Lockhart's Lament

School teacher and professional mathematician Paul Lockhart has written a brilliant denunciation of what is wrong with the teaching of mathematics in schools. Much of what he says applies equally well to other subjects, I expect. Certainly much of what passes for learning reading in schools takes something lively and beautiful and does its best to render it dull and lifeless, just like mathematics. And exposure to computing in secondary schools seems more likely to turn off and misdirect students then to prepare them to continue the subject in university.

I particularly enjoyed Lockhart's opening, an extended metaphor:

'A musician wakes from a terrible nightmare. In his dream he finds himself in a society where music education has been made mandatory. “We are helping our students become more competitive in an increasingly sound-filled world.” Educators, school systems, and the state are put in charge of this vital project. Studies are commissioned, committees are formed, and decisions are made—all without the advice or participation of a single working musician or composer.

'Since musicians are known to set down their ideas in the form of sheet music, these curious black dots and lines must constitute the “language of music.” It is imperative that students become fluent in this language if they are to attain any degree of musical competence; indeed, it would be ludicrous to expect a child to sing a song or play an instrument without having a thorough grounding in music notation and theory. Playing and listening to music, let alone composing an original piece, are considered very advanced topics and are generally put off until college, and more often graduate school.'



On Extending Wand’s Type Reconstruction Algorithm to Handle Polymorphic Let

Years ago, I asked Mitch Wand whether it was possible to extend his lovely constraint-based inference algorithm to handle polymorphic let. Now Sunil Kothari and James Caldwell have done just that. (François Pottier has also done nice work along these lines, which these authors don't cite.)

Postscript: Didier Rémy writes to let me know that the material in François Pottier's notes that I cite above also appears in a definitive textbook form: François Pottier and Didier Rémy. The Essence of ML Type Inference. In Benjamin C. Pierce, editor, Advanced Topics in Types and Programming Languages, Chapter 10, pages 389-489, MIT Press, 2005. Didier confirms that this work subsumes the work of Kothari and Caldwell.

This page is powered by Blogger. Isn't yours?