1, the basic mathematical thinking method is of great significance to the development of students.

Mi Shan Kunsan, a famous Japanese mathematics educator, pointed out: "Mathematics, as knowledge, may be forgotten less than two years after leaving school, but its spirit, thoughts, research methods and key points are deeply remembered in the mind, and it plays a role anytime and anywhere, benefiting students for life."

Mathematical thinking method is the soul and essence of mathematics. Mastering the scientific mathematical thinking method is of great significance to improve students' thinking quality, the follow-up study of mathematics, the study of other disciplines and even the lifelong development of students. It is the key to strengthen students' mathematical concepts and form good thinking quality to consciously infiltrate some basic mathematical thinking methods in primary school mathematics teaching. Not only can students understand the true meaning and value of mathematics, learn to think and solve problems with mathematics, but also can organically unify the learning of knowledge with the cultivation of ability and the development of intelligence.

2. Infiltrating the basic mathematical thinking method is the requirement of implementing the spirit of the new curriculum standard.

The revised mathematics curriculum standard takes "four basics": basic knowledge, basic skills, basic ideas and basic activity experience as the target system. The basic idea is one of the goals of mathematics learning, and its importance is self-evident. The new textbook presents some important mathematical thinking methods through the simplest examples in students' daily life, and solves these problems through intuitive means such as operation, experiment and guess. So as to deepen students' understanding of mathematical concepts, formulas, theorems and laws and improve students' mathematical ability and thinking quality. This is an important way to realize mathematics education from imparting knowledge to cultivating students' ability to analyze and solve problems, and it is also the real connotation of the new curriculum reform of primary mathematics.

2. What mathematical thinking methods are permeated in the new textbook?

By combing the whole set of textbooks, we can grasp the relationship between knowledge points in the system more deeply and accurately. It is not difficult to find that the characteristics of textbook arrangement are the gradual transition from focusing on concrete image thinking to focusing on abstract thinking, and many mathematical thinking methods are also spiral deepening.

First of all, there is a certain connection between the contents, and accurately grasping the connection points of each textbook is helpful to interpret the textbooks. For example, the rational arrangement of the seventh volume, the problem of finding defective products in the tenth volume, and the pigeon coop principle in the twelfth volume all need to consider the problem of "at least" when solving problems, and all need to use the ideas of reasoning and infiltration optimization to find the best strategy in various schemes. When solving the problem of planting trees in closed squares, we need to use the "overlapping problem" to interpret it; Both the problem of planting trees and the problem of keeping chickens and rabbits in the same cage attach great importance to the construction of mathematical models, and generally have to go through the learning process of "problem situation-establishing models-explaining application models" ...

Secondly, many teaching contents emphasize the infiltration of mathematical culture. For example, chicken and rabbit in the same cage, pigeon hole principle and other issues need to introduce mathematical knowledge background to improve students' interest in learning mathematics. In the teaching process, we should always pay attention to the embodiment of emotional attitude and values.

Third, how to effectively penetrate mathematical thinking methods?

1, with the infiltration of mathematical thinking method as the core, grasp the target positioning.

Teaching goal is the soul of classroom teaching and the starting point and destination of teaching. Therefore, whether the teaching goal is set properly or not directly determines the degree of achieving the goal in the teaching process, and also directly determines the teaching effect of a class. The standard points out: "Important mathematical concepts and ideas should be gradually deepened." Mathematical thinking method belongs to tacit knowledge, and students can't master it all in a short time. It takes long-term infiltration and constant experience to understand. Therefore, teachers should implement it in stages according to students' age characteristics and cognitive rules, and should not set the teaching goal too high. So how to accurately locate the teaching objectives?

First of all, from the perspective of grasping the teaching objectives, it should be oriented to let students feel the basic mathematical thinking methods, learn to use mathematical thinking methods to try to solve problems, and experience the strategies and methods to solve problems through mathematics teaching activities. Because mathematics classroom teaching is for all students, the original intention is to let every student get the training of mathematical thinking, and gradually form the interest and desire to explore mathematical problems, discover and appreciate the beauty of mathematics.

Secondly, from the perspective of the decomposition of teaching objectives, we should also take care of individual differences and reflect the hierarchy of teaching objectives. The differences in students' learning starting point and personality require us to deal with the relationship between facing the whole and paying attention to differences in teaching, to ensure that every student gains something, and to truly "ensure the bottom, not the top".

Obviously, based on the goal orientation of mathematical thinking method, teachers are bound to fully explore and understand the mathematical thinking method embodied in the teaching materials, and pay attention to making students feel the charm of mathematical thinking method through observation, comparison and analysis in teaching.

2. Use mathematical thinking methods to lead and integrate teaching resources.

As a developer of curriculum resources, teachers should choose teaching materials reasonably and integrate teaching resources. That is, combining the teaching content with the course objectives, consciously selecting and integrating the course resources, so that the course content can be more closely combined with the students' mathematics teaching activities, which can better reflect the infiltration and edification of mathematical thinking methods.

(1) Pay attention to whether the "textbook" is suitable for your classroom.

