Mathematical abstraction is the basic idea of mathematics and an important basis for forming rational thinking. It reflects the essential characteristics of mathematics and runs through the whole process of its emergence, development and application. Mathematical abstraction makes mathematics a highly generalized, accurate, universal and orderly multi-level system.
In the process of the formation of mathematical abstract core literacy, we have accumulated experience from concrete to abstract. Students can better understand mathematical concepts, propositions, methods and systems, understand and grasp the mathematical essence of things through abstraction and generalization, gradually develop the habit of thinking about problems as a whole, and actively use mathematical abstract thinking methods to solve problems in the study of other disciplines.
logical inference
Logical reasoning refers to the thinking process of deducing a proposition from some facts and propositions according to logical rules. It mainly includes two categories: one is reasoning from special to general, and the main forms of reasoning are induction and analogy; One is from general to special reasoning, and the main form of reasoning is deduction.
Logical reasoning is an important way to obtain mathematical conclusions and build a mathematical system, a basic guarantee of mathematical rigor, and a basic thinking quality for people to communicate in mathematical activities.
In the process of forming the core literacy of logical reasoning, students can find problems and put forward propositions; Be able to master the basic form of reasoning and express the process of argumentation; Be able to understand the relationship between mathematical knowledge and build a knowledge framework; Form argumentative, organized and logical thinking quality and enhance mathematical communication ability.
mathematical modeling
Mathematical modeling is a process of abstracting realistic problems mathematically, expressing problems in mathematical language, and establishing models to solve problems with mathematical knowledge and methods. It mainly includes: finding problems, putting forward problems, analyzing problems, establishing models, solving conclusions, verifying results and improving models in actual situations, and finally solving practical problems.
Mathematical model builds a bridge between mathematics and the outside world and is an important form of mathematical application. Mathematical modeling is the basic means to solve practical problems by applying mathematics, and it is also the driving force to promote the development of mathematics.
In the process of forming the core literacy of mathematical modeling, we accumulate experience in solving practical problems with mathematics. Students can find and ask questions in actual situations; Able to establish mathematical model of the problem; Be able to use mathematical knowledge to solve the model, and try to verify and improve the model based on the realistic background; Can improve the application ability and enhance the sense of innovation.