时间：2022-09-07 09:16:41
Abstract. Teaching content of Higher Mathematics is systematic and rigor with a high degree of abstraction. Because different students are on the different basis and different disciplines have various requirements， mathematics is generally difficult for students. In order to improve the quality of teaching mathematics， we should make use of individualized teaching and teaching by different levels in order to achieve the best teaching results.
Key words： Higher Mathematics； Individualized； Level Teaching
1. Introduction
With the depth of China's education reform， the traditional education system and education method have been in a severe test. Education needs to face the world and the future， continues to explore and innovate， with full respect for the status of the students， and to play the initiative of students， and accelerating the training of a large number of qualified reserve personnel， which is an important issue of mathematics education of our universities. Level teaching is a reform of the traditional teaching content and teaching methods closely integrated student practical and professional characteristics， and is one of the effective education reform attempts. Classroom instruction is specific use of individualized hierarchical principle in the classroom teaching. In teaching practice， teachers according to the individualized principles， presented different teaching objectives and requirements for different grades of the students， to make teaching more in line with the actual situation of students and to adapt to students at all levels； Using uniform materials， according to the same schedule in accordance with the syllabus， they teach students in the implementation of the specific circumstances of different requirements. Level teaching enhances students' sense of competition， increases exchanges between the students， and makes the learning atmosphere intensity， which is incomparable of the old way of teaching.
2. The theoretical basis of level of teaching
2.1 Individualized is the theoretical basis of teaching levels
Recognizing students’ differences and teaching in accordance with difference is the individualized. The idea is fine tradition of education. As early as two thousand years ago， Confucius is good at teaching students with different choices of teaching content and teaching methods according to different characteristics， who can be recognized as the individualized pioneer. Teaching should recognize individual differences and reflect the principle of individualized， giving full play to students' individual strengths. Implementing level teaching in the process of teaching mathematics should both grasp the overall characteristics of the students， and take into account of the individual characteristics of the students， so as to effectively promote the sound development of all students in higher mathematics lessons.
2.2 Level teaching is the need of full implementation of quality education
Level teaching of higher mathematics is in line with the teaching theory of "the educational process optimization". Soviet educator Babanski proposed in "education system optimization methods" that， for different levels of students， in conditional regions， the class can be divided into three groups of strong， medium and weak， and design optimization task of teaching according to the appropriate standard， whose essence is level teaching. Teaching arrangements of level teaching meet students’ practical condition， to make all types of students choose their learning speed， practice different levels of difficulty， knowledge and information， so that they can learn and earn， which reflects the quality of education for all students.
2.3 It is the need of university mathematics reform.
Higher education gradually shifts from elite to mass education， which changes require university education reformed. In order to adapt to students’ different levels of college， it is necessary to implement the "level teaching". Only implement the "level teaching"， for all students and individualized， we can achieve a large area to improve the quality of teaching purposes and to adapt future society highly competitive environment.
3. The significance of teaching at different levels
Soviet educator Babanski said： teaching should follow the "acceptable" principle， which requires arrangements to meet the possibility of students’ practical learning ability， so that they intellectually， physically and mentally will not feel too heavy burden". American educator Bloom also said： " Any thing which can be learnt in the world， can be learnt by almost all the people ─ just provide them with proper premise and appropriate learning conditions".
3.1 Teaching at different levels is in line with individual differences in students' mathematics learning process
"Uniform" teaching mode is regardless of the student's acceptance and basic conditions and just provides the same content in the same schedule， seriously dampening the enthusiasm of teachers and enthusiasm of some students. Requirements for different professional knowledge of higher mathematics are different， so we should determine different learning objectives and requirements with different levels of teaching guidance for different types of students； At the same time， teaching arrangements and method selection are combined with professional features and play a role in promoting professional courses for students studying math， making students confident.
