First, understand the requirements of the new mathematics curriculum and master the teaching methods.
The so-called mathematical thought is the essential understanding of mathematical knowledge and methods and the rational understanding of mathematical laws. The so-called mathematical method is the fundamental procedure to solve mathematical problems and the concrete embodiment of mathematical thought. Mathematical thought is the soul of mathematics, and mathematical method is the behavior of mathematics. The process of solving problems by mathematical methods is the process of accumulating perceptual knowledge. When this quantity accumulates to a certain extent, it produces a qualitative leap and thus rises to mathematical thought. If mathematical knowledge is regarded as a magnificent building based on a clever blueprint, then mathematical methods are equivalent to architectural means, and this blueprint is equivalent to mathematical thoughts.
1. The new curriculum standard requires "hierarchical" teaching.
The new mathematics curriculum standard divides the mathematical ideas and methods infiltrated into junior middle school mathematics into three levels: cognition, understanding and application. In teaching, we should carefully grasp the three levels of "understanding", "knowing" and "being able to apply", and we should not arbitrarily raise the level of "understanding" to the level of "being able to apply", otherwise students will feel that their mathematical thoughts and methods are abstract and unfathomable when they first come into contact, thus losing confidence. For example, the first volume of junior middle school mathematics clearly puts forward the teaching idea of "reduction to absurdity" and reveals the general steps of applying it, but the new mathematics curriculum standard only positions "reduction to absurdity" on the level of understanding the meaning of reduction to absurdity through examples, so we must firmly grasp this "degree" in teaching, and we must never arbitrarily raise or deepen it, otherwise,
2. Understand "thought" from "method" and guide "method" with "thought".
At present, there is no accepted definition of the connotation and extension of mathematical thinking methods in junior high school mathematics. In fact, in junior high school mathematics, many mathematical ideas and methods are consistent, and it is difficult to separate them. The two complement each other and contain each other. Only the method is more specific, which is a technical means to implement relevant ideas; Thought is a mathematical concept and abstract. Therefore, in junior high school mathematics teaching, it is necessary to strengthen students' understanding and application of mathematical methods, so as to achieve understanding of mathematical ideas and integrate mathematical ideas and methods.
For example, the idea of conversion can be said to run through the whole junior high school teaching, which is reflected in the transformation from unknown to known, from general to special, from part to whole. Many mathematical methods are introduced into the textbook, such as substitution method, elimination and simplification method, mirror image method, undetermined coefficient method, matching method and so on. In mathematics teaching, through the study of specific mathematical methods, students can gradually realize the mathematical ideas contained in the methods; At the same time, the guidance of mathematical thought deepens the application of mathematical methods. This treatment can perfectly combine "method" and "thought", put innovative thinking and spirit into teaching, and make teaching fruitful.
Second, follow the cognitive law, grasp the teaching principles and implement innovative education.
In order to meet the basic requirements of the new mathematics curriculum standard, the following principles should be followed in teaching:
1. Infiltrate "method" and understand "thought".
For example, the chapter "Rational Numbers", the first volume of junior high school mathematics textbook published by Beijing Normal University, lacks a section ── "Comparison of Rational Numbers" compared with the original textbook, and its requirements run through the whole chapter. After the teaching of number axis, it leads to "two numbers represented on the number axis, the number on the right is always greater than the number on the left" and "all positive numbers are greater than 0, all negative numbers are less than 0, and positive numbers are greater than all negative numbers". Compare the whole process of two negative numbers, and solve them separately after absolute value teaching. Teachers should grasp the principle of gradual progress in teaching, not only to make this chapter important and difficult, but also to infiltrate the idea of combining numbers and shapes into students to make them easy to accept.
2. Train "methods" and understand "thoughts".
For example, when teaching multiplication with the same base number, students should be guided to study the operation methods and results of the same base number with a specific base number and exponent, so as to summarize the general methods. After obtaining the general law that A stands for base and M and N stands for exponent, students are required to apply the general law to guide specific operations. In the whole teaching, teachers have infiltrated the mathematical methods of induction and deduction at different levels, which has played an important role in cultivating students' good thinking habits.
3. Master "method" and apply "thought".
For example, the mathematical method of analogy can make students easy to understand and master in the process of putting forward new concepts and teaching new knowledge points. When learning functions, you can use multiplication formula for analogy; When studying the properties of quadratic function, we can compare it with the properties of roots and coefficients of unary quadratic equation. Through repeated demonstrations, students can truly understand and master the mathematical method of analogy.
4. Refine "method" and improve "thought".
In teaching, we should refine and summarize the mathematical methods in time and properly, so that students can have a clear impression. Because mathematical ideas and methods are scattered in different parts, the same problem can be solved by different mathematical ideas and methods, so it is very important for teachers to summarize and analyze. Teachers should also consciously cultivate students' ability to refine themselves and try to figure out how to summarize mathematical thinking methods, so as to implement the teaching of mathematical thinking methods.
In teaching, it is incomplete to only pay attention to imparting superficial knowledge without infiltrating mathematical thinking methods, which is not conducive to students' real understanding and mastery of what they have learned, so that students' knowledge level will always remain in the primary stage and it is difficult to improve; On the other hand, if we simply emphasize mathematical thinking methods and ignore the teaching of superficial knowledge, it will make teaching a mere formality, and it will be difficult for students to understand the true meaning of deep knowledge. Therefore, the teaching of mathematical thought should be integrated with the teaching of the whole surface knowledge. As long as our instructors carefully design and organize before class, give full play to students' main role, create more situations, provide more opportunities and persevere, we can achieve the goal of teaching and educating people.