Advanced mathematics is the earliest important basic course for science and engineering students in higher education. Because advanced mathematics is abstract, logical and reasoning, there are many concepts and theorems, and many students are afraid. In view of how to improve the teaching effect of advanced mathematics, we can explore some practical methods and skills from different aspects such as teaching links [1], teaching means [2] and the use of multimedia [3]. Based on emotion, this paper puts forward some practical suggestions from all aspects of teaching, and deeply analyzes some problems encountered in the teaching process, and puts forward specific measures.
First of all, teachers should attach importance to all teaching links.
1, teachers should pay attention to personal status.
Personally, as a college math teacher, we should first stand upright, dress well, be neat and decent; Secondly, the standard of Putonghua is required, and the voice is loud and powerful, and the speech speed cannot be too fast; Finally, the contents of the courses taught and studied in this major are systematically accumulated. This is the basic quality that a teacher should have.
In addition, teachers should maintain a good mental state. People's mental states will influence each other. In class, if more than half of the students are sleeping, the students' mood is likely to affect the teacher's mood. Therefore, teachers should be full of energy and smile from the beginning of entering the classroom. Some people may think that you can relax yourself before starting class. In fact, the students have been watching you since the teacher stepped into the classroom. Your state will affect the state of students in class, so even if you have a serious lack of sleep the night before, you can't appear sleepy and groggy in front of students. If the teacher can scan the students in the classroom with a smile when they enter the classroom, instead of going straight to the teaching equipment to prepare for class, it will also achieve good results.
Teachers should pay attention to preparing lessons before class.
Preparing lessons is an important prerequisite for a good class, a basic guarantee for improving teaching quality, and an important way for teachers to continuously enrich their teaching experience and improve their professional ability. So what should teachers do? Teachers should seriously study the syllabus and teaching materials, thoroughly understand the teaching materials, and accurately grasp the difficulties, key points and keys. We should prepare the teaching content carefully, fully and meticulously, and what content should we make clear? What do you mean? When preparing lessons, you should think carefully and design carefully.
"Be prepared before class and be familiar with the teaching content, …" is a sentence that a teacher often hears. However, how can we get ready and be familiar with the teaching content?
For the advanced mathematics course, I personally think we should at least do the following: first, make clear the difficulties and key points of this course, allocate time reasonably, pave the way for the difficulties or prepare some simple examples to help students understand, so that students can feel where the difficulties are from the teacher's explanation and know where the key points are from the allocation of time; Second, the concepts and names in the course must not be misspelled or misspelled, and those with multiple names or expressions should be introduced one by one; Basic concepts should be thoroughly understood, and the meanings of keywords and words in concepts should be clearly understood; The difference and connection between concepts and similar concepts should be grasped in place; Thirdly, the reasoning of the basic theorem is clear, and the thinking of solving problems is clear, so as to realize the possible wrong solutions in the process of solving problems; Fourthly, the rational use of multimedia is an issue under discussion. The biggest problem in the use of multimedia is that when the speed is fast, the ideological process of students' independent analysis and discussion is omitted, which is not conducive to cultivating students' autonomous learning ability.
3. Teachers should know the teaching objects.
The teaching object of teachers is students, and the teaching object of advanced mathematics course is freshmen. Teachers should not only be familiar with the teaching content, but also understand the learning attitude of freshmen before teaching.
For some freshmen, first of all, they finally ended their crazy senior three studies and entered the university as they wished. Many things outside of study (such as various societies, part-time cadres, etc. ) is very attractive to them, resulting in insufficient learning energy; Secondly, the study in junior high school and senior high school is extremely hard, and the purpose of hard work is to be admitted to an ideal university. Now that the goal has been achieved, learning seems less important, resulting in insufficient learning motivation; What's more, after graduation, my family will help me solve my work problems, so that I can muddle through my studies in college. Of course, there must be some students who can arrange the relationship between study and other activities well and achieve ideal results in all aspects of study, work and life.
