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Arts major cracks hard math through practice, practice, practice

Arts major cracks hard math through practice, practice, practice
Arts major cracks hard math through practice, practice, practice

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In an older story that Nautilus recently republished, a woman seemingly born to be an English or languages major, ended up as a professor of engineering as an adult. Barbara Oakley’s story sheds an interesting light on the current war on math. In her own words,

I was a wayward kid who grew up on the literary side of life, treating math and science as if they were pustules from the plague. So it’s a little strange how I’ve ended up now—someone who dances daily with triple integrals, Fourier transforms, and that crown jewel of mathematics, Euler’s equation. It’s hard to believe I’ve flipped from a virtually congenital math-phobe to a professor of engineering…

Learning math and then science as an adult gave me passage into the empowering world of engineering. But these hard-won, adult-age changes in my brain have also given me an insider’s perspective on the neuroplasticity that underlies adult learning.

Barbara Oakley, “How I Rewired My Brain to Become Fluent in Math,” Nautilus, September 11, 2014

So what did she do? Not what popular culture might lead us to expect. She did not master math by self-expression or group discussion.

Oakley contrasts that with Japan’s Kumon Math, to which millions of parents send their kids after school, for “plenty of practice, repetition, and yes, intelligently designed rote learning, to allow them to gain hard-won fluency with the material.” In fact, the first words on Kumon’s English-language website are “practice makes possibilities.”

That’s certainly how Oakley seems to have done it. Having become fluent in Russian through constant practice, she successfully applied the same approach to mathematics. She compares the process to learning to be a chess master via “chunking”:

Chunking was originally conceptualized in the groundbreaking work of Herbert Simon in his analysis of chess—chunks were envisioned as the varying neural counterparts of different chess patterns. Gradually, neuroscientists came to realize that experts such as chess grand masters are experts because they have stored thousands of chunks of knowledge about their area of expertise in their long-term memory… This level of true understanding, and ability to use that understanding in new situations, comes only with the kind of rigor and familiarity that repetition, memorization, and practice can foster.

Oakley, “How I Rewired

Remembering moves that worked is easier than reinventing them. Professors of math and science repeatedly reassured Oakley that her approach, constant memorization and practice, was vital to success.

The ongoing war on math

Oakley’s (and Kumon’s) approach is less popular today, probably for cultural reasons. Last year, for example, Marquette University hired a math educator who has little use even for the concept that math is universal: “Different cultures, different groups of folks have different ways of doing and practicing math. We just assume that everyone does it the same way.”

Indeed. U.S. math scores typically fall below international rankings. A high proportion of lower income students borders on innumeracy. Scores took another tumble in the 2023 test (the COVID school shutdowns should be factored in). And if students don’t learn successful methods for reasons of “culture,” they’re the losers. But many teachers may resist a Kumon-like curriculum, even if it works, because philosophy may feel more important to them than outcomes.

A scorched earth policy for math

As math scores continued to decline, some math educators launched an assault on the idea that 2 + 2 = 4. It may have begun as a joke tweeted by social scientist and mathematician James Lindsay in 2020. Sensing a trend, he wrote ironically: “2+2=4: A perspective in white, Western mathematics that marginalizes other possible values.” Lindsay, of course, was riffing off George Orwell’s iconic insight in Nineteen Eighty-Four: “Freedom is the freedom to say that 2+2=4. If that is granted, all else follows.”

But Lindsay promptly discovered that a number of mathematicians and math educators are quite comfortable with the idea that 2+2 might = 5 or that it doesn’t matter what it equals. Among many respondents was a teacher and PhD student who replied, “Nope, the idea of 2+2 equaling 4 is cultural and because of western imperialism/colonization, we think of it as the only way of knowing.” A number of educators then piled in, attempting to show that 2 + 2 does not necessarily equal 4. In 2021 news media began to report the underlying controversy, with headlines like “Is math racist? As many students of color struggle with the subject.” Portland State University philosophy professor Peter Boghossian chided them, “No, math is not racist. Major venues like @USATODAY even asking this question is a sign of cultural sickness.”

Very well, what sort of a cultural sickness is it? Mathematics underlies our entire universe at its most basic level. Correct answers conform to reality. Thus planes fly, bridges stand, and dosages heal patients instead of poisoning them.

A pause in the war?

African American smiling woman math teacher stands at black board with pointer.

It’s too soon to tell but parents, employers, and others may be starting to tire of the elite educators’ war on math. A straw in the wind: Stanford’s Jo Boaler, a stalwart in the fight against traditional math teaching, has been cited for poor scholarship, according to a recent article in Chronicles of Higher Education: “The 100-page document details 52 instances in which Boaler, a professor of math education at the university’s Graduate School of Education, allegedly misstated or misconstrued outside studies about learning, neuroscience, and math education in her own articles, lectures, and books.” It has been summarized as a “reckless disregard for accuracy” — at the very time that educators are walking back some of her unsuccessful innovations.

The war on math is certainly not over but the warriors may be starting to find themselves on the back foot.

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