Research shows that college students' learning ability is generally not strong at present, and students learn passively under the guidance of teachers. Students' knowledge acquisition and application ability (knowledge memory, understanding and application), self-monitoring ability in learning process (setting learning objectives, selecting and adjusting learning methods, implementing and controlling learning process, reflecting and summarizing learning results), and management and application ability of learning resources (learning time, learning environment, learning motivation and learning behavior). Therefore, improving college students' learning ability as soon as possible is an important topic facing higher education reform.
College mathematics is an important basic course for science, engineering and economic management majors in colleges and universities. It plays a very important role in innovating students' learning concepts, improving learning methods and cultivating their learning ability. It directly cultivates students' learning ability and provides students with the necessary basic mathematical knowledge and common mathematical methods for learning other subjects. Therefore, college mathematics teaching undertakes not only the teaching of simple mathematical knowledge, but also the development of students' mathematical quality and the cultivation of students' abstract thinking ability.
Traditional college mathematics teaching has always been aimed at imparting knowledge. It is difficult to cultivate students' learning ability under the domination of values aimed at coping with exams. In the relationship between knowledge, ability and quality, too much emphasis is placed on the teaching of knowledge and the cultivation of students' learning ability is ignored; In the relationship between teaching and learning, teachers' leading role is overemphasized, while students are neglected as the main body of learning. This teaching mode, which emphasizes knowledge memory, examination and innovation, can no longer meet the demand of innovative talents in modern society, and it is urgent to build a new teaching mode.
Compared with the traditional teaching mode, three-dimensional teaching is a brand-new teaching mode. It pays attention to the overall design of teaching material content, teaching form and teaching space in college mathematics teaching, which can effectively play the leading role of teachers and fully realize students' independent construction in emotion and cognition. The three-dimensional teaching mode has three meanings: one is the hypertext of teaching materials, the other is the diversification of teaching forms, and the third is the expansion of teaching space. Because these three aspects examine a concept from three dimensions and are an inseparable unity, this teaching mode is called three-dimensional teaching mode. This teaching mode has played an active role in improving teaching efficiency, improving teaching effect, expanding teaching information, cultivating students' practical ability and improving their comprehensive quality in all aspects. Then, how to cultivate students' learning ability in three-dimensional college mathematics teaching? I think we can start from the following five aspects.
First, effectively improve the quality of classroom teaching
Whether it is the traditional college mathematics teaching mode or the three-dimensional college mathematics teaching mode, the classroom is the main channel for students to acquire knowledge, but there are obvious differences between them: the former has a small classroom capacity and the students receive limited knowledge; The latter class capacity is greatly increased, and students receive more knowledge. In this way, it is necessary to improve the quality of classroom teaching. And if the content is too much for students to accept, the result will be counterproductive. So students must prepare well before class. Before class, the teacher should tell the students the content of the next lecture, so that students can "come prepared" and attend class with questions, so that the teaching effect will be greatly improved. In class, teachers should pay attention to the choice of teaching methods and adopt multimedia teaching methods, but their functions should not be exaggerated too much. "Blackboard+chalk" is still an important means of modern educational technology, which has incomparable advantages over multimedia teaching methods, such as teacher-friendly and infectious teaching. In the classroom, teachers should combine the two organically, so as to get twice the result with half the effort and effectively improve the quality of classroom teaching. In addition, we should also pay attention to the integration of multimedia teaching methods and mathematics courses: the application of multimedia should not only cause profound changes in the depth and breadth of teaching, but also guide students from classrooms and books to the broad outside world. Thirdly, teachers can adopt better teaching strategies and inspire students to think. Only in this way can it really help to cultivate students' learning ability.
Second, arrange the teaching content of college mathematics reasonably to make the teaching method more humanized and personalized.
One of the key points of college mathematics course is to cultivate students' rational thinking ability. Learning college mathematics well requires rational thinking. It is through this powerful guidance and fluidity that mathematics further cultivates students' abilities of induction, calculation and spatial imagination, so mathematics is known as "gymnastics of thinking". We must master some principles and methods of mathematics, which is the main channel to cultivate students' logical thinking. By studying mathematics, students' logical thinking ability will be greatly improved, and these principles and methods are also the source of students' future development. Therefore, it is essential to learn mathematical principles and methods. However, if the teacher only deduces step by step in class and the students keep taking notes, this boring teaching method will easily lead to students' unwillingness to learn mathematics or even talk about it. In order to create an active mathematics classroom atmosphere, teachers can appropriately insert stories about the development history and trends of mathematics and some mathematicians in the classroom, which can not only cultivate students' innovative consciousness and scientific spirit, but also stimulate students' interest in learning.
In classroom teaching, teachers can try to teach by classroom discussion. We advocate interactive and discussion-based teaching methods, that is, students respond to teachers' questions, and there is dialogue and communication between students and teachers. Students can discuss problems with teachers at any time in class, instead of cramming from beginning to end. Teachers can also try to get all students to prepare lessons and randomly choose a student to give lectures, which not only respects the students' dominant position in teaching, but also enlivens the classroom atmosphere and makes the teaching methods more humanized and personalized. Long-term persistence in this way will greatly improve students' learning ability.
