The Faulty Logic of the Math Wars (NYT) is a critique of “progressive” math instruction. I agree that every domain has a particular mode of thought and action, the author misses an important point.
First, math is most often used for decision making. This is a step both before and beyond the “algorithm” used. Context is important.
Math reformers are correct when the assert that while students may be able to “do” the algorithm, they are unlikely able to be successful with a word problem that requires the algorithm.