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.
While U.S. teachers have more formal education than their colleagues almost anywhere in the work, they do not have the benefit of the long-term structured apprenticeship in the profession which is characteristic of the German and Japanese system. Furthermore, those systems have demanding entry requirements for anyone who wishes to attend the university, including individuals who wish to become teachers. U.S. and German teachers do not have the opportunities for rich, informal discussion and the chance to learn from each other and share questions about teaching-related issues that are characteristic of the Japanese teachers' environment. Algebra and geometry are studied by all Japanese and German eight graders, but in the U.S. they are reserved for students in higher tracks. Indeed, our eight grade math curriculum more closely resembles the seventh grade curriculum in Germany and generally mathematics instruction in the U.S. requires less sophisticated mathematics thinking than does instruction in Germany and Japan.