The Godfather, or G as I’m going to call him, is very observant about the crimes we commit against students in mathematics classes. The less serious one he mentions is drill, which in my opinion does have some benefits. It’s nice not to have to worry about getting things like 4 times 8 or 7 times 9 correct without having to pull out a calculator. Once such basic pathways are set in the brain, it becomes easier to concentrate on deeper mathematical concepts. The problem occurs when the subject reduces entirely to drill – either due to students’ perceptions, or due to limitations of the teaching methods used. Math cannot be forced into students like stuffing, it cannot be squeezed or hammered in. There has to be some play involved, something that moves it into the realm of ideas, of games.
The other point G makes is more serious. A lot of mathematics is cumulative, and if you miss something along the way, it can have a cascading effect. So we’ll just have to make sure that doesn’t happen while we read along. I will point out, however, that the way G seems to have written his book, you should be able to skip some of the details, and it shouldn’t affect your understanding of what’s to come. Same with these notes I’ve added. So feel free to read ahead if you feel bogged down or stuck.