (A: $450)
Eighth graders ought to be able to solve this problem no matter how it’s presented. Still, my guess is that basic computation wasn’t the real hangup here. Most of them could probably solve Problem B. What they couldn’t do was convert Problem A into Problem B.
So what would make me happier: A student who could convert A to B but then used a calculator to get the numerical answer? Or a student who could solve Problem B in their head but couldn’t get there in the first place? If I were forced to choose, I’d choose the former. And if I had to give up some teaching time dedicated to basic skills in order to make kids better at converting A to B, I’d do it. After all, in a real world version of this problem with real numbers that didn’t divide nicely, I’d end up using a calculator myself.
Of course, the big question is: does “reform” mathematics actually succeed at teaching kids to apply mathematics better? Or does it stint on basic skills and end up getting nothing in return? Unfortunately, that’s an empirical question, and the critics don’t seem much interested in empirical evidence.
For example, here’s Richard Neill. Neill is a member of the Texas State Board of Education, and this is what he wrote in 1997 about the infamous “Rainforest Algebra” text:
My point is this: Addison-Wesley’s watered down algebra destroys the true beauty of mathematics. You see, math helps mold children. It teaches them perseverance, attention to detail, critical thinking skills and discipline.
Here we get to the core issue: not teaching math but fighting moral decay. Neill doesn’t seem to care whether this textbook does or doesn’t teach kids how to use algebra. What he cares about is molding children via perseverance and discipline. Apparently, if math is tedious and hard to learn, that’s a good thing.
Count me out. If math can’t be made fun and interesting, that’s too bad. Kids have to learn it anyway. But if it can be made fun and interesting, surely we should welcome that. After all, if Texans want to teach their children perseverance and discipline, there’s always football.