First, analyze the causes of difficulties in learning advanced mathematics
1. The characteristics of advanced mathematics determine the difficulty of students' learning.
Higher mathematics is variable mathematics first, and the research object is the change of the relationship between variables, that is, functions; Secondly, the logical reasoning method of conceptual abstraction is relatively difficult to understand and accept. Advanced mathematics is very different from elementary mathematics, which requires students' knowledge transfer ability. Only when students fully understand the concept, master the theorem and grasp the knowledge as a whole can they use it thoroughly and accurately. Therefore, advanced mathematics will be very difficult for those students with relatively poor mathematical foundation.
2. The quality of students is declining year by year.
In recent years, colleges and universities all over the country have adopted the policy of "lenient entry" to attract students, which leads to the lower overall quality of students. Students' basic knowledge of mathematics is not solid enough, and their mathematics learning ability is poor. Most students still have not developed good study habits, and their self-discipline and self-control ability need to be improved. They are not interested in learning mathematics, which increases the difficulty of higher mathematics teaching.
3. Teachers' teaching methods are backward.
Most of the classroom teaching of advanced mathematics is still a teaching mode of "a blackboard and a piece of chalk", and most of the mathematics experiment classes can only be on paper, and students have little chance to really do it. The single teaching method affects students' interest in learning advanced mathematics, and then affects the improvement of teaching quality.
Second, improve the quality of higher mathematics classroom teaching methods
1. Optimize the teaching content, strengthen the pertinence and reflect the application.
Reasonable arrangement of teaching content, according to the characteristics of majors and students, break the dogma of unified teaching syllabus and unified teaching plan, adjust teaching content, and make reasonable choices and supplements. From the beginning, let students know the purpose of learning, the significance of learning, the main contents and functions of the course, and help students correct their learning attitude. When preparing lessons, teachers should understand and master the contents of textbooks, determine the key and difficult contents, clarify the background and context of knowledge points, and analyze the role of teaching contents in students' knowledge structure, skill training and development ability. Teachers should not only prepare textbooks, but also prepare students. They should deeply understand the students' knowledge level and psychological characteristics, feel the teaching content from the students' point of view, distinguish the priorities of the teaching content, and avoid "covering everything", thus further changing the situation that teachers talk too much and students are sleepy.
2. Improve teaching methods and try diversified teaching methods.
(1) Vivid, interesting and intuitive teaching methods. Because mathematics is more abstract than other subjects, we choose intuitive teaching methods to improve students' understanding ability. Use graphics, charts, emotions and other means to let students get a clear representation through perception. Psychological experiments show that people can generally remember 25% of the knowledge gained from vision, 15% only from hearing; If people can combine hearing with sight, what they can remember will increase to 65%. Using the above rules and comprehensively mobilizing students' sensory organs for teaching can greatly improve the quality of mathematics teaching. Specifically, there are the following ways:
First, the description is visual. Calculus contains many important mathematical ideas and methods, which is the focus of the course, but it is often difficult. It can be vividly described by examples and metaphors, and it can often get twice the result with half the effort. For example, when talking about the left and right limits, there is an important mathematical idea, that is, the idea of two sides approaching, so we can use the example of docking with the International Space Station to help students understand the idea of two sides approaching.
Second, the combination of numbers and shapes. Graphics are indispensable to mathematics. We can demonstrate some difficult concepts or figures through the geometric sketchpad, so that students can have an intuitive understanding, so that it is easier to understand and master relevant knowledge points.
Third, combined with the mathematical and cultural background. When we talk about Newton-Leibniz formula, we can start with Newton and Leibniz's schooling experience, and then how they "walked" together. Through the edification of students' mathematical culture, students' interest in learning advanced mathematics is stimulated.
Fourth, make full use of network resources to optimize students' learning environment. With the rapid development of information technology, colleges and universities will gradually develop into a new digital campus with information as the center, network as the medium and colleges and universities as the platform, and enjoy and optimize the allocation of various information resources to the maximum extent. As a university teacher, we should combine the background of the times, try our best to teach knowledge with students' favorite teaching methods, and try our best not to stay at the level of electronic text textbooks, which requires teachers not only to enrich teaching experience, but also to master the necessary multimedia technology and network technology.
(2) Embody the idea of mathematical modeling. The traditional mathematics teaching thought pays attention to the cultivation of students' logical thinking ability, but ignores the students' ability to extract mathematical thoughts from reality and solve practical problems with mathematical knowledge, which leads to the phenomenon that students learn a lot but can't use it. Advanced mathematics gives students the impression that it is boring to recite theorem formulas and complicated calculations, which can't arouse students' subjective initiative in learning mathematics. Therefore, it is necessary to inject mathematical modeling ideas into classroom teaching, which can not only stimulate students' interest in learning mathematics, but also change the embarrassing situation that students can only learn but not use it.
Three. conclusion
Through the study of advanced mathematics, we can not only cultivate students' abstract generalization ability, logical thinking ability and rigorous thinking and analytical judgment ability, but also lay a solid foundation for the study and scientific research of other disciplines. As a front-line teacher of advanced mathematics teaching, this paper analyzes the reasons for students' difficulties in learning advanced mathematics according to their own teaching practice for many years, and makes relevant exploration and analysis on how to improve the classroom teaching methods of advanced mathematics and improve the quality of classroom teaching.
refer to
[1] Liang Lijing. Analysis and Reflection on the Present Situation of Mathematics Teaching in Higher Vocational Colleges, Vocational Education Forum .2007, (48).
[2] Li Ming. Suzhou Institute of Industrial Technology. Career research. 2007, ( 12).
[3] Chen Qi. Educational psychology. Higher education press. 2005, (8).