Fundamental Research on Constructing an Idea of the Teaching and Learning Processes, emphasis on Student's Understanding of Mathematics-Concentration in connecting elementary, junior high and high school-

在建构数学理解课时，要明确学生理解的对象、理解的手段以及学生是否理解，其中理解的确认尤为重要。此外，有必要从小学、初中和高中相结合的角度仔细教授变量的意义和证明的价值。最后，如果我们想在表现和理解之间给予更多的关注，教师花时间让学生通过写日记来反映他们的元认知过程是非常重要的。同时这个过程也会培养学生的理解力。

When we are constructing how to understand mathematics lesson, it is important to clarify the following : objects that we want the students to understand ; devices to make them understand ; and confirm whether student understood them.Confirmation of understanding is especially important. Moreover, it is necessary to teach carefully the meaning of variables and the value of proofs from the viewpoint of connecting elementary schools, junior high school and high schools. Finally, if we would like to pay more attention between performance and understanding, it is very important for teachers to take time to let students reflect their meta-cognitive processes through journal writing. Simultaneously this process will foster student's understanding.