It’s long been recognized that American kids suck at math, at least when compared to kids in Singapore, Finland, etc. What’s less well known is that the steep decline in proficiency only starts when kids are taught algebra. That, at least, is the conclusion of a new government report:
“The sharp falloff in mathematics achievement in the U.S. begins as students reach late middle school, where, for more and more students, algebra course work begins,” said the report of the National Mathematics Advisory Panel, appointed two years ago by President Bush. “Students who complete Algebra II are more than twice as likely to graduate from college compared to students with less mathematical preparation.”
The problem with algebra in America actually extends far beyond the international comparisons. More kids drop out of high school because they fail introductory algebra than for any other academic reason. In the fall of 2004, 48,000 ninth-graders took beginning algebra in the Los Angeles Unified School District. Forty-four percent of students flunked the class, nearly twice the failure rate of English. An additional seventeen percent finished with Ds. The vast majority of these students will never graduate. They will fail algebra again and again, and then they will give up.
Why is algebra so hard to learn? Because it’s so abstract. No other high school subject is as disconnected from the real world. When students open their algebra textbook, they enter into a world of pure ideas, with page after page of elusive equations and intangible theories. In fact, supporters of mandatory algebra classes tout this as one of the subject’s benefits: it is often a student’s only introduction to abstract thinking.
But this abstraction, especially when it is taught abstractly, comes at a steep cost. Algebra uses an idiom of symbols and variables to express mathematical relationships. Unfortunately, students rarely understand how these relationships map onto everyday experience. Although algebra was invented to solve practical problems, struggling students rarely grasp what problems algebra can actually help them solve. A study commissioned by the Los Angeles Unified School District concluded that the single biggest problem in algebra instruction was its “systematic failure to teach algebraic concepts which students could then knowingly apply.”
The solution, I think, lies in the pedagogy of John Dewey. While Dewey’s educational philosophy goes in and out fashion, I think he got a basic fact of learning right, which is that the brain learns by doing. Abstract concepts, untethered to experience, are never internalized by our neurons.
In November 1894, John Dewey described his educational philosophy in an excited letter to his wife, “When you think of the thousands & thousands of young ‘uns who are practically being ruined by the Chicago schools every year, it is enough to make you go out & howl on the street on the street corners. There is an image of a school growing up in my mind all the time; a school where some actual and literal constructive activity shall be the centre & source of the whole thing, & from which the work should be always constructive industry.”
A little more than a year later Dewey opened the University Elementary School at the University of Chicago, where he was already employed as a philosophy professor. For Dewey, the school wasn’t just about practicing a new way of teaching. It was also “a laboratory of applied psychology”. In fact, its official name was “The Laboratory School.” As Dewey wrote in a planning letter, “This school is a place to work out in the concrete, instead of merely in the head or on paper, a theory of the unity of knowledge.” The students were his metaphysical guinea pigs.
But how could a small private school demonstrate the “unity of knowledge”? Dewey’s insight was that primary education was the ideal place to collapse what he called “the invidious distinction between learning and doing.” At the Laboratory School, knowledge was viewed as a by-product of activity. Of course, this is a radically unconventional way of teaching children. Traditionally, things worth knowing are handed down from teacher to pupil as a disembodied encyclopedia of information. The job of a student is to memorize as much of this information as possible.
Dewey thought this approach was not only a terrible way to teach children (“its primary effect is boredom,” he once remarked) but was rooted in a false theory of thinking. Even worse, it reinforced this same erroneous distinction in its students, who grew up believing that learning and doing were separate activities. As a result, education became a useless exercise, nothing but the memorization of “truths ready made”.
At the Laboratory School, Dewey was determined to make knowing and doing part of the same learning process. His mission was to “reinstate experience into education”. The Laboratory students spent most of their day outside of the classroom, engaging in activities like sewing, carpentry and cooking. (Unlike other schools at the time, Dewey made boys and girls participate in activities together. Girls learned how to use a hammer and boys learned how to bake.) But these activities weren’t simply exercises in manual labor. Rather, they were demonstrations of “active learning”. “If a child realizes the motive for acquiring a skill,” Dewey argued, “he is helped in large measure to secure the skill. Books, the ability to read and bookish knowledge are, therefore, regarded as tools.”
Take cooking. At the Laboratory School, the children were often responsible for preparing their own lunch. Dewey’s insight was to build into this activity a wealth of related academics. Before students could boil an egg, they had to conduct experiments to determine the proper temperature at which to cook the egg. When they graduated to the preparation of more complicated dishes, the students had to weigh and measure the ingredients (arithmetic), understand the process of digestion (biology), analyze the process of cooking (chemistry and physics), and so on.
The secret, of course, was to sneak in the science. The knowledge had to seem indivisible from the lunch. “Absolutely no separation is made between the ‘social’ side of the work, its concern with people’s activities and their mutual dependencies, and the ‘science,’ regard for physical facts and forces,” Dewey wrote in 1899, in his best-selling pamphlet The School and Society. If the teaching was done right, the children wouldn’t even realize they were being taught.
I wrote about Bob Moses’ Algebra Project – a modern version of the Laboratory School – a few years ago in Seed. For more on Dewey, check out The Metaphysical Club, by Louis Menand.