1
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.
2
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.
three
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.
four
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.
five
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.
six
Inspection method
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.
seven
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.
The following Xiao Lang introduces several problem-solving skills:
Multiple choice answer strategy
1. exclusion method
Using the information provided by the known conditions and options, three wrong answers are eliminated from the four options, so as to achieve the purpose of correct selection. This is a common method, especially when the answer is a fixed value or has a numerical range, special points can be used instead of verification to exclude it.
2. Special value test method
For a general mathematical problem, in the process of solving it, the problem can be specialized, and the principle that the problem does not hold in special circumstances and does not hold in general circumstances can be used to achieve the purpose of removing the false and retaining the true.
3. The principle of extremism
Analyze the problem to be studied to the extreme state, so that the causal relationship becomes more obvious, thus achieving the purpose of solving the problem quickly. Extreme value is mainly used to find extreme value, range and analytic geometry. Many problems with complicated calculation steps and large amount of calculation can be solved instantly through extreme value analysis.
4. Forward cracking method
Using mathematical theorems, formulas, rules, definitions and meanings, the method of obtaining results through direct calculus and reasoning.
5. Reverse verification method
The method of substituting the options into the stem of the question for verification, thus negating the wrong options and getting the correct answer.
6. If it is difficult, it is illegal.
When it is difficult to solve the problem from the front, we can gradually find out the qualified conclusions from the options, or draw conclusions from the opposite side.
7. Number-shape combination method
According to the conditions of the topic, make a graph or image that conforms to the meaning of the topic, and get the answer through simple reasoning or calculation with the help of the intuition of the graph or image. The advantage of the combination of numbers and shapes is intuitive, and you can even measure the result directly with a square.
8. Recursive induction
Through the conditional reasoning of the topic, we can find the law and sum up the correct answer.
9. Characteristic analysis method
Analyze the characteristics of questions and options, find the rules and summarize the correct judgment methods.
10. Appraisal selection method
Some problems cannot (or are not necessary) be accurately calculated and judged due to the limitation of subject conditions. At this time, we can only get the correct judgment method from the surface by means of estimation, observation, analysis, comparison and calculation.
fill (up) a vacancy
Math fill-in-the-blank questions are mostly computational (especially inferential calculation) and conceptual (qualitative) judgment questions, which can only be answered by actual calculation or logical deduction and judgment according to rules.
The basic strategy to solve the fill-in-the-blank problem is to work hard accurately, skillfully and quickly. Commonly used methods include direct method, specialization method, multi-line combination method, equivalent transformation method and so on.
1 direct method
This is the basic method to solve the fill-in-the-blank problem, starting directly from the problem setting conditions, using the knowledge of definition, theorem, nature, formula, etc., and directly obtaining the result through the processes of deformation, reasoning and operation.
2. Specialized methods
When the conclusion of the fill-in-the-blank question is unique or its value is fixed, we only need to replace the parameter variables in the question with special values (or special functions, special angles, special series, special positions of graphs, special points, special equations, special models, etc.). ) come to a conclusion.
3. Number-shape combination method
With the help of the intuitive shape of graphics and the combination of numbers and shapes, the method of making quick judgments is called image method. Venn diagram, trigonometric function lines, images of functions and curves of equations are all commonly used graphics.
4. Equivalent transformation method
By "simplifying complexity and turning strangeness into familiarity", the problem is equivalently transformed into an easy-to-solve problem and the correct result is obtained.