When carrying out practical teaching work, primary school mathematics teachers should first abandon traditional and outdated teaching methods and adopt new teaching methods to adapt to the social development trend and keep pace with the times. In addition, in order to make students have a profound knowledge and understanding of knowledge, teachers should properly use classified knowledge to solve many practical problems and infiltrate mathematical ideas into practical teaching activities. On the one hand, the application of these ideas can improve the efficiency of mathematics teaching, on the other hand, it can stimulate students' interest in learning mathematics and let students participate in learning independently, thus opening a new chapter in primary school teaching with the joint efforts of teachers and students.
First, an overview of mathematical thought
Mathematics thought was put forward from 65438+90' s. The application of this idea should be matured in the long-term development. However, there are still many incomplete places in the study of China's mathematical thoughts, so there are still many places that are not clear enough, but China can classify the mathematical thoughts well in his development. In fact, it can be divided into two categories: mathematical thought and mathematical method. Mathematical thinking is mainly a cognitive activity based on the essence of mathematics. One is to re-understand the known mathematical content and put forward new ideas and opinions. That is, in the process of primary school mathematics teaching, teachers should learn to understand mathematics ideologically and understand the essential content of their thoughts, so as to better guide students to learn mathematics knowledge, solve problems in mathematics and consolidate all review links. Comparatively speaking, mathematical methods are more practical. Teachers should carry out different forms of ideological activities under the control of mathematical thought, and understand the problems in the process of mathematical activities with the help of practical discovery. The contents of mathematical methods mainly include forms, means and methods.
Second, the method of infiltrating mathematical thought in teaching
(A) the idea and method of classification
The main idea of classification is to classify all the problems in detail, classify the fragmentary individuals into a whole, classify them according to certain principles, and finally divide the whole into parts. Analyze different parts and realize the solution of the whole content. The idea of classification is of great significance in mathematics teaching, and it is also widely used in primary mathematics. Using the idea of classification, complex mathematical knowledge can be classified and applied.
The classification of complex ideas has a positive impact on the method. In the face of complex mathematical classification, it is necessary to display the contents of different attributes on the premise of the same object attribute. In this way, students can have a clear understanding of concepts and laws, thus improving their ability to solve problems. For example, in teaching activities, students can directly divide triangles into acute triangles, right triangles and obtuse triangles, which is convenient for students to understand the essential contents of the three types of triangles and clarify the differences and connections between them. The establishment of classification ideas should follow the following principles: First, the principle of standard identity. All standards should be unified for each classification, and two or more standards cannot be put forward at one time. The same standard can be regarded as the same factor or composed of two or more factors. For example, if a number that can be both odd and even is found among natural numbers, then this classification standard contains two classification factors. The second is the principle of not repeating or omitting. After the classification is completed, there can be no duplication or omission between the parts, so that under the same standard, the parts are mutually exclusive but do not intersect. For example, when learning quadrilateral classification, we can divide quadrilateral into parallelogram, trapezoid and arbitrary quadrilateral, and then divide parallelogram into general parallelogram and rectangle.
(2) Explore mathematical ideas from the perspective of mathematical design.
When teachers carry out teaching activities, they should first do a good job in teaching design. At the beginning of teaching design, teachers need to take the excavation of mathematical thoughts as the main starting point of thinking methods, deeply understand the contents of teaching materials, refine methods, and then carry out practical mathematics work in combination with these methods. For example, in teaching, teachers should first explain the problem of planting trees to students, and use different mathematical ideas to carry out teaching activities in combination with the contents of textbooks, so that students can master cases and deeply explore the "two-headed planting", "one-headed planting" and "two-headed planting" in textbooks. In-depth exploration of these three types of cases, and can understand the relevant knowledge points in the exploration, so as to associate cases and solve problems in the future.
(C) the way of thinking in the process of cognitive knowledge formation
In mathematics teaching, thinking method and knowledge are closely related, because they are difficult to exist independently. In this case, teachers should infiltrate methods in the process of forming teaching knowledge, so that students can learn related mathematics knowledge better. For example, teachers let students know the numbers within 10, and then play them by video, or use animation to let students have a vivid understanding of the numbers within 10, and induce relevant digital contents by induction. Based on this, students can not only have a clear understanding of numbers within 10, but also have a deeper understanding of inductive thinking methods.
(D) Reflection on the infiltration of mathematical ideas in teaching
In mathematics teaching, teachers should let students have a deep understanding of knowledge after teaching students the basic knowledge. In order to make students have a good sense of reflection, teachers should infiltrate mathematical ideas throughout the reflection period, so that students can have a deep understanding of the learning process of mathematics.
(E) the idea of combining numbers with shapes
In mathematical research, it is mainly to have a simple understanding of the spatial form and quantitative relationship in the real world. Spatial form can be regarded as "shape" and quantitative relationship as "number". Numbers and shapes represent two different aspects of the same thing. They are interrelated, but they can also be transformed into each other. Using the idea of combining numbers with shapes requires the complementary advantages of abstraction and concreteness, which requires highlighting the graphic relationship between them, and then intuitively expressing the corresponding quantitative relationship, thus helping tangible students to solve problems better. In addition, the properties or characteristics of graphics can be transformed into algebraic problems, and the problems can be obtained with the help of numerical assistance.
Mathematics is an important learning subject, and it is also the key and difficult point in teaching. In order to better carry out mathematics teaching in teaching activities, teachers should take various measures to infiltrate thinking methods in teaching, so that mathematics teaching can achieve good results and students can master more mathematics knowledge.