Before the implementation of case teaching of advanced mathematics, teachers need to carefully prepare teaching cases according to the requirements of teaching content and teaching objectives, and inform students in advance what they should preview and review, and students need to complete tasks before class according to the requirements of teachers.

Advanced mathematics is an important course, which is the basis for students to learn other professional courses. However, due to the characteristics of advanced mathematics, students' enthusiasm in the learning process is not high, which leads to unsatisfactory teaching effect. Introducing CDIO teaching concept into advanced mathematics teaching and using case teaching mode to let students solve practical problems by themselves with mathematical knowledge will certainly stimulate students' interest in learning advanced mathematics, thus improving the quality of advanced mathematics classroom teaching.

Keywords: advanced mathematics; CDIO； Case teaching

Everyone says that mathematics is very useful, but how to use it? This is a topic worth discussing. Advanced mathematics is a course offered by all colleges and universities. The content and methods of this course have an important influence on students' future study of specialized courses. So it is a tool class, which also shows the importance of learning advanced mathematics well. However, the study of advanced mathematics is boring, and students are in great pain in the process of learning. We should change the traditional teaching methods of advanced mathematics, improve students' enthusiasm for learning advanced mathematics, and thus effectively improve the teaching quality of advanced mathematics. With the help of CDIO concept, the introduction of case teaching method in advanced mathematics teaching will certainly stimulate students' interest in learning advanced mathematics, thus improving the teaching effect of advanced mathematics.

A higher mathematics teaching status quo

For a long time, the teaching of advanced mathematics has been based on lectures, that is, teachers talk and students listen. Although the teacher talked in Kan Kan on the platform, some students were sleepy because of the boring and abstract characteristics of mathematics, and their learning interest and enthusiasm were not high, which could not achieve the ideal teaching effect. Many teachers pay more attention to the explanation of definitions, the proof of theorems and the derivation of formulas. As for the historical background and cultural value of mathematical knowledge, and how to use mathematical knowledge to solve practical problems, there are few introductions, which makes students feel that it is useless to learn mathematics, and they don't realize the role of advanced mathematics in their subsequent study of professional courses and later life, so they don't pay attention to the study of advanced mathematics. The disadvantages of the traditional teaching mode of advanced mathematics are more and more obvious, and it is urgent to find an effective teaching mode to change this situation.

Introduction to CDIO concept

CDIO is a very popular educational concept, which is implemented in the field of higher education engineering. CDIO stands for concept, design, implementation and operation. It is a new engineering education model [1-] jointly founded by Massachusetts Institute of Technology, chalmers university of technology, Sweden, Linxueping University and Royal Swedish Institute of Technology. This model emphasizes students' dominant position, requires students to actively participate in teaching, tries to mobilize students' enthusiasm, allows students to actively practice engineering technology, emphasizes the cultivation of students' practical ability, and advocates? Doing middle school? Guide students? Listen to math? Become? Do math? . Since the introduction of CDIO education concept in Shantou University, combining CDIO education mode with the teaching situation in China universities and strengthening the education of honesty, professional ethics and professional quality can guide students to become interested in the study of core professional courses, make them learn in practice and cultivate their practical application ability. CDIO mode requires teachers as the leading factor and students as the main body, strengthening practical teaching, further cultivating their cooperation and communication skills, and improving their innovation ability and teamwork ability.

Brief introduction of case teaching

Case teaching method is a teaching method in which teachers take cases as teaching materials, let students enter certain situations and play certain roles, encourage students to think and communicate under the guidance and support of teachers, find out problems and their causes, find opportunities and make decisions [4]. The case teaching method originated from Harvard Business School in the 1920s, and gained popularity in the United States in the 1950s and 1960s. However, it was not until the 1990s that domestic educational circles began to explore the case teaching method. At first, case teaching method was widely used in economy, trade, management, law and other fields, and now it has been widely used in MBA teaching in China. In the teaching of advanced mathematics, there are not many examples of using cases to teach, which is mainly related to the characteristics of advanced mathematics itself. Advanced mathematics is a professional basic course, and the study of subsequent professional courses needs to solve problems with the help of advanced mathematics knowledge. Many classic cases exist in subsequent professional courses, and there are some problems in the connection between them. However, due to the characteristics and advantages of case teaching method, it is still worth learning.

