Paul became interested in mathematics when he was about 14 (outside of the school math class, he points out) and read voraciously, becoming especially interested in analytic number theory. He dropped out of college after one semester to devote himself to math, supporting himself by working as a computer programmer and as an elementary school teacher. Eventually he started working with Ernst Strauss at UCLA, and the two published a few papers together. Strauss introduced him to Paul Erdos, and they somehow arranged it so that he became a graduate student there. He ended up getting a Ph.D. from Columbia in 1990, and went on to be a fellow at MSRI and an assistant professor at Brown. He also taught at UC Santa Cruz. His main research interests were, and are, automorphic forms and Diophantine geometry.
After several years teaching university mathematics, Paul eventually tired of it and decided he wanted to get back to teaching children. He secured a position at Saint Ann's School, where he says "I have happily been subversively teaching mathematics (the real thing) since 2000."
He teaches all grade levels at Saint Ann's (K-12), and says he is especially interested in bringing a mathematician's point of view to very young children. "I want them to understand that there is a playground in their minds and that that is where mathematics happens. So far I have met with tremendous enthusiasm among the parents and kids, less so among the mid-level administrators," he wrote in an email to me. Now where have I heard that kind of thing before? But enough of my words. Read Paul's dynamite essay. It's a 25-page PDF file.
Awesome. What a great article. I bet kids learn under this man because he KNOWS how to teach!!! Those kids... all grades should get down on their knees and be thankful because they have someone in such an important subject who CARES...genuinely cares about them without all the “fluff” that it out there today. Besides... St. Ann’s was the name of the 8 year elementary school we attended as well. :) Thank you!!!!
Awesome. What a great article. I bet kids learn under this man because he KNOWS how to teach!!! Those kids... all grades should get down on their knees and be thankful because they have someone in such an important subject who CARES...genuinely cares about them without all the “fluff” that it out there today. Besides... St. Ann’s was the name of the 8 year elementary school we attended as well. :) Thank you!!!!
Thanks, it reminds me of Feynmann’s complaint about mathematics textbooks when he was reviewer for the Berkley school department. One book, in particular, consisted of nothing but blank pages. When he called the publisher, she apologized and said that all the reviewers had been accidently sent blank trade show props, with the correct glossy covers. Yet some of the reviewers had already submitted favorable recommendations!
I hated high school math, and in freshman year in college we were taught by a Chinese TA who could barely speak English, and then not intelligibly. (I got 795 on the SAT math level II achievement test, but never did math homework, I was somewhat like Lockhart, but I plugged through the hateful experience, because I needed a j-o-b.)
I came to the conclusion fairly early that it is the rigor of what is taught, and how well the assigned math is taught that is most important.
I had rigorous Algerbra, Trig, Physics, and so on in high school. No calculus, but tough problems. Hit a college in NYC where half my math year was Regis Prep School grads. Epsilon and Delta day one. Fit right in.
Did grad school until Uncle Sam gave me chance to join the Air Force, and remembered that in my last semester I sat next an 18-year old from Brooklyn College whose goal in life was to solve a word problem. Fell in love with computers in the AF and stayed in it.
Love math, but like many other things, too. Probability knowledge is handy for calculating pot odds, though.
Wow. Thank you for posting that link! Excellent article that should be required reading for every math teacher and high school student in the country.
Excellent read, sp. Thanks.
In Confucian thought, children are "jugs to be filled"; in Lockhart's view, they are "candles to be lit".
I think the truth is that they are "lanterns, which must be filled before they can be lit".
Let's just try applying Lockhart's prescription to a real-world problem: the failure of Senate Democrats to propose a budget in 3+ years. Should be just "wait until their own natural curiosity about [budget] numbers kicks in"?
I'm not just taking a cheap, partisan shot with that last example: I think that politicians - of both sides - have only been able to get away with the destruction they've wrought because of the numerical illiteracy of a majority of the population and of the attorney/bureaucrat beltway ruling class.
Feel-good, finger-painting, "kumbaya" Math education is unlikely to improve the situation.
Lockhart has an interesting critique of the standard mathematics curriculum.
Unlike Galileo’s 17th century debate on world systems, however, I think the optimum solution is somewhere in between that of Simplicio and Salviati.
Like Simplicio, I rather liked the formalism of my late ‘60s instruction in Euclidian geometry. Things have gotten worse rather than better since then: the standard curriculum now just teaches geometry facts without proofs.
But, like Salviati, I rather disliked the curiousity-killing pedagogy of elementary school. I still remember my 4th grade teacher telling me that there were no such things as negative numbers when I argued that, yes, you can subtract 5 from 4.
And, Lockhart is absolutely correct about trig being a two week course that gets expanded to fill an entire semester with useless definitions and purposeless manipulations.
It’s taking me all day to read this thread. Lockhart’s Lament is interesting, but it lambasts the traditional math curriculum in favor of dreamy ideals. Not exactly the touchy feely approach, maybe, but it could be taken that way. His blast at Geometry is particularly disconcerting. I guess he’s just trying to make a point.
I did learn of Gauss’s “notions vs. notations” quote and tracked it down to an online edition of the Disquisitiones Arithmeticae ( linked by Wikipedia. ) I wondered what the Latin might be. Well, it’s “notionibus” and “notationibus”. I believe this is the “ablative of means” applied to “notio” and “notatio”. So that was interesting.