Textbooks can't design all the questions perfectly, nor can they take into account all the students' situations. It is inevitable that some topics will be divorced from the reality of students. Therefore, teachers should break through the shackles of teaching materials, creatively use teaching materials and tap their potential value. They should be good at starting from the reality of students, adjusting and changing the presentation mode and arrangement order of teaching materials, and changing "teaching materials" into "teaching by teaching materials". For example, in the second volume of Senior Two, the author takes the second floor layout as the main material for teaching, presents the theme map step by step, and makes secondary use of the theme map. This arrangement gives students ample space to explore, changing two pictures of the same level into different levels, which is conducive to students' further discovery and consolidation of the law.

(2) Pay attention to whether the awareness of "talents" is in place.

The consciousness of "talent" is mainly manifested in: teachers pay attention to students' knowledge base, cognitive characteristics, hobbies, emotional attitudes and other factors, search for "materials" from the perspective of realizing teaching objectives around the main line of infiltrating mathematical thinking methods, be good at observing and understanding students, study textbooks from the perspective of students, and grasp the "degree" of handling textbooks. For example, in order to reorganize the teaching materials in the overlapping process, the survey results of "your favorite sports" and "your favorite TV programs" can be used as research materials from the students' actual life and interests.

(3) Pay attention to whether the "material" is combed and perfected.

If the same material is used evenly or lacks refinement, its teaching value may not be fully reflected. Learning materials should reflect hierarchy and development, need orderly combination, need to be combed and improved in consolidation and application, refine mathematical thinking methods, and give full play to the educational value of mathematics textbooks.

3. Take the activity experience as the basic form to realize the mathematical thought.

Mathematical thinking method is a kind of tacit knowledge based on and higher than mathematical knowledge, which is more abstract than mathematical knowledge. Therefore, it is necessary to design some lively and interesting mathematical activities for students, and observe, operate, experiment, guess, reason and communicate in these activities to fully realize the wonders and functions of mathematical thinking methods. Then, how should we pay attention to mathematical thinking when designing activities?

First of all, pay attention to experience and gradually abstract.

The teaching difficulty in mathematics textbooks lies in how to make students realize abstract mathematical thinking methods in intuitive problem solving. The key to solve this difficulty is to let students actively participate, because without active participation, they can't experience mathematical knowledge and mathematical thinking methods; Without experience, the infiltration of mathematical thinking methods can only be empty talk. Therefore, in the teaching process, it is necessary to create various situations that students are interested in, so that students can actively participate in the mathematics teaching process in a positive state and gradually understand the mathematical thinking methods according to their own experiences.

In the teaching process, we should avoid the process of intuition, without abstraction, or there is no ladder, transition and progression between intuition and abstraction. Instead, we should guide students to actively participate, experience feelings through activities such as observation, operation, experiment, guessing, reasoning and communication, and infiltrate abstract mathematical thinking methods from intuitive problem solving.

Secondly, develop thinking by combining numbers and shapes.

Hua, a famous mathematician, said: "If you count less, you will have less consciousness. If you count less, it will be difficult to be nuanced. No matter how good the combination of numbers and shapes is, it will be difficult to separate everything." The idea of combining numbers and shapes can make some abstract mathematical problems intuitive and vivid, and can turn abstract thinking into thinking in images, which is helpful to grasp the essence of mathematical problems. It can be seen that teachers should often use visual teaching methods such as objects, teaching AIDS, charts, life experiences and humorous language to help students understand mathematical thinking methods and improve learning efficiency.

4. Take problem-solving as the basic mode, and cultivate application consciousness.

Judging from the characteristics and formation process of mathematical thinking methods, the infiltration of students' mathematical thinking methods is not immediate, but requires a continuous infiltration process, step by step, from the shallow to the deep. And this requires teachers to become the leaders of this "process", and constantly temper students' thinking with mathematical ideas, so that students can constantly reflect, accumulate and feel in the process of tempering again and again until they can take the initiative to apply. Therefore, in mathematics teaching, we should constantly pay attention to the general process of problem solving in class or after class, cultivate students' strategies of applying mathematical thinking methods to solve problems, and even more, we should "reflect" after solving problems, and experience the mathematical thinking methods and application values in this process.

In order to let students experience the thinking method of "simplifying complex problems", I am afraid that students are still not impressed by the experience. Therefore, on the basis of trying to solve the problem, the author organized a review of the learning process, designed the strategy problem, clearly demonstrated the thinking process of "clarifying the problem-exploring the law-establishing the model-solving the problem" by combining pictures and texts, and intuitively presented the mathematical methods and strategies involved in studying the tree planting problem.

After making students feel the solution strategy of planting trees, design problems different from planting trees, such as installing street lamps, going up stairs, sawing wood, queuing and so on. To enable students to further use "transformation thinking" to migrate and solve similar planting problems, and to apply and feel the thinking method of planting trees in solving such similar problems.

Problem is the heart of mathematics, method is the behavior of mathematics, and thought is the soul of mathematics. Whether it is the establishment of mathematical concepts, the discovery of mathematical laws, the solution of mathematical problems, or even the construction of the whole "mathematical building", the core problem lies in the infiltration and establishment of mathematical thinking methods.