Case teaching of advanced mathematics under the concept of CDIO

It is a brand-new attempt to introduce CDIO concept and implement case teaching mode in higher mathematics teaching. Case teaching is intuitive and vivid, and it is easy to stimulate students' enthusiasm for learning mathematics. The case scale can be large or small, which has good operability in teaching and conforms to CDIO theory. CDIO requires learning by doing. In teaching, teachers should introduce cases, and students should use their own mathematical knowledge to discuss and find solutions, so as to cultivate students' ability to solve problems. In teaching, we should not only learn mathematics, but also use mathematics, that is? Learning while doing, learning while practicing? This is the concept of CDIO.

(A) the choice of cases should be scientific and reasonable.

In advanced mathematics, not all the contents are suitable for case teaching. Therefore, before case teaching, teachers should choose appropriate mathematics content and design teaching cases with practical projects related to their majors. On the one hand, the selected cases should meet the requirements of teaching objectives. On the other hand, case selection should comprehensively consider students' cognitive structure and personality characteristics, and make clear what problems case teaching can solve and what abilities students can solve. For example, the application of derivative, the application of definite integral, the extreme value of multivariate function and so on. These contents are convenient for selecting cases related to the actual background of the major, guiding students to analyze and discuss, thus improving students' ability to solve practical problems.

(B) The role of teachers should be accurate.

In the process of case teaching of advanced mathematics, teachers and students are two important roles in teaching, and teachers should play the role of organization and guidance, that is, teachers should be the main body. First of all, teachers should choose appropriate cases according to students' cognitive level before class; Then, organize students in class and guide them to carry out the whole process of case analysis and discussion. In this process, teachers need to solve the problems existing in the case, consciously guide students to think towards the established goals, find all kinds of mathematical knowledge and thinking methods that need to be used, and pay attention to all kinds of possibilities of problem development and change; Finally, the whole process of case analysis is summarized and commented to meet the requirements of teaching objectives. Teachers should also update cases at any time, so that cases can adapt to the development of the times and truly reflect the needs of professional learning, and cases that do not meet the actual needs of development should be eliminated in time.

(3) Students can actively participate in teaching.

CDIO engineering education mode requires students as the main body and improves students' initiative and enthusiasm. In case teaching, students are important participants. Students should analyze cases, collect information, participate in discussions and express their opinions. The concepts and theorems in advanced mathematics are very logical and abstract, and students are prone to be tired of learning. When organizing students to carry out case discussion activities, it is the key to let students actively participate.

(D) The implementation of case teaching should be well organized.

Before the implementation of case teaching of advanced mathematics, teachers need to carefully prepare teaching cases according to the requirements of teaching content and teaching objectives, and inform students in advance what they should preview and review, and students need to complete tasks before class according to the requirements of teachers. In class, teachers show cases, help students divide into groups reasonably, guide students to discuss cases, solve problems raised by students in time, and help students find solutions to problems together. After the case discussion, each group will send a representative to speak and report the discussion opinions of the group, so that everyone can choose the best scheme together. Finally, teachers should summarize and evaluate the methods of case teaching, then list some similar cases, analyze the ideas of case solving, find out the uniqueness through comparison, and fully affirm the reasonable opinions of students. Only by completing these four stages can the teaching objectives be better realized.

Five summaries

The introduction of CDIO teaching concept in higher mathematics teaching and case teaching fully reflect the process of teacher-student interaction. Teachers no longer take the initiative to teach, students no longer passively accept, teachers become the organizers and guides of the classroom, and students really become the masters of the classroom. Starting from practical problems, students can experience the fun of solving problems through their own discussion and design, cultivate their innovative consciousness and mathematical practice ability, and let them learn how to solve practical problems with mathematical knowledge.

refer to

Edward Crawley, John Ma Yueran, Sonos Luna, Doris Broder, Gu Peihua, Shen Minfen, translated by Lu Xiaohua. Reflection on Engineering Education: Dialogue Method [m]. Beijing: Higher Education Press, 2009 (4): 86544

[2] Cha Jianzhong. Open? Doing middle school? CDIO mode under strategy [J]. Research on Higher Engineering Education, 2008(3): 1-6.

Wang Ping. Research on the Project Driving of Advanced Mathematics Based on CDIO [J]. Educational Modernization, 2015 (15):143-145.

[4] Gao Zhenbin, Shen, Application of Case Teaching Method in Mathematical Modeling [J]. Educational Exploration, 201(5): 65.

;