Indeed, compared to Japan and Germany, the mathematics taught in our eighth grade classes is based on easier material, not of high mathematical quality and less challenging. U.S. and German eight grade mathematics teachers usually explained that the goal of a lesson was to have students acquire particular skills, i.e., to learn how to do something. Japanese teachers' goals were more likely to resemble the recommendations of reform experts. Teacher poses a complex thought-provoking question. Students struggle with the problem.
Various students present ideas or solutions to the class.
The teacher leads a class discussion of the various solutions. Teacher summarizes conclusions and makes connections to mathematical concepts. Teacher instructs students in a concept of skill. Teacher solves example problems with the class. Students practice on their own while the teacher assists individual students.