First, gradually infiltrate cognitive symbols.
There are many symbols in our life, for example, the symbol "P" stands for parking, railways, highways and aviation all have their own signs, and there are various signs on the map, as well as KFC, which children like. These are symbols in life, which all represent specific meanings, and mathematics is also full of symbols. There are several types of symbols appearing in primary school textbooks: (1) Individual symbols: symbols representing numbers. A, B, c…, π, X and symbols of decimals, fractions and percentages. (2) The operation symbols of numbers:+,-,× (? ) ,÷( /, ∶) 。 (3) Relation symbols: =, >,<, etc. (4) Combination symbols: () [] and so on, as well as measurement unit symbols indicating angles and separator symbols indicating vertical operations. Of course, they also have specific meanings. The current textbook has arranged the teaching of various mathematical symbols from the first grade, which runs through the whole six years 12 volumes. Faced with so many symbols, we must respect students' original experience, let students experience the symbolic process of abstract quantitative relations and changing laws from specific situations, let students know symbols and gradually understand their meanings.
1. Understand with the help of specific situations.
The thinking of junior children is mainly the concrete thinking of images. Teachers should learn to create situations to make them interested in the materials they have learned, arouse their existing experience and go through the process of knowledge symbolization. For example, when children learn the knowledge of 1 to 5, the textbook does not directly present the number of 1 to 5, but counts 1 teacher, 2 potted flowers, 3 girls and 4 balloons in a specific situation through objects and pictures, and then presents the corresponding disks and numbers, so that students can clearly know the meaning of these numbers, which enables them to know. Another example is the statistics teaching in the second volume of the new textbook. The teacher created the actual situation of "counting which small animals are most popular with the children in the class", and some students used 1, 2, 3 to express it; Some students use numbers such as ○, △, □, and 4, while others use the method of "√". Students use their own personalized symbols to solve statistical problems and feel the value of symbols by digging their own life experiences.
2. Use arguments to change ideas.
From the first grade, you can use "□" or "()" instead of the variable X, so that students can fill in the numbers. 2 + 2 = □ ,3+( )=8 , 5= □+□+□+□+□; Another example: the school has 10 balls and bought five more. How many are there now? Students are required to fill in □□□□□ =□ (1). Although such a topic only requires students to fill in a number in the "space", the teacher should understand that if the symbol □ is replaced by X, the above topic is a linear equation with one variable. This is the idea of argument. It can be said that the idea of variables is the basis of solving application problems with equations. Once students understand and master the idea of variables, it will be of great help to solve application problems in the future.
3. Dig the meaning of the symbol itself.
When teaching addition for the first time, in order to help students understand the meaning of "plus sign", the teacher can first present a scene map and ask how many people are there. Teachers can ask students to relate the meanings of these two pictures. Students think that addition is to combine two numbers through their own language expression. The teacher listed the formulas and connected the two numbers with "+". The blackboard is 3+2=5. Teachers can continue to ask students to talk about the meaning of the plus sign, so that students can understand the meaning of the symbol through the mutual transformation of daily language and mathematical language, and lay a solid foundation for the correct use of the symbol. Teachers should not simply teach students mathematical symbols as "prescribed symbols", but should infiltrate symbolic thinking into the whole teaching, cultivate students' abstract thinking ability and gradually cultivate their sense of symbols.
Second, use symbols flexibly.
1, realize the superiority of using letters to represent numbers.
From the second learning period, it is an important step to express numbers with letters. From studying a specific number to expressing an approximate number by letters is a leap in understanding. The arithmetic and simple operation of grade four make full use of letters to express multiplication commutative law, associative law and multiplication distribution rate. Obviously, it is more general and clear than using specific numbers, and more concise and easy to remember than using everyday language. The rectangular area formula in the second volume of Grade Three is described in language as: rectangular area = length × width, but in Grade Five, the formula for calculating the area of parallelogram is changed to s=ah. Through the gradual transition of the above stages, students will gradually understand the superiority of using letters to represent numbers, and the idea of symbolization will gradually take shape.
2. Feel the convenience of solving equations.
Using equations to solve practical problems, the solution itself contains symbolic ideas, which are mainly reflected in the following aspects: (1) algebraic assumption, using letters instead of unknowns, participating in operations on an equal footing with known numbers; (2) Algebraic translation, which translates the known conditions expressed in natural language into equations expressed in symbolic language. (3) Solving algebraic equations. Taking letters as known numbers, four operations are carried out to achieve the purpose of solving. It can be said that it is a concentrated expression of symbolic thought in mathematics, which is of great value to students' understanding of mathematical symbolic thought and its significance. For example, "cheetah is the fastest animal in the world, and its speed can reach 1 10KM, which is more than 30KM twice that of elephant. How many kilometers per hour can an elephant reach at the earliest? " The first step is to assume the speed of the elephant, the second step is to list the equation according to the conditions, and the third part is to solve the equation. By solving problems, students can be familiar with and skillfully use symbols, and also feel the simplicity of solving problems with symbols, thus cultivating students' sense of symbols.
Because the symbolic thinking method is scattered in different parts of the textbook, and the same problem can be solved by different mathematical thinking methods, it is very important for teachers to summarize and analyze. In addition, teachers should consciously cultivate students' ability to refine themselves and try to figure out symbolic thinking methods, so as to implement the teaching of mathematical thinking methods.