The curriculum standard (revised edition) changes "two basics" to "four basics", that is, about mathematics: basic knowledge, basic skills, basic ideas and basic activity experience.

"Basic thought" mainly refers to deduction and induction, which should be the main line of the whole mathematics teaching and the highest thought. Deduction and induction are not contradictory, nor are their teaching. By summarizing the prediction results, the results are verified by deduction. In specific problems, it will involve mathematical ideas such as mathematical abstraction, mathematical model, equivalent substitution, combination of numbers and shapes, but the most important idea is deduction and induction. The reason why we use "basic thought" instead of basic thought method is to distinguish it from concrete mathematical methods such as method of substitution, recursive method and collocation method. Each specific method may be important, but they are all individual cases and are not universal. There is no need to master it as an idea. After a period of time, students are likely to forget it. The idea mentioned here is a big idea, which is the kind of thinking method that students hope to benefit for life after understanding it.

Professor Shi Ningzhong thinks that the main function of deductive reasoning is to verify the conclusion, not to discover it. What we lack is the ability to "predict the results" according to the situation; The ability to "explore the reasons" according to the results. And this is the ability of inductive reasoning.

As far as methods are concerned, inductive reasoning is very complicated, including enumeration, induction, analogy, statistical inference, causal analysis, observation experiment, comparative classification and comprehensive analysis. Contrary to deductive reasoning, inductive reasoning is a kind of "reasoning from special to general". Inductive reasoning can cultivate students' ability to "predict results" and "explore reasons", which is incomparable to deductive reasoning. From the perspective of methodology, the lack of inductive ability in "double-basic education" is not conducive to students' going to society in the future and to the cultivation of innovative talents.

First, what is the primary school mathematics thinking method?

The so-called mathematical thought refers to people's understanding of the essence and content of mathematical theory, as well as some viewpoints extracted from some specific mathematical understanding processes. It reveals the universal law in the development of mathematics, which directly dominates the practical activities of mathematics and is a rational understanding of the laws of mathematics.

The so-called mathematical method is the method to solve mathematical problems, that is, the methods, ways and means to solve specific mathematical problems, and it can also be said that it is a strategy to solve mathematical problems.

Mathematical thought is macroscopic, and it has more universal guiding significance. Mathematical method is microscopic, and it is a direct and concrete means to solve mathematical problems. Generally speaking, the former gives the direction to solve the problem, while the latter gives the strategy to solve the problem. However, because the content of primary school mathematics is relatively simple and knowledge is the most basic, it is difficult to completely separate the hidden ideas and methods, which are more reflected in the connection, and their essence is often the same. For example, the commonly used classification thinking method, set thinking method and intersection method are all connected in essence, so primary school mathematics usually regards mathematical thinking method as a whole concept, that is, primary school mathematical thinking method.

Second, what are the thinking methods of primary school mathematics?

1, corresponding thinking method

Correspondence is a way of thinking about the relationship between two set factors, while primary school mathematics is generally an intuitive chart with one-to-one correspondence, which is used to conceive the idea of function. For example, there is a one-to-one correspondence between points (number axes) on a straight line and specific numbers.

2. Hypothetical thinking method

Hypothesis is a way of thinking that first makes some assumptions about the known conditions or problems in the topic, then calculates according to the known conditions in the topic, makes appropriate adjustments according to the contradiction in quantity, and finally finds the correct answer. 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.

3. Comparative thinking method

Comparative thinking is one of the common thinking methods in mathematics, and it is also a means to promote the development of students' thinking. In the application of teaching scores, teachers are good at guiding students to compare the situation before and after the change of known quantity and unknown quantity, which can help students find solutions quickly.

4. Symbolic thinking method

Symbolic thinking is to use symbolic language (including letters, numbers, graphics and various specific symbols) to describe mathematical content. For example, in mathematics, all kinds of quantitative relations, quantitative changes and deduction and calculation between quantities all use lowercase letters to represent numbers, and use condensed forms of symbols to express a large amount of information. Such as laws, formulas, etc.

