Advanced mathematics is an important basic course for undergraduates majoring in economics, which plays a key role in mastering professional course knowledge and engaging in higher-level research in this major. In order to make the students of this major learn this course well, our school has tried out the teaching mode of layered teaching for the teaching of advanced mathematics. This paper analyzes and expounds the advantages of stratified teaching from the aspects of necessity, mode and effect. Keywords: advanced mathematics; Hierarchical teaching; Teaching students in accordance with their aptitude. The Necessity of Implementing Hierarchical Teaching Advanced Mathematics is an important basic course for undergraduates majoring in economics. Its importance lies in that learning this course well is not only the basic guarantee for learning its specialized courses well, but also an indispensable tool for improving the quality of thinking and conducting higher-level research. Therefore, ordinary undergraduate colleges offer advanced mathematics courses to economic students from the beginning of their freshman year. However, after the enrollment expansion of colleges and universities, China's higher education has developed from elite education to mass education, which makes it an indisputable fact that the enrollment of various majors in colleges and universities has soared and the quality of students has declined. Moreover, students come from all provinces and cities in China, and their math scores and levels are uneven; Different students have different hobbies and development directions. However, the textbooks, teaching plans and syllabus used by the same major are the same, and students and teachers have basically no choice. This unified teaching mode has seriously hindered the further improvement of higher mathematics teaching quality. At present, the biggest problem facing the teaching of this course is the decline of students' interest in learning and academic performance. There are many factors that cause this problem, one of which is the neglect of students' different needs for teaching methods and teaching contents. Therefore, according to students' math scores, hobbies and development aspirations, it is imperative to implement different requirements and different teaching methods for students with full respect for personal wishes. Based on the scientific theory and the teaching practice in our school, this paper analyzes and discusses the implementation methods and effects of hierarchical teaching. Second, the theoretical basis of hierarchical teaching The theoretical basis of hierarchical teaching is the theory of "mastering learning" by American psychologist and educator B.S. Bloom, who believes: "As long as we provide appropriate materials and teaching, and provide appropriate help and sufficient time for each student, almost all students can complete their learning tasks or achieve the prescribed learning goals." The theory of "mastering learning" requires teachers to teach according to students' actual development level, learning style and personality characteristics. Students from ordinary colleges and universities come from all provinces and cities in China. In recent years, the expansion of colleges and universities has also caused a decline in the quality of students. This has caused the students' mathematics level to be uneven and quite different, and hierarchical teaching can better reflect the above ideas. The layered teaching method is also based on the theory of multiple intelligences, respects students' personality differences, attaches importance to personality development, follows the principle of teaching students in accordance with their aptitude, and takes students' development as the starting point and destination of teaching, which truly embodies the educational reform requirements of "taking students' development as the center, taking social needs as the guide and taking subject knowledge as the basis" and can also truly reflect the spiritual connotation of quality education. In addition, in fact, in ancient China, Confucius, an educator and thinker, had put forward that educating people should be "deep, shallow, beneficial and respectful", that is, he advocated "teaching students in accordance with their aptitude, which varies from person to person". In other words, teachers' "teaching" must be suitable for students' "learning". Thirdly, the implementation of hierarchical teaching is to set learning objectives, design course content and create different teaching situations and teaching methods according to students' different learning levels and abilities, as well as students' own interests and requirements in mathematics, so as to teach students in accordance with their aptitude, promote students' all-round exercise and development, and then realize a more efficient and effective teaching model. Since the 2008 school year, with the strong support of the Academic Affairs Office of our university, we have tried the hierarchical teaching mode in the teaching of advanced mathematics for economic majors. Compared with the previous non-hierarchical teaching mode, the teaching effect has been improved obviously in the past two years. The specific implementation method is that for the two schools of the School of Economics, the School of Economics and Trade and the School of Business Administration, we adopt the method of not disrupting the departments, or we can divide classes by layers. The level is divided into two layers, namely, layer A and layer B. Layer A is a higher level in mastering basic knowledge, flexibly applying theory and combining theory with practice. The teaching plan and content are aimed at in-depth research in postgraduate entrance examination and professional fields. The corresponding requirements of layer B are lower, but the basic principle is to lay a solid foundation and make mathematics a powerful tool for subsequent professional courses. At the same time, due to the high requirements of Class A, it is not easy to grasp, and teachers with many years of teaching experience are responsible for teaching. The basis of stratification is objective and subjective. The objective basis is the students' mathematics achievement level. On the one hand, we should refer to the results of the college entrance examination; On the other hand, at the beginning of freshmen's entrance, there should be a "bottom-up" exam in mathematics. The test questions of "finding the bottom" are given by teachers with rich teaching experience, most of which are average in difficulty, and a few are more difficult, which shows that students' math scores are high or low. The subjective basis of stratification is students' own interests and requirements for mathematics courses. For example, some students are very interested in mathematics, although their grades are average, or they are interested in continuing their research in this field, such as postgraduate entrance examination. We can consider dividing students into advanced classes. On the other hand, some students have high test scores, but they are not interested in mathematics, and just regard it as a compulsory basic course. Then, they can ask the students' opinions and divide them into class B. Considering the class size and teaching effect, we regard quite three "natural classes" as a teaching class. The fundamental purpose of hierarchical teaching is to teach students in accordance with their aptitude. Therefore, after the end of the final exam of the first semester, some students' mathematics scores and interest in mathematics may no longer be suitable for the original class teaching objectives, which requires the adjustment of classes, that is to say, hierarchical teaching has certain mobility. Adjustment also follows the above hierarchical basis, because adjustment is hierarchical. On the one hand, it is the students' test scores, on the other hand, it also takes into account the students' subjective wishes. However, practice has proved that the fluctuation should not be too large, and it is appropriate not to exceed 5%. Fourthly, the effectiveness and thinking of hierarchical teaching have achieved certain results. Compared with students who did not implement hierarchical teaching before Grade 08, the failure rate has been greatly reduced. The number of people with scores of 60-69 and 70-79 increased significantly, and the excellent rate above 90 increased slightly, and the average score increased significantly. The distribution of grades is normal. It can be seen that hierarchical teaching meets the wishes and requirements of most students and should be adhered to and improved. Hierarchical teaching is targeted and personalized, which can improve students' interest in learning and reduce the burden brought by the abstract and boring subject itself. Make some students who have no confidence in mathematics and lose interest in learning meet the requirements of the syllabus, and better solve the contradiction between the two levels of mathematics learning of college students. After Grade 08, students' recognition of hierarchical teaching is getting higher and higher, and their adaptability and confidence in learning mathematics are greatly enhanced. Practice has proved that hierarchical teaching ensures teaching students in accordance with their aptitude, so that "top students eat well, middle students eat well, and poor students eat well", and at the same time reduces students' academic burden, which is an effective way to comprehensively improve teaching quality and implement quality education. Although the implementation of hierarchical teaching has greatly improved all aspects of higher mathematics teaching, there are still some problems to be solved urgently. For example, students from different "natural classes" have math classes in the same class, which causes difficulties in classroom and homework management and puts forward new requirements for teachers and counselors. In addition, students' grades need to be ranked according to "natural courses" after the exam, which also causes some troubles. Our work is just the beginning, and we will continue to improve the teaching methods of hierarchical teaching in the future practice. For example, when assessing students' grades, not only written test scores can be considered, but also other forms of assessment results can be considered; In the teaching process, multimedia teaching can be carried out with the help of computers to improve students' interest in learning.