Third, set up mathematical experiment courses to improve students' mathematical application ability.
College mathematics is the foundation and is widely used in other disciplines. The basic knowledge and thinking method of mathematics have penetrated into various fields of science and engineering, such as scientific research and engineering technology. At the same time, the application of mathematics in humanities and social sciences has also promoted the innovation and development of these disciplines, such as the application of probability theory in moral philosophy. With the progress of science and technology, especially the rapid development of computer technology, mathematics has more extensive influence on contemporary science and even the whole society, and mathematics has become the main pillar of scientific research. It has become a common mode to solve practical problems by establishing mathematical models, applying mathematical theories and methods and combining computers, so modern society has put forward higher requirements for the mathematical quality and ability of scientific and technological talents.
Mathematical experiment course has adapted to the requirements of modern society for the cultivation of scientific and technological talents. Its purpose is to make students understand and gradually apply mathematical knowledge and methods to solve practical problems and conduct "experiments" with computers. For example, mathematical software such as Mathematic and Matlab can improve students' practical application ability of mathematics and stimulate students' interest in learning mathematics. The energy generated by the combination of mathematics and computer is enormous, and students' learning ability will be greatly improved.
Fourth, guide students to carry out extracurricular autonomous learning.
Class time is limited, so it is necessary to cultivate students' learning ability after class. We should actively guide students to participate in some extracurricular activities to improve their autonomous learning ability. For example, the national mathematical modeling competition for college students is one of the largest extracurricular scientific and technological activities in colleges and universities in China, and it is a mass scientific and technological activity for college students. Its purpose is to stimulate students' enthusiasm for learning mathematics and improve their comprehensive ability to use computer technology to build mathematical models and solve practical problems. Participating in such extracurricular activities will greatly improve students' comprehensive ability.
There are extremely rich mathematical resources on the Internet. If we can make full use of the rapidly growing and frequently updated network resources properly, it will be very beneficial to the cultivation of students' autonomous learning ability. Online learning resources are unlimited. If students want to get the learning information they need, they only need the help of the internet, and all kinds of information will come in droves, not only browsing, but also downloading. This opens a fast door for the study of mathematics courses, which is far more convenient and quick than the previous library to consult materials, with strong timeliness and wide sources of information. At the same time, students' learning is not limited by time and space, but also fully embodies their autonomy. Network provides a place for cultivating students' autonomous learning ability. Learning mathematics through network not only meets the requirements of "autonomous learning" advocated by mathematics teaching today, but also cultivates students' interest in inquiry, scientific research ability and innovative spirit.
Many colleges and universities have online course resource banks and excellent course resource banks, and the online learning resources are very rich. The biggest feature of college mathematics is the abstraction of knowledge, the abstraction of mathematical concepts and theorems, and it is difficult for students to understand and accept knowledge. In addition, many colleges and universities recruit students for the whole country, resulting in uneven quality of students. Normal classroom teaching cannot guarantee the learning quality of all students. Therefore, we can use the online course resource library and excellent course resource library to show the more abstract concepts in college mathematics in the form of multimedia, such as limit, derivative, definite integral and so on. In addition to the normal classroom teaching, students can also learn independently with the help of the Internet according to their own needs, which can not only consolidate the classroom teaching content, deepen their understanding of concepts, but also stimulate their interest in learning and cultivate their learning ability.
Fifth, introduce mathematics application cases in the classroom, so that students can really feel that learning is useful.
An important reason why some students don't like learning mathematics is that they think mathematics is of little use. Mathematics is not as obvious as the practical application of other subjects, so students feel tired of learning, which is very unfavorable to their future development and will certainly affect the cultivation of their learning ability. College mathematics curriculum has a subtle influence on the cultivation of students' learning ability.
In fact, the knowledge of calculus, linear algebra, probability theory and mathematical statistics in college mathematics has broad application space. If the teacher only takes pains to teach the calculation methods and skills of limit, derivative, integral and linear equations, but ignores the elaboration of their basic ideas and the analysis of application cases, then students will be at a loss when facing practical problems. In this regard, teachers can try to carry out mathematics case teaching and introduce some practical application cases of mathematics in other disciplines in the classroom, that is, draw mathematical knowledge from practical problems and then use mathematical knowledge to solve practical problems in life and engineering.
Some educators in China have noticed this and done some pioneering work. For example, the book "Engineering Linear Algebra (Matlab Edition)" co-authored by Chen, Gao Shuping and Yang Wei lists a large number of practical application examples of linear algebra, which can be solved by Matlab and other software. By studying Engineering Linear Algebra (Matlab version), students will find it very useful to study mathematics, and their ability to analyze and solve practical problems by using mathematical thinking mode will naturally be improved.
References:
Yuan Weixin. A summary of foreign science teaching models based on constructivism [J]. Comparative Education Research, 2003, (8).
[2] Zhao Guodong. The application of modern educational technology and the modernization of teaching process in colleges and universities [J]. Higher Education Research, 2000, (2).
[3] Text assistance. Professional Education Model of China University and Its Reform [J]. Higher Education Research, 2000, (2).