First, junior high school mathematics thinking method
There are many ways of thinking in junior high school mathematics, but the most basic ones are function and equation, combination of numbers and shapes, classified discussion and problem transformation.
1. Function and Equation Thought
Function thought refers to a corresponding thought between variables. The idea of equation refers to transforming the quantitative relationship between known quantities and unknown quantities in mathematical problems into equations or mathematical models such as equations. For example, an engineering team wants to recruit 700 workers with two types of jobs. The monthly wages of the two types of workers are 800 yuan and 1200 yuan respectively. At present, the number of workers in Class B is required to be not less than three times that of Class A. When asking how many people to recruit for each type of work, can the monthly salary be the least?
2. The idea of combining algebra with graphics
The idea of combining algebra with graphics is often said to be the idea of combining numbers with shapes, which is the oldest and most common way of thinking in mathematics. The combination of numbers and shapes is to combine abstract mathematical language, quantitative relations with intuitive geometric figures and positional relations. Through the combination of "helping numbers with shapes" or "solving shapes with numbers", that is, through the combination of abstract thinking and image thinking, complex problems are simplified and abstract problems are concretized, so as to achieve the purpose of optimizing problem-solving methods. For example, as shown in the figure, how to infiltrate mathematical thinking methods into junior high school mathematics teaching?
3. Discuss the idea of mathematical classification.
There are many theorems, formulas, rules and exercises in junior high school mathematics textbooks, which need our classified discussion. When teaching these contents, we should consciously strengthen the students' idea of classified discussion, so that students can realize these problems. Only after classified discussion can the conclusion be complete and correct. If we don't discuss them separately, we will easily miss or make mistakes. In problem-solving teaching, classified discussion also helps students to generalize and summarize regular things, thus strengthening the order and meticulousness of students' thinking. For example, after learning rational numbers, the size of the letter A is compared with 0, and the image distribution of the function y=(k- 1)x+b needs to be classified and discussed.
4. The transformation of the problem
Transformational thinking, also known as transformational thinking, refers to mathematical thinking that transforms unknown, unfamiliar and complex problems into known, familiar and simple problems through deduction and induction, so that the problems can be solved smoothly. Mathematical theories such as trigonometric function, geometric transformation and factorization are permeated with the idea of transformation. Common transformation methods include: general special transformation, equivalent transformation, complex simple transformation, associative transformation, analog transformation and so on. For example, the solution of binary linear equations, ternary linear equations are essentially transformed into one-dimensional linear equations.
Second, the way to infiltrate mathematical thinking methods in teaching
Every knowledge link in mathematics teaching contains mathematical thinking methods, which can stimulate students' interest in learning, infiltrate mathematical thinking methods and improve students' learning efficiency through various ways.
1. In the process of exploring knowledge, pay attention to infiltrating mathematical thinking methods.
The new curriculum requires that teaching should pay attention to the process of students' knowledge formation, especially the derivation of theorems, properties and formulas and the solution of examples. Basic mathematical ideas and methods are formed and developed in this process. Therefore, teachers should pay attention to the deduction process in the process of teaching concepts, properties and formulas, and lose no time in infiltrating relevant mathematical thinking methods in the process of knowledge generation and development, so that students can master surface knowledge and understand deep mathematical thinking methods, thus improving their thinking quality. In the teaching process, students should be guided to actively participate in the process of exploration, discovery and deduction of conclusions, find out the causal relationship among them, understand its relationship with other knowledge, and let students experience the mathematical ideas and methods they have experienced and applied in creative thinking activities.
2. Through the teaching of examples and solving problems, comprehensively apply mathematical thinking methods.
In teaching, teachers carefully analyze examples and think about how to guide students to cultivate mathematical ideas in examples. In teaching, teachers should do well in problem-solving and reflection activities. Every time they finish a math problem and an example, they should sum up the problem-solving methods to students, form mathematical ideas, attach importance to the problem-solving process, and use mathematical ideas and methods to associate and transform the problem-solving methods. Many typical examples are designed in the new junior high school mathematics textbook, and many excellent questions will appear in the middle school exam every year. Teachers are good at choosing inspiring and creative topics to practice, and displaying mathematical ideas and teaching methods in the process of analyzing and thinking about these issues.
3. Summarize the gradual internalization of mathematical thinking methods in time.
Mathematical thinking is implicit in the mathematical knowledge system of teaching materials. A content can contain many different mathematical thinking methods, and the same mathematical thinking method is often used in many different basic knowledge. After explaining a topic, the teacher should reveal the thinking mode of solving the problem, the knowledge points involved and the thinking methods used, and encourage students to talk about their own thinking process of solving the problem. The teacher will give students some related topics to strengthen and stimulate, so that students can learn to summarize and summarize mathematical thinking methods and consciously internalize them in their minds.
4. In the process of solving problems, deepen the mathematical thinking method.
In teaching, students often understand it at that time, but they don't know what to do after class, especially when they encounter new problems. The reason is that teachers solve problems when they get them in teaching, and get bored and tired when they encounter similar problems. Therefore, when exploring mathematical problems, we should guide students to learn to think and truly understand the thinking methods contained in mathematical problems.
The ocean of mathematical problems is boundless, but the thinking method of mathematics is limited. In our teaching, we should strengthen and consolidate the basic knowledge of mathematics, infiltrate and master the basic mathematical thinking methods in the process, and students will solve problems by methods. Make good use of teaching materials, carefully analyze the intention of compiling examples, carefully select examples, infiltrate and summarize mathematical thinking methods in the teaching and learning activities of teachers and students, and transform the learned mathematical knowledge into the ability to learn mathematics, so that students can learn mathematics easily and happily and improve their mathematics scores.