There was a study done in Japan, Germany and the United States, where teachers were video taped and researchers studied the videos to find out what the differences were among the teaching styles. The conclusion was that Germany has a "developing advanced procedures" teaching style, Japan has a "structured problem solving" teaching style, and the United States has a "learning terms and practicing procedures" teaching style.
The teaching style I have observed thus far in my class (mind you I have only been in class for a total of 5 days) is the American Style of teaching. What I mean by this is that the teacher goes over a simple process and expects the students to copy down the process. She then does some examples and goes over definitions and assigns the students homework problems that mirror the practice problems she had already done with the class. The main difference I have noticed is the type of questioning she asks the students and the type of questions in the book. The book asks more conceptual questions such as is this example true or false and why. Putting the why in there is asking students to be able to explain, which will demonstrate the students complete understanding. Also, during the initial note taking and examples, the teacher tends to ask a lot of conceptual questions such as "What is the difference between (-4)^10 and -4^10?" and "compare and contrast an integer and a whole number." It is this type of questioning that puts a little more of the "developing advanced procedures" technique, because the students will be able to carry their conceptual knowledge to more advanced questions. Another thing is the teacher will bring up more challenging examples or concepts that are not in the book, such as "Can we write (2)(2)(2)(a)(a) in exponential form?" This requires students to fully understand the concept of base, exponent and how the grouping works. Students came up with a variety of answers, but in majority of the classes students were able to come up with (2^3)(a^2). I say it is more of an American style teaching because although she introduces a more complicated problem, she still goes mainly from the book, and does not start off the class with any complicated problems to allow students to come up with their own questions.