(Successful Teaching 1946, pp. 21, 23).
Mathematics teachers in Japan cover fewer topics but their students achieve better results on tests. These teachers report that their aim is conceptual understanding, and their teaching practices reflect these aims.
In Japan, the goal of a lesson is for students to develop mathematical thinking whereas in other countries the goal is to acquire a specific mathematical procedure.
The emphasis on understanding is evident in the steps typical of Japanese eighth grade mathematics lessons:
- Teacher poses a complex, thought provoking problem
- Students struggle with the problem
- Various students present ideas or solution to the class
- The teacher summarizes the class' conclusions
- Students practice similar problems.
- Teacher instructs students in a concept or skill
- Teacher solves example problems with the class
- students practice on their own while the teacher assists individual students.
Wiggins, G. & McTighe, J. (2005) Understanding by Design (2nd ed.)