5. Analogical thinking method

Analogy means that based on the similarity between two types of mathematical objects, the known attributes of one type of mathematical object can be transferred to another type of mathematical object. Such as additive commutative law's sum-multiplication commutative law, rectangular area formula, parallelogram area formula, triangle area formula, etc. The idea of analogy not only makes mathematical knowledge easy to understand, but also makes the memory of formulas natural and concise.

Step 6 change your way of thinking

Changing ideas is a way of thinking from one form to another, and its own size is unchanged. Such as geometric equal product transformation, homotopy transformation for solving equations, formula deformation, etc. A-B = A × 1/ B is also commonly used in calculation.

7. Classified thinking method

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 divisors. 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.

8. thinking set Law

Set thinking is a way of thinking that uses set concept, logical language, operation and graphics to solve mathematical problems or non-pure mathematical problems. Primary schools use intuitive means, graphics and objects to infiltrate and gather ideas. When talking about common divisor and common multiple, we adopt the thinking method of intersection.

9. The thinking method of combining numbers and shapes

Numbers and shapes are two main objects of mathematical research. Numbers are inseparable from shapes, and shapes are inseparable from numbers. On the one hand, abstract mathematical concepts and complex quantitative relations are visualized, visualized and simplified through graphics. On the other hand, complex shapes can be expressed by simple quantitative relations. When solving application problems, we often use the intuitive help of line segment diagram to analyze the quantitative relationship.

10, statistical thinking method:

Statistical charts in primary school mathematics are some basic statistical methods, and finding the average application problem is the thinking method of data processing.

1 1, extreme thinking method:

From quantitative change to qualitative change, the essence of limit method is to achieve qualitative change through the infinite process of quantitative change. When talking about "the area and perimeter of a circle", the idea of limit division of "turning a circle into a square" and "turning a curve into a straight line" is to imagine their limit states on the basis of observing the limit division, which not only enables students to master the formula, but also germinates the limit idea of infinite approximation from the contradictory transformation of curves and straight lines.

12, alternative thinking method:

He is an important principle of solving equations, and one condition can be replaced by other conditions when solving problems. If the school buys four tables and nine chairs, it will cost 504 yuan. The price of a table and three chairs is exactly the same. What is the unit price of each desk and chair?

13, reversible thinking method:

It is the basic idea in logical thinking. When the positive thinking is difficult to solve, we can seek the way to solve the problem from the condition or problem thinking, and sometimes we can use the line segment diagram to push back. For example, a car from A to B left in the first hour 1/7, and left in the second hour 16 kilometers, leaving 94 kilometers. Find the distance between a and b. ..

14, turn to thinking method:

Through the transformation process, the problems that may or may not be solved are classified into one class, so as to solve the problems that are easy to solve and get a solution, which is called "transformation". But mathematical knowledge is closely related, and new knowledge is often the extension and expansion of old knowledge. Undoubtedly, it is of great help for students to think in a reductive way in front of new knowledge and improve their ability to acquire new knowledge independently.

15, grasp the unchanging thinking method in the change:

In the complicated changes, how to grasp the quantitative relationship and take the constant quantity as the breakthrough point is often solved by asking questions. For example, there are ***630 science and technology books and literature books, of which science and technology books account for 20%. Later, I bought some science books. At this time, science and technology books account for 30%. How many science books did you buy?

16, mathematical model thinking method:

The so-called mathematical model idea means that for a specific object in the real world, starting from its specific life prototype, it makes full use of the so-called processes of observation, experiment, operation, comparison, analysis, synthesis and generalization to get 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.

17, holistic thinking method:

It is often a more convenient and time-saving method to observe and analyze mathematical problems from the macro and overall situation and grasp the whole.

Third, how to teach students mathematical thinking methods:

1, delve into the textbook and seriously explore the factors of mathematical ideas and methods infiltrated in the textbook.

2. In the process of the occurrence, formation and development of knowledge, mathematical thinking methods should be infiltrated in time.

3. In the process of summarizing and reviewing knowledge, pay attention to the use of comparison and classification methods to help students sort out some clear and commonly used mathematical thinking methods.

4. Guide students to apply mathematical thinking methods to solve some practical problems in life.

5. Some questions should be designed properly during the exam to examine students' understanding and application ability of mathematical thinking methods.