1. Solutions to problems

What is the method? Some scholars have given the following levels of problem-solving methods:

For primary school mathematics, the problem-solving methods we refer to mainly refer to specific problem-solving methods, but some of them have the characteristics of subject thinking methods, so they can be said to be a combination of the two.

2. The method system of solving mathematics problems in primary schools.

Based on the reality of primary school mathematics, the following commonly used problem-solving methods are preliminarily constructed:

3. Basic methods and special methods.

In the special method series above, there is a method "transformation method" that can be included, but cannot be written. This is because "transformation" or "transformation" is essentially the most basic idea and train of thought to solve mathematical problems, and it is always accompanied by primary school mathematics learning to transform the unknown into the known.

Second, the basic methods of problem solving in teaching practice

1. Two meanings of analytical method and comprehensive method.

Analysis method (look at the problem and think about the conditions):

Start with the problem or conclusion, think about what conditions are needed to solve this problem or draw this conclusion, and trace back step by step until you know all the conditions. This method or thinking of "holding the fruit" from "unknown" to "need to know" and gradually approaching "known" is called analytical method.

Comprehensive method (thinking according to conditions):

Starting from the known conditions, think about how to get the answer or conclusion of the question step by step through operation or reasoning. This method or idea of "from cause to effect", from "known" to "knowable" and then gradually leading to "unknown" is called comprehensive method.

Moreover, because the mathematical conditions and problems (conclusions) are always interrelated and interdependent, analysis and synthesis tend to penetrate each other, and the two meanings of analysis and synthesis can be used in combination, which can be briefly described as follows:

2. Teaching practice of analytical method and comprehensive method

As the basic methods to solve mathematical problems, the study and teaching of analytical method and comprehensive method can be arranged in three stages.

(1) The first stage: derivation of analytical method and comprehensive method.

The practice of analysis and synthesis and pregnancy can start from the first year of high school. The practical problems of two-step calculation in learning to solve problems can be clearly deduced, from which two different ideas can be summarized: "thinking about conditions according to problems" and "thinking about problems according to conditions". As for the terms "analytical method" and "comprehensive method", it is more appropriate not to mention them.

Generally speaking, the idea of comprehensive method can be combined with reading questions, which is more natural and analytical, and sometimes needs the guidance of teachers.

(2) The second stage: the understanding of analytical methods and comprehensive methods.

Follow-up teaching can make students feel through examples. Some problems are more suitable for thinking from problems, while others are the opposite. Therefore, when showing examples, we might as well cover the conditions first, so that students can only see the problems.

(3) The third stage: the flexible application of analytical methods and comprehensive methods.

Undoubtedly, considering the relationship between part and whole, condition and problem, and accumulating relevant practical experience is an important basis for further learning other problem-solving methods and improving mathematics problem-solving ability, and its learning effect is fundamental and long-term.

In short, listing analysis and synthesis as the basic methods to solve problems has both sufficient theoretical basis and long-term practical support.