Singing the Blues About Pelham's Elementary Math Program

Tom Lehrer, brilliant satirical songwriter and very smart mathematician, penned these words:

It won't do you a bit of good to review math.
It's so simple,
So very simple,
That only a child can do it!

Pelham parents struggling to help their elementary kids with the Math Investigations textbooks would be forgiven if they thought Lehrer wrote the lyrics yesterday. As he says in his introduction to the song, which is about a subtraction problem, “but in the new approach, as you know, the important thing is to understand what you're doing rather than to get the right answer.”

In fact, Lehrer’s song is called “New Math” because it is about the New Math of the mid-1960s, the new math of set theory and base-8, the new math I suffered through for several of my elementary years. That the song still delivers its message now underlines one my conclusions about math: A curriculum cannot be approved until research demonstrates it will make no sense to the current generation of parents.

Kidding aside, there is grand irony in the wars over math education. Math is the most objective of subjects; the answers are the answers. Things add up. And at the same time, math is the subject that has been most beset by educational fads and philosophical debates. How can there be so many questions about teaching a subject where the answers never change?

Math has even suffered under the burden of ideology, both political and educational. New Math was created during the Cold War, a response to Sputnik. America had a collective panic attack and decided if we changed how kids learned math and science, we could throw a bleeping little bit of metal into orbit to match the Soviets. Several years of that program’s abstraction accompanied by plummeting student performance brought in the back-to-basics movement, with lots of drills and learning by rote. And that, in turn, spawned Reform Math and a renewed focus on conceptual understanding. Reform Math is sometimes called “New New Math,” and Investigations is firmly in that camp.

Investigations follows a very specific Reform Math ideology called “constructivism,” I learned from a cool Wired magazine article on the excellent, free education website Khan Academy. Wired wrote, “This school of thought holds that kids lose interest in math because it’s so often taught as a bunch of mechanical routines you follow to solve problems disconnected from everyday life. Constructivists argue that it’s better to give kids activities that let them discover the principles of math and physics on their own.”

Sounds good, right? Everyone loves a fun manipulative lesson or two. Makes it all feel real. That is until kids are still counting with fingers, or number lines, or blocks, or grids when in the fifth grade. Because, you see, math in the end does become abstract, and to do the abstract stuff you need to have those awful mechanical routines down cold. So-called “discovery” will be of no use when you hit quadratic equations. As Khan Academy creator Salman Khan told Wired, “Isaac Newton would not have invented calculus had he not had textbooks on algebra.”

Bill Gates, whose foundation is a funder of the non-profit Khan Academy, was more blunt: “If you can’t do multiplication, then tell me, what is your contribution to society going to be?”

Investigation’s greatest sin is that it puts ideology before all else, including math content, and so forces districts like Pelham to misdirect precious training dollars. The Prince William County Education Reform Coalition in Maryland wrote in a report that “mathematical content must be a priority over the pedagogical ideology that serves as the foundation for the Investigations curriculum... evidence suggests that the program is rich in ideology and weak in content."

In a brilliant bit of citizen journalism, the coalition discovered and reported that 36 out of 70 school districts listed in a marketing brochure as successful adopters of Investigations had actually dropped the textbook series, or were in the process of doing so. (That’s a little more than 50 percent, by my old-math thinking.) I don’t have room for them here, but the quotes from curriculum staff at some of those 36 districts are highly instructional. One highlight: there were multiple complaints about the amount of professional development time that must be spent on the Investigations text itself, versus using that time for mathematical concepts.

I would add, from my two years reading the workbooks closely, they are poorly written and edited, and confusing (to kids, not this old head, since they’re meant to confuse me).

As it turns out, Investigations and other constructivist curricula do not represent the last battle in the math wars. Singapore math is the hot new favorite, already adopted by Scarsdale (which means Pelham will get it around 2018). I honestly don’t know enough about Singapore to say it is the better way to go—and Scarsdale’s purchase of it isn’t enough, by itself, to convince me—but my reading tells me the program at least favors math over ideology.

“Singapore math’s added appeal is that it has largely skirted the math wars of recent decades over whether to teach traditional math or reform math,” reported the New York Times. “Indeed, Singapore math has often been described by educators and parents as a more balanced approach between the two, melding old-fashioned algorithms with visual representations and critical thinking.”

So the best of both worlds.

This school year, the Pelham district is doing a formal study of Investigations, though with the likely goal of showing why it was the right choice, rather than replacing it. If you have a view, express yourself to teachers, principals, administrators and school board members. I have.

But if you don’t want to become a curriculum wonk like me (and I don’t blame you), then check out Khan Academy. I’m already one-third of the way through pre-alegbra—for the day when “discovery” isn’t enough for Patrick to understand the topic—while he has been reviewing the arithmetic modules. It’s refreshingly direct, straightforward and ideology-free, and Sal Khan makes math interesting without wood blocks or fingers counting.