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2. Logically, there are "complete induction and incomplete induction, synthesis, analysis, deduction, reduction to absurdity, and the same method".
3. There is another kind of mathematical method which is completed by several specific operation steps in the textbook, such as elimination method, collocation method, method of substitution method, undetermined coefficient method, equal product method, basic graphic method, etc. Mathematical thought is the basic viewpoint of mathematical activities. In teaching, students should be made aware of its inherent laws and essence. Mathematical thought is a high generalization of the inherent laws and essence of mathematical knowledge and methods, which is of guiding significance for solving mathematical problems.
Cultivation of Mathematical Thinking Quality
Because solving mathematical problems is a transformation process from conditions to conclusions, which has certain directionality. Therefore, in teaching, the training of concentrated thinking and divergent thinking is the main content of cultivating students' thinking quality. From the formal point of view, concentrated thinking is "directional, hierarchical and convergent" in content, and it is "seeking sameness and concentration".
From the analysis of the logical structure of the textbook, the directionality, hierarchy and cohesion are obvious, but the process of guiding students to explore every knowledge point is implicit in it. Therefore, students should be guided to read the textbook carefully and systematically after learning a unit or a chapter. Combine the form and content of concentrated thinking, write the thoughts after reading or make the thinking chart of teaching materials, so that students can understand the connotation of concentrated thinking.
By analyzing the process of solving mathematical problems, create a situation of concentrated thinking, guide students to comprehensively analyze the existing information in the conditions, and divide the problems into several small problems in turn according to the conclusion direction. Every time a small problem is solved, students can understand that its conclusion directly affects the thinking direction of the next small problem, and the scope of thinking search will be narrowed and the problem will be finally solved. Obviously, in the process of solving problems, the quality of students' concentrated thinking is cultivated.