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 children 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 children must learn and master when learning mathematics. But children must have a correct and profound understanding of formulas, laws, rules and rules, 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) Comparison must be conducted under the same relationship (same standard), which is the basic condition of "comparison".
(4) To compare the main contents, try to use the "exhaustion method" as little as possible, which will make the key points 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
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.
5. Analytical method
A way of thinking that decomposes the whole into parts, decomposes complex things into various parts or elements, and studies and deduces these parts or elements is called analytical method.
Foundation: The whole is made up of parts.
Thinking: In order to better study and solve the whole, first separate all parts or elements of the whole, and then compare the requirements separately, so as to straighten out the problem-solving ideas.
That is to say, starting from the problem to be solved, the two required conditions are correctly selected and deduced in turn until the problem is solved. This problem-solving model is "tracing the cause from the result". Analytical method is also called inverse method. "Branch diagram" is often used to illustrate this idea.
6. Integrated approach
A way of thinking that combines all parts or aspects or elements of an object into an organic whole to study, deduce and think is called comprehensive method.
When solving mathematical problems by comprehensive method, each problem is usually regarded as a part (or element). After analyzing the internal relationship between each part (or element) layer by layer, the problem requirements are gradually deduced. Therefore, the problem-solving mode of comprehensive method is based on cause and cause, also called forward deduction method. This method is suitable for mathematical problems with few known conditions and simple quantitative relationship.
7. Equation method
Unknown numbers are represented by letters, and expressions (equations) containing letters are listed according to the equivalence relation. Column equation is an abstract and generalized process, and solving equation is a deductive process. The biggest feature of equation method is that the unknown quantity is regarded as the known quantity and participates in formulation and operation, which overcomes the deficiency that arithmetic method must avoid the formulation of knowledge. It is beneficial to the transformation from known to unknown, thus improving the efficiency and accuracy of solving problems.
8, parameter method
A method of expressing related quantities by letters or numbers that only participate in formulas and operations without solving them, and listing formulas according to the meaning of the questions is called parametric method. Parameters are also called auxiliary unknowns and intermediate variables. Parametric method is the product of the extension and expansion of equation method.
9. Exclusion method
The result of eliminating opposition is called exclusion.
The logical principle of exclusion is that everything has its opposite. In all kinds of right and wrong results, excluding all wrong results, the rest can only be correct results. This method is also called exclusion, screening or disproof. This is an indispensable method of formal thinking.
1 1, reduction method
Through some transformation process, the method to solve the problem by simplifying it into a typical problem is called simplification. Transformation is an important way of knowledge transfer and the first step to expand and deepen cognition. The logical principle of reduction is that things are generally related. Transformation is a common dialectical thinking method.