Thanks greatly Wes,
I am glad that my essay meets your approval. I hadn't heard before about Bee's comments on perspective in Art, but that link is most welcome. You are absolutely correct about teaching fundamental concepts, and how learning solutions naturally flows from understanding them. This is sadly left out of many curricula, but it was one of the things Alfie Kohn stressed the importance of, in his lecture at the James Earl Jones theater - up the hill from me. Lately I've been conversing with a retired local Physics prof, Greg Kirk, and he also extols the virtue of that approach.
Unfortunately; this is not always easy. In a conversation with (then active, now retired) RPI Chemistry professor John Carter; he told me of trying to deliver the conceptual basis - and having his students complain, asking 'is this going to be on the test?' and urging him to go directly to the next equation they could memorize. I told this story to UNAM Physics prof, Jaime Keller after FFP11 in Paris, when he asked me "Why at an international symposium, with Nobel laureates and other top experts presenting, were there so many stupid questions?" But comments like that are part of my motivation for this essay.
As to the Maths; I am an oddball, both a Constructivist and a Platonist. And my purview admits the outlooks of Tegmark and Wolfram equally well, while positioning me somewhere between them. Much more can be said on that later, on the FQXi forums or in a private exchange, or you can look at my work cited in the references and previous FQXi essays for some details.
All the Best,
Jonathan