1. Abstract:
Mathematics is a unique symbol system created by human beings. This symbol is a symbol, which comes from concrete things in the real world and is the result of human brain's induction and generalization of objective reality, but it is different from concrete things and higher than reality. For example, numbers are symbols of equivalent sets.
What is an equivalent set? Sets with the same number of elements are called equivalent sets. For example, five people, five cats, five keys, five trees, five bars of soap, five rooms, five applause and so on. , can be represented by the number 5, that is, 5 can represent any set with the number 5. For another example, form comes from the shapes of various objects in the objective world. Geometric figures in mathematics are the result of a high generalization of the shapes of objects in the real world.
For another example, the formula 1+ 1=2 indicates that all elements are the combination and result of two groups of 1. Real life is the source of mathematical abstraction, and mathematics comes from life and is higher than life. This tells us that children must learn mathematics from the concrete things they are familiar with in life and gradually begin the abstract process of mathematics. This is also the requirement of "feeling the quantitative relationship of things from life and games" in the outline.
2. Logic:
Logic usually means that people think about problems and deduce reasonable conclusions or laws from some known conditions. It usually arranges a bunch of chaotic and unrelated things according to certain laws and rules, and establishes a certain relationship, that is, logical relationship.
Logical thinking is a process in which people reflect reality with the help of concepts, judgments and reasoning, and this process is inseparable from the knowledge and understanding of the logical relationship of things. Mathematics is a unique language of human beings and a symbol system, which is characterized by replacing complex things with simple symbols and concrete relationships with abstract logic.