Only by understanding the students' mentality can students have all kinds of "bad learning" behaviors (for example, not previewing on time, sleeping in class, not completing homework as required, etc.). ), teachers can really understand students, and understanding students is to relax the teacher's own mood, and then actively think of some better ways to improve the bad situation. Will an angry or angry person calm down and try to solve the problem?
In addition, teachers should have a certain understanding of students' disciplines and majors, mathematics foundation, and the dependence of the follow-up courses of this major on advanced mathematics knowledge, as well as students' regional characteristics and teaching level, so as to have a clear idea and be targeted. Teachers and students should be in full contact. Teachers should understand students' state, adjust the original teaching methods, and guide students to be familiar with and adapt to their own teaching style.
4. Teachers should grasp the teaching process.
Paying attention to personal status, preparing lessons before class and understanding the teaching objects are the purposes of better grasping the classroom, mobilizing students' learning enthusiasm, mastering the basic courses of advanced mathematics and laying a solid foundation for future study.
The classroom teaching of advanced mathematics is mainly to explain concepts, formulas, theorems, examples and exercises that are easy to make mistakes in students' homework. The content is a bit boring than other courses. Literature 2 puts forward many measures on how to teach advanced mathematics well. However, the classroom is a matter for both parties. In order to achieve better results, in addition to a series of measures taken by teachers, students also need to actively cooperate.
If you want students to follow the teacher's ideas, you can't arbitrarily or unintentionally discourage students from learning. To take good care of students' enthusiasm for learning, we should start from the usual dribs and drabs. For example, when reviewing the content of the last class before class, you can't criticize the students who answered incorrectly. In fact, he already felt embarrassed. Students who do problems on the blackboard can't even use them directly. Teachers must not be angry. They can explain it themselves or ask other students to do it. I believe all the students who can't do it understand. In short, for the mistakes made by students because they don't understand the principle, teachers should first look for problems from themselves, whether they have not explained clearly, and there may be other aspects that were not expected, and so on.
Second, the analysis of several typical problems in the teaching process
1. What should teachers do if they find students sleeping in the teaching process?
It has become a big problem for students to sleep in class. In view of this problem, some teachers take measures to ignore it. The reason is that if students are willing to study, they will naturally not sleep in class. If they don't want to learn, they may not be able to listen well even if they don't sleep. It certainly sounds so. Is that really the case?
Students always sleep for a reason. Teachers should first understand their current state from the heart, and must not be angry, and then give effective guidance. One of the purposes of university study is to cultivate students' good personal study habits and personal living habits, which is more important for freshmen. Advanced mathematics is a compulsory course for freshmen, which belongs to the category of basic courses, and the corresponding mathematics teacher is also called the basic course teacher. Because the basic course teachers are in contact with freshmen, the course lasts for a long time and there are many class hours, so the basic course teachers have a greater influence on students and shoulder a heavier burden. Therefore, as the first responsible person in class, teachers must not ignore the problem of students sleeping in class.
As we all know, students in local universities are managed by administrators, while students in military schools are managed by captains. When dealing with students' sleep problems, teachers should avoid training students in class or making them stand up and listen (it doesn't matter if students stand up by themselves), and avoid telling managers (at least don't let students know). Try not to be emotionally opposed to students. This is not to say that it will be ineffective, but that we can find some better treatment methods or measures.
In fact, on the issue of students sleeping, everyone has their own methods. Personally, I think we should start from two aspects: preparing lessons and classroom management. First of all, when preparing lessons, we should consciously simplify difficult knowledge. We can give some simple examples, or give simple explanations intuitively to avoid the situation that most students don't know what to say. Because the math course itself is boring, students are more likely to get sleepy if the teacher just keeps explaining it by himself. Therefore, when preparing lessons, students should give some simple examples of the required knowledge points and try to let students do it first, so as to prevent students from falling asleep. Secondly, in classroom teaching, if the teacher finds that the students are sleeping, he can pause and talk to the students about some topics that are related to the students but have nothing to do with the content of the class at that time. The topic should be as short as possible, which will not affect the teaching progress but make students awake. When students are doing classroom exercises, teachers can also walk around the classroom at the right time, patting the sleeping students as long as they wake up. Try not to teach him any more, let alone lecture him in front of the whole class.
