Traditional Math (2): Prefatory Remarks, Disclaimers and Warnings

This is part 2 of a series that will eventually be a book by the same name as this blog. Enormous changes to what you read here will likely happen at the last minute before publication, so enjoy this raw version while you can.

I believe strongly in how math should be taught and even more strongly in how it should not be taught. Nevertheless, when I am involved in teaching it as I believe it should be taught, (which happens to be in the traditional mode) I feel vaguely guilty, as if I am doing something against the rules and perhaps even wrong.

I have heard from other teachers who identify and empathize with this. Traditional math teaching is vilified by education schools, education consultants and other educational rent-seekers that have pervaded in the profession over the last three decades. Teachers feel bad for teaching using a method that…