Just take three socks,
You can guarantee to take out a pair of socks of the same color.
There are only red and blue socks in the box.
If you take out a blue sock, there are two pairs of red socks.
If you take out two blue socks, there is a red sock.
If you don't take out blue socks, take out three red socks.
These three results ensure the production of a pair of socks with the same color.
Methods and skills of solving mathematical problems.
Mathematics in primary and secondary schools, including Olympic Mathematics, needs appropriate methods in learning. With good methods and ideas, you may get twice the result with half the effort! Then what methods can be based on? I hope everyone can use these thinking and methods to solve problems!
Thinking in images means that people use thinking in images to understand and solve problems. Its thinking foundation is concrete image, and its thinking process is developed from concrete image.
The main means of thinking in images are objects, figures, tables and typical image materials. Its cognitive feature is that it is average in individual performance and always retains its intuition about things. Its thinking process is represented by representation, analogy, association and imagination. Its thinking quality is manifested in the active imagination of intuitive materials, the processing and refining of appearances, and then the essence, law or object are revealed. Its thinking goal is to solve practical problems and improve thinking ability in solving problems.
Physical demonstration method
Demonstrate the conditions and problems of mathematical problems and the relationship between them with the physical objects around you, and analyze and think on this basis to find a solution to the problem.
This method can visualize the content of mathematics and concretize the quantitative relationship. For example: the problem of meeting in mathematics. Through physical demonstration, we can not only solve the terms of "simultaneity, relativity and encounter", but also point out the thinking direction for students.
In the second grade math textbook, "Three children meet and shake hands, every two people shake hands once, and * * * shakes hands several times", "How many digits can * * * put into two digits with three different digital cards". If such permutation and combination knowledge is demonstrated in kind, it is difficult to achieve the expected teaching goal in primary school teaching.
Especially some mathematical concepts, if there is no physical demonstration, primary school students can't really master them. Learning the area of rectangle, understanding the cuboid and the volume of cylinder all depend on physical demonstration as the basis of thinking.
diagram
With the help of intuitive graphics, we can determine the direction of thinking, find ideas and find solutions to problems.
Graphic method is intuitive and reliable, easy to analyze the relationship between numbers and shapes, not limited by logical deduction, flexible and open-minded. However, the graphic method depends on the reliability of human processing and arrangement of representations. Once the graphic method is inconsistent with the actual situation, it is easy to make the association and imagination on this basis appear fallacy or go into misunderstanding, which will eventually lead to wrong results.
In classroom teaching, we should use graphic methods to solve problems. Some topics, pictures come out, and the results come out; Some questions have good pictures, and students will understand the meaning of the questions; For some problems, drawing can help to analyze the meaning of the problem and inspire thinking, as an auxiliary means of other solutions.
Tabulation method
The method of analyzing, thinking, looking for ideas and solving problems through lists is called list method. List method is clear, easy to analyze and compare, prompt the law, and is also beneficial to memory.
Its limitation lies in the small scope of solution and narrow applicable problems, which are mostly related to finding or displaying rules. For example, "list method" is mostly used in the teaching of positive and negative proportion content, sorting out data, multiplication formula, numerical order and so on.
proof technique
Is your result correct? You can't just wait for the teacher's judgment. It is important to have a clear mind and a clear evaluation of your own study, which is an essential learning quality for excellent students.
Verification method has a wide range of applications and is a basic skill that needs to be mastered skillfully. Through practical training and long-term experience accumulation, I constantly improve my verification ability and gradually develop a good habit of being rigorous and meticulous.
(1) is verified in different ways. Textbooks have repeatedly suggested that subtraction is tested by addition, subtraction, multiplication and division.
(2) Substitution test. Is the result of solving the equation correct? See if both sides of the equal sign are equal by substitution. You can also use the result as a condition for reverse calculation.
(3) Whether it is practical. Mr. Tao Xingzhi's words, "A thousand teachers teach people to seek truth, and ten thousand teachers learn to be human beings", should be implemented in teaching. For example, it takes 4 meters of cloth to make a suit, and the existing cloth is 3 1 meter. How many suits can you make? Some students do this: 3 1÷4≈8 (set)
It is undoubtedly correct to keep the approximate figures according to the rounding method, but it is not realistic, and the rest of the cloth for making clothes can only be discarded. In teaching, common sense should be valued. The approximate calculation of the number of clothes sets should use the "tail cutting method".
(4) The motivation of verification lies in guessing and questioning. Newton once said, "Without bold speculation, there will be no great discovery." "Guess" is also an important strategy to solve the problem. It can develop students' thinking and stimulate the desire of "I want to learn". In order to avoid guessing, we must learn to verify. Verify whether the guessing result is correct and meets the requirements. If it does not meet the requirements, adjust the guess in time until the problem is solved.