2. What should teachers do when they have conflicts with students in the teaching process?
If you are a young teacher, you just started school for two weeks, and a class has the following situations, what will you do? The teacher talked earnestly for half an hour and asked the students, "Did you understand all the knowledge just now? Are there any questions? " A stubborn voice: "No!" Teacher: "Who said that just now? Stand up. " Hoo, a classmate stood up ... Teacher: "What don't you understand?" Student: "I don't understand!" " "The dialogue reached an impasse and the classroom was silent. ...
Faced with such a situation, improper handling will have two consequences. First, the teacher's prestige among students is gone, and the future courses are not easy to be carried out in a friendly atmosphere, and the teacher himself may not be willing to discipline this student from the bottom of his heart; Secondly, students are opposed to this course from the heart, and the basic concepts at the beginning are not fully mastered, so the later study may be very difficult. The key is that the later study may be a kind of mental torture for him.
When I first talked about the course of advanced mathematics, I was lucky to meet this situation. At that time, the course had just started less than a month, and my experience was not enough to cope with the scene at that time. I think if I keep a tough attitude, it may not end well, so I suppressed my anger and asked the students' names, and then said, "Come to me after class, and we will find time to make up for what you don't understand." You sit down. "The student didn't come to see me after class. I went to see him and asked him when he was free. He told me that he didn't need to trouble the teacher. He will go and have a look for himself. If not, he can ask his classmates. Finally, judging from the results, the student has been at the upper-middle level. It seems that the measures I took at that time were right.
In practice, when there is a real conflict between teachers and students, many teachers will choose to tell the students' managers. Personally, I think this kind of measures to deal with problems is not desirable, because managers usually associate students' various behaviors with their final evaluation, which will cause emotional opposition between students and teachers. On the surface, the student may no longer make trouble in class, but he is not sure whether he has solved the problem fundamentally.
The math course itself is rather boring. As teachers, we can make the course simple and interesting, so that students can enjoy it. It can also make students like this course because they like the humor of the teacher's speech or some styles of the teacher. At least, students should not dislike this course because of the way some teachers do things.
3. What should teachers do if they make mistakes in the teaching process?
Advanced mathematics teachers must be very familiar with the theoretical knowledge of the course, but it is not enough to be familiar with the content. They should also analyze from the students' point of view, find out what is difficult to understand and easy to make mistakes, and analyze what ideas students may have, how these ideas come about, where the root causes of mistakes are, and so on. In this way, you can be handy when explaining the theoretical part. If time permits, you can also deliberately "make mistakes" and then correct them, so that students will have a deeper understanding of the knowledge points.
Teachers may have had this experience in the teaching process, and made mistakes in the specific derivation of topics on the blackboard, especially since multimedia courseware was widely used in classroom teaching, such clerical errors have occurred from time to time.
What should I do if I make a mistake? If you have realized before the end of this topic or found that it is getting more and more complicated or contradicted with other places in the process of derivation, you can test the students, let them correct their mistakes, and let them know where this type of topic is prone to mistakes, which requires students to be particularly careful. If a student finds out first, shout: "Something is wrong, it should be ……". At this point, you can calmly say, "It seems that this place is prone to mistakes. Students should learn a lesson and don't make similar mistakes in the future ... ". At the same time, let students understand that teachers are human beings and may make mistakes, so they should have their own views in future study. Errors are inevitable, and whether they need to be covered up depends on the specific situation.
5. Conclusion
The role of mathematical literacy in all walks of life is becoming more and more obvious. How to continuously improve students' mathematical foundation and lay a solid foundation for future study? As a math teacher, I will continue to explore and think positively in this respect, so as to accumulate experience for future teaching.