There are two kinds of mathematical thinking methods, image thinking method and abstract thinking method. Primary school mathematics should cultivate students' thinking ability in images, and lay a solid foundation for developing abstract thinking ability on this basis.
Image thinking method
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.
1, 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. Not only can it be solved through physical demonstration? Walk in opposite directions at the same time, meet? And so on, and pointed out the thinking direction for students. Another example is the problem of planting trees around a round (square) pond If you can do an actual operation, the effect will be much better
In the second grade math textbook, three children meet and shake hands. Every two people shake hands. * * * How many times do I have to shake hands? With what? Put three different digital cards into two digits. * * * How many seats can you put? . 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.
Therefore, primary school math teachers should make as many math teaching (learning) tools as possible, and these teaching (learning) tools should be kept well before use. This can effectively improve classroom teaching efficiency and students' academic performance.
Performance.
2, graphic method
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. For example, some math teachers love to draw mathematical figures by hand, which will inevitably lead to inaccuracies and misunderstandings among students.
3. List 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, positive-negative ratio, sorting out data, multiplication formula, numerical order, etc. are most used in teaching? List method? .
Solving the traditional mathematical problem with list method: the problem of chickens and rabbits in the same cage. Make three tables: the first table is an example. According to the conditions of 20 chickens and rabbits, assuming that there are only 1 chicken, there are 19 rabbits and 78 legs, and list them one by one until you find the desired answer; In the second table, after several enumerations, the rule of counting only and the number of legs is found, thus reducing the enumeration times; The third table is listed from the middle. Because there are 20 chickens and rabbits, each chicken is taken as 10, and then the marketing direction is determined according to the actual data.
Step 4 explore methods
According to a certain direction, trying to explore the law and explore the way to solve problems is called inquiry method. Hua, a famous mathematician in China, said that in mathematics, the difficulty lies not in having a formula to prove, but in how to find it before there is no formula. ? Suhomlinski said: In people's hearts, there is a deep-rooted need to become discoverers, researchers and explorers, and this need is particularly strong in children's spiritual world. ? Learning should be centered on inquiry? , is one of the basic concepts of the new curriculum. When it is difficult for people to turn a problem into a simple, basic, familiar and typical problem, a good way is often to explore and try.
5. Observation
Through a large number of concrete examples, the method of summarizing and discovering the general laws of things is called observation. Pavlov said, "You should learn to observe first. Unless you learn to observe, you will never become a scientist." ?
Elementary school math? Observation? The general contents are as follows: ① the changing law and position characteristics of numbers; ② Relationship between conditions and conclusions; (3) the structural characteristics of the topic; (4) The characteristics of graphics and the relationship between size and position.
6. Typical method
According to the topic, the method of associating the problem-solving laws of the solved typical problems to find out the problem-solving ideas is called the typical method. Typical is relative to universal. To solve mathematical problems, some need general methods and some need special (typical) methods. Such as normalization, multiple ratio and induction algorithm, travel, engineering, eliminating similarities and seeking differences, averaging and so on.
When using the typical method, we must pay attention to:
(1) Master the key and laws of typical materials.
(2) Be familiar with typical materials, and be able to quickly associate them with applicable models, so as to determine the required problem-solving methods.
(3) Typical is associated with skill.
7. Scaling method
The method to solve the problem by estimating the scale of the studied object is called scale method. Scaling method is flexible and ingenious, but it depends on the ability to expand knowledge and imagination.
8. Verification method
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. ? Thousands of teachers in Qian Qian teach people to seek truth, and thousands of students in Qian Qian learn to be human? Mr. Tao Xingzhi's words 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 (sets)
Follow? Rounding method? It is undoubtedly correct to keep the approximate figure, but it is not realistic. The rest of the cloth for making clothes can only be discarded. In teaching, common sense should be valued. How is the quantity of clothes calculated? Tailing method? .
(4) The motivation of verification lies in guessing and questioning. Newton once said: Without bold speculation, there is no great discovery. Guess what? It is also an important strategy to solve the problem. Can develop and stimulate students' thinking? I want to learn? Desire. 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.
Abstract thinking method
The thinking process of reflecting reality with concepts, judgments and reasoning is called abstract thinking, also called logical thinking.
Abstract thinking is divided into formal thinking and dialectical thinking. Objective reality has its relatively stable side, and it can adopt the form of thinking; Objective existence also has its constantly developing and changing side, and we can adopt dialectical thinking. Formal thinking is the basis of dialectical thinking.
Formal thinking ability: analysis, synthesis, comparison, abstraction, generalization, judgment and reasoning.
Dialectical thinking ability: contact development and change, law of unity of opposites, law of mutual change of quality, law of negation of negation.
