Number and shape are two aspects of the research object in mathematics teaching. Combining the relationship between numbers and spatial forms to analyze and solve problems is the idea of combining numbers with shapes. The combination of numbers and shapes, with the help of simple illustrations made by figures, symbols and words, can promote the coordinated development of students' thinking in images and abstract thinking, communicate the connection between mathematical knowledge, and highlight the most essential characteristics from the complex quantitative relationship. It is an important principle in the arrangement of primary school mathematics textbooks, an important feature of primary school mathematics textbooks and a common method to solve problems.

For example, we often use the method of drawing line segments to solve application problems, which is a method of replacing quantitative relations with graphics. You can also study the perimeter, area and volume of geometric figures by algebraic method, which embodies the idea of combining numbers with shapes.

Second, the method of thinking set

Putting a group of objects together as the scope of discussion is an early way of thinking of human beings, and then putting some abstract thinking objects, such as points, numbers and formulas in mathematics, together as the research objects. This way of thinking is called collective thinking. As an idea, set thought is embodied in primary school mathematics. In primary school mathematics, the concept of set is infiltrated by drawing a set diagram.

For example, the concept of set is intuitively infiltrated into students with a circle diagram (Wayne diagram). Let them perceive that all the objects in the circle have some * * * same attributes, which can be regarded as a whole, and this whole is a collection. Using the relationship between graphs, we can penetrate the relationship between sets to students, for example, rectangular sets contain square sets, parallelogram sets contain rectangular sets, and quadrilateral sets contain parallelogram sets.

Third, the corresponding way of thinking.

Correspondence is the grasp of the problem connection between two sets by human thinking, and it is the most basic concept of modern mathematics. In primary school mathematics teaching, dashed lines, solid lines, arrows, counters and other graphics are mainly used to connect elements, objects, numbers and formulas, and quantities, thus infiltrating corresponding ideas.

For example, in the first volume of the first grade textbook published by People's Education Press, rabbits and bricks, pigs and wood, rabbits and radishes, apples and pears correspond to each other, and how many comparative studies have been made to infiltrate the corresponding relationship between things into students and provide them with thinking methods to solve problems.

Function thought has penetrated into the first volume of the first grade textbook of People's Education Press. For example, let students observe the "addition table brought back to the car within 20 minutes" and look for the changing law of sum caused by the change of addend, which well permeates the idea of function and aims to help students form the initial concept of function.

Fourthly, inductive thinking method.

Before studying general problems, we should first study several simple, individual and special situations, so as to sum up general laws and properties. This way of thinking from special to general is called inductive thinking. The occurrence of mathematical knowledge is the application of inductive thinking. By using inductive thinking in solving mathematical problems, we can not only recognize the laws of solving given problems, but also discover new objective laws and put forward new principles or propositions on the basis of practice. Therefore, induction is an important way of thinking to explore problems and discover mathematical theorems or formulas, and it is also a leap in the thinking process.

For example, when teaching "the sum of internal angles of triangles", first calculate the sum of internal angles of right triangles and equilateral triangles, then deduce the sum of internal angles of general triangles through guessing, operation and verification, and finally get that the sum of internal angles of all triangles is 180 degrees. This uses the inductive thinking method.

Verb (abbreviation of verb) symbolic thinking method

Today, mathematics has become a symbolic world. Symbol is the concrete embodiment of mathematical existence. Russell, a famous British mathematician, said, "What is mathematics? Mathematics is symbols plus logic. " Mathematics is inseparable from symbols, and symbols are everywhere in mathematics. Whitehead once said: "As long as we analyze it carefully, we can find that symbolization has brought great convenience and even necessity to the expression and demonstration of mathematical theory." Mathematical symbols are not only used to express, but also contribute to the development of thinking. If mathematics is gymnastics of thinking, then the combination of mathematical symbols becomes "gymnastics March". The current primary school mathematics textbooks attach great importance to the infiltration of symbolic ideas.

In the content of primary school mathematics, symbolic thought can be seen everywhere, and teachers should consciously infiltrate it. Mathematical symbols are the crystallization and foundation of abstraction. If we don't understand its meaning and function, it is as daunting as a "heavenly book". Therefore, teachers should pay attention to students' acceptability in teaching.

Sixth, statistical thinking method.

In production, life and scientific research, people usually need to investigate and analyze some problems purposefully, and sort out some original data collected to infer the overall characteristics of the research object. This is the idea and method of statistics. For example, average is an idealized statistical method. We should compare the learning situation of the two classes, and it is convincing to take the average class size as the symbol of class performance. This is the most commonly used and simple statistical method.

In addition to the above mathematical thinking methods, primary school mathematics also uses transformation thinking method, hypothetical thinking method, comparative thinking method, classified thinking method, analogy thinking method and so on. From the teaching effect, the infiltration and application of these teaching ideas and methods in teaching can increase students' interest in learning and stimulate their interest and initiative in learning; Can enlighten thinking and develop students' mathematical intelligence; It helps students to form a solid and perfect cognitive structure. In short, in teaching, teachers should not only pay attention to the imparting of mathematical knowledge and skills, but also pay attention to the infiltration and application of mathematical ideas and methods, which will undoubtedly help students improve their mathematical literacy in an all-round way and contribute to their lifelong learning and development.