Mathematics learning thinking

Reverse thinking. Contrary to the thinking process of inferring conclusions from conditions, giving a conclusion or answer first requires various conditions to make it hold. For example, given a concentration problem, we list an equation; Conversely, given an equation, a concentration problem can be worked out. The latter belongs to reverse thinking.

Case-making thinking Some conditions or conclusions are often illustrated by examples, and their irrationality is often proved by counterexamples. Constructing examples according to needs is often a thinking process of returning from abstraction to concreteness and comprehensively applying all kinds of knowledge. For example, try to find a function whose inverse function is equal to itself.

Inductive thinking. Through observation and experiment, the general law is put forward in several examples.

Open mind. That is, only the object or certain conditions of the research question are given, and the problems or conclusions that can be inferred from it are explored by the students themselves. For example, let students observe the image of y = sinx, tell its main properties and explain them one by one.