I have no idea where you get the idea that Don Knuth opposes Lockhart's approach. I guess we'd not know without asking him, but having waded through much of TA

I have no idea where you get the idea that Don Knuth opposes Lockhart's approach. I guess we'd not know without asking him, but having waded through much of TAOCP, Concrete Mathematics (a book filled to the brim with the kind of delightful discovery of pattern that Lockhart describes as optimal in learning math), Knuth's marvelously playful book "Selected Papers on Fun and Games"[2], and the novel he wrote about Conway's astonishing "Surreal Numbers"[3]...listening to him lecture on "importunate permutation" at the last local (SF) Joint Meeting of the American Mathematical Association, hearing about Knuth's thoughts on the mathematics of pipe organs, and even seeing the play/pattern-making that went into the entrance mosaic in his home [1]....I think you're way off base about what you think Knuth thinks about math education. Lockhart: "...if I had to design a mechanism for the express purpose of destroying a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being done— I simply wouldn’t have the imagination to come up with the kind of senseless, soulcrushing ideas that constitute contemporary mathematics education." Knuth [Preface to Concrete Mathematics]: "Some people think that mathematics is serious business that must always be cold and dry; but we think mathematics is fun, and we aren't ashamed to admit the fact. Why should a strict boundary line be drawn between work and play? Concrete mathematics is full of appealing patterns; the manipulations are not always easy, but the answers can be astonishingly attractive." I make an annual pilgrimage to Palo Alto for Knuth's Christmas Tree lecture[4], which content continuously emphasizes exactly the kind of joy in experimenting, discovering, and learning real math that Lockhart is talking about in his paper. Everything I know about Don Knuth speaks to his amazing playfulness and joy in pattern finding and making - a delight in the music of math...and a denial of the value of making sure everyone's labeled their axes and memorized their circle of fifths. [1]: https://www.youtube.com/watch?v=v678Em6qyzk https://www.youtube.com/watch?v=v678Em6qyzk [2]: http://www-cs-faculty.stanford.edu/~uno/fg.html http://www-cs-faculty.stanford.edu/~uno/fg.html The preface states "I've never been able to see any boundary between scientific research and game-playing. ... The topics treated here were often inspired by patterns that are visually compelling, or by paradoxical truths that are logically compelling, or by combinations of numbers and/or symbols that fit together just right. These were papers that I couldn't not write. I believe that the creation of a great puzzle or a great pattern is a scholarly achievement of great merit, an important contribution to world culture, even though the author of such a breakthrough is often an amateur who has no academic credentials. Therefore I'm proud to follow in the footsteps of the pioneers who have come up with significant new “mind-benders” as civilization developed. Many years ago I wrote an essay that asked “Are toy problems useful?” [reprinted as Chapter 10 in Selected Papers on Computer Science] in which I discussed at some length my view that students are best served by teachers who present them with well-chosen recreational problems. And I've carried on in the same vein ever since, most recently on pages 7--9 of The Art of Computer Programming, Volume 4A, in a section entitled “Puzzles versus the real world.” [3]: http://www-cs-faculty.stanford.edu/~uno/sn.html http://www-cs-faculty.stanford.edu/~uno/sn.html Surreal Numbers: "How two ex-students turned on to pure mathematics and found total happiness" - In 1973 during a week of relaxation in Oslo, Knuth wrote an introduction to Conway's method in the form of a novelette. ... I believe it is the only time a major mathematical discovery has been published first in a work of fiction. ... The book's primary aim, Knuth explains in a postscript, is not so much to teach Conway's theory as ``to teach how one might go about developing such a theory.'' He continues: ``Therefore, as the two characters in this book gradually explore and build up Conway's number system, I have recorded their false starts and frustrations as well as their good ideas. I wanted to give a reasonably faithful portrayal of the important principles, techniques, joys, passions, and philosophy of mathematics, so I wrote the story as I was actually doing the research myself.'' ... It is an astonishing feat of legerdemain. An empty hat rests on a table made of a few axioms of standard set theory. Conway waves two simple rules in the air, then reaches into almost nothing and pulls out an infinitely rich tapestry of numbers that form a real and closed field. Every real number is surrounded by a host of new numbers that lie closer to it than any other ``real'' value does. The system is truly ``surreal.'' [4]: http://www-cs-faculty.stanford.edu/~uno/musings.html http://www-cs-faculty.stanford.edu/~uno/musings.html