3.2 Teaching at different levels is for all， ensuring the dominant position of students
Education is for all students， so it should be responsible for every student and meet certain requirements. The development of students' knowledge， skills， capabilities， inclination and expertise is different， so we should highlight the dominant position of students and reform from the entire professional teaching programs， teaching content and teaching methods. Student-centered is a very important concept of modern international education circles. The implementation of student-centered teaching strategies refers to the basic principles of teaching and learning activities to induce independent learning， so that students have a learning initiative to create a harmonious collaborative learning environment. We should cultivate students' interest in learning， pay attention to the needs of students learning and personalized education， and create a democratic and harmonious and entertaining classroom， and create a good learning environment and other extracurricular effective strategy. Level teaching adhere to the "people-oriented" principle， for various types of learning objectives with many types of teaching content to match； this mode of education can design different media teaching learning materials based on objective conditions， study type， study habits， etc. of students， so that each student's personality and potential capacity can be more fully exploited， form a unique self while adapting to the needs of social development. This respect for individual self-development and respect for the status of teaching in the form of personal survival is people-oriented and student-centered， which fully reflects humanistic care of teacher. Teaching at levels ensures the dominant position in the process of teaching students.
4. The basic way of teaching at different levels
Higher mathematics is an important foundation of professional theory courses of most institutions and the essential foundation of in-depth study of professional courses. By learning advanced mathematics to cultivate students’ scientific spirit and scientific literacy， with applications of mathematics in various disciplines increasingly widespread， both in the future engaging in research or teaching work， they should have the ability to sound mathematical foundation and flexible application of mathematics.
4.1 Correctly grasp the levels of mathematics teaching process
Teaching method of taking the class as a whole， although is able to focus on training students in problem-solving， ignore the scientific process and the social significance of science. As a teacher， you need to go deep into the students' preparation， lectures， review， process assignments， tests， examinations and others. The process of students understanding knowledge is in line with the law that from part to the overall， from analogy to compare， and from the approach to the thought， so we make use of hierarchical propulsion method， difficulty dispersing gradually deepening spiral， guide students from basic scientific facts and phenomena of view to form a scientific the basic principles and methods， and then apply it to practice， so that students truly appreciate the scientific process of development of things. Scientific theoretical level， the first is the original concept and the original relationship， and then the basic concepts of their own logic and higher unity， the unity of the final is the biggest imaginable， as well as by their own senses observed compatibility. Thus in the teaching of higher mathematics， we should based on the levels of mathematical theory and the basic principles of nature and acceptability principle， implement hierarchical teaching methods to make students acquire knowledge step by step and form the ability to solve practical problems in mathematics.
4.2 Choose the relevant materials
With training objectives of institutions of higher education， we can determine the dimensions of the four goals as the quality of teaching， namely science， advanced， practical， standardized， quality materials as determining the merits. With analysis of objective needs of college students’ physical and mental development， the selected materials should be scientific and thoughtful. Through learning mathematics curriculum， we need to improve the quality of mathematics， and establish the scientific method to cultivate the spirit of science to meet the needs of the knowledge economy and society of highly qualified personnel； With analysis of the needs of society for talent， the selected materials should include some links between social production and life of content with applied nature； With analysis disciplines of knowledge， the selected materials should have a new development in mathematics， advanced and with relevant disciplines. The content of teaching materials should be from easy to the difficult， step by step， in line with the student's understanding of the law and the ability to accept， and strive to use modern ideas， methods and language.
4.3 Unified and flexible treatment for teaching content
Higher mathematics is one of the professional basic courses in science， which provides the necessary mathematical knowledge to prepare for the professional follow-up courses. Because mathematics has its own knowledge structure and theoretical system， even students in different professional and in individual differences， it still requires every student to master basic mathematics ideas and methods and concepts， theorems， nature and formula ...... such as knowledge limit， derivative， differentiation and integration， which are unified in the teaching and learning requirements.
In the actual teaching， teachers can grasp some flexibility， and according to the actual situation of the students on different levels of classes， make appropriate adjustments in the teaching content part. In accordance with the basic requirements of teaching specialized courses in applied mathematics content available on demand were selected differential equations， series， integral transforms， part of probability theory and mathematical statistics to be professor of exercise can also choose more specialized course content and related content， such as the financial class can study prices， prices of securities to emphasize the application of knowledge. The mathematical concepts and theories focused primarily on the basic concepts of mathematics and important mathematical principles， highlighting the mathematical concept formation and proof of theorems with strong theoretical nature. For example， in the limit concept teaching， physics， computer and other related professionals have higher requirements on mathematical concepts and theories. Calculation and application of Advanced Mathematics mainly introduce the basic formulas and basic methods， introducing important conclusions without proof， highlighting the conclusions of the application， to enhance awareness and simple mathematical modeling capabilities to develop students' applications capacity.