course content
The object and characteristics of mathematics, the thinking method and function of mathematics.
(b) Learning and assessment requirements
Understand the connotation of mathematical language, mathematical method, mathematical model and other concepts, understand the characteristics of mathematical abstraction and rigor, and clarify the characteristics of axiomatic method and random thinking method.
1. From the research object of mathematics, mathematics is summarized as a science that studies various quantities, quantitative changes and their relationship between numbers and shapes in the real world.
2, the characteristics of mathematics:
(1) Abstract:
① thoroughness of mathematical abstraction;
② the hierarchy of mathematical abstraction;
③ Abstraction of mathematical methods.
(2) rigidity; Logically impeccable, the conclusion should be very certain.
(3) wide applicability.
2. Talk about your understanding of mathematical rigor.
The rigor of mathematics means that the logic should be impeccable and the conclusion should be very certain. Judging from the history of mathematical development, the rigor of mathematics is relative and closely related to the level of mathematical development. With the development of mathematics, the degree of rigor is constantly improving. People demand absolute strictness, which promotes the study of mathematics and greatly changes the essence and appearance of mathematics.
3, the role of mathematics:
(1) has a great influence on human progress and social development.
(2) Language and tools for exploring natural and social phenomena.
(3) Improve cultural quality and develop scientific thinking.
1. Mathematical language: Like the object of mathematics, it comes from human practice. It comes from human language. With the development of abstraction and rigor of mathematics, it has gradually evolved into a unique language symbol system. Mathematical language is mainly composed of written language (terminology), symbolic language (symbol) and image language.
2. Mathematical method: it is a method of scientific research and problem solving with mathematics as a tool, that is, it expresses the state, relationship and process of things with mathematical language, and forms the method of explanation, judgment and prediction through reasoning, operation and analysis. Mathematical methods also have three basic characteristics of mathematical science:
(1) is highly abstract and generalized.
(2) Accuracy, that is, the rigor of logic and the certainty of conclusions;
(3) universality and operability of application.
3. Mathematical model: a model that simulates reality with mathematical language.
3. Mathematical model method: refers to the basic method of mathematical generalization, description and abstraction of the quantitative relationship and spatial form contained in a certain thing or phenomenon. The process of establishing mathematical model is a scientific and abstract process.
4. Axiomatic method: It began with Euclid's "The Original" in ancient Greece. Starting from five postulates and five axioms, it deduces all the geometric knowledge known at that time by deduction, and makes it organized and systematic, forming a logical system.
5, the characteristics of axiomatic method:
(1) pure deductive system;
(2) an orderly whole;
(3) The system is formal.
5. The function and significance of axiomatic method.
First of all, it is helpful to summarize and sort out mathematical knowledge and improve cognitive level. Secondly, promote the establishment of new theories. Such as non-Euclidean geometry, argumentation or proof theory, model theory and so on. Thirdly, because the axiomatic thought of mathematics expresses the simplicity, conditionality and structural harmony of mathematical theory, it has played an exemplary role in the expression of other scientific theories, and other sciences have followed suit and established their own axiomatic system.
6. Random method: Random method, also known as probability statistics method, refers to a method that people use probability statistics as a tool to effectively collect and sort out data affected by random factors, find out certain quantitative laws, and quantitatively describe and analyze these random effects, so as to infer and predict observed phenomena and problems until they provide basis and suggestions for future decisions and actions.
7, random method, also known as the characteristics of probability and statistics method:
Induction of probability and statistics methods;
B. The processed data is influenced by random factors;
The problems dealt with by C are generally complex problems with unclear mechanisms;
Probability features are hidden in D probability data.
Chapter II Overview of Mathematics Curriculum
course content
The related theories of mathematics curriculum, the factors influencing the development of mathematics curriculum, the modern development of mathematics curriculum and the arrangement system of mathematics curriculum in middle schools.
(b) Learning and assessment requirements
Understand the connotation of popularizing mathematics and the characteristics of mathematics curriculum in the sense of popularizing mathematics, and explain the understanding of the connotation of "problem solving" and what characteristics of mathematics curriculum pay attention to problem solving.
