First, the development of symbolic thinking.
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 operator 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".
Western countries introduced symbols into mathematical research earlier. /kloc-in the 6th century, the mathematician Veda made many improvements on mathematical symbols. He was the first to consciously and systematically represent numbers with letters, which brought about a significant expansion of algebraic research and laid the foundation for symbolic algebra. Later, the great mathematician Descartes improved the letters used in Vedas. Using symbolic language (including letters, numbers, graphics and various specific symbols) to describe the content of mathematics is symbolic thinking.
Second, the embodiment of symbolic thought in primary school mathematics textbooks
1. Introduce mathematical symbols into teaching.
The current primary school mathematics textbooks also attach great importance to the infiltration of symbolic ideas. For example, introduce some letters: a, b, c …; ; The operation symbols of numbers:+,-,×, ÷, etc. Relation symbols: =, >,<, ≦, etc. , and combination symbols (), [], {} and so on. Reflecting the management level; The introduction of these symbols is not chaotic and aimless. They are introduced step by step according to the age and thinking characteristics of primary school students, in a certain order and in line with certain logic. The infiltration of symbolic thoughts in primary school mathematics textbooks is carried out according to the specific conditions of different teaching stages. Mainly from the following aspects of planned and step-by-step infiltration. For example, when learning the knowledge of 1-5, the textbook does not directly present the numbers of 1 to 5, but counts 1 elephant, 2 rhinoceroses, 3 giraffes and 4 clouds in a specific situation through objects and pictures, and then presents the numbers, so that students can clearly know the meanings of these numbers. This is very beneficial to the study of children who have just entered school. It can make students fully realize the meaning expressed by mathematical symbols and lay a foundation for students to study mathematics in the future. This is a bright spot to deal with the symbol infiltration in primary school mathematics textbooks under the new curriculum standard.
2. Controversial views
According to the age characteristics and knowledge level of primary school students, the idea of variables is infiltrated in different forms, aiming to let students gradually understand the idea of variables. For example, from the first grade, textbooks began to use "mouth" or "()" instead of the variable X, and asked students to fill in numbers. For example: l+2= mouth, 6+( )=8, and another example: the school has 7 balls and bought 4 more. How many are there now? Another example is to ask students to fill in the appropriate numbers in their mouths. For example:
9-□>4 8< 16-□
12>3+□ 8+□