Kevin·Z

Since the middle of last century, with the rapid development of computer technology and modern information technology, the subject of mathematics has also developed rapidly, and the requirements for mathematics and applied mathematics are getting higher and higher. There is an increasing demand for mathematics talents in the new century, but there are some problems in the current mathematics teaching in colleges and universities, which are divorced from reality and lack of application and intuition. In order to adapt the talents in colleges and universities to the needs of the times, this paper discusses some problems existing in mathematics teaching in colleges and universities, so as to improve the literacy and teaching quality of talents in colleges and universities. Mathematics teaching; Intuitive; Applicability; quality of teaching

With the rapid development of high and new technology, quantitative research in science and technology and various professional fields has become increasingly popular and in-depth, and the application of mathematics has become increasingly extensive. In the new century, scientific and technological talents have higher and more comprehensive requirements for college students' mathematical quality. However, at present, there are many problems in the teaching of undergraduate mathematics courses in colleges and universities, which are not suitable for the current situation of reducing class hours and expanding students' enrollment in colleges and universities as a whole. How to strengthen the intuitive and applied teaching, pay attention to the teaching efficiency and effect of the course, and effectively improve the quality of college mathematics education is particularly important. First, the problems in college teaching

Due to the lack of intuitive and applied teaching, the following common phenomena have appeared in the current college mathematics teaching:

(A) "definition+theorem+calculation (example)" phenomenon is serious.

This method belongs to the traditional teaching mode, and I personally think it is more suitable for the education of middle school students. But in the education of colleges and universities, we should pay attention to improving students' imagination, creativity and independent thinking ability. This teaching mode is single. Although there are many knowledge points taught, there are few explanations about the source of knowledge points and the relationship between knowledge and surrounding things. Lack of application, boring teaching content, it is difficult to arouse students' interest, let alone application. (2) Over-abstraction of concepts In some mathematics teaching, the lecturer overemphasizes the abstract concepts of mathematics without paying attention to reality, which makes mathematics difficult to be practical. It is not only difficult to stimulate students' interest in learning, but also makes them feel noisy and disgusted. Too much emphasis on the rigor of mathematics makes mathematics lose its universality and practicality. Lack of or little attention to intuition, especially geometric intuition teaching, makes students know what they know but don't know why, and to a great extent falls into a state of "getting carried away", "getting" the literal definition, nature and theorem of mathematical knowledge, and "forgetting" the original motivation and intuition of mathematical knowledge (3) Students are tired of learning.

The lack of practical and applied mathematics teaching makes students have no passion to learn mathematics effectively, while pure theoretical teaching can not only improve students' practical ability, but also stifle students' imagination and creativity. This leads to a high degree of students' weariness of learning mathematics, and even thinks that learning mathematics has no practical use, let alone students' dedicated study and application of what they have learned. Some students even don't listen to the teacher in class and do their own things, which is not conducive to students' study and teachers' teaching. (D) the lack of applied teaching

Let students think that mathematics is "x+y = z", and learning well has nothing to do with their future development. The source and application of mathematical knowledge are rarely introduced, which does not fully reflect the importance of mathematics and its promotion and support for the development of science and technology and other disciplines. It is not fully realized that making students understand the wide application of mathematics is also one of the tasks of mathematics teaching, which will often play a multiplier role in improving the quality of mathematics teaching. And students are not allowed to use mathematical models themselves, such as doing some mathematical modeling. Computer simulation of economic development and so on. Make students not strengthen the application of mathematics. Second, the reasons behind the phenomenon

Is it an inherent feature of mathematics that mathematics is difficult to understand, or is it a math teacher's lack of ability to spread mathematical knowledge? The above phenomenon should be caused by the mathematics discipline itself and the teachers themselves. Briefly summarized as follows:

(A) the subject characteristics of mathematics

Mathematics is a subject with strong rational thinking, which requires students' rich imagination and strong rational thinking. Mathematics itself has the characteristics of preciseness, abstraction, systematicness and relevance, which also brings great difficulty to mathematics teaching. How to make mathematics teaching intuitive and applicable requires a deep understanding and attainments of mathematics. (B) the development of mathematics

Modern mathematics has developed rapidly, and the development speed has been greatly improved. Mathematics knowledge is updated faster. Maybe a theory is practical today, but it may not be practical in the future. Some conclusions are valid today and may be overturned tomorrow. In addition, the category of mathematical science is very complex, the development of mathematical discipline is beyond imagination, and the abstraction and complexity of mathematics are increasing day by day. Nature puts forward high requirements for the teaching and learning of mathematics. And the development speed of modern mathematics is much higher than that of ancient mathematics. If we don't strengthen the updating of mathematical knowledge, mathematical knowledge may be eliminated, let alone taught to students.

