We do need, however, the kind of direction and guidance for our curriculum that the NCTM Standards have begun to provide. Teacher solves example problems with class. Students practice on their own while the teacher assists individual students. Teacher poses complex thought-provoking problem. Students struggle with the problem.
Various students present ideas or solutions to the class.
Class discusses the various solution methods. The teacher summarizes the class' conclusions. Students practice similar problems. The expectations in our lessons differ from those in both Japan and Germany. But many Japanese students practice skills in paid tutoring sessions after school.