A, serial number and operation content
Establish the basic structure of number system from natural number, rational number to real number. The content requirements include: introducing irrational numbers to form the concept of real numbers; Establish the structure of number system, mainly including sequence structure (size comparison) and operation structure (basic operation rules, properties and order).
Second, the content of equations and algebraic systems
Focusing on the study of equations, the foundation of elementary algebra is constructed. The content requirements include: algebra as the basis, equation as the center, and preliminary inequality; Highlight mathematical thinking methods, such as reduction thought and method of substitution, elimination method, formula method, reduction method, etc.
In the overall arrangement, the first is to provide basic foundations such as the universality of number system and the properties of equality, such as algebraic expressions and their operations; The second is to systematically study the basic elementary algebraic equations and form the basic theory about elementary algebraic equations (mainly referring to the basic solutions of various algebraic equations and the existence, number and distribution of solutions, as well as the general solutions of equations, etc. ).
Three, graphics and geometry series content
Taking the study of graphic properties as the carrier, the foundation of elementary geometry is formed. The content requirements include: taking empirical geometry as the starting point and paying attention to intuitive perception; Based on experimental geometry, it focuses on reasonable reasoning such as analogy, induction and operational reasoning; Demonstrating geometry is the key point, paying attention to deductive reasoning.
Focus on basic graphics, such as simple lines and circles; Attach importance to the application of research methods, such as intuitive experience, operational experiments, deductive reasoning, quantitative analysis, mutual transformation between special and general, and reverse thinking.
IV. Functions and Analysis Series
The basic task is to form the concept of function, intuitively learn simple elementary functions and lay the foundation for mathematical analysis.
The content requirements include: establishing the concept of function from concrete to abstract, intuitively understanding the essence of function with images, and entering the preliminary analysis; In the study of basic functions such as linear function, quadratic function and inverse proportional function, the elementary analysis method is displayed.
V. Data Processing and Probability Statistics Series
Focus on the basic thinking method of probability statistics and introduce the preliminary knowledge of probability statistics. The content requirements include: perfecting the basic methods of data processing and establishing a preliminary knowledge base of probability and statistics; Explain and solve some simple probability and statistics problems in real life.
Extended data:
Understand mathematical concepts
Mathematical concept is the cornerstone of junior high school mathematics, and it is the carrier of mathematical thinking mode and method. Many students encounter difficulties in solving math problems. Tracing back to the source, they often find that they have a problem with a certain mathematical concept, which prevents them from solving the problem.
Concept belongs to rational knowledge, and its formation depends on perceptual knowledge. The psychological characteristics of students are easy to understand and accept specific perceptual knowledge. Learning methods of mathematical concepts: In the learning process, we should understand the occurrence and formation of concepts, clarify the differences and connections between concepts, and form a network of related concepts in our minds to achieve a comprehensive and flexible application.
Before learning new concepts of mathematics, it will help to promote the formation of new concepts if students can make some structural changes to the original appropriate concepts in their cognitive structure to introduce new concepts. The teaching of some concepts can proceed from reality, so that children can discover the occurrence and development process of concepts in operation.
Improve the efficiency of classroom learning
The learning of new knowledge is mainly carried out in the classroom, so we should pay attention to the learning efficiency in the classroom and seek the correct learning methods. The secret of improving classroom listening efficiency can be summarized as follows: First, prepare in advance, which requires students to prepare in advance.
Second, listen attentively, follow the teacher's ideas in class, and master the basic knowledge and key points in class; Third, we should speak boldly, speak actively on problems and exercise our expressive ability, so that we can review our true level and feel the joy of success; The fourth is to take notes.
Finally, at every stage of learning, we should sort out and summarize, and combine the points, lines and surfaces of knowledge into a knowledge network and bring it into our own knowledge system.
Do targeted exercises.
Many students work very hard in the process of learning mathematics, and they also know that they have to do a lot of exercises, but in the end, the improvement of mathematics scores is not obvious. Why is this? I think it is largely because the exercises done by my classmates are not targeted. My point is not only to do the problem, but also to do it well.
References:
Baidu encyclopedia-junior high school mathematics