I often wonder if the issue is that many educators feel there is an aspect of teaching that can be learned and mastered separate from the subject matter. In other words many think one can be a good math teacher without a passion for and a love of mathematics. The author's tone in discussing arithmetic conveys an attitude I often see with respect to one of the most powerful tools a child learns.

We see this in programming shops with the pointy-haired boss phenomenon. Management is taught as a science unto itself.

I'm reminded of a recent essay I read by the category theorist Eugena Cheng (http://cheng.staff.shef.ac.uk/illogic/illogic.html).

Imagine your children learning the "trivial" facts and algorithms of arithmetic from a teacher with this world view of what math is.