First, preview before class and find out the difficulties.
Preview can fully improve the efficiency of classroom lectures, and good preview habits can lay a solid foundation for improving self-study ability in the future. Therefore, before class, students should preview the content of the new lesson to be taught that day, at least understand more than half, and have a preliminary understanding of the whole content, instead of relying on teachers to solve problems, so as to stimulate their potential. Write down what you don't understand. As the focus of the new course and the content of asking questions, we can boldly give up the tedious and difficult derivation and proof process.
Second, listen carefully in class and dare to ask questions.
The acceptance of new knowledge of advanced mathematics and the cultivation of mathematical ability are mainly carried out in the classroom. Students should report their strong interest in acquiring energetic new knowledge and all kinds of problems in preview, and listen carefully to the teacher how to ask questions, analyze problems and solve problems in class. Therefore, in class, we should closely follow the teacher's thinking, actively develop our thinking, predict the next steps, compare our thinking of solving problems with what the teacher said, correct the subjective understanding in preview, and enhance our understanding and memory of new textbooks. When a teacher proves theorems and deduces formulas, the most important thing is to understand ideas. As long as you get the general idea, it doesn't matter if you don't hear some details clearly. Under the guidance of this idea, I can make up all the details and finally draw a conclusion. At the same time, class notes are an important means for students to think positively and ensure the effect of lectures, and they are also good reference books. Good notes can get twice the result with half the effort Therefore, students should be good at taking notes in class, because what the teacher said in class is in most textbooks, so there is no need to pursue completeness in taking notes.
Third, review carefully after class.
Confucius said, "It's okay to learn and learn from the times!" This paper puts forward the importance of review, but review is not a simple repetition. We should use our own expressions to reproduce what we have learned. When reviewing, we should combine class notes and teaching materials, refine the main content of this lesson, grasp the essentials, extract the essence, deepen understanding and strengthen memory. At the same time, it should be noted that the idea of review should not just copy the teacher's lectures or textbooks, and a reference method is to use flashbacks. From the conclusion of the theorem, we can deduce how to reason to get the conclusion of the theorem and where the conditions of the theorem are used, but we must make the basic concepts clear, the basic theories accurate and the basic reasoning methods skilled. In this way, the reverse thinking mode is a creative thinking activity. Finally, remember to arrange periodic review, sort out and summarize at each learning stage, and combine the points, lines and surfaces of knowledge into a knowledge network and bring it into your own knowledge system.
Fourth, finish the homework assigned by the teacher independently.
If doing a good preview is a sufficient condition for improving the efficiency of classroom lectures, then completing homework in time is a necessary condition for reading advanced mathematics well. Some students copy their classmates' homework because they are lazy or can't do some problems, or deal with them at random regardless of quality. These are irresponsible behaviors, and they don't respect teachers or themselves. Be sure to read the homework approved by the teacher carefully, which is a respect for the teacher's hard work and a good way to correct mistakes and avoid repeating them. In addition, you can't do homework for the sake of homework. When doing homework, you should think more, compare with what you have learned in the past, and constantly improve your problem-solving ability.
Five, participate in mathematical modeling
Generally speaking, there is not only one correct model for a practical problem. The same problem can be solved by many different models, and the same abstract model can be used to solve different specific problems. It has no fixed methods and prescribed mathematical tools, and there are no ready-made answers and models to follow. The result is only better, not the best. In this way, mathematical modeling itself provides students with a practical process of independent learning, independent thinking and serious exploration. It brings students a flexible way of thinking and broadens their horizons. It encourages students to think deeply about problems and provides atmosphere and conditions for students to play their creative talents. Through modeling, students should grasp the main points of complex practical problems, make the problems clear gradually, classify the problems into one category, reveal their essential characteristics, get the key points and difficulties to solve the problems, and consciously use the given conditions to seek the best solutions and ways to solve the problems. This process can give full play to students' rich imagination and innovative ability, thus improving their learning enthusiasm and cultivating their interest.
Sixth, read more relevant books to improve self-study ability.
Reading more reference books will broaden your horizons, increase your knowledge and deepen your understanding of knowledge. Reading reference books is also the second classroom for learning, and it is the supplement and continuation of classroom learning. It is often impossible for us to read a reference book carefully because of the time. So I suggest that you can selectively look at other reference books around a problem that you are interested in or want to study in depth, find relevant parts in these reference books, study this problem in depth and see how these reference books are discussed. We should also take notes when reading. On the basis of what we have learned, through comparison with the teaching materials, we should be brave enough to absorb what is superior to the teaching materials, and the discussion of what is inferior to the teaching materials should not be affected, so as to make a summary for the exercise.
Teachers use multimedia in class to improve students' interest in learning.
Multimedia teaching is a vivid teaching form, which can be changed from abstract to intuitive, so that students can deepen their understanding and mastery of mathematical theory and stimulate their interest in learning mathematics. Appropriate introduction of multimedia teaching can increase the amount of classroom information, extend the teaching content, help students obtain more perceptual materials, make teaching more intuitive and improve the quality of classroom teaching, thus helping to cultivate students' thinking ability in images, and at the same time arouse students' curiosity and interest in learning.
In a word, as a higher vocational student, the key to learn advanced mathematics well is to use appropriate learning methods. We should sincerely sum up and explore suitable learning methods in our usual study, so as to learn advanced mathematics well, cultivate our logical thinking ability and innovation ability, and lay a good foundation for the cultivation of our abilities in all aspects.