First, change ideas and attach importance to mining mathematical thinking methods.
Mathematical concepts, laws, formulas, properties and other knowledge are clearly written in the textbook, with a "shape", while mathematical thinking methods are implicit in the mathematical knowledge system, without a "shape", and are scattered in all chapters of the textbook systematically. Teachers don't talk, talk more and talk less, which is arbitrary. They often squeeze it out as a "soft task" because of the tight teaching time. The requirement for students is to calculate as much as they can. Therefore, as a teacher, we should first renew our ideas, constantly improve our understanding of the importance of infiltrating mathematical thinking methods, integrate both mastering mathematical knowledge and infiltrating mathematical thinking methods into teaching purposes, and integrate the requirements of teaching mathematical thinking methods into lesson preparation. Secondly, we should study the teaching materials deeply and try our best to find out all kinds of factors that can penetrate mathematical thinking methods. For each chapter and section, we should consider how the specific content permeates mathematical thinking methods, which mathematical thinking methods permeate, how to permeate, and to what extent. It is necessary to have an overall design and put forward specific teaching requirements at different stages. In primary school mathematics teaching, teachers should not only be satisfied with the conclusion that students acquire correct knowledge, but should pay attention to guiding students to understand the process of knowledge formation. Let students gradually understand the mathematical thinking method contained in it. In other words, it is equally important to attach importance to the process and the result in mathematics teaching. Teachers should stand on the height of mathematical thought, analyze the teaching content in a simple way with appropriate language, and prompt the thinking method hidden behind the knowledge content. For example, the teaching of the concept of circle cognition can be carried out according to the following procedures: (1) abstract the object into geometric figures and establish the representation of the circle; (2) On the basis of representation, point out the radius, diameter and characteristics of the circle, so that students can have a deeper understanding of the circle; (3) Using various representations of the circle, the essential characteristics are analyzed and abstractly summarized as the concept of the circle expressed in written language; (4) Related concepts of symbolic circle. Obviously, this mathematical process not only conforms to the cognitive law of students from perception to representation to concept, but also enables students to understand how teachers use mathematical thinking methods, compare relevant materials, abstract and summarize spatial forms and formalize teaching concepts.
Second, the camera moves and introduces mathematical thinking methods in time.
In order to better infiltrate mathematical thinking methods in primary school mathematics teaching, teachers should not only study teaching materials, but also pay attention to the means and methods of ideological infiltration. In primary school, intuitive method, problem method, reappearance method and analysis method are commonly used in the infiltration of mathematical thinking methods. The so-called intuitive method is to visualize and visualize the mathematical thinking method in the form of charts. The viewpoint of intuitive method is to turn the highly abstract mathematical thinking method into concrete materials that students can easily perceive, especially vivid and interesting pictures, leaving a vivid impression on students. The problem method means that students, inspired by teachers, gradually understand the regularity of mathematical problems through reviewing, thinking and summarizing in the process of exploring the answers to questions, and then deepen their understanding of problem-solving methods and skills. Repetition means that students can continue to accept the influence of a certain mathematical thinking method through the repetition of the same situation. Anatomy is a typical example of anatomy. From the perspective of methodology, mathematical phenomena are described and mathematical laws are explained in mathematical language that children can understand. In the process of teaching, teachers should master methods and lose no time to infiltrate mathematical thinking methods into students. Teachers can penetrate through the following channels: (1) in the process of knowledge formation. For example, the formation of concepts and the derivation of conclusions are excellent opportunities to penetrate mathematical thinking methods, train thinking and cultivate ability. (2) Infiltration in the process of solving problems. For example, in the teaching process of "reverse reasoning", students can gradually understand the mystery of this strategy by using charts and extracting conditions in the process of solving problems. (3) Infiltrate in the review summary. In the mathematics teaching of chapter summary and review, we should pay attention to the summary and review of mathematical thinking methods from both vertical and horizontal aspects, so that teachers and students can experience the relaxed and happy feeling of understanding mathematical thinking, using mathematical methods, improving training effect, reducing the burden on teachers and students and getting out of misunderstandings. For example, after teaching the unit "Understanding Circle", students can rely on the derivation process of circle area to help them recall the derivation method of polygon area formula in time, so that students can clearly realize that "conversion" is an effective method to solve problems. (4) Infiltrating into teaching activities such as mathematics lectures. Mathematics lecture is a form of extracurricular teaching activities, which is not only loved by students, but also widely used by mathematics teachers. In particular, the proper infiltration of mathematical thinking methods in activities such as mathematics lectures has brought vitality to mathematics teaching, changed the stagnant face of exam-oriented teaching in the past, and rejuvenated its vitality.
Third, temper-consciously use mathematical thinking methods.
The teaching of mathematical thinking method is not only to guide students to use mathematical knowledge effectively and explore the direction and entrance to solve problems, but also to cultivate people's thinking quality. It belongs to the stage of "osmosis" in the new teaching, and enters the stage of clear and systematic in practice and review, which is also the acquisition process and application process of mathematical thinking method. This is a leap from vagueness to clarity. And such a leap is achieved through systematic analysis and problem-solving exercises. Students will not only consolidate and deepen their already mastered mathematical knowledge and mathematical thinking methods, but also summarize and refine new mathematical thinking methods from them. The teaching process of mathematical thinking method begins with imitation. As an example, students solve the same type of exercises according to the program and format of the example teacher, which is actually the mechanical application of mathematical thinking method. At this time, it is not certain that students have understood the mathematical thinking method used. Only when students apply it to new situations, solve other related problems and be creative can they ensure that students have a deep understanding of this teaching essence and mathematical laws.
We know that for learners, the best learning effect is active participation and personal discovery, and the learning of mathematical thinking methods is no exception. In teaching, through the extensive application of mathematical thinking methods, students attach importance to the study of mathematical thinking methods subjectively, and then enhance their consciousness of consciously refining mathematical thinking methods. Teachers should also consider the design of exercises from the perspective of mathematical thinking methods, and arrange exercises as much as possible so that students at all learning levels can answer in plain language. There are not only specific methods or steps, but also thinking or grasping from the solution of a class of problems, forming a problem-solving method, and then deepening into mathematical thinking. For example, after teaching the calculation of circle area, solving several practical problems by moving and cutting can not only make students understand the transformed mathematical thinking method, but also be of great benefit to improving their interest in learning. Let students master in operation, understand after mastering, and let mathematical thinking methods be generated together in the process of knowledge and ability formation.
Mathematical thinking method is a systematic project, which is influenced and restricted by many factors. Only by attaching importance to the study and research of mathematical thinking methods and exploring its teaching rules can our primary school mathematics teachers meet the needs of curriculum teaching reform. Of course, it should be noted that the infiltration of mathematical thinking methods is long-term and repeated. Infiltrating students' mathematical thinking methods is bound to go through a cyclical and spiraling process, and often several thinking methods are intertwined. In the teaching process, teachers should focus on infiltrating and clarifying a mathematical thinking method in a certain period of time according to the specific situation, so that students can really understand it after repeated training.