(c) The level of teachers and their understanding of mathematics

The level of teachers will have a great influence on students' learning. A good teacher may not teach a good student, and a bad teacher will not teach a good student. Sometimes, due to the limitation of their own level, teachers can't explain mathematical concepts deeply and popularly, which leads to students' learning difficulties. Moreover, if teachers don't really understand mathematics knowledge and culture, it is easy to mystify, complicate and symbolize mathematics. Become only talking about mathematics, not teaching and not talking. Third, the solution to the problem.

Intuitive teaching is an important principle of teaching activities. /kloc-in the 7th century, the Czech educator Comenius declared that intuitive teaching is the golden rule of teaching: "whenever possible, we should accept everything with sensibility". From the psychological level, we can know that one hundred stories are worth reading. In mathematics learning, we should do everything possible to link abstract mathematical conclusions with intuitive images. Because intuitive images are generally clear and stable in memory, it is easy to remember abstract mathematical conclusions through them. (A) to avoid traditional teaching methods

Strengthen the interest of mathematics teaching, change the traditional teaching methods in the past, and really stimulate students' interest, instead of simply explaining definitions+theorems+calculations, we should cultivate students' practical ability and creativity. In order to improve the teaching quality, modern mathematics teaching methods should be properly used. Strengthen the intuition of teaching, such as explaining functions and derivatives with computer software to make the changes of functions more intuitive. Applying modern science and technology to teaching has become an important means of modern teaching. This requires our teachers to master modern computer application technology skillfully. This is not only conducive to their own learning, but also can make the teaching methods break away from tradition and stimulate students' interest and ability in learning. (B) to strengthen the practicality and application of mathematics teaching

In order to avoid excessive abstraction in mathematics teaching, mathematics teaching should be easy to understand and more practical. Instead of making mathematics mysterious and complicated. Let mathematics be closer to real life and let students really feel that learning is useful. So as to really stimulate students' inner enthusiasm for learning mathematics. Instructors can encourage students to do some mathematical modeling and guide students to participate in mathematical modeling competitions, so that the learned mathematical knowledge can be applied, and the application of mathematics can be consolidated and improved. Make mathematics not boring but full of practical significance. If possible, you can also lead students to participate in social internships, so that students can do it themselves and truly understand the usefulness of mathematics. Only in this way can the practicality of mathematics be brought into play and the teaching quality be improved. (C) Lecturers to strengthen their own learning, improve their ability.

As the saying goes, there is no end to learning. Lecturers should also strengthen their learning and understanding of mathematics to improve their level, and constantly explore new teaching schemes and innovations in mathematics teaching to make mathematics teaching more attractive, thus improving students' level. A good teacher can teach a good student, starting with himself. If a person's ability is insufficient, students will naturally not be interested in learning, on the contrary, they may have an aversion to learning mathematics, which will not only harm students, but also harm themselves. And now the speed of mathematics development is also quite fast. If teachers themselves do not update their knowledge and keep up with the times, then teachers themselves may be eliminated. Therefore, teachers should strengthen the study and cultivation of their own abilities.

(D) Improve students' learning mood

Students' learning mood in mathematics is very important, and a good teacher knows how to stimulate students' interest in learning. Even if the teacher speaks well, students will not be in the mood to learn mathematics, so they will not actively cooperate with the teacher in class, let alone follow the teacher's ideas to think. Therefore, while teachers are doing their best, they should also consider how to improve students' interest. Of course, students should have their own learning emotions, actively cooperate with teachers, let both sides reach an understanding and create a good learning atmosphere. abstract

In short, the development of mathematics in today's society is extremely rapid. In order to meet the needs of the times, we must strengthen the practicality and intuition of mathematics teaching, improve the quality of teaching, and make college talents really learn knowledge and really use and contribute to society. This not only fulfilled the responsibility as a teacher, but also failed to live up to our teacher's expectations.