Xu Zhiyun said that the position and score of mathematics in the college entrance examination are extremely important. It can be said that "those who get mathematics in the college entrance examination win the world", and learning mathematics well will play a great role in entering an ideal university. This is especially true for liberal arts students, because many liberal arts students have little difference in Chinese and English, and the first grade is mathematics. In the usual exams and college entrance examinations, some math scores even differ by 30-60 points. Judging from the past, according to the characteristics of liberal arts students in mathematics learning, it is necessary to learn mathematics well with the help of "external force" if you want to improve your mathematics performance at present.
One is to attend a cram school. This is a useful supplement to school teaching, which can be one-on-one tutoring or a small class of 4-8 people. If there are too many people, the effect will be greatly reduced.
Second, students learn from each other. Including the timely discussion and exchange of what you have learned in your daily study. For example, when you learn new knowledge of projection drawing, you can use recess or other time to ask your classmates for advice immediately about what you have not learned or have little knowledge, so that you can solve problems anytime and anywhere, so as to solve problems that day.
The third is to ask the teacher for help. When studying and doing homework in each class, once there is something you don't understand, you can solve the learning difficulties and problems in time through face-to-face tutoring, telephone, SMS, email, qq and other different ways, so as to be shameless. This is also a valuable experience for liberal arts students to learn mathematics well.
[study guide]
Positioning should be reasonable, emphasizing basic knowledge.
Chen said that through the research and analysis of the college entrance examination questions in recent years, it was found that most of the liberal arts mathematics questions were medium, accounting for as much as 80% of the total score. For most liberal arts students, it is very important to do this sub-topic well. Students should increase independent problem-solving and psychological simulation training in the examination room, which can further improve and greatly improve the overall math scores. Students should correctly estimate their mathematics level and learning ability, and establish their own starting point of mathematics review practice and learning goals of mathematics achievements. For most students who take the liberal arts and art test in senior three, the foundation of mathematics is relatively poor. Therefore, math review must pay close attention to basic review. Through review, you can use what you have learned to analyze problems and solve the most basic fill-in-the-blank questions and intermediate questions. For difficult problems, learn to give up voluntarily, there is no need to waste time. If you really understand the basic things, make sure that the fill-in-the-blank questions (before 10) and multiple-choice questions (before 3) do not lose points or less, and firmly grasp 40% (the proportion of easy, medium and difficult papers is 4: 4: 2). If possible, complete the easy part of the intermediate questions, and the college entrance examination can completely exceed 100.
We should use teaching materials reasonably.
Chen stressed that the test point of the college entrance examination is "no textbook will never change", and many test questions come from examples and exercises in textbooks. Students should pay more attention to the textbooks, and the examples and exercises in the textbooks are valuable resources for senior three liberal arts students to review. Redo the typical exercises in the textbook, so that students can re-examine and summarize the difficulties, problem-solving methods and mathematical ideas contained in them from a global perspective, so as to have a brand-new understanding of mathematics learning. There are always many undigested problems in the process of mathematics learning for senior one and senior two students, which have been puzzling the development of their mathematical thinking ability and affecting their confidence in mathematics learning. It is very important to master the chapters of the whole textbook first, then refine the specific content, build a knowledge system in your mind by association, understand the essential relationship between problem-solving ideas and knowledge methods, and improve your practical application ability. Returning to textbooks is not about memorizing questions and conclusions, but focusing on mastering the knowledge covered by examples and problem-solving methods, and selecