Thinking method is the result of objective existence reflected in human consciousness through thinking activities. It is a product obtained from a lot of thinking activities. After repeated refining and practice, it has been proved to be correct again and again, and it can be repeatedly applied to new thinking activities and produce new results. Mathematical thinking method refers to reflecting the spatial form and quantitative relationship in the real world to people's consciousness, which is the result of thinking activities. It is an essential understanding of mathematical facts and mathematical theories (concepts, theorems, formulas, laws, etc.). Therefore, mathematical thought is an essential understanding of mathematical knowledge, a rational understanding of mathematical laws, and a mathematical viewpoint refined from some specific mathematical contents and the process of understanding mathematics. Repeated use in cognitive activities has universal guiding significance and is the guiding ideology for establishing mathematics and solving problems with mathematics. Mathematical method refers to all kinds of ways, means and ways used in the process of putting forward and solving problems (including internal problems and practical problems in mathematics) from a mathematical point of view. Mathematical thinking is closely related to mathematical methods. Generally speaking, emphasizing the guiding ideology is called mathematical thought, and emphasizing the operation process is called mathematical method.
Mathematical thinking method is the link to form students' good cognitive structure and the bridge from knowledge to ability. It is clearly pointed out in the middle school mathematics syllabus that the basic knowledge of mathematics refers to the concepts, properties, laws, formulas, axioms, theorems and mathematical thinking methods reflected in mathematics. Incorporating mathematical thinking method into basic knowledge shows that the teaching of mathematical thinking method has attracted the attention of education departments, and also reflects the understanding of mathematics educators in China on the development of mathematics curriculum. This is not only a measure to strengthen the cultivation of mathematics literacy, but also the necessity and requirement of the modernization process of mathematics basic education. This is because the modern teaching of mathematics is to base the basic education of mathematics on modern mathematical ideas and use modern mathematical methods and languages. Therefore, explore the teaching of mathematical thinking methods.
A series of problems have become an important topic in modern mathematics education research.
According to the law of psychological development, junior high school students' thinking is a transition from formal thinking to dialectical thinking, while senior high school students' thinking is the formation of dialectical thinking. The teaching of mathematical thinking method not only helps students to transition from formal thinking to dialectical thinking, but also is an important way to form and develop students' dialectical thinking.
From the perspective of cognitive psychology, the process of mathematics learning is the process of the development and change of mathematical cognitive structure, which is realized through assimilation and adaptation. Assimilation means that subjects bring new mathematics learning content into their original cognitive structure, and process and transform new mathematics materials to adapt them to the original cognitive structure of teaching and learning. The so-called adaptation means that when the original mathematical cognitive structure of the subject can not effectively assimilate the new learning materials, the subject adjusts and transforms the original mathematical internal structure to adapt to the new learning materials. In assimilation, the basic knowledge of mathematics does not have the characteristics of thinking and initiative, and can not guide the process of "processing". The psychological component only provides the subject with desire and motivation, and provides the cognitive characteristics of the subject, and cannot realize the "processing" process alone. Mathematical thinking method not only provides thinking strategies (design ideas), but also provides specific means to achieve goals (problem solving methods). In fact, the transformation and regression in mathematics is to realize the assimilation of old and new knowledge. Like assimilation, adaptation is also carried out under the guidance of mathematical thinking methods. Actively teaching mathematical thinking methods will greatly promote the development and perfection of students' mathematical cognitive structure.
From the perspective of learning transfer, mathematical thinking method is beneficial to students' learning transfer, especially the transfer of principles and attitudes, which can greatly improve learning quality and mathematical ability. Bruner thinks
"The purpose of learning the basic principles is to promote the loss of memory, not to completely lose it, but the legacy will make us rethink one thing at a time when necessary. Brilliance theory is not only a tool to understand the present phenomenon, but also a tool to recall the phenomenon tomorrow. " Therefore, as the "general principle" of mathematics, mathematical thinking method is very important in teaching. Therefore, for middle school students, no matter what they do in the future, only the mathematical thinking method deeply engraved in their minds will play a role anytime and anywhere and benefit for life.
Second, the teaching principles of mathematical thinking methods
The teaching principle of mathematical thinking method is to explain the teaching law of mathematical thinking method. The content of middle school mathematics curriculum is an organic whole composed of concrete mathematical knowledge and mathematical thinking methods. The arrangement of current mathematics textbooks is generally carried out along the longitudinal direction of knowledge, and a large number of mathematical thinking methods are only included in the system of mathematical knowledge, without clear disclosure and summary. In this way, the problem of how to deal with the teaching of mathematical thinking methods arises. In the teaching of mathematical thinking method, we must explore the law in practice and form the guiding principle of mathematical thinking method teaching. The construction of mathematical thinking method has three stages: subconscious stage, clear forming stage and deepening stage. Generally speaking, we should take the principle of permeability as the main line and combine the principles of repeatability, systematicness and clarity. They are interrelated and complement each other, which together constitute the guiding ideology of mathematical thinking and method teaching.