Mathematics itself is established in an abstract way and develops continuously. The degree of symbolization and formalization of mathematical language is unmatched by any discipline, which provides great convenience for people to learn and communicate mathematics and explore and discover new mathematical problems. Although abstraction is not unique to mathematics, in terms of its form, mathematical abstraction has the characteristics of multi-level, symbolization and formalization, which is the characteristic that mathematical abstraction is different from other scientific abstractions. Therefore, cultivating students' abstract ability naturally becomes one of the goals of middle school mathematics curriculum.
(2) strict logic. The object of mathematics is formal ideological material, and whether its conclusion is correct can not be tested by repeated experiments like physics and other disciplines, but mainly by strict logical reasoning; Once the conclusion is proved by reasoning, then this conclusion is correct. Axiomatic method in mathematics is essentially the direct application of logical method in mathematics. In the system of mathematical axioms, all propositions are linked by strict logic. Starting from the original concept directly adopted without definition, other derived concepts are gradually established with the help of logical definitions; Starting from the axiom based on unproven direct adoption, with the help of logical deduction, a further conclusion, namely theorem, is gradually drawn; Then all the concepts and theorems are combined into a whole with internal logical connection, that is, an axiomatic system is formed. The solution of a mathematical problem should conform to the laws of mathematics on the one hand and logic on the other. The process of solving problems must be gradual, the words must be well-founded, and strict logical reasoning and argumentation must be carried out. Therefore, it is also one of the goals of middle school mathematics curriculum to cultivate students' logical thinking ability such as analysis, synthesis, generalization, reasoning and argumentation.
(3) universality of application. As we all know, in people's daily life, work, productive labor and scientific research, mathematical knowledge is used in all disciplines of natural science. With the rapid development of modern science and technology, mathematics has become an indispensable tool. In the research of every science, qualitative research will eventually be reduced to quantitative research to reveal its essence. Mathematics only solves the pure quantification problem of every science, and the quantitative research of every science is inseparable from mathematics. Nowadays, mathematics is more infiltrated into other sciences, which affects the development of other sciences. Some people even think that which science introduces mathematics marks the beginning of its maturity.
Mathematics is one of the important basic courses in middle school education. Learning mathematics well provides favorable conditions for the study of physics, chemistry and other courses, and is very beneficial for further study and participation in social productive labor. Therefore, the universality of mathematics application must be fully considered when determining the goal of middle school mathematics curriculum.
(4) Dialectical connotation. Mathematics is rich in dialectical materialism and reveals many basic laws of materialist dialectics. The emergence and development of mathematics itself shows that its power ultimately comes from the materialistic point of view, that is, the production of objective materials needs such a materialistic point of view. The content of mathematics is full of the basic laws of dialectics, such as interrelation, movement change, unity of opposites and quantitative change to qualitative change. For example, positive and negative numbers, constants and variables, necessity and randomness, approximation and accuracy, convergence and divergence, finite and infinite, and so on. Are the prerequisites for each other's existence. Without one party, the other party will cease to exist and can be transformed into each other under certain conditions. Mathematical methods also embody dialectics. For example, the limit method in mathematics is to study and solve the contradictory problems in mathematics, such as "straight and curved", "finite and infinite" and "consistent and inconsistent", which determines the dialectical nature of the limit method. The development of mathematics is also full of dialectics. The emergence and solution of three mathematical crises have given us profound enlightenment. In middle school mathematics teaching, fully revealing many dialectical contents contained in mathematics is a good form to educate students on dialectical materialism and form a correct view of mathematics.
Middle school mathematics is the mathematics to be learned in middle school. Be able to operate, draw or draw pictures and make simple reasoning according to certain procedures and steps. This is clearly stipulated in the junior high school mathematics syllabus. Simply put, I can calculate, draw and reason. Its specific requirements are clearly listed in the teaching requirements of the syllabus. that is