Two unrelated incidents. First, I attended a talk by Sergiy Klymchuk who talked about misconceptions in mathematics, especially in calculus. He also pointed out an example of a disastrous error in a paper published in a highly rated mathematics education journal. The exact reference was not given but with a little clever searching I found the passage.
The second, also from a lecture, which quoted this observation from the book The Teaching Gap (page 25-26). Mind you, this is really from the horse’s mouth since lecturer was the one who was quoted in the book.
“I believe I can summarize the main differences among the teaching styles of the three countries.” Everyone perked up at this, and here is what he had to say:
“In Japanese lessons, there is the mathematics on one hand, and the students on the other. The students engage with the mathematics, and the teacher mediates the relationship between the two.
In Germany, there is the mathematics as well, but the teacher owns the mathematics and parcels it out to students as he sees fit, giving facts and explanations at just the right time.
In U.S. lessons, there are the students and there is the teacher. I have trouble find the mathematics; I just see interaction between students and teachers.”