Mathematical problem-solving methods are developed with the in-depth study of mathematical objects. Teachers studying exercises and mastering problem-solving methods can promote teachers to further master middle school mathematics textbooks, practice basic problem-solving skills, improve problem-solving skills, accumulate teaching materials, and improve their professional level and teaching ability. The following are the most commonly used methods to solve problems in junior high school mathematics, and some methods are also required to be mastered in the middle school syllabus. 1, the so-called formula of matching method is to match some items of an analytical formula into the sum of positive integer powers of one or more polynomials by means of constant deformation. The method of solving mathematical problems with formulas is called matching method. Among them, the most common method is to make it completely flat. Matching method is an important method of constant deformation in mathematics. It is widely used in factorization, simplifying roots, solving equations, proving equality and inequality, finding extreme values of functions and analytical expressions. 2. Factorization Factorization is to convert a polynomial into the product of several algebraic expressions. Factorization is the basis of identity deformation. As a powerful mathematical tool and method, it plays an important role in solving algebra, geometry and trigonometry problems. There are many methods of factorization, such as extracting common factors, formulas, grouping decomposition, cross multiplication and so on. Middle school textbooks also introduce the use of decomposition and addition, root decomposition, exchange elements, undetermined coefficients and so on. 3. method of substitution method of substitution is a very important and widely used problem-solving method in mathematics. We usually refer to unknowns or variables as elements. The so-called method of substitution is to replace a part of the original formula with new variables in a complicated mathematical formula, thus simplifying it and making the problem easy to solve. 4. Discriminant Method and Discriminant of Vieta Theorem The unary quadratic equation ax2+bx+c=0(a, B, C belongs to the root of R, a≠0), and△ = B2-4ac is not only used to judge the properties of the root, but also used as a problem-solving method to solve algebraic deformation, equations (groups), inequalities, functions and even geometry. Vieta's theorem not only knows one root of a quadratic equation, but also finds another root. Knowing the sum and product of two numbers, we can find the symmetric function of the root, calculate the sign of the root of quadratic equation, solve the symmetric equation and solve some problems about quadratic curve. , has a very wide range of applications. 5. When solving mathematical problems, the undetermined coefficient method is called the undetermined coefficient method. If it first judges that the obtained results have a certain form and contain some undetermined coefficients, then it lists the equations about the undetermined coefficients according to the problem setting conditions, and finally finds out the values of these undetermined coefficients or finds out some relationship between them, thus solving mathematical problems. It is one of the commonly used methods in middle school mathematics. 6. Construction method When solving problems, we often use this method to construct auxiliary elements through the analysis of conditions and conclusions. It can be graphs, equations (groups), equations, functions, equivalent propositions, etc. And establish a bridge connecting conditions and conclusions, so that the problem can be solved. This mathematical method of solving problems is called construction method. Using construction method to solve problems can make algebra, trigonometry, geometry and other mathematical knowledge permeate each other, which is beneficial to solving problems. 7. The reduction to absurdity is an indirect proof method. It is a way to put forward a hypothesis contrary to the conclusion of the proposition, and then proceed from this hypothesis and lead to contradictions through correct reasoning, thus denying the opposite hypothesis and affirming the correctness of the original proposition. The reduction to absurdity can be divided into reduction to absurdity (with only one opposite conclusion) and exhaustive reduction to absurdity (with more than one opposite conclusion). The steps to prove a proposition by reduction to absurdity can be roughly divided into: (1) reverse design; (2) return to absurdity; (3) conclusion. Anti-design is the basis of reduction to absurdity. In order to make correct anti-design, we need to master some commonly used negative expressions, such as: yes/no; Existence/non-existence; Parallel/non-parallel; Vertical/not vertical; Equal to/unequal to; Large (small) inch/small (small) inch; Both/not all; At least one/none; At least n/ at most (n-1); At most one/at least two; Only/at least two. Reduction to absurdity is the key to reduction to absurdity. There is no fixed model in the process of derivation of contradiction, but it must be based on reverse design, otherwise the derivation will become passive water and trees without roots. Reasoning must be rigorous. There are the following types of contradictions: contradictions with known conditions; Contradicting with known axioms, definitions, theorems and formulas; There are dual contradictions; Contradictions 8. Area method The area formula in plane geometry and the property theorems related to area calculation derived from the area formula can be used not only to calculate the area, but also to prove that plane geometry problems sometimes get twice the result with half the effort. The method of proving or calculating plane geometric problems by using area relation is called area method, which is commonly used in geometry. The difficulty in proving plane geometry problems by induction or analysis lies in adding auxiliary lines. The characteristic of area method is to connect the known quantity with the unknown quantity by area formula, and achieve the verification result through operation. Therefore, using the area method to solve geometric problems, the relationship between geometric elements becomes the relationship between quantities, and only calculation is needed. Sometimes there may be no auxiliary lines, even if auxiliary lines are needed, it is easy to consider. 9. Geometric transformation method In the study of mathematical problems, the transformation method is often used to transform complex problems into simple problems and solve them. The so-called transformation is a one-to-one mapping between any element of a set and the elements of the same set. The transformation involved in middle school mathematics is mainly elementary transformation. There are some exercises that seem difficult or even impossible to start with. We can use geometric transformation to simplify the complex and turn the difficult into the easy. On the other hand, the transformed point of view can also penetrate into middle school mathematics teaching. It is helpful to understand the essence of graphics by combining the research of graphics under isostatic conditions with the research of motion. Geometric transformation includes: (1) translation; (2) rotation; (3) symmetry. 10. Method of solving objective questions Multiple-choice questions are a kind of questions that give conditions and conclusions and require correct answers according to certain relationships. Multiple-choice questions are ingenious in conception and flexible in form, which can comprehensively examine students' basic knowledge and skills, thus increasing the capacity and knowledge coverage of test papers. Fill-in-the-blank question is one of the important questions in standardized examination. Like multiple-choice questions, it has the advantages of clear test objectives, wide knowledge coverage, accurate and fast marking, and is conducive to examining students' analytical judgment and calculation ability. The difference is that the fill-in-the-blank question does not give an answer, which can prevent students from guessing the answer. In order to solve multiple-choice questions and fill-in-the-blank questions quickly and correctly, in addition to accurate calculation and strict reasoning, there are also methods and skills to solve multiple-choice questions and fill-in-the-blank questions. The following examples introduce common methods. (1) Direct deduction method: Starting directly from the conditions given by the proposition, using concepts, formulas, theorems, etc. Carry out reasoning or operation, draw a conclusion and choose the correct answer. This is the traditional method of solving problems, which is called direct deduction. (2) Verification method: find out the appropriate verification conditions from the questions, and then find out the correct answer through verification, or substitute alternative answers into the conditions for verification to find out the correct answer. This method is called verification method (also called substitution method). This method is often used when encountering quantitative propositions. (3) Special element method: substitute appropriate special elements (such as figures or numbers) into the conditions or conclusions of the topic, so as to get the solution. This method is called the special element method. (4) Exclusion and screening method: for multiple-choice questions with only one correct answer, according to mathematical knowledge or reasoning and calculus, the incorrect conclusion is excluded and the remaining conclusions are screened, so that the solution to make the correct conclusion is called exclusion and screening method. (5) Graphic method: The method of judging and making a correct choice through the properties and characteristics of the graphics or images that meet the conditions of the topic is called graphic method. Graphic method is one of the common methods to solve multiple-choice questions. (6) Analysis method: directly through the conditions and conclusions of multiple-choice questions, make detailed analysis, induction and judgment, so as to select the correct result, which is called analysis method.