When people think or talk about mathematics learning ability, they are often used to linking it with computing ability, spatial imagination ability, mathematical observation ability, mathematical memory ability and mathematical thinking ability. The listening, speaking, reading and writing abilities discussed in this paper are considered to be related to the learning activities of Chinese, foreign languages and other disciplines, so the cultivation of these abilities is often ignored in mathematics learning activities. In fact, in mathematics learning activities, listening, speaking, reading and writing have their specific connotations, which are also the premise and indispensable learning ability of mathematics classroom learning activities, and also the guarantee to improve the efficiency of mathematics classroom learning, which should be paid enough attention to.

This paper analyzes the four activities of listening, speaking, reading and writing from the viewpoint of modern information theory, in which listening and reading belong to the processing form of information input, while speaking and writing belong to the processing form of information output. According to the theory of cognitive psychology and information processing, "the process of mathematics learning is divided into four stages: information input, interaction, operation training and information output". [1] Input stage is an indispensable link in individual cognitive processing. Information input runs through the whole cognitive processing process, and information output perfects the initial mathematical cognitive structure, and finally forms a good mathematical cognitive structure. Therefore, students' information input function and information output function, that is, the ability of listening, reading, speaking and writing, largely determine the efficiency of their mental work in class, and directly affect their ability to understand and master mathematical ideas, methods and knowledge, as well as the development of mathematical thinking ability.

We know that language is the carrier of information, and listening, speaking, reading and writing are inseparable from language, and classroom is an environment where language is always dispersed. "In the traditional and more formal classroom, teachers and students exchange information through language. On average, teachers or students spend more than 70% of their time using language." [2] Math class is no exception. In fact, mathematics teaching includes various forms of language activities, such as teaching, explaining, asking questions, answering, retelling, reading, writing and discussing. Language is always accompanied by mathematics teaching activities of teachers and students.

Mathematical language is widely used in mathematics classroom, which is not only the carrier of mathematical thinking, but also the concrete embodiment of mathematical thinking. It is not only a tool of expression but also a tool of communication. Students' listening, speaking, reading and writing abilities in mathematics learning are directly related to the development of their mathematical thinking and their understanding, mastery and application of mathematical knowledge. As Stolyar pointed out: "The root of students' superficial knowledge is often the improper coordination of semantic processing and syntactic processing in mathematical language learning. The disconnection between form and content is essentially the disconnection between mathematical language symbols and formulas and what they represent. " 〔3〕

Mathematical language is a scientific and specialized language different from natural language, and it is a special expression form formed by human mathematical thinking in the long-term development. "Specific teaching background and specific teaching content all affect the syntax, semantics and effectiveness of language in mathematics teaching, because they are different from everyday language in form and connotation." [4] It takes mathematical symbols as its main vocabulary and mathematical rules, theorems and formulas as its grammatical rules. Its writing form is based on natural language and a symbol system different from natural language, such as+,-,> and letters and numbers, which are combined according to special rules to produce reasonable expressions. They have the following three characteristics: (1) the trinity of word, meaning and symbol; (2) Concise, accurate, clear, concise and changeable; (3) Mutual interpretation and translation between intuitive language (graphics and symbols) and abstract language. Therefore, the requirements for students' listening, speaking, reading and writing ability in mathematics learning are necessarily different from those in general language learning. It requires students to input information accurately, process information quickly and flexibly, and output information correctly. Students are also required to have the ability to change from one language form to another, and to "master the correct relationship between the form of mathematical language and the content expressed, mathematize natural language, symbolize and schema mathematical language, and communicate with each other". [5] For example, when a student hears "the intersection of set A and set B" or reads the symbol "a∩b", he can not only understand that this mathematical language refers to "a set composed of all elements belonging to set A and set B (that is, the common elements of A and B)", but also associate it with the Wayne diagram representing the intersection. For another example, when students hear or read the concept of "increasing function", they should be able to associate with the properties and images of increasing function: the function is in a monotonous interval, and the value of the function increases with the increase of independent variables. The image shows a monotonous upward trend from left to right at monotonous intervals. However, if we can say or write that "any two of x 1 x2 belong to a monotonous interval, and if both X 1 > X2 have f(x 1) > F (X2), it is said that f(x) is increasing function in this monotonous interval", then we can judge the increase or decrease of a function.

This also means that the training of students' listening and reading ability in mathematics learning should aim at understanding and expressing relevant mathematical languages, while the training of students' oral and writing ability aims at mastering and applying mathematical languages. Therefore, students' listening and reading ability in mathematics learning is to integrate and organize the physiological feelings caused by external stimuli (mathematical materials and backgrounds) and accurately transform them into psychological perception. In the process of listening or reading, driven by a certain need or purpose, students' knowledge related to the new knowledge they want to learn in the mathematical cognitive structure is activated, making some expectations and predictions, constantly verifying or correcting assumptions, and thus understanding, extracting and absorbing information. In mathematical language, the meanings of a word difference and a symbol difference are very different, such as "divide" and "divide", "contain" and "contain in", > and "

