The author suggested that studier study modern mathematics thought and method and instruct teaching based on middle school mathematical content.

According to the property of entire structure and forming rule of modern scientific mentality, the general principles that researching modern scientific mentality should be obeyed are put forward, the used often several methods of modern scientific mentality research are introduced.

To foster exploration ability through cultural values, we may make some trials, such as introducing man s cognition on mathematics to help student comprehend mathematics; recurring the process of mathematical knowledge by the material of mathematical history; co-discussing mathematical methods in teacher-student by launching monographic study; reappearing cultural factors of advanced mat.

Mathematical Methods for teaching and research.

The idea of conversion,an important mathematical way of thinking winds through a course of analytic geometry.

This paper describes the importance of strengthening the teaching of mathematical way of thinking,analyzes the mathematical way of thinking implied in the concepts of limit,derivative and definite integral and dialectically analyzes the law of the unity of opposites of different variables of the concepts in the change process.

Taking the theory of educational psychology as the guide, this paper proposes the ways of optimizing the students mathematical cognitive structure, that is, the innovation of the traditional method of preparing lessons, the flexible use of teaching strategy and the emphasis on mathematical way of thinking.

There are such kinds of mathematics idea and method as sign and graph, function, inversion; discussion and so on in the mathematics teaching in the middle school.