The teachers in both videos were extremely good at what they were doing, which brought home an unsettling realization to me: You can be very good at doing something that is absolutely horrible.
So what was going on that was horrible? Discovery learning, in which teachers spend an inordinate amount of time trying to get students to "discover", or figure out, what it took the best minds the human race has to offer several centuries to figure out.
An in another indictment of ed schools:
Mr. NCTM moved on to the next comment from another woman who in all seriousness and with no sarcasm intended said “The teacher was very good at not answering the students’ questions.” There was unanimous agreement.
The mind boggles.