Students' poor ability of listening or reading, speaking or writing in mathematics learning may be due to insufficient internal conditions or external conditions, which should be carefully analyzed and treated differently. The inherent basic conditions for students to have the ability of listening, speaking, reading and writing in mathematics learning are: 1. Appropriate knowledge preparation, including mathematical knowledge, mathematical experience and mathematical language; 2. Psychological tendency of active processing, including cognitive strategies and emotional factors. The required external basic conditions are: 1. The degree of stimulation, that is, the clarity of the provided mathematical materials and background and the rigor of logic; 2. Evaluate the appropriateness and timeliness of feedback. Students' listening, speaking, reading and writing abilities in mathematics learning are formed and developed in mathematics learning, but not any mathematics learning process can promote the formation and development of these abilities. Teachers should carefully analyze the factors and conditions that affect the formation of students' listening, speaking, reading and writing abilities in mathematics learning, try their best to create conditions conducive to the formation of students' listening, speaking, reading and writing abilities in classroom teaching, and constantly explore the rules and methods of training.

There are many factors that affect students' ability of listening, speaking, reading and writing in mathematics, among which language is the first factor, and teachers' "higher language literacy is an important condition for rational use of mathematics time". Therefore, first of all, teachers should pay attention to the use of language in class. Specifically, we should do the following two things. 1. Teachers' speech must conform to the general grammatical rules and logical requirements. In class, the sentences spoken by teachers should be complete and fluent, the main components and additional components in the sentences should be clear and definite, the procedure of judgment and reasoning should be accurately grasped, the speech should be coherent and distinct, and the causal relationship should be appropriate. 2. Teachers should use standardized mathematical language. Teachers' language is a role model for students, and its influence on students' language habits and abilities is cumulative and subtle. If the teacher's mathematical language is inaccurate and irregular, students will have a vague understanding of mathematical knowledge, which will affect the correct use of mathematical language. Therefore, mathematics teachers must master mathematical terms and expressions of definitions, theorems, formulas and rules in mathematical science language, so that their words are orderly and reasonable, which is also of great benefit to cultivating students' rigorous scientific spirit and mathematical thinking methods. If the logic of the language spoken by teachers is confusing, it is difficult for students to understand, or the language writing is incorrect and irregular, it will interfere with students' listening and reading ability, and will also cause negative transfer to students' oral and writing.

Secondly, teachers should actively create conditions to cultivate students' listening, speaking, reading and writing abilities. 1. Teachers should pay attention to the art of teaching language and be good at using language skills. The language in the classroom should be vivid, interesting, concrete, simple and infectious, so that students can learn the process of teachers' thinking, learn good thinking methods and experience the happiness in the process of thinking through the superb language art of teachers, so that their thinking state can naturally enter the mathematical thinking environment, stimulate students' interest in learning and arouse their enthusiasm for learning. 2. Teachers should be good at "colloquialism", popularize and visualize abstract mathematical language, and translate and explain mathematical language and natural language, so that students can understand and master mathematical language. For example, "any non-zero integer" can be expressed as "any integer not equal to zero", and "a≥b" can be interpreted as "A is greater than B or A is equal to B" or "A is not less than B" and so on. This can help students overcome the obstacles in understanding mathematical language and better master and use mathematical language. Teachers should provide more opportunities for students to cultivate and exercise these abilities. An expert in mathematics education once analyzed: "In mathematics teaching, students are usually not explicitly taught to read, write and speak, because everyone thinks that with the deepening of teaching content, the ability of these activities will naturally develop. Nevertheless, we often ask students to imitate the language of books or teachers. " [7] Therefore, we can't let the development of students' mathematical language ability die. Instead, we should purposefully induce students to listen and read in class, so that students can "listen-think" and "read-learn" the mathematical language. More importantly, we should set aside some time for students to talk and write, create a veritable communication situation, and provide students with opportunities to practice their listening, speaking, reading and writing skills. Students should be allowed to participate in teaching activities. In participating activities, students can experience the cognitive process by moving their mouths, hands and brains, so that they can think and express clearly, accurately and unambiguously, so that everything they say comes from my mouth and everything they say comes from my heart, so as to truly achieve mastery of knowledge.

Finally, teachers should make appropriate and timely feedback and evaluation on the results of students' listening, speaking, reading and writing activities. Teachers generally evaluate students' learning effect through their homework or tests, and occasionally ask questions in class, but the feedback is very little, so the evaluation is often too simple to achieve the role of regulation. Teachers should not miss any opportunities for feedback. For example, students' classroom expression or homework writing should be particularly affirmed to cultivate students' self-confidence. Don't simply say that mistakes are wrong or cross-cutting, but point out mistakes more specifically and provide correct demonstrations if possible to help them correct them in time. Make students experience "joy" in affirmation and "gap" from deficiency, and then produce the thoughts and feelings of "not learning enough" or "not knowing enough, and then reflecting".

The cultivation of students' listening, speaking, reading and writing abilities in mathematics learning and even the language problems in mathematics education have not been studied enough in China. This paper only makes a superficial exploration of the previous problems, hoping that more colleagues in the mathematics education circle will care about, attach importance to, study and experiment these topics, so as to promote the improvement of the quality of mathematics education.