[al2o3cr]

+1 to teaching concepts - but I don't agree with the author's opposition to word problems and learning to apply a "bag of tricks". I'd argue that "deciphering vaguely-phrased word problems and figuring out which of a selection of tricks to apply" is the MOST transferrable skill somebody can take away from a math class, because it's a major component of working in lots of other fields. For instance, the biggest difficulties I've observed in novice developers are in breaking apart a big challenge ("write a program that solves this Sudoku board") into digestible / implementable pieces and in understanding which piece of information they already know can get the result they want.

[amoonki]

I agree, but I think the "word problems" the author was referring to are much lower quality than the ones you're thinking of. I imagined some highly-contrived exercises where all of the relevant information is already pre-processed for you, removing any need for problem decomposition. For example, "if the angle between the ground and a tree's shadow is 45 degrees and a 50 ft tall telephone pole that's 10 ft away from the tree casts a shadow..." (substitute a similar differential equation problem). As you point out, half the fun is defining a problem and breaking it down, and these kinds of word problems don't give you a chance to do that.