1, the mathematics curriculum in the sense of popular mathematics must be geared to all students and promote all students to learn mathematics well. Its basic meaning includes the following three aspects:
(1), everyone learns useful math.
(2) Everyone can master mathematics (the primary strategy to realize everyone's mastery of mathematics is to let students learn and develop mathematics in real life).
(3) Different students study different mathematics.
2. Reflect the characteristics of mathematics curriculum of popular mathematics:
(1) Pay attention to the universality of the course content, that is, choose the basic knowledge of mathematics that students need, like and accept in the future society as the course content.
(2) Choosing and arranging the teaching content with the essential mathematical thinking method of future citizens as the main line.
(3) Presenting mathematics content suitable for students' age characteristics in a popular and life-oriented way.
(4) Let students learn and develop mathematics in activities and real life.
(5) dilute the form and focus on the essence.
3. What are the specific aspects of the mathematics curriculum that focuses on the application of mathematics?
(1) Increase the mathematical knowledge with broad application prospects;
(2) Strengthen the connection between traditional mathematics content and practice;
(3) Practical research.
3. Mathematics curriculum focuses on problem solving: the connotation of problem solving can be explained from three aspects:
(1), solving problems is a goal of mathematics teaching. The most fundamental purpose of attaching importance to the cultivation of problem-solving ability and developing students' problem-solving ability is to enable students to master the ability and skills to survive and develop in the fierce competition and rapid development of the information society in the future.
(2) Problem solving is a process of mathematical activities, that is, through problem solving, students can personally participate in the process of discovery, exploration and innovation.
(3) Problem solving is a skill. But it is not a single problem-solving skill, but a comprehensive skill, including the understanding of the problem, the design of mathematical model, the search for solving strategies, and the reflection and summary of the whole problem-solving process.
4. The basic principles of arranging the mathematics curriculum system:
(1), which conforms to the law of students' cognition and psychological development: acceptability, intuition, interest and stages;
(2) It conforms to the basic characteristics of mathematical science. The arrangement of curriculum system should not only conform to students' cognitive law and psychological development law, but also not violate the logical order of subject content. Only in this way can students' knowledge learning and cognitive level develop from one height to another.
5, the specific presentation form of the curriculum system:
(1), linear and spiral;
(2), conclusion type and process type;
(3), comprehensive type and branch type.
6. What are the factors that affect the development of mathematics curriculum?
(1) Social factors.
A's influence on mathematics curriculum objectives;
B's influence on mathematics curriculum content and teaching methods. Adapt to the needs of modern social life; Adapt to the needs of the rapid development of science and technology; Adapt to the needs of mathematics education for all students)
(2) Mathematics subject factors
First, the establishment of modern mathematics concept
B's influence on the content of mathematics curriculum
(3) Student factors
Mathematics curriculum must adapt to students' physical and mental development
Mathematics curriculum must promote students' physical and mental development.
Chapter III Foreign Mathematics Curriculum Reform
course content
The general situation of mathematics education reform movement in the 20th century, and the large-scale international comparative study of mathematics education and mathematics curriculum reform in various countries facing the new century.
(b) Learning and assessment requirements
Understand the reform movement of mathematics education in the 20th century (Bailey-Klein movement, new mathematics movement, returning to basics, problem solving, etc. ), understand the significance of these movements to the development of mathematics curriculum, and grasp the reference significance of foreign new mathematics curriculum reform in China.
1 and Bailey-Klein movement 190 1 in, British mathematician Bailey gave a famous lecture on mathematics teaching, and put forward the ideas that "mathematics education should be geared to the public" and "mathematics education must attach importance to application", as well as clear ideas for reforming mathematics education, most of which were aimed at geometry courses. At the same time, the famous mathematician Lacken also expressed his views on mathematics education on various occasions and put forward the so-called "Milan Outline". These views strongly criticized the mathematics field at that time as a response to Bailey and Klein. Paulie of France and Moore of the United States also put forward the idea of mathematics education reform, which was later called Bailey-Klein Cloud.