1. Abstract thinking: Mathematics is an abstract subject, which requires us to abstract general laws from concrete things. For example, when we study geometry, we need to abstract basic elements such as points, lines and surfaces from concrete graphics, and then study the properties of graphics through these basic elements.
2. Logical thinking: Mathematics is a rigorous discipline, which requires us to use logical thinking for reasoning and proof. For example, when we study algebra, we need to use logical thinking to deduce formulas and theorems, and then solve practical problems through these formulas and theorems.
3. Model thinking: Mathematics is a widely used subject, and we need to build mathematical models to solve practical problems. For example, when we study calculus, we need to establish a functional model to describe physical phenomena, and then solve this model through calculus.
4. Change thinking: Mathematics is a flexible subject, which requires us to be good at turning complex problems into simple ones to solve. For example, when we study probability theory, we need to turn complex probability problems into combinatorial mathematics problems to solve.
5. The idea of classified discussion: Mathematics is a clearly classified subject, which requires us to discuss different types of problems in a classified way. For example, when we study series, we need to discuss arithmetic progression and geometric progression separately.