To cultivate students' preliminary abstract thinking ability in primary school mathematics, the key points are: (1) thinking quality, which should be agile, flexible, connected and creative. (2) In the way of thinking, we should learn to think methodically and systematically. (3) in terms of thinking requirements, the thinking is clear, the cause and effect are clear, the words must be reasonable, and the reasoning is strict. (4) In thinking training, we should require correct application of concepts, proper judgment and logical reasoning.
1, control mode
How to correctly understand and apply mathematical concepts? The common method of primary school mathematics is comparison. According to the meaning of mathematical problems, the method of solving problems through understanding, memorizing, identifying, reproducing and transferring mathematical knowledge is called contrast method.
The thinking significance of this method lies in training students to correctly understand, firmly remember and accurately identify mathematical knowledge.
2. Formula method
Methods to solve problems by using laws, formulas, rules and rules. It embodies the deductive thinking from general to special. Formula method is simple and effective, and it is also a method that primary school students must learn and master when learning mathematics. But students must have a correct and profound understanding of formulas, laws, rules and regulations, and can use them accurately.
3. Comparative method
By comparing the similarities and differences between mathematical conditions and problems, we study the reasons for the similarities and differences, so as to find a solution to the problem, which is the comparative method.
Comparative law should pay attention to:
(1) Finding similarities means finding differences, and finding differences means finding similarities, and being indispensable means being complete.
(2) Find the connection and difference, which is the essence of comparison.
(3) comparisons must be made under the same relationship (same standard). What is this? Compare? The basic conditions of.
(4) Compare the main contents and use them as little as possible? Exhaustive method? By comparison, that will make the focus less prominent.
(5) Because of the rigor of mathematics, comparison must be meticulous, and often a word or a symbol determines the right or wrong conclusion of comparison.
Step 4 classify
As the saying goes, birds of a feather flock together.
According to the similarities and differences of things, things are divided into different categories, which is called classification. Classification is based on comparison. According to the * * * similarity between things, they are grouped into larger classes, and the larger classes are subdivided into smaller classes according to differences.
Classification is to pay attention to the different levels between categories and subcategories to ensure that subcategories in categories are not duplicated, omitted or crossed.
Primary school mathematics learning methods
1, grab the class
Science is mainly based on general study and is not suitable for surprise review. In every class the teacher tells us, we should concentrate, listen carefully and follow the teacher's ideas closely. Listen more and remember the math ideas and learning methods the teacher said. Don't be limited by a certain problem. Like what? Turn to thought? 、? Combination of numbers and shapes? The way of thinking is far more important than the answer to a question.
2. Finish the homework with high quality
The so-called high quality refers to high precision and high speed.
When writing homework, I sometimes repeat the same type of questions. At this time, we should consciously examine the speed and accuracy, and we can have deeper thinking on such problems every time we finish. Such as investigating its content, using mathematical thinking methods, solving problems and skills. In addition, the thinking questions assigned by the teacher should also be carefully completed. If not, don't give up easily. Do you want to carry it forward? Nails? Spirit, meditate whenever you have time, and inspiration always comes to you inadvertently. More importantly, this is an opportunity to challenge yourself.
Success will bring self-confidence, and self-confidence is very important for learning science, and it will also urge you to meet more difficult challenges again and again. Even if you fail, this truth will leave a deep impression on you, so that when you encounter the same type of problems in the future, you will unconsciously reflect on the reasons for the mistakes at that time and how to avoid them.
3. Think hard and ask more questions.
First of all, the laws and theorems given by the teacher should not be just? Do you know? More? You know why? . When you don't know how to study, you should get to the bottom of it. Secondly, you should be skeptical about learning any subject, especially science. Ask questions about the teacher's explanation and the content of the textbook at any time and discuss with the teacher. Don't pile up problems, finish what you do on the same day. In short, thinking and asking questions are the best ways to eliminate hidden dangers in learning.
4. Summarize and compare, and clear your mind.
(1) summary and comparison of knowledge points. After learning each chapter, you should make a frame diagram of the content of this chapter or go through it in your mind to clarify the relationship between them. Similar and confusing knowledge points should be summarized and compared separately, and sometimes they can be distinguished by association.
(2) Summary and comparison of topics. Students can set up their own question bank. One is wrong and the other is accurate. Write down the mistakes in your homework or exam selectively and note them with a red pen. Just read the red pen before the exam. There are also some extremely clever or difficult problems written down, and all the methods and ideas of this problem are also marked in red pen. After a long time, I can sum up some types of problem-solving rules and write them down in red notes. In the end, they will become your precious wealth and be of great help to your math study.
5. Do extracurricular exercises selectively.
For primary school students, after-school time is very precious. Therefore, when you do extracurricular exercises, you should be less and more precise. Every question type has mastered the learning method. As long as you do two or three questions every day, over time, your mind will be much broader.
Correct learning methods are important, but what is more important is the spirit of perseverance and Excellence. As long as you think more, ask more questions and integrate this learning attitude into your life, you will certainly learn every subject well. Believe in yourself and master the learning methods, and you will be full of interest and passion for all your studies.