What is the connection and difference between mathematical thinking and olympiad?
① When dealing with many problems in life and work, we need to analyze, judge, speculate and even regulate the development of things. With internal relations and data, there will be mathematical thinking. Whether it is an Olympic math problem or not, almost every math problem needs logical thinking, and it can't be said by temper. I think this question is equal to several.
② Mathematical knowledge is a mathematical concept and conclusion. Methods include measurement, calculation, statistics and comparison. The purpose is to analyze and explore problems with mathematical thought, and the essence is a kind of thinking. Can mathematical thought and mathematical knowledge system be separated?
Example-classification idea
Classification is the most basic and widely used idea in mathematics. Classified according to scientific and reasonable standards and studied one by one.
Preschool children will know to find out different kinds of goods.
In primary school, we divide numbers into natural numbers, decimals, fractions and percentages.
The classification idea should be used in the classification enumeration, geometric counting, arrangement and combination of Olympic numbers.
Discussion on various classifications in junior high school.
Can olympiad help children improve their thinking ability?
Thinking is the angle and way for a person to look at and think about objective existence. Although the complexity and diversity of objective existence have far exceeded our cognitive ability, we can summarize, summarize and refine it with the participation of thinking. How to develop thinking? This is a very complicated problem.
Then, can an ordinary child cultivate some logical thinking and creative thinking ability in the process of learning Olympic Mathematics?
In this respect, everyone's experience is naturally different.
Have positive experiences and opinions:
A former Olympic math student and now an Olympic math teacher said: With my personal experience, Olympic math has brought me a brand-new way of thinking. I will also pass this way on to the children I have taught. The essence of Olympic Mathematics is to encourage students to explore thinking, and the purpose of the topic "tricky" is to encourage students to solve problems in ways that he can't learn in class.
I remember when I was studying Olympic Mathematics, the teacher would write a question in class and then give everyone half an hour. When he goes out for a walk, he will come back and ask, Is there a trick? Then everyone will say what to do, and then he will challenge everyone's ideas. Then people will think that if someone solves it, they will be encouraged to think of other solutions. This exploratory way of thinking has benefited me a lot.
Another teacher said: I'm opposed to learning Olympic Mathematics, but I am very supportive of capable children to play it, which is really helpful to improve their thinking. Everyone should practice running to exercise, but not everyone should take part in the track and field training of the Olympic Games. Under the current situation of China Olympic Mathematics, if you want to play Olympic Mathematics, you should stay away from those remedial classes that are oriented to further studies (is there? )。
A parent said: Although his son is not particularly clever, it is easier to understand with a little guidance. It was not painful to learn, and later entered the experimental class of key middle schools, which made great contributions to the Olympic Mathematics. Therefore, for him, the greatest help of Olympic Mathematics is to easily enter key middle schools. As for how far he can go, it depends on the future.
But on the whole, most people are critical of the China Olympic Games (at least in the media).
The focus of criticism is: The essence of China's Olympic Mathematics is to take a math class, but he learned something outside the syllabus and taught some methods that are not used at ordinary times. This is an exam. People who benefit from these Olympic math industries often teach problem-solving routines step by step, and the mathematical knowledge they teach is not systematic, but chaotic so-called "skills." It is very easy for children to misunderstand mathematics, thinking that mathematics is intelligence, which can not only improve their thinking, but also destroy the real creative thinking.
An Olympic math teacher said: I have been tutoring children who have passed the Olympic math test for half a year in Beijing. Under the oppression of China's exam-oriented education system, the original intention of the Olympic Mathematics simply can't be reflected. In terms of teaching methods, although the textbooks compiled by some educational institutions can greatly enliven the teaching content, they are still inseparable from the cramming teaching mode. Developing students' thinking is pure nonsense.
But objectively speaking, for gifted students, Olympic Mathematics can really improve their abstract thinking ability. Under the current Olympic environment in China, I can't comment on whether we can cultivate elite talents in mathematics. However, what I see is a very painful consequence of the Olympic Games for the whole people, which makes countless children misunderstand, fear and hate mathematics, a very interesting and important science!
A summary of the types of Olympic mathematical thinking training in primary schools
Conversion type
This is a form of thinking, which changes the problem from one form to another when it is blocked, making it simpler, clearer and easier to solve. In teaching, this kind of training can greatly improve students' problem-solving ability. For example, there is a rule for selling fish. Anyone who buys fish must buy half of the fish in the basket and add another half. According to this selling method, after four people buy it, the fish in the basket is used up. How many fish are there in the basket? For some students who have not been trained in transformational thinking, this question will feel at a loss. Even students with a good foundation can only solve complex equations.
But after the training of transforming thinking, students become smarter. They know that buying fish is converted into 1 person, and obviously there are 1 fish. Then it is converted into 2 people, so there are 3 fish; Three more people, then seven; Four more people, then 15.
System type
This is an advanced holistic thinking form, which considers things or problems as a system from different levels or different angles. In addition to comprehensive application problems, senior three can also compile many intellectual training questions to cultivate students' systematic thinking ability. For example: 123456789, under the premise of not changing the order (that is, several adjacent numbers can be combined into one number, but not reversed), add and subtract symbols between them to make the operation result equal to 100. A problem like this involves the training of systematic thinking. Teachers can guide students to regard 10 as a system and consider it from different levels. Level 1: Find the nearest number to 100, that is, 89 dogs are smaller than 1 1 00. Level 2: Find the nearest number 1 1, which is obviously the previous 12. Level 3: The whole procedure for solving the multiple L problem is as follows:12+3+4+5-6-7+89 =100.
Enhanced type
This is a jumping, lively and highly transferable thinking form. Teachers can train students through quick questions and answers. For example, what is the sum of three fives? Students answer: 5+5+5= 15 or 5×3= 15. The teacher asked again: What is the product of three fives? Student's answer: 5×5×5= 125. Then ask: What is the product of 3 and 5? Answer: 3×5= 15, or 5×3= 15. Through this quick question-and-answer training, it is found that students' thinking is more and more active, flexible and accurate.
Analogy type
This is a form of thinking to identify the similarity of parallel things. This kind of training can cultivate the accuracy of students' thinking. For example:
(1) Jinhu Grain Store delivered 6 tons of rice. 1/4 tons is less than the flour shipped. How many tons of flour were shipped?
② Jinhu Grain Store delivered 6 tons of rice, less than the flour delivered 1/4. How many tons of flour were delivered?
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8. Primary school mathematics application problems and mathematical thinking teaching methods
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