1, mathematical abstraction
Mathematical abstraction refers to the thinking process of obtaining mathematical research objects by giving up all physical attributes of things. 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 with mathematical symbols or mathematical terms.
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.
2. Logical reasoning
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.
3. 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.
4. Intuitive imagination
Intuitive imagination refers to the process of perceiving the shape and change of things with geometric intuition and spatial imagination, and understanding and solving mathematical problems with graphics. It mainly includes: understanding the position relationship, morphological change and motion law of things with the help of space; Describe and analyze mathematical problems with graphics; Establish the connection between form and number; Construct an intuitive model of mathematical problems and explore solutions.
Intuitive imagination is an important means to discover and put forward mathematical problems, analyze and solve mathematical problems, and it is the thinking basis for exploring and forming argumentation ideas, logical reasoning and constructing abstract structures.
In the process of forming the core literacy of intuitive imagination, students can further develop their geometric intuition and spatial imagination, enhance their awareness of graphic thinking and spatial imagination, enhance their ability to combine numbers with shapes, understand the essence of things and cultivate innovative thinking.
5. Mathematical operations
Mathematical operation refers to the process of solving mathematical problems according to the operation rules on the basis of clear operation objects. It mainly includes: understanding the operation object, mastering the operation law, exploring the operation direction, selecting the operation method, designing the operation procedure and obtaining the operation result.
Mathematical operation is the basic form of mathematical activities, a form of deductive reasoning and an important means to obtain mathematical results. Mathematical operation is the basis for computer to solve problems.
In the process of forming the core literacy of mathematical operation, students can further develop their mathematical operation ability; Can effectively solve practical problems with the help of operation methods; It can promote the development of mathematical thinking through operation and form the habit of programmed thinking; Form a meticulous, rigorous and realistic scientific spirit.
6. Data analysis
Data analysis refers to the process of obtaining relevant data from the research object, analyzing and inferring useful information in the data by statistical methods, and forming knowledge. It mainly includes: collecting data, sorting out data, extracting information, establishing models, analyzing and inferring information, and drawing conclusions.
Data analysis is the main method of mathematics application in the era of big data, which has penetrated into all aspects of modern social life and scientific research.
In the process of forming the core literacy of data analysis, students can improve their data processing ability, enhance their awareness of expressing real problems based on data, develop the habit of thinking through data, and accumulate experience in exploring the essence, correlation and law of things based on data.
Extended data:
The basic characteristics of mathematics core literacy can be summarized into three aspects: comprehensiveness, stages and persistence. Let me explain these three aspects in detail.
1, comprehensiveness refers to the comprehensive expression of basic mathematical knowledge, learning attitude and thinking ability, in which basic learning ability and knowledge need students to learn and think about which method to solve problems besides basic operation methods, reasoning and calculation, which is a comprehensive ability, and basic mathematical knowledge and ability are the basis of this ability, and mathematical core literacy can also promote students' further understanding and learning of basic knowledge.
2. Stage Because each student's learning ability is different, there will be differences at different levels and stages in the performance of mathematics core literacy. Just like the same problem, students of different grades have different learning styles, and it will be difficult and easy to solve it, fast and slow, and their understanding ability and thinking ability will be different, so there will be a phenomenon that people of different levels form an understanding of mathematics core literacy at different stages. This situation is a problem that needs further study.
3. Persistence is not only worthy of attention in the process of students learning mathematics knowledge, but also plays an important role in students' future work and study, which will guide students to think and solve problems by using the way of thinking they have learned. It can be said that mathematics learning can not be learned overnight, and it takes long-term practical accumulation to acquire knowledge, and they will also have and use what they have learned for a long time and become students' wealth.
Mathematics subject network-the core accomplishment of mathematics subject in ordinary high schools