Predigested Formalisms, Spoonfeeding of
Finally, the van Kampen paper which is not available in the Premier Institute of Social Engineering has arrived from Oxford (thanks to a friend there who got her friend in the college that had the book in its library to photocopy it — yes, socialising comes in useful sometimes). I’m lucky enough to be in a job where I actually have access to whatever passes for a university library here, but the thought that I could have gotten the paper in ten minutes rather ten days if I was still in Chicago makes me a little unappreciative of my situation. I will probably write a bit on van Kampen’s take on the Gibbs Paradox soon, but for now, van Kampen’s opening message to Dirk ter Haar is worth quoting:
Beste Dik,It is a long time since we both attended the lectures by Mrs de Haas-Lorentz on thermodynamics. They were excellent from a paedagogical point of view since they forced you to figure out almost everything yourself. That is a much better way of learning physics than the spoonfeeding of predigested formalisms which is nowadays regarded as the highest wisdom in education. I remember how puzzled I was by the sudden appearance of the term
in the entropy. After I figured it out I found that there is still much confusion about it in the literature. That is my excuse for bothering you with such a time-worn subject.
“spoonfeeding of predigested formalisms” — how appropriate that this description should also be so undigested.
And, just because it’s also about pedagogy and because I have said similar things: Timothy Gowers explains why “examples first” is his favourite pedagogical principle. I couldn’t agree more.
October 21, 2007 at 4:26 pm
I ratify that “examples first” dictum too, and specifically within the larger pedagogical aim of showing what it’s actually like to do mathematics, rather than easily regurgitating the formalism after the hard work of — well, formulating it, has already been done. This was essentially the substance of my argument with James Cook, where I disagreed that Bourbaki-style texts are appropriate for first-year graduate courses, for any number of reasons — but most of all because, well, you’re still learning, and such a presentation completely obscures the intellectual thrust that led to the formalism in the first place. This isn’t merely a matter tracing the historical development of a field, but rather in showing how, say, the axiomatized notion of ‘topological space’ came to be out of thinking about what we would come to call ‘topological’ properties of spaces.
To my delight, I was elated to see Gower’s Explanation 2, which I independently used, nearly verbatim, in explaining “the idea of mathematical structure” in a talk I once gave to high school students about the foundations of higher mathematics.
Unrelatedly, what kind of job are you in now?