Last month, as I read Christopher J. Phillips’ brief and engrossing The New Math: A Political History, I found myself reciting the ominous line from Battlestar Galactica:
Early in my teaching career, I spent a lot of time and life-force railing against the shortcomings of a rote math education. The mindless manipulations. The paper-thin comprehension. The lack of critical thought. I saw it as my duty to name (and blame, and shame) these patterns.
As the years went by, I realized these critiques were not as fresh as they felt. People like me had been decrying methods like those not just for years, but for centuries. Such critiques did not really disrupt the system; they were a longstanding element therein.
Far from challenging the status quo, I was playing a comfortable role within it.
These thoughts came rushing back as I read Phillips’ pithy and potent history. There is nothing new under the sun—at least, not in our philosophies of math pedagogy. The arguments just go round and round.
Witness this passage, about the rival textbooks of Pike and Colburn:
Pike emphasized the importance of memorizing arithmetic rules and then applying them to various examples…
Colburn’s [approach] was to reverse rule and example: instead of presenting rules, he presented simple examples in an effort to lead children to form rules for themselves….
Contemporaries understood the differences between the textbooks to be about differences in reasoning…
[One critic] proclaimed… that rule-based methods failed because a student would not have “been called upon, in this process, to exercise any discrimination, judgment, or reasoning…”
[Another critic] claimed that inductive methods would… ultimately undermine authority by erasing the traditional grounding of rigorous knowledge in rules.
Is this about the Common Core battles of the 2010s? Sure sounds like it.
But no, it’s about the New Math controversy of the 1960s. Right?
Wrong again. Colburn published his book in the 1820s. Pike wrote his in the 1780s.
All of this has happened before. All of this will happen again.
As Phillips elucidates, a silent assumption underlies both sides of the Colburn/Pike debate. “Even—perhaps especially—at the most elementary levels,” he writes, “evaluating mathematical methods entailed assumptions about the virtues of intellectual training.”
Let me spell that out: the shared assumption, the axiom that both sides accept, is that math education shapes the intellect. Arithmetic is not just arithmetic. However you manage matters of multiplication, that’s how you’ll also approach matters of democracy.
In the 1960s, New Math reformers worried that rote drill would breed blind deference to authority. They hoped instead to create a society of mini-professors, seeing the world in terms of flexible, abstract structures.
In the 1970s, “back to basics” counter-reformers held the opposite hope, and the opposite fear. They believed rote drill inculcated discipline and diligence, and that the New Math would breed a feckless generation that was forever confusing true with false, right with wrong.
The rival camps favored opposite kinds of minds, and opposite kinds of math. But they shared a deep principle: Math makes minds.
I’ve long operated on this same principle. Vital to a free and thriving intellect—and thus, to a free and thriving society—is great mathematical thinking, whatever that is.
At the moment, I can’t help wondering if we’ve all got it wrong. Maybe math education isn’t about broader intellectual habits. Maybe it is not, as 17th-century Jesuits believed, a model of how divine authority flows forth from unquestionable axioms. Maybe it is not, in Underwood Dudley’s lovely phrase, about “teaching the race to reason.” Maybe it’s none of those things.
Maybe, if we want to break the Battlestar Galactica cycle of endless “math wars,” we need to embrace a new axiom: math education is just about math. Maybe those stakes are high enough.
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Published
December 18, 2023December 5, 2023
