Interesting to note that an article that begins "The Faulty Logic" might as easily be renamed "An Introduction to Logical Fallacy by Example." As in Dude's observation, repeating progressive is a slick ad hominem argument.
One bit in there that gets me is:
"the most efficient — and most elegant and powerful — algorithms for specific operations"
I think that is quite a distortion of the classic algorithms which strike me as foolproof and consistent but neither elegant nor efficient.
My proof:
49,999 + 7 =
I believe the investigations type philosophy is in the right place, but the systems are likely flawed in their execution by being too dogmatic. You can't train creativity or creative problem solving. Forcing a kid to keep guessing at solution approaches until they match the fixed set in the answer guide is a fail.
Reflecting on other threads perhaps in the ideal execution of "reform mathematics" requires both a certain amount of talent in the instructor as well as the learner to realize its intent.
