First, the importance of cultivating junior high school students' mathematical thinking methods
The so-called mathematical thought is the understanding of the essence of mathematical knowledge. It is the guiding ideology of establishing mathematics and solving problems with mathematics, such as modeling, statistics, optimization, reduction, classification, integration, combination of numbers and shapes, transformation, equations and functions. The so-called mathematical method refers to various ways, means and approaches adopted in the process of raising and solving problems (including internal problems and practical problems in mathematics) in mathematics. The mathematical methods that junior middle school students should master are collocation method, method of substitution method, undetermined coefficient method, parameter method, construction method and special value method. Mathematical thinking is closely related to mathematical methods. When emphasizing the guiding ideology, it is called mathematical thought, and when emphasizing the operation process, it is called mathematical method.
According to the requirements of the mathematics syllabus, the nine-year compulsory education syllabus has clearly included the mathematical thinking method into the basic knowledge category, which refers to the mathematical thinking method reflected by the concepts, properties, laws, formulas, axioms and their contents in mathematics. The mathematics content of middle school students includes mathematical knowledge and mathematical thinking methods. Mathematical thinking method produces mathematical knowledge, and mathematical knowledge contains thinking method, which is conducive to revealing the spiritual essence of knowledge and improving students' comprehensive quality and mathematical literacy.
From the perspective of education, mathematical thinking method is more important than mathematical knowledge. This is because: mathematical knowledge is stereotyped and static, while thinking method is developing and dynamic. The memory of knowledge is temporary, and the mastery of thinking methods is permanent. Knowledge can only benefit students for a while, and thinking methods will benefit students for life. Strengthening the cultivation of mathematical thinking methods is more important than imparting knowledge, and mastering mathematical thinking methods is beneficial to solving any practical problems. Therefore, mathematics teaching must attach importance to the teaching of mathematical thinking methods.
Practice has proved that cultivating junior high school students' mathematical thinking methods can effectively stimulate students' interest in learning, fully mobilize their enthusiasm and initiative in learning, constantly improve and develop their cognitive structure, enable students to apply existing thinking methods to the process of learning new knowledge, turn complex problems into simple ones to solve, improve learning efficiency and improve their ability to analyze and solve problems. At present, the combination of numbers and shapes, classified discussion, equations and functions are the focus of examination papers in various places. Therefore, we should also attach importance to the cultivation of junior high school students' mathematical thinking methods, and examining students' mathematical thinking methods is the only way to examine students' ability.
Second, the main mathematical thinking methods in junior high school
There are many mathematical thinking methods in junior high school mathematics, the most basic and main ones are: reduction thinking method, combination of numbers and shapes thinking method, classified discussion thinking method, function and equation thinking method and so on.
1. Corresponding ideas and methods
In the introduction teaching of algebra in grade one, there is a calculation problem of algebra evaluation. Through calculation, it is found that the value of algebraic expression is determined by the value of letters in algebraic expression, and different letter values can get different calculation results. Here, there is a correspondence between the value of letters and the value of algebra, then there is a correspondence between real numbers and points on the number axis, and there is a correspondence between ordered real numbers and points on the coordinate plane ... In this teaching design, attention should be paid to infiltrating corresponding ideas, which not only helps students to see problems from a changing point of view, but also helps to cultivate their functional concepts.
2. The idea and method of combining numbers and shapes.
The idea of combining numbers and shapes refers to a thinking strategy that combines numbers and shapes to analyze, study and solve problems. Mr. Hua, a famous mathematician, said: "Numbers and shapes are interdependent, how can they be divided into two?" If there are fewer numbers, there will be less intuition, and if there are fewer shapes, it will be difficult to be meticulous. The combination of numbers and shapes is good, and everything is separated. " This fully shows the importance of the combination of numbers and shapes in mathematical research and application.
3. Overall ideas and methods
Holistic thinking means that when considering a mathematical problem, we should not focus on its local characteristics, but on the overall structure of the problem, understand the essence of the problem from a macro perspective through comprehensive and profound observation, and treat some independent but closely related quantities as a whole. Holistic thinking is widely used to deal with mathematical problems.
4. The idea and method of classification
There are many examples of classification in the textbook, such as rational number, real number, triangle, quadrilateral, etc., which can not only let students know the importance of classification: First, make related concepts systematic and complete; The second is to make the extension of the concept of classification clearer, deeper and more specific, and also to enable students to grasp the main points of the score: (1) classification is carried out according to certain standards, and the classification results are different with different standards;
(2) It should be noted that the classification results are neither missing nor overlapping;
(3) The classification should be gradual, and it can't be overstepped.
5. Ideas and methods of analogy and association
When considering some problems, mathematics teaching design often puts forward assumptions and conjectures based on the similarity between things, thus extending the attribute analogy of known things to similar new things.