One way for freshmen to learn advanced mathematics well: to complete two transformations quickly
Freshmen should complete two changes as soon as possible through personal efforts in the first semester.
One is the change of learning style.
The difference between middle school mathematics and advanced mathematics is that middle school mathematics mainly studies constants and advanced mathematics mainly studies variables. The contents and methods of the two are essentially different, which determines that the learning methods of universities are necessarily different from those of middle schools. In fact, middle school mathematics is mainly based on full practice, and the understanding of concepts is not high. Solving problems basically adopts the thinking mode of pattern recognition and method recall, and the methods and skills of solving problems are imitated, memorized and applied. Most students don't have the habit of mathematical thinking, and they don't master mathematical thinking methods. Therefore, in middle school learning, students are all imitating and learning under the direct guidance of teachers. In learning advanced mathematics, we must pay attention to the source of the concept, the starting point of the concept and some specific applications related to it, and ask students to carry out creative learning under the guidance of teachers, that is, take the key and difficult points mentioned by teachers in class as clues, fully digest and master the knowledge learned in class by reading a large number of textbooks and similar reference books, and then consolidate it through exercises and personal review. Therefore, freshmen should take the initiative to communicate with teachers and seniors, learn from others' experience in time, and complete the change of learning style as soon as possible.
The second is the change of learning psychology.
Learning in middle school is often passive learning under the constant urging and supervision of teachers or parents. Mathematics teaching in middle schools generally emphasizes teaching over learning, knowledge over ability, imitation over innovation. Teachers spend a lot of energy to cultivate students' skills through a large number of topic drills, and provide timely guidance and consolidation, and supervise students more strictly. In universities, teachers mainly play a guiding role. Teachers pay more attention to rigor and logic, emphasize the mastery of concepts and principles, and have a deep understanding of thinking methods. Students may not have examples to follow when applying independently. Students' learning is a conscious and active behavior, and exercises are more personal behaviors. Therefore, freshmen should get rid of the psychology of relying on teachers as soon as possible in their studies, and take the initiative to find themselves with teachers (not teachers) if they have learning or ideological problems! ) communicate in time and get guidance.
Be able to restrain yourself in a relaxed environment, study actively and consciously, and be the master of learning, so as to master what you have learned as soon as possible and learn what you have learned solidly.
The second way for freshmen to learn advanced mathematics well: to achieve three societies as soon as possible
One is to learn to attend classes as soon as possible.
This question will be dismissed by freshmen, who think that they have studied for more than ten years, can they still attend classes? But for beginners of advanced mathematics, there is indeed a question of whether they will attend classes.
When studying advanced mathematics, the most important thing for the teacher in class is to understand the whole, rather than sticking to whether every detail is clear or not. Teachers should pay special attention to understanding the ideas when proving theorems or deducing formulas. As long as you master the main idea, it doesn't matter if you don't hear some details clearly. Because I can completely turn the whole process of proof into my own under the guidance of this main line. We know that no listener can guarantee that he can always concentrate and concentrate in a class. Therefore, it is very important to allocate attention reasonably in class: when listening to theorem proving ideas, you must follow the teacher's explanation.
In order to realize the reasonable distribution of classroom attention, preview before class is particularly important. Through preview, you can have a general impression of what you want to learn. In class, you can see the difference between your understanding in the preview and the teacher's explanation, and you should discuss any problems with the teacher or classmates. Only through preview can we have a preliminary understanding of the difficulties and key points in the content to be studied, so as to become an active participant rather than a bystander in the classroom learning process.
The second is to learn to teach yourself as soon as possible.
2 1 century college students are future scientific and technological talents with the mission of knowledge innovation, so they should actively cultivate their self-learning ability and initiative. A certain degree of self-study is the key to learn advanced mathematics well. Self-study should deal with the following relations:
1, the relationship between review and problem solving. It is necessary to change the practice of doing problems after class and taking solving problems as a measure of learning quality. It is impossible to master the thinking method in advanced mathematics just by burying one's head in doing problems. Review should be carried out in time after class, which is impressive and efficient. In fact, the process of review is the process of active thinking and the process of cultivating future scientific research ability.
2. The relationship between thinking and asking questions. Problems in higher mathematics learning advocate problems based on independent thinking. The deeper you drill in your study, the more you can find problems. Make full use of the question and answer time and try to get help from the teacher. At the same time, learn advanced mathematics, don't ask specific exercises, but ask the corresponding knowledge points. If a problem cannot be solved, it means that the knowledge points corresponding to the problem have not been mastered well. If you don't know the knowledge point corresponding to this question, it means that the specific application method of this knowledge point is not well mastered.
3. The relationship between teaching materials and reference books. Review should be based on textbooks and notes, supplemented by reference books. Reading reference books is very beneficial to enrich the knowledge learned and cultivate self-study ability. However, reading reference books should conform to the learning progress, have a clear purpose to read the required content, and then enrich the harvest in the notes.
4. The relationship between planning and flexibility. In the study of advanced mathematics, strengthening planning is an effective measure. Freshmen should take the initiative to ask the teacher about the teaching plan so that they can make a study plan for the next week every week. Only by leaving room in the study plan can there be flexibility in implementation and appropriate adjustments be made according to specific conditions. In this way, with the accumulation of experience, the plans made in the future will be more and more in line with their own reality. The third way for freshmen to learn advanced mathematics well is to learn to summarize as soon as possible.