What are the core concepts of the new math curriculum standards

The core concepts of the new curriculum standards for mathematics are number sense, symbolic awareness, spatial concepts, geometric intuition, concepts of data analysis, arithmetic skills, reasoning skills, modeling ideas, sense of application, and sense of innovation.

1. Number sense mainly refers to the sense about number and quantity, quantitative relationships, and estimation of arithmetic results. The second layer of meaning is the function of number sense. Mathematics a core is abstract, and the abstract understanding of numbers is the most basic. The learning of number sense is actually connected with the abstraction of numbers and the application of numbers. For example, the estimation of length, area, and volume units in elementary school and the estimation of irrational numbers in middle school are all related to number sense. The formation of number sense is a long-term process.

2. Symbolic consciousness mainly refers to the ability to understand and use symbols to represent numbers, quantitative relationships and patterns of change. It is to use symbols to represent, to represent what, to represent numbers, quantitative relationships and patterns of change, this is a layer of meaning. Another layer of meaning is to know that the use of symbols can be used to perform operations and reasoning, in addition to obtaining a conclusion, and obtaining a conclusion with generality. In the teaching of Quadratic Equations, the formula for finding the root of a quadratic equation is a conclusion that can be generalized and can be operated. The use of the symbolic language of mathematics is critical in the teaching of mathematics. There is also the formula for the vertex coordinates of the quadratic function, also in the training and use of symbolic awareness.

3, spatial concept mainly refers to the characteristics of the object, the abstraction of geometric shapes, according to geometric shapes to imagine the depiction of the physical object, imagine the orientation of the physical object and their positional relationship with each other, describing the movement of the figure and change, according to the language of the description, the drawing of shapes and so on. This is a portrayal of the concept of space. The concept of space has several latitudes. First, it is the relationship between figures and objects, which is a very important latitude. Second, it is the sense of direction that is portrayed in the standards, which is commonly referred to as the sense of direction. Third, the study of views must have a spatial conception of the drawing of the main, top and left views of a given physical object.

4, geometric intuition mainly refers to the use of graphics to describe and analyze the problem, with the help of geometric intuition, you can make complex mathematical problems into a concise image, help explore the idea of geometric problems. Cultivate geometric intuition to let students develop a good habit of drawing, pay attention to the transformation of graphics, so that the students' minds stay graphics, so in the usual teaching to strengthen the understanding of the basic graphics, help to improve the students' geometric intuition. Such as in the line segment perpendicular bisector, angle bisector of the nature and determination to strengthen the understanding of graphics, help students understand and master the theorem.

5, the concept of data analysis refers to: understanding in real life, there are many issues should first do research, collect data, make judgments through analysis. Appreciate the information contained in the data, understand that for the same data can be analyzed in a variety of ways, according to the background of the problem, the need to choose the appropriate method, through data analysis to experience randomness. On the one hand, for the same thing, the data received each time may be different, on the other hand, as long as there is enough data, patterns can be found from it, data analysis is the core of statistics. In math teaching, the study of frequency distribution of data directly develops students' data analysis ability. Only the concept of data analysis, can this part of the content of more thorough study and research.

6, arithmetic ability, as long as it refers to the ability to be able to carry out correct operations according to the laws and operations. Cultivate arithmetic ability to help students understand the operation, seek reasonable, simple arithmetic way to solve the problem. For the teaching of junior high school mathematics in the simplification of value, equation solving, operations with real numbers, and other parts of the development of students' arithmetic ability, arithmetic ability is particularly critical, it is a foundation of number and algebra.

7, reasoning ability, first of all, reasoning is the basic way of thinking in mathematics, reasoning generally includes sympathetic reasoning and deductive reasoning, sympathetic reasoning extends to include two major aspects, one is sympathetic reasoning, one is deductive reasoning. Deductive reasoning starts from known facts, follows some definite rules, and then reason logically to prove and calculate. In other words, from the point of view of the form of thinking, the process from the general to the particular, in the geometric proofs, are actually such a form of reasoning. Sensible reasoning is a way of thinking that starts from the existing facts, reviews some experiences, intuition, and makes inferences through induction and analogy to obtain some possible conclusions. And deductive reasoning is not the same from the particular to the general such a kind of reasoning, so sympathetic reasoning to get the conclusion, know is not necessarily right, usually may be called conjecture, speculation, is a possibility of conclusion. Geometric proof problems in middle school math are all about developing students' reasoning skills. Sympathetic reasoning is important throughout the development of mathematics, the formation of many concepts and theorems in mathematics have undergone sympathetic reasoning, such as the concepts of equations and functions, and the sample looks at the whole in statistics.

8, the establishment of modeling ideas, so that students appreciate and understand the basic ways of mathematics and the external world connection, the process of establishing and solving models include, from real life or specific situations, abstract mathematical problems, using mathematical symbols, the establishment of equations, inequalities, functions and other mathematical models of the quantitative relationship and the law of change, and then find the results, and discuss the significance of the results. Practical problems modeling ideas, both equations, inequalities, functions and solving right triangles in a particularly wide range of applications.

9, application awareness is to emphasize the connection between mathematics and reality, mathematics and other subjects, how to use the mathematics learned, to solve the reality and other subjects in some of the problems, of course, also includes the use of mathematical knowledge to solve another mathematical problem. Equation application problems, function application problems, solving right triangle application problems and so on is to develop students' ability to apply math. The standards say that students' ability to identify and formulate problems is the basis of innovation, and that independent thinking and learning to think are the core of innovation. Therefore, in the classroom teaching important to encourage students to boldly question, encourage students to constantly raise questions and find problems, and give enough time and space to independent thinking, communication, verification, to provide students with opportunities for innovation.

10. Creative consciousness

Consciousness of innovation may be more important, mathematics is very abstract and rigorous, but at the same time the application of mathematics is very broad, should reflect the innovative, creative application. In teaching I let students learn first, find and solve problems; teachers after the lead, students *** with the same exchange, comparison, access to different ways of solving problems and ideas, cultivate the students a problem more than one solution, a problem more than one variation of variation of thinking, improve their ability to innovate. With the help of teachers, students do math by themselves, use their hands and brains, collect materials by means of observation, imitation, experiment, conjecture, etc., get experience, and make analogy, analysis, induction, and gradually form their own mathematical knowledge. At the same time, I also let students in the math classroom to dare to question, doubt books, teachers, not satisfied with the ready-made answers or results, dare to be different, with the help of different thinking, from different perspectives to explore the solution of mathematical problems. In the actual teaching, I also let students learn math must listen carefully to the explanation, using their own minds to think. Let the students start from the "mathematical observation", so that students understand that mathematical knowledge is obtained through the process of exploration. Students do it themselves, get first-hand information, under the guidance of the teacher, the students are engaged in observation, operation process, discussion, organization, and finally come up with similar results and conclusions, which is conducive to the development of students to cooperate **** attitude and good interpersonal relationships.