The Teacher's crucial role

Mursell, J.L. says, "Teaching may best be defined as the organization of learning. It follows, therefore, that the problem of successful teaching is to organize learning for authentic results...(This) is distinctly preferable as a definition to the familiar definitions of teaching either as the direction or guidance of learning. It saves us from arguments about whether the teacher ought to guide or to direct, arguments that are somewhat futile since the truth is he/she should do both"
(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:

1. Teacher poses a complex, thought provoking problem
2. Students struggle with the problem
3. Various students present ideas or solution to the class
4. The teacher summarizes the class' conclusions
5. Students practice similar problems.

In contrast, the emphasis on skill acquisition is evident in the steps common to most U.S. and German mathematics lessons:

1. Teacher instructs students in a concept or skill
2. Teacher solves example problems with the class
3. students practice on their own while the teacher assists individual students.

"Teachers in Japan emphasize problem-based learning in which rules and theorems are often derived, not merely stated and reinforced through drill."


Wiggins, G. & McTighe, J. (2005) Understanding by Design (2nd ed.)