Function and equation thought: Function thought is the abstraction, generalization and refinement of function content at a higher level, which plays an important role in learning equations, inequalities, series, analytic geometry and other contents. Equation thought is the basic idea to solve all kinds of calculation problems and the basis of calculation ability. The idea of combining numbers with shapes: the object of mathematical research is the relationship between numbers and spatial forms, that is, numbers and shapes. Classification and integration thought: classification is the basic logical method in natural science and even social science research. The idea of transformation: turn complex problems into simple problems, turn difficult problems into easy problems, and turn unsolved problems into solved problems. Special and general thinking: from shallow to deep, from phenomenon to essence, from part to whole, from practice to theory, from special to general, and then from general to special. The thought of finiteness and infinity: it is the only way to solve the infinite problem to change the study of infinity into the study of finiteness. The idea of possibility and inevitability: two basic characteristics of random phenomena, one is the randomness of results, and the other is the stability of frequency. Find inevitability in the accident, and then use the law of inevitability to solve the accident.