1. Mathematical abstraction
Mathematical abstraction refers to the abstraction of quantitative relations and spatial forms in order to obtain the literacy of mathematical research objects. It mainly includes: abstracting the relationship between mathematical concepts and concepts from the relationship between quantity and shape, abstracting general laws and structures from the specific background of things, and expressing them in mathematical language.
Mathematical abstraction is the basic idea of mathematics, an important basis for forming rational thinking, which 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.
Mathematical abstraction is mainly manifested in obtaining mathematical concepts and rules, putting forward mathematical propositions and models, forming mathematical methods and ideas, and understanding mathematical structures and systems.
Through the study of senior high school mathematics curriculum, students can abstract mathematical concept propositions, methods and systems in situations, and accumulate activity experience from concrete to abstract; Develop the habit of thinking in daily life and practice, grasp the essence of things, and control complexity with simplicity; Thinking and solving problems with mathematical abstract thinking.
2. Logical reasoning
Logical reasoning refers to the completion of deducing other propositions from some facts and propositions according to 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.
Logical reasoning is mainly manifested as: mastering the basic forms and rules of reasoning, finding problems and putting forward propositions, exploring and expressing the argumentation process, understanding the proposition system and making logical expression and communication.
Through the study of high school mathematics course, students can master the basic form of logical reasoning and learn logical thinking; Be able to grasp the relationship between things and grasp the context of their development under more complicated circumstances; Form an argumentative, organized and logical thinking quality and rational spirit, and enhance communication skills.
3. Mathematical modeling
Mathematical modeling is the result of mathematical abstraction of real problems, expression of problems in mathematical language and establishment of models to solve problems in mathematical methods. The process of mathematical modeling mainly includes: finding problems, raising problems, analyzing problems, establishing models, determining parameters, calculating solutions, testing results, improving models, 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.
Mathematical modeling mainly includes: finding and putting forward problems, establishing and solving models, testing and perfecting models, and analyzing and solving problems.
Through the study of mathematics course in senior high school, students can consciously express the real world in mathematical language, find problems, ask questions, and realize the relationship between mathematics and reality: learn to use mathematical models to solve practical problems, accumulate mathematical practical experience, understand the role of mathematical models in science, society, engineering technology and many other fields, enhance practical ability, and enhance innovative consciousness and scientific spirit.
imagine
Intuitive imagination refers to the quality of perceiving the shapes and changes of things with the help of geometric intuition and Kong Wen's imagination, and using spatial forms, especially graphics, to understand and solve mathematical problems. It mainly includes: understanding the position relationship, morphological change and motion law of things with the help of spatial form; Describe and analyze mathematical problems with graphics; Establish the relationship between shape and number, establish an intuitive model of mathematical problems, and explore solutions.
Intuitive imagination is an important means to find and put forward problems, analyze and solve problems, and it is the thinking basis for exploring and forming argumentation ideas, conducting mathematical reasoning and constructing abstract structures.
Intuitive imagination is mainly manifested in establishing the relationship between shape and number, describing problems with geometric figures, helping geometry to understand problems intuitively and using spatial imagination to understand things.
Through the study of high school mathematics course, students can improve the ability of combining numbers with shapes and develop geometric intuition and spatial imagination; Enhance the consciousness of thinking with geometric intuition and spatial imagination; Form a mathematical intuition and understand the essence of things in its context.
5. Mathematical operation
Mathematical operation refers to solving mathematical problems according to the operation rules on the basis of clear operation objects. It mainly includes: understanding the operation object, mastering the migration law, exploring the operation idea, selecting the operation method, designing the operation program and obtaining the operation result.
Mathematical operation is the basic means to solve mathematical problems. Mathematical operation is deductive reasoning and the basis for computer to solve problems.
Mathematical operation is mainly manifested as: understanding the object of operation, mastering the operation rules, exploring the operation ideas and obtaining the operation results.
Through the study of high school mathematics course, students can further develop their mathematical operation ability; Effectively solve practical problems with the help of operation methods; Promote the development of mathematical thinking through operation, form the quality of standardized thinking, and cultivate the scientific spirit of being meticulous, rigorous and realistic.
6. Data analysis
Data analysis refers to obtaining data from the research object, sorting, analyzing and inferring the data by mathematical methods, and forming knowledge literacy about the research object. The process of data analysis mainly includes: collecting data, sorting out data, extracting information, establishing models and drawing conclusions.
Data analysis is an important mathematical technology to study random phenomena, the main method of mathematical application in the era of big data, and also the main mathematical method in the related fields of "internet plus". Data analysis has penetrated into all aspects of science, technology, engineering and modern social life.
Data analysis mainly includes: collecting and arranging data, understanding and processing data, obtaining and interpreting conclusions, and summarizing and forming knowledge.
Through the study of senior high school mathematics courses, students can improve their awareness and ability to obtain valuable information and make quantitative analysis; Adapt to the needs of digital learning and enhance the awareness of expressing real questions based on data. Form the thinking quality of knowing things through data; Relying on data accumulation to explore the essence, correlation and law of things.