experience preferred

Scientistjenluc"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
Behind legislation.

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,Pitcher
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.

10 thoughts on “experience preferred”

  1. An instinct for science

    Yesterday after reading this NYT editorial, I started writing a piece about the continuing slide of math and science education in this country, but Jennifer has a much more interesting (and much better written) take on the situation. (also, follow…

  2. A timely quote from my Google home page:
    “The things we know best are the things we haven’t been taught.”
    – Marquis de Vauvenargues

  3. > What can I say? I was young and
    > naive.
    You were learning from experience… ironically.
    Ahh… Jack Chick. How wonderful that Battleaxe Ministries is still passing them out. I wrote to them and then sent me a sample pack of all 50 or so tracts that they had at the time. Good reading!
    My daughter’s recent experience in learning to read has taught me in no uncertain terms that whole-word reading and phonics are two different modes of learning to read and she is most definitely a whole-word reader. If we’d not found an old Dick & Jane book, she’d have learned to read from her school’s phonics lessons months after she did.

  4. An instinct for science

    Yesterday after reading this NYT editorial, I started writing a piece about the continuing slide of math and science education in this country, but Jennifer has a much more interesting (and much better written) take on the situation. (also, follow…

  5. My father taught me to read when I was about two years old. No clue how he did that — I don’t remember it happening, but the skills have always been with me. One of the first things I do remember reading is the sign in the South Parkway Waffle House of Huntsville, Alabama, telling customers to reserve booths for parties of eight or more. My father, the professional photographer, snapped a picture of me at age three or so devoutly reading a book entitled “Toilet Training in a Day” (or some such). It’s the sort of photograph mothers frame and trot out to embarrass their children in front of guests.
    Fonix lessons in elementary school always seemed like studies in absurdity. I was able to **do** them, but it was startlingly easy to stump the teacher by asking “Why do we write this word like that?” I understood a little of the “why” years later, when I started studying linguistics for fun. The silliness which puzzled us kids so much goes back to the Great Vowel Shift, the Norman Conquest — all sorts of history which, as a first-grader, I had no idea impinged upon my silent Es.

  6. Wow. I had no idea you were raised as a born-again Christian. I was too! With that in mind, you might enjoy this book by Randall Balmer, a critique of the religious right by an evangelical Christian.
    Thy Kingdom Come: How the Religious Right Distorts the Faith and Threatens America: An Evangelical’s Lament
    by Randall Balmer
    Here’s a description taken from Amazon:
    Book Description
    The distinguished author of Mine Eyes Have Seen the Glory returns with a searing examination of a new generation of evangelical leaders who have hijacked the Christian faith on behalf of the Republican Party
    For much of American history, evangelicalism was aligned with progressive political causes. Nineteenth-century evangelicals fought for the abolition of slavery, universal suffrage, and public education. But contemporary conservative activists have defaulted on this majestic legacy, embracing instead an agenda virtually indistinguishable from the Republican Party platform. Abortion, gay marriage, intelligent design–the Religious Right is fighting, and winning, some of the most important political battles of the twentyfirst century. How has evangelical Christianity become so entrenched in partisan politics?
    Randall Balmer is both an evangelical Christian and a historian of American religion. Struggling to reconcile the contemporary state of evangelical faith in America with its proud tradition of progressivism, Balmer has headed to the frontlines of some of the most powerful and controversial organizations tied to the Religious Right. With a skillful combination of grassroots organization, ideological conviction, and media savvy, the leaders of the movement have mobilized millions of American evangelical Christians behind George W. Bush’s hard-right political agenda.
    Deftly combining ethnographic research, theological reflections, and historical context, Balmer laments the trivialization of Christianity–and offers a rallying cry for liberal Christians to reclaim the noble traditions of their faith.
    Balmer’s earlier book and PBS series, Mine Eyes Have Seen the Glory give a glimpse of what it’s like to be an evangelical to those on the outside. I don’t think you can really ever understand it totally without experiencing it for yourself, but this book and series come pretty close to providing the flavor.

  7. Fascinating stuff. It’s certainly true that many people learn subjects like maths and science more easily if they can relate it to their real life experience. But isn’t part of the benefit of studying mathematics that it does train the mind to deal in abstractions? The deeper one delves into science and maths the more one is dealing with the abstract, and the harder and harder it is to relate eveything back to day to day experience.

  8. Well, certainly that is part of the value of studying mathematics. But in the process of learning to do so, it helps to have some visual or other contextual help. It’s a bit like learning to ride a bike: it helps to have training wheels (or your dad holding on t the back of the bicycle seat) the first few times out, and you get the hang of it, and gain confidence, the training wheels can come off. Sometimes physicists and other scientists give the impression that they think one explanation should suffice, the get frustrated when laypeople don’t automatically “learn” things and retain it. That’;s just not how learning works, IMHO, and I was pleased that these studies are looking into that. Learning is a lifelong process, a series of stepping stones. Project Albegra, from the SEED description, appears to be an important first step in getting students to embark on a lifelong learning process for mathematics.

  9. You can’t argue with of learning from experience. Though I did well in my academic training, I feel that the only physics ideas that I understand well are those that touch my own research. It’s fine to have memorized the lensmaker’s formula, but so much better to have designed, constructed and aligned an apparatus using real lenses!
    Memorization is often an obstacle to understanding, not an aid to it. Too frequently students believe that because they can solve a homework problem, they understand it. I felt this way about statistical mechanics in school. You had to guess the right ensemble and then take a bunch of partial derivatives, none of which required any real insight into the problem. I only feel like I’m starting to under statistical mechanics now, after 20 years out in the trenches.
    Too bad about Project Algebra. School bureacracies appear to be the major obstacle to real education.

  10. ObsessivemathsFreak

    Speaking as an applied mathematician, I can safely tell you that the problem of abstractness extends even unto the most advanced mathematical topics. I can also tell you that it is holding back progress not only in mathematics, but in virtually every science. It’s a serious problems mathematicians simply won’t address.

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