High abstraction is the most essential feature of mathematics, which leads to great generality. Abstraction and generalization constitute the essence of mathematics, and mathematical thinking is abstract and generalized thinking. Therefore, the ability of abstract generalization constitutes the first element and the core of mathematical thinking ability.
Mathematical thinking:
1, thinking is an advanced form of psychological activity.
2. Mathematical thinking is what people usually call mathematical thinking ability, that is, the ability to think and solve problems from a mathematical perspective. For example, reduction, from general to special, from special to general, the idea of function/mapping and so on.
Generally speaking, people with strong mathematical ability basically have two abilities, one is association, and the other is digital sensitivity. The former can link two seemingly unrelated problems, among which structural ability is the most convincing; The latter is the most exposed so-called geek, such as Nash and so on. Of course, there are also two abilities combined.
4. It is clearly pointed out in China's junior and senior high school mathematics teaching curriculum standards that thinking ability mainly refers to: observation, experiment, comparison, guess, analysis, synthesis, abstraction and generalization; Able to use induction, deduction and analogy for reasoning; Will logically and accurately explain their own ideas and opinions; Can use mathematical concepts, ideas and methods to distinguish mathematical relations and form good thinking quality.
Theoretical basis:
1, mathematics is a study of patterns, or a patterned process (abstraction). Mathematics is to abstract a specific problem into a pure mathematical problem. The solution of this abstract problem has practical significance and is helpful to solve practical problems.
2. Therefore, mathematics has two attributes, namely abstraction and reality (or application). When children learn mathematics, they must start with the concrete things they are familiar with in life and gradually start the abstract process of mathematics.
3. It is against the essential attribute of mathematics to teach abstract mathematical operations only by solving specific problems, not starting from specific things and not divorced from specific practice. Children are in the period of germination and initial development of logical thinking, and it is also the period of initial formation of mathematical concepts.
4. Mathematics knowledge has a strong logic and abstraction, and learning mathematics can exercise the logic and abstraction of children's thinking.