Re-reading a classic by Philip J. Davis and Reuben Hersh that I first encountered in college. They are the perfect guides to math as a human endeavor, and its many touch points with non-STEM disciplines. Here they are quoting Herman Weyl about the uses of infinity…
…purely mathematical inquiry in itself, according to the conviction of many great thinkers, by its special character, its certainty and stringency, lifts the human mind in to closer proximity with the divine than is attainable through any other medium. Mathematics is the science of the infinite, its goals the symbolic comprehension of the infinite with human, that is finite, means. It is the great achievement of the Greeks to have made the contrast between the finite and the infinite fruitful for the cognition of reality. Coming from the Orient, the religious intuition of the infinite, the άπειροv, takes hold of the Greek soul…
This tension between the finite and the infinite and its conciliation now become the driving motive of Greek investigation.
To my surprise, Elizabeth Green’s sensible article about math education reform in the NYTimes has become a “most emailed” hit. Certainly several people have emailed it to me, one not knowing that I’ve done a fair amount of work doing online courses on math education and have a strong interest in the subject.
Although it’s got an unfortunate headline, “Why Do Americans Stink at Math?” points out that we haven’t had the follow up to train teachers in new approaches, even when they are promising–and have yielded great results in other countries. Instead, we get stuck in some kind of paradoxical nostalgia. We may have had bad math experiences at school, but we would prefer our children have those to new ones that we don’t understand or trust, we also let everyone off the hook, students, our teachers, and perhaps most importantly ourselves, when we categorize math competence as an immutable characteristic.
In a broader piece, I’ll vapor on about my speculation that fighting over curriculum is really ideological battle by other means, but in the meantime recommend reading the article which sites the baleful effect of giving the same bad old experiences to students in classrooms: places where using time tested methods that don’t work is the preferred way of doing most things wrong.
The unschooled may have been more capable of complex math than people who were specifically taught it, but in the context of school, they were stymied by math they already knew. Studies of children in Brazil, who helped support their families by roaming the streets selling roasted peanuts and coconuts, showed that the children routinely solved complex problems in their heads to calculate a bill or make change. When cognitive scientists presented the children with the very same problem, however, this time with pen and paper, they stumbled. A 12-year-old boy who accurately computed the price of four coconuts at 35 cruzeiros each was later given the problem on paper. Incorrectly using the multiplication method he was taught in school, he came up with the wrong answer. Similarly, when Scribner gave her dairy workers tests using the language of math class, their scores averaged around 64 percent. The cognitive-science research suggested a startling cause of Americans’ innumeracy: school.