First, understand the outline requirements and grasp the teaching methods.
1. Clarify the basic requirements and infiltrate the "layered" teaching. "Mathematics Outline" divides the mathematical thinking method infiltrated into junior middle school mathematics into three levels, namely, cognition, understanding and application. In teaching, students are required to "understand" mathematical ideas such as the combination of numbers and shapes, classification, transformation, analogy and function. What needs to be explained here is that some mathematical ideas are not clearly put forward in the outline. For example, in the process of learning new knowledge and solving problems with new knowledge, the solution of equations (groups) runs through the thinking mode from "generalization" to "specialization" In the teaching process, teachers should stimulate students' curiosity and thirst for knowledge in learning mathematics, constantly pursue new knowledge through independent thinking, and discover, propose, analyze and creatively solve problems. In teaching, we should carefully grasp the three levels of "understanding", "knowing" and "using". We should not arbitrarily raise the level of "understanding" to the level of "understanding" and raise the level of "understanding" to the level of "being able to apply", otherwise students will feel that their mathematical ideas and methods are abstract and unfathomable when they first come into contact, thus losing confidence.
2. Understand "thought" from "method" and guide "method" with "thought". In junior high school mathematics, many mathematical thinking methods are consistent, and it is difficult to separate them. The two complement each other and contain each other. Therefore, in junior high school mathematics teaching, strengthening students' understanding and application of mathematical methods to achieve an understanding of mathematical ideas is an effective way to integrate mathematical ideas and methods. For example, the idea of transformation can be said to be mathematics that runs through the whole junior high school stage, which is reflected in the transformation from unknown to known, from general to special, and from local to whole. Many mathematical methods are introduced into textbooks, and students can gradually appreciate these mathematical ideas by learning specific mathematical methods in teaching. 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, the principles of infiltrating mathematical ideas and methods
1. The principle of gradual and spiral rise.
Students' understanding and mastery of mathematics, mathematical ideas and methods has a cognitive process of "from special to general, from concrete to abstract, from perceptual to rational, from low to high". Students first have perceptual knowledge of certain ideas and methods, and after repeated practice, they gradually generalize them into rational knowledge. Finally, in mastering mathematical knowledge, they verify and develop the formed mathematical ideas and methods, and further deepen their rational understanding by solving problems with mathematical knowledge.
2. Adhere to the principle of studying teaching materials and infiltrating at different levels. "Mathematics Outline" divides the mathematical thinking method infiltrated in junior middle school mathematics into three levels: understanding and application. We should conscientiously grasp the three levels of "understanding", "understanding" and "using". The idea and method of infiltrating hierarchical mathematics teaching are often contained in textbooks. On the basis of being familiar with and studying the textbook, we can understand the mathematical ideas and methods hidden between the lines of the textbook. For example, the equation thought of "using letters to represent numbers" in the first day of junior high school is a leap from special to general and from concrete to abstract.
Third, in the process of showing the formation and application of mathematical knowledge, refine mathematical thinking methods.
The process of mathematical knowledge is also the process of its thinking method. In this process, students are provided with rich, typical and correct intuitive background materials, and the mode of "problem situation-modeling-explanation, application and expansion" is adopted. Through the study of relevant problem situations as an effective starting point, the process of knowledge generation is displayed, so that students' thinking and experience are all devoted to accepting problems, analyzing problems and feeling the challenges of thinking methods, and in this process, they understand the meaning of numbers, symbols, spatial concepts and ideas.
Four, planned, purposeful, organized to do a good job in the ideological and methodological training courses.
Summary class and review class are the best class types for systematic knowledge, deepening knowledge and internalizing knowledge, and also the best opportunity to infiltrate mathematical thinking methods. By systematically combing the learned knowledge, we can dig and refine the guiding ideology of solving problems, sum up and rise to the height of thinking methods, grasp the essence and reveal the law. There are many knowledge and skills that embody the idea of "classified discussion" in junior middle school mathematics. Such as the classification of (1) real numbers; (2) Classify triangles according to the size of angles and the relationship between sides; (3) The absolute value of any real number can be divided into three situations: greater than zero, equal to zero and less than zero. (4) The way to reveal the shape-size relationship between two triangles is to divide the two triangles into two categories: similar and dissimilar; ..... All these fully reflect the thinking method of classified discussion, which is helpful for students to understand the connections and differences between things in the material world.
Mathematical thinking method is the essential reflection of mathematical problems, and the pursuit is "giving people fish". Infiltrating mathematical thinking methods into classroom teaching and updating mathematical teaching concepts can not only help students understand the essence of problems, but also help students understand the essential characteristics of mathematical problems outside the teaching materials through the transfer of mathematical thinking methods, enrich their thinking world and make them become creative and sustainable talents in the new era.