OK, my argument against Lockhart shouldn't have included the words "playfulness", because now everyone has latched on to that and portrayed me into the Grinch w

OK, my argument against Lockhart shouldn't have included the words "playfulness", because now everyone has latched on to that and portrayed me into the Grinch who Stole Math. As a personal anecdote, I hated the way math was taught in elementary and high school, as a dry series of formulas to be memorized (particularly geometry, which I took in the 7th grade). Math should be fun, but for many students, it shouldn't be a series of abstract problems unconnected to the real world. My main complaint here is about learning in the abstract vs learning in specifics. That's my sole argument against Lockhart's piece. I regret ever using the word "playfulness", because that has nothing to do with my main argument (and if you re-read my top comment, I think you'll understand this). My concern is about abstract-to-specific versus specific-to-abstract learning. But let's quote a little more from the preface of "Concrete Mathematics": "Abstract mathematics is a wonderful subject, and there's nothing wrong with it: It's beautiful, general, and useful. But its adherents had become deluded that the rest of mathematics was inferior and no longer worth of attention. The goal of generalization had become so fashionable that a generation of mathematicians had become unable to relish beauty in the particular, to enjoy the challenge of solving quantitative problems, or to appreciate the value of technique. Abstract mathematics was becoming inbred and losing touch with reality; mathematical education needed a concrete counterweight in order to restore a healthy balance". So, that basically sums of my feelings about how I was taught math in college. I'm not going to pretend to know what Knuth or Lockhart believe, but that paragraph describes my personal concerns about math education. I'm not a professional mathematician, nor even a math major, but I am an educated parent and informed citizen, and so fall directly into Lockhart's intended audience for this piece. I've now read it 5 times, and each time I get more and more the feeling that he wants mathematics to be taught deductively, as an abstraction. I base this interpretation on how much "pure" and "abstract" learning is emphasized in the essay, and how much disdain he has for practical math applications. I'm not going to pull out all the quotes, but if you disagree, then I don't know what to say. Unfortunately, I honestly can't afford to spend any more time on this argument, so I'll have to read your rebuttal (if any) and stop there.