How to cultivate students' mathematical language ability in mathematics teaching? Mathematical language, as the universal language to express scientific thoughts and the best carrier of mathematical thinking, contains many contents. Among them, narrative language, symbolic language and graphic language are more prominent, with the characteristics of accuracy, strictness and conciseness. Because mathematical language is a highly abstract artificial symbol system, it often becomes a difficult point in mathematics teaching. Some students are afraid of mathematics, on the one hand, because mathematics language is difficult to understand and learn; On the other hand, teachers don't pay enough attention to the teaching of mathematical language and lack of training for students, which makes students unable to master mathematical language accurately and skillfully.

Then, in the process of mathematics teaching, how to cultivate students' mathematical language ability?

First, cultivate students' mathematical language understanding ability

As we know, mathematical language has three basic attributes, namely accuracy, rigor and conciseness. Accuracy means that when describing mathematical things, we should pay attention to the appropriateness of words, which conforms to the characteristics of mathematics and does not violate the scientific requirements of mathematics; Stiffness means that in mathematics teaching, the expression and thinking activities of mathematical language are well-founded, not empty or leaking; Conciseness means that when describing mathematical things, the language should be concise and powerful, without nonsense, and avoid meaningless mechanical repetition.

Therefore, in mathematics teaching, teachers' descriptions of mathematical definitions, theorems and axioms must be accurate, and students should not be confused or misunderstood. As a teacher, we must first have a thorough understanding of the essence of concepts and the meaning of terms. Whether the language is standardized or not will not only affect the effect of teachers' expression, but also affect the effect of students' acquisition of knowledge and training skills. Secondly, the language should be rigorous. This requires teachers' teaching language not to be empty and disjointed, but to be reasonable and well-founded. Finally, teachers must purify the teaching language according to the concise characteristics of mathematical language, fully reveal the essence of mathematical knowledge, guide students to think actively, correctly understand the mathematical content represented by language symbols, mathematical symbols, terms and formulas, be familiar with their interaction, and pay attention to characteristics and key points.

Therefore, in mathematics teaching, teachers should first set an example, and then ask students to learn, understand and express mathematics language according to its three basic attributes at all times. In this way, through teachers' requirements and students' intensive training, middle school students will consciously study according to the three attributes of mathematical language, and then students' understanding ability of mathematical language will be greatly improved, laying a solid foundation for learning mathematics well.

Second, cultivating students' ability to transform mathematical language is the key to learning mathematical language well, and it is also the key to learning mathematics well.

The transformation of mathematical language mainly refers to the interaction between ordinary language and narrative language, symbolic language and graphic language (namely mathematical language). How should teachers cultivate students' mathematical language conversion ability in mathematics teaching?

(1) Pay attention to the translation between ordinary language and mathematical language.

Ordinary language is the language used in daily life and is familiar to students. Students feel cordial and easy to understand what they express with it. The learning of any other language must take the common language as the interpretation system. The same is true of mathematical languages. Through the mutual translation of the two languages, the abstract mathematical language can be used for reference in real life, so that it can be thoroughly understood and used freely.

"Mutual translation" has two meanings: one is to translate ordinary language into mathematical symbol language or graphic language, commonly known as "mathematicization". An equation, for example, is to turn the conditions of literal expression into mathematical symbols, which is a necessary procedure to solve practical problems by using mathematical knowledge. The other is to translate mathematical language into common language. Mathematical practice tells us that all students can retell the definition of concepts in common language and explain the essential attributes revealed by concepts. Then they have a deep understanding of the concept. Because mathematical language is an abstract artificial symbol system, it is not suitable for oral expression. Only by translating it into common language to make it popular can it be convenient for communication.

(2) Pay attention to the learning process of students' mathematical language conversion and arrange teaching reasonably.

The formation of mathematical concepts and symbols generally includes three links: logical process, psychological process and teaching process. Logical process can reveal various logical relationships between concepts, facilitate the overall understanding of mathematical structure, and help students understand and understand the essence of mathematics. Psychological process refers to the process from learning mathematical language to mastering mathematical language, which often varies from person to person. Mathematical symbols and rules get their meanings from the real world. It also acts on reality in a larger scope. Only when students understand the context and meaning of mathematical language and master various usages of mathematical language can they describe it flexibly in various equivalent ways in mathematics learning and apply it correctly in an abstract symbol system. So as to reach the highest level of learning mathematical symbol language. The teaching process of mathematical language is a process in which teachers explain, analyze, give examples and test a certain mathematical symbol. Teachers should be good at mastering mathematical language in teaching. They should be good at scrutinizing the key words and expressions of narrative language .5438+0

Narrative language is the most basic way to introduce mathematical concepts, in which every keyword and phrase has an exact meaning, which needs to be carefully scrutinized to clarify the dependence and restriction between keywords. For example, the key words in the concept of parallel lines "two straight lines that do not intersect in the same plane are called parallel lines" are: "in the same plane", "do not intersect" and "two straight lines". In teaching, it should be emphasized that parallel lines reflect the mutual positional relationship between straight lines. Emphasizing the premise of "in the same plane", students can observe that two straight lines that are not in the same plane do not intersect; By extending the straight line, students can understand the correct meaning of "disjoint". Through the scrutiny, modification and deletion of keywords, students can realize that the two keywords "on the same plane" and "two non-intersecting straight lines" are indispensable, thus deepening their understanding of parallel lines.

2. Explore the mathematical meaning of symbolic language.

Symbolic language is the symbolization of narrative language. When introducing a new mathematical symbol, we should first introduce various representative concrete models to students and form a certain perceptual knowledge. Then, according to the definition, leave the concrete model to analyze the essence of symbols rationally, so that students can really grasp the concept (connotation and extension) at the abstract level; Finally, back to the concrete model, the concrete model has dual significance in the teaching of mathematical symbols: one is as the starting point of generalization to prepare for the introduction of abstract symbols, and the other is as a professional way to facilitate the application of symbols.

Mathematical symbolic language is often difficult to understand because of its dense, abstract and rich connotation, which requires students to have considerable symbolic language understanding ability and be good at translating simple symbolic language into common mathematical language, which is conducive to the transformation and handling of problems.