(1) On the overall goal, the standard proposes that students should "experience the process of using mathematical symbols and graphics to describe the real world, establish the consciousness of numbers and symbols, and develop abstract thinking."
It can be seen that understanding the meaning of numbers and symbols is very important for students to establish the meaning of numbers and symbols in the process of mathematics learning and is the basis for entering mathematics learning. In the compulsory education stage, students should learn concepts such as integer, decimal, fraction, rational number and real number. These concepts are abstract in themselves, but through the study of mathematics, students can relate the concepts of these numbers with the practical meanings they represent, such as how big a million is, how many soybeans there are in a handful, and so on. In the curriculum standards, we should attach importance to the understanding of logarithmic meaning, cultivate students' sense of numbers and symbols, dilute the requirements of excessive "formalization" and memory, and let students exercise independently in the process of learning mathematics, which not only improves their own mathematical literacy, but also helps them understand and explain practical problems with their mathematical minds.
Mathematics is closely related to real life. As early as the early 1980s, UNESCO put forward that "solving mathematical problems should be the center of school mathematics education". Therefore, valuable mathematics is more reflected in students' observation and understanding of daily life phenomena with mathematical vision and thinking, to solve problems in life, and to acquire or improve their ability to adapt to life. In the past, teachers always attached great importance to the accuracy and proficiency of students' written calculations, and students lacked estimation consciousness and estimation methods. But in daily life, it is estimation that is more widely used than written calculation. We often need to estimate the time needed to go to school and work, and the time needed to complete a task (cooking, buying food, doing homework, etc.). ), the amount of paper needed to write an article, the size of the place needed to put the refrigerator, and the cost of a trip. Therefore, it is of great value to strengthen estimation, cultivate students' estimation consciousness and develop students' estimation ability. The new curriculum standard also repeatedly emphasizes the need to strengthen estimation and downplay written calculation.
(B) "Number and Algebra" is conducive to the development of students' thinking and ability, and cultivate mathematical emotions.
Today, when "everyone learns valuable mathematics" is advocated, implementing this concept in middle schools requires us teachers to pay attention not only to how students master knowledge and skills, but also to the cultivation of students' emotions, attitudes, values and general abilities. Students' thinking ability, thinking methods, habits, emotions and attitudes are of inestimable value to students' future life creation. Therefore, "number and algebra" as a basic part, its main content is to study the mathematical model of quantitative relationship, movement and change law in the real world. It can help people to understand, describe and grasp the real world more accurately and clearly from the perspective of quantitative relations, and it is a valuable mathematics that can effectively develop students' thinking and cultivate mathematical emotions.
From ancient times, knots and nicks were used to count, to the use of abacus, to the use of calculators, to the emergence of modern large computers, and to the widespread use of microcomputers today. All show the value of innovation. Therefore, only people with innovative spirit can constantly create a more wonderful world. Therefore, mathematics that can cultivate students' innovative spirit is valuable mathematics. This is mainly reflected in the diversification of problem-solving strategies. If we can think about a problem from many angles and levels, explain a thing in many ways, express an object in many ways and solve a problem in many different ways, then we can not only develop our thinking ability, but also have a more comprehensive and profound understanding of this problem, which is helpful to cultivate students' innovative spirit.
The basic part of "number and algebra" is to build a bridge of this kind of thinking. It can not only promote students' exploration and discovery by exploring the quantitative relationship and its changing law in real situations, but also cultivate students' initial innovative spirit and practical ability. We can also use the idea of unity of opposites contained in the concepts of positive and negative numbers, precision and approximation, equation and solution, known and unknown, and the idea of movement and change contained in the concepts of variables and functions to promote students to understand the real world from the perspective of mathematical science.