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The problem-solving methods of mathematics have developed with the deepening of the study of mathematical objects. Teachers can further master middle school mathematics textbooks, practice the basic skills of problem solving, improve problem-solving skills, accumulate teaching materials, and improve their professional level and teaching ability. The problem-solving methods introduced below are the most commonly used in junior high school mathematics, and some of them are also required to be mastered in the middle school syllabus.
1. Matching method The so-called formula is to use the method of identity deformation of an analytical formula to match some of the terms into the sum form of one or several polynomials to the power of positive integers. The method of solving a mathematical problem through a recipe is called the matching method. Among them, the most used is the perfect flat method.
The matching method is an important method of identity deformation in mathematics, and it is widely used in factorization, simplifying radicals, solving equations, proving equations and inequalities, finding extreme values and analytic formulas of functions, etc. 2. Factorization Factorization is the form of multiplying a polynomial into several integer products. Factorization is the basis of identity deformation, which plays an important role as a powerful tool in mathematics and a mathematical method in solving problems in algebra, geometry, trigonometry, etc.
There are many methods of factorization, in addition to the method of extracting common factors, formula method, group decomposition method, cross multiplication method, etc., which are introduced in middle school textbooks, there are also methods such as using split terms to add terms, finding root decomposition, commutation, pending coefficients, etc. 3. The commutation method is a very important and widely used method of solving problems in mathematics. We usually call unknowns or variables as elements, and the so-called commutation method is to replace a part of the original formula with a new variable or transform the original formula in a more complex mathematical formula, so that it is simplified and the problem is easy to solve.
4. Discriminant formula method and Vedic theorem The discriminant discrimination of the root of the quadratic equation ax2+bx+c=0 (a, b, c belong to r, a≠0), =b2-4ac, is not only used to determine the properties of the root, but also as a method of problem solving, it has a very wide range of applications in algebraic deformation, solving equations (groups), solving inequalities, studying functions and even geometry and trigonometric operations. Vedic theorem finds another root in addition to knowing one root of a quadratic equation; In addition to simple applications such as finding the sum and product of two numbers, you can also find the symmetry function of the root, calculate the symbol of the root of the quadratic equation, solve the symmetry equation, and solve some problems about the quadratic curve. 5. Pending coefficient method When solving mathematical problems, if the desired result is judged to have a certain definite form, which contains some undetermined coefficients, and then the equation about the undetermined coefficients is listed according to the problem conditions, and finally the value of these undetermined coefficients is solved or a certain relationship between these undetermined coefficients is found, so as to solve the mathematical problem, this solution method is called the undetermined coefficient method.
It is one of the commonly used methods in middle school mathematics.
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