① Common mathematical methods: collocation method, method of substitution method, undetermined coefficient method, mathematical induction method, parameter method, elimination method, etc.
② Mathematical logic methods: analysis, synthesis, induction, induction, deduction, etc.
③ Mathematical thinking methods: observation and analysis, generalization and abstraction, analysis and synthesis, special and general, analogy, induction and deduction.
④ Common mathematical ideas: function and equation, combination of numbers and shapes, classified discussion and transformation.
Compared with the basic knowledge of mathematics, mathematical thinking method has a higher status and level. Mathematical knowledge is the content of mathematics, which can be recorded and described by words and symbols. As time goes on, memory declines and may be forgotten in the future. Mathematical thinking method is a kind of mathematical consciousness, which can only be understood and applied and belongs to the category of thinking. It is used to understand, deal with and solve mathematical problems and master mathematical thinking methods. Not for a while, but for a lifetime. Even if the knowledge of mathematics is forgotten, the mathematical thinking method still works for you.
Among the mathematical thinking methods, the basic mathematical method is the embodiment of mathematical thinking and mathematical behavior, which has the characteristics of patterning and operability and can be chosen as a specific means to solve problems. Mathematical thought is the soul of mathematics, and it and the basic methods of mathematics are often acquired while learning and mastering mathematical knowledge.
It can be said that "knowledge" is the foundation, "law" is the means and "thinking" is deepening. The core of improving mathematics quality is to improve students' understanding and application of mathematical thinking methods, and the comprehensive embodiment of mathematics quality is "ability".
In order to help students master the golden key and thinking method of solving problems, this book first introduces the basic mathematical methods commonly used in the college entrance examination: collocation method, method of substitution method, undetermined coefficient method, mathematical induction method, parameter method, elimination method, induction method, analytical synthesis method, special and general method, analogy and induction method, observation and experiment method, and then introduces the mathematical ideas commonly used in the college entrance examination: function and equation thought, combination of numbers and shapes and so on. Finally, the problem-solving strategies and several hot issues in the college entrance examination are discussed, and the college entrance examination papers in recent years are provided in the appendix.
In each section, the method or problem is first described comprehensively, and then it appears in the form of three problem groups. Reproducible problem group is a set of simple reproduction methods for choosing fill-in-the-blank questions, and demonstrative problem group gives detailed answers and analysis, demonstration methods and questions. The consolidation problem group aims to check the effect of learning and play a consolidation role. The exercise selection of each problem group is also integrated into the mathematical knowledge of algebra, trigonometry and geometry as far as possible.