Using symbolic language (including letters, numbers, graphics and various specific symbols) to describe the content of mathematics is symbolic thinking. The idea of symbols is to integrate all data examples into one, and express complex languages and characters with simple and clear letter formulas, which is convenient for memory and use. It is a process from concreteness to representation, and then to abstract symbolization, which abstracts things, phenomena and their relationships into mathematical symbols and formulas. The mathematical language embodied by symbols is a worldwide language and a comprehensive reflection of a person's mathematical literacy.

(2) convert to thought

Transforming thinking is the most commonly used thinking method in mathematics. Its basic idea is to transform the solution of problem A into the solution of problem B, and then get the solution of problem A through the inverse of the solution of problem B ... generally refers to irreversible "transformation". Its basic forms are: turning difficulty into ease, turning life into maturity, turning complexity into simplicity, turning the whole into parts, turning music into straightness and so on. For example, when calculating the area of combined graphics, cut the combined graphics into simple graphics, and then calculate the sum or difference of the areas of each part, so that students can understand the essence of reduction.

(3) decomposition ideas

Decomposition thinking is a kind of thinking method that first decomposes the original problem into several easy-to-solve sub-problems, then decomposes several easy-to-solve areas, then decomposes several easy-to-advance problem-solving steps layer by layer, and then solves them one by one, so as to successfully solve the original problem. For example, the problem-solving strategy of "reverse thinking" in the teaching of "Problem-solving Strategy" in grade five embodies this idea.

(4) change your mind

Transforming ideas is an important strategy to solve mathematical problems, and it is a way of thinking from one form to another. The transformation here is reversible bidirectional transformation. Reduction is a very useful strategy to solve mathematical problems. When the problem is transformed, both the known conditions and the conclusion of the problem can be transformed. Transforms can be equivalent or not. Solving mathematical problems with the idea of transformation is only the first step, the second step is to solve the problem of transformation, and the third step is to reverse the solution of the problem of transformation into the solution of the problem. If the equivalence relation is used for conversion, the solution can be obtained directly without inversion.

5] classification thought

The thinking method of classification is not unique to mathematics, but embodies the classification of mathematical objects and its classification standards. For example, the classification of natural numbers can be divided into odd and even numbers according to whether they can be divisible by 2; Divide prime numbers and composite numbers according to the number of factors. Another example is a triangle that can be divided by edges or angles. Different classification standards will have different classification results and produce new concepts. The correct and reasonable classification of mathematical objects depends on the correct and reasonable classification standards, and the classification of mathematical knowledge is helpful for students to sort out and construct their knowledge.

[6] inductive thinking

Mathematical induction is a mathematical proof method, which is usually used to determine whether an expression is valid in all natural numbers or another form is valid in an infinite sequence. There is a generalized formal view used in mathematical logic and computer science, pointing out that the expressions that can be found are equivalent expressions, which is the famous structural induction.

An Analogical Thinking

Mathematical analogy refers to the idea that according to the similarity between two kinds of mathematical objects, the known properties of one kind of mathematical object can be transferred to another kind of mathematical object, which can solve some seemingly complicated and difficult problems. The idea of analogy not only makes mathematical knowledge easy to understand, but also makes the memory of formulas natural and concise, which can stimulate students' creativity.

As a hypothetical idea

Hypothetical thinking is a commonly used speculative mathematical thinking method, which can be used to solve some fill-in-the-blank problems, judgment problems and application problems. The quantitative relationship of some topics is hidden, so it is difficult to establish the quantitative relationship, or the quantitative relationship is abstract and impossible to start. A way of thinking that you can make some assumptions about the known conditions or questions in the topic, then calculate according to the known conditions in the topic, and finally find the correct answer according to the contradiction of quantity. Hypothetical thinking is a meaningful imaginative thinking, which can make the problem to be solved more vivid and concrete after mastering it, thus enriching the thinking of solving problems.

Levies comparative thinking

People's understanding of everything is based on comparison, either distinguishing differences from similarities or seeking common ground from differences. Russian educator ushinski said: "Comparison is the basis of all understanding and all thinking." While learning mathematical knowledge, primary school students need to understand the essential meaning of new knowledge and master the connections and differences between knowledge by comparing mathematical materials.

In the application problem of teaching scores, teachers should be good at guiding students to compare the known and unknown quantities in the problem before and after the change, which can help students find the solution quickly.

⑽ restrictive thinking

From quantitative change to qualitative change, the essence of limit method is to achieve qualitative change through the infinite process of quantitative change. There are many places in the current primary school textbooks that pay attention to the infiltration of extreme thoughts.

⑾ deductive thought

Deduction is also a rational activity, but unlike intuition, they are not simple rational activities. We must first assume some truths (or definitions), and then draw some conclusions with these definitions.

⑿ model thought

It refers to a specific object in the real world, starting from its specific life prototype, making full use of the so-called processes of observation, experiment, operation, comparison, analysis, synthesis and generalization, and getting simplification and hypothesis. It is a way of thinking to turn practical problems in life into mathematical problem models.

It is the highest realm of mathematics and the goal of students' high mathematical literacy to cultivate students to understand and deal with the surrounding things or mathematical problems with mathematical vision.

[13] correspondence thought

Correspondence means that an item in one system is equivalent to an item in another system in nature, function and position. Corresponding thinking can be understood as a way of thinking about the connection between two set elements. Infiltrating corresponding ideas in primary school mathematics teaching is helpful to improve students' ability to analyze and solve problems.

[14] setting ideas

A certain number of distinct (whether concrete or abstract) things are combined together and regarded as a whole, which is called a set, and each thing is called an element of the set. In layman's terms, it is to regard some identifiable different objects as a whole, and this whole is the collection of all these objects.

⒂ combination of numbers and shapes

According to the internal relationship between the conditions and conclusions of mathematical problems, it not only analyzes its algebraic significance but also reveals its geometric significance, so that the quantitative relationship and spatial form of the problem can be skillfully and harmoniously combined, and the mathematical problems can be solved through the mutual transformation of numbers and shapes.

Expressed the idea of statistics.

The significance of adding statistics and probability courses in primary school mathematics lies in forming the ability to explain data reasonably, improving the ability to understand the objective world scientifically and developing the ability to solve practical problems in realistic situations.

⒄ system thought

Systematic thinking is an organic whole with specific functions, which is composed of several elements (or components) that think of correlation and function. The method of systematic thinking is to ask people to study the object from the relationship between system elements, the relationship and interaction between system and elements, and from the system to the external environment, so as to get the best scheme for studying and solving problems.