"A wise man learns through the mistakes of others. Only a fool learns by experience." At least that’s what I was taught growing up; I think it’s from the Book of Proverbs. I distinctly recall self-righteously parroting this adage at the ripe old age of 15, as if it was some profound insight that explained everything about the world. What can I say? I was young and naive. I was also the progeny of born-again fundamentalist Christians. Pat Robertson’s 700 Club was a weekday morning staple over breakfast, and I witnessed my first exorcism at the age of 10 — it scared the hell out of me, quite literally. I was dragged to Pentecostal prayer meetings, faith healing sessions, James Dobson seminars, and educated on "the four Christian temperaments" by Tim and Beverly LaHaye (basically a reworking of the medieval concept of the four "humours"). While other kids my age were discovering the Marvel and DC Comics universes, I was reading the schizophrenic rantings of Jack Chick comics (amusing parodies of Chick comix can be found here).
Needless to say, it was not an environment that fostered intellectual independence or critical thought. Religion is the opiate of the masses precisely because it discourages thinking for oneself. (Since people’s hackles tend to rise at the merest hint of any god-related criticism, let me state quite plainly that this comment pertains to organized religion as a social — and these days, political — infrastructure, not to private, personal beliefs.) Conformity was (and is) the rule du jour, and believe me, the Bible-thumping community is ruthless when it comes to squelching opposing viewpoints. Yet somehow, I developed those attributes in spite of myself, thanks to voracious reading habits and an insatiable curiosity about the world around me that my upbringing couldn’t quite dampen. I may have been outwardly docile to avoid attracting negative attention, but even back then, Jen-Luc Piquant was lurking in the background of my psyche with her sharp, snarky tongue, healthy skepticism, and common sense — just waiting for me to wake up and acknowledge her.
By the time I was 17, I’d figured out that personally, I preferred to learn by experience, the proverbial "school of hard knocks." I’ve been following that pedagogical model ever since. Sure, sometimes it hurts a bit more than mere book-larnin’, but the lessons learned, and knowledge gained, is much more concrete and lasting. There’s a difference between knowing something is right in an intellectual, abstract sense because you’ve been told, and knowing something is right because you’ve tested it in the real world. The entire scientific enterprise is based on learning through experience: forming abstract hypotheses, making predictions, and testing those predictions through rigorously designed experiments.
Yet somehow, when it comes to actually teaching math and science in our schools, the element of experience is often overlooked in favor of cramming abstract knowledge into students’ brains so they can pass the requisite standardized tests. That’s the gist of a fascinating article in the new issue of SEED by Jonah Lehrer (available online), entitled "How We Know."
Lehrer opens with the story of Cambridge math teacher Bob Moses, who took it upon himself in 1982 to instruct his daughter and her junior high school class in algebra because her public school didn’t offer such a course. Frustrated that most of the students couldn’t grasp the basic concepts, Moses realized it was because his pedagogical approach was, well, just plain wrong. And it inspired him to create a new curriculum called the Algebra Project that grounded the lessons of algebra in the real world: for instance, "a ride on the T became a lesson in coordinate graphing and negative numbers…. The first rule of Moses’ math class was that students always had to ‘participate in a physical event.’"
Gosh, I wish I’d had Moses as my teacher for high school algebra. As mentioned in a prior post, I consider myself functionally innumerate, despite having performed very well, academically, in all my math and science classes. Just because I got straight As didn’t mean I took away much lasting knowledge. Mostly, I was just crunching out rote answers, with very little comprehension of how it all fit together. I’ve been highly suspicious ever since of the standard metrics used to measure academic achievement. What was lacking in the classroom was a real-world context. Most of us just aren’t abstract thinkers, so it helps to have something concrete that illustrates in some way the concepts we’re supposed to be learning. Experience is definitely preferred when it comes to acquiring true understanding of a subject; indeed, I’d argue that it’s essential.
According to Lehrer’s article, my instincts on this issue are pretty accurate. Moses found that students responded beautifully to his innovative pedagogical approach; not only were they learning, they were retaining the new knowledge, precisely because they could relate their lesson plan to real-world experiences. Quoth Moses: "What you’re really doing is developing a new way of thinking. Instead of just trying to memorize these strange equations, you’re busy relating the math to your own experiences. All of a sudden, you’re finding math spilling over into other areas of your life."
Nor is his success merely anecdotal; the numbers back him up. Some 92% of those who graduated from the Algebra Project went on to take upper-level math courses, which Lehrer reports is twice the rate of those students not in the program. The Algebra Project’s success was even more noticeable at Lanier High School inJackson, Mississippi, where the percentage of students receiving a passing grade on the state math exam went from close to zero to 55% within two years. Alas, despite its demonstrable success, apparently the Algebra Project
has been discontinued, yet another victim of the pressure to conform to
standardized testing requirements and the ill-conceived No Child Left
It’s worth quoting from Lehrer’s article at length on this point: "Bob Moses’ insight was that the math curricula these schools follow misunderstand the mind. The same abstraction that many educators celebrated… stifled learning for many students…. He realized that the brain wasn’t designed to deal with abstractions it doesn’t know how to use, or to solve variables while sitting at a desk. Our knowledge, Moses intuited, is a by-product of activity. What we end up knowing is what we can learn how to use. We learn by doing."
That’s probably not news to Jeff Francis, the 25-year-old southpaw pitcher for the Colorado Rockies, who was a physics and astronomy major at the University of British Columbia before hitting the major leagues. Francis is profiled in the latest issue of Symmetry magazine,
focusing specifically on his understanding of the Magnus force, so named because it was first demonstrated in 1852 by the German physicist Gustav Magnus. Magnus showed that a spinning object moving through a fluid (like a baseball moving throgh air) experiences a sideways deflection in its path (like a curve ball).
The article goes into the physics behind pitching and hitting in a bit more detail, but I was most intrigued by Francis’ comment that good pitchers and hitters are natural, instinctive physicists, even though most have never heard of the Magnus force. They learn "by just being around baseball and observing," says Francis. "For example, you’ll always see hitters tapping their bat with their hand and then listening to it like a tuning fork, knowing that a higher sound means a higher frequency, which means harder wood, which, in turn, means the ball will jump off the bat more." In other words, first-hand experience counts.
Perhaps some of you are still a bit skeptical — especially those who do happen to perform well at abstract thinking, and therefore do just fine with the way math and science is traditionally taught. And being trained to be skeptical, why should you trust my intuition — or Moses’ anecdotes, or Francis’ first-hand view from the mound — on the matter? Well, according to Lehrer’s article, studies in modern neuroscience back us up. So there. Learning by doing turns out to be how the human mind functions best, thanks to the presence of so-called "mirror neurons": brain cells in the motor cortex that — in the case of an Italian study involving monkeys — enable the brain to combine the reason we are moving with the actual movement itself. Mirror neurons "translate our ideas into action," because, says Lehrer, "The human mind understands the world by interacting with it."
The Francis profile also illustrates my earlier comment about different styles of learning. It’s a myth that math and physics phobes aren’t capable of understanding the basic concepts; they simply aren’t drawn to the way it’s traditionally taught. But "different" does not automatically equate with "inferior." This point is especially relevant to the perennial debate about supposedly innate gender differences in math and science abilities. Yet another round in the ongoing battle has been playing out in the blogosphere this past week, sparked by a New York Times article about transgender biologist Ben A. Barres, who has a commentary in Nature on the question of gender in science.
There’s been a lot of truly eloquent blogging on the subject, so I don’t feel the need to expound at length about it here. My favorite take comes courtesy of Joanne Hewitt at Cosmic Variance, who dismisses the gender argument
as, well, complete bullshit, listing at random a dozen or so gifted
women just in her own field of high energy physics that defy the
stereotypes. I happen to be a woman who fits the prevailing stereotypes: my talents
lie more in writing and communication than in math and the hard
sciences. But I am far from incapable in those latter fields, even if they
aren’t where I truly shine. I would add that there are plenty of men who also excel more at the
humanities than in math and science. What’s the gender-based excuse for
their supposed "shortcomings"?
That men and women are different in many ways is indisputable — although whether or not those differences relate to math and science ability remains unproven — and I’m
one of those people who relish the differences and find them enriching
and rewarding. I only get testy if someone insists that one set of innate abilities (or style of learning) is somehow inferior (or superior) to another. We are different, yet equal, bringing complementary strengths to the table; it’s that simple. Experience has taught me that.