How to use mathematical language correctly
I. Introduction Mathematical language is the carrier of mathematical thinking, mathematical learning is essentially a mathematical thinking activity, and communication is an important link in the thinking activity. Therefore, the curriculum standard points out that "hands-on practice, independent exploration and cooperative communication are important forms for students to learn mathematics". UNESCO regards effective mathematical communication as one of the goals of learning mathematics, and the premise of achieving effective communication is to learn and master mathematical language. Second, the characteristics of mathematical language Mathematical language can be divided into abstract mathematical language and intuitive mathematical language, including mathematical concepts, terms, symbols, formulas, graphics and so on. Mathematical languages can be divided into three categories: written languages, symbolic languages and graphic languages. Each form of mathematical language has its own advantages, such as strict concept definition and revealing essential attributes; Terminology is introduced into Science and Nature, and the system is complete and standardized; Symbols are concise, easy to write and concentrate on expressing mathematical content; The formula dissolves the relationship in form, which is helpful for operation and thinking. The graphic representation is intuitive and helpful to remember, think and solve problems. As a basic part of mathematical theory, mathematical language has "high abstraction, strict logic and wide application". Simply put, mathematical language is scientific, concise and universal. Third, the teaching strategy of mathematical language 1. Pay attention to the training of mutual translation between mathematical languages and infiltrate the dialectical thought of unity of opposites. On the one hand, "mutual translation" refers to transforming ordinary language into mathematical language (that is, mathematicization), such as gradually abstracting the concepts of mapping and function from concrete correspondence, and internalizing the understanding of abstract mathematical language with the help of ordinary language or concrete examples, such as constructing mapping and function examples according to the definitions of mapping and function; On the other hand, it also includes the transformation between different mathematical languages, such as natural language representation, symbolic language representation and Wayne diagram representation of sets. "Mutual translation" helps to stimulate students' interest in learning, deepen their understanding of the essence of mathematics and enhance their ability to distinguish. The process of mutual translation embodies the idea of unity of opposites, which is helpful to the transformation of different ideas and the reduction of problems. For example, the function y=f(x) is on [a, b]. 3. Attach importance to the teaching of propositional conditional relations, strengthen conditional awareness, and integrate abstraction into concrete examples. The essence of conditional relation is the concrete expression of abstract logical evidence supporting relation. Strengthening the teaching of conditional relations is helpful to cultivate the ability of meticulous logical reasoning. For example, in teaching, we should emphasize that two straight lines li:aix+biy+ci=0(i= 1, 2) are parallel if and only if a 1b2=a2b 1, but the slopes of the two straight lines are not equal. 4. Attach importance to the teaching of thinking methods and integrate the teaching of mathematical thinking into the teaching of mathematical language. Mathematics language teaching cannot be isolated. In the process of mathematical language teaching, we should consciously sum up skills and methods, refine strategies, sublimate ideas, and dissolve the teaching of thinking methods into the teaching of mathematical language. Teaching examples show that sporadic thoughts converge into useful thoughts and special skills, effective thoughts evolve into systematic methods and strategies, and scientific methods evolve into scientific thoughts. For example, we can learn from the special solutions of some special equations: experimental evaluation → deformation arrangement → addition, subtraction and substitution skills → elimination method → the idea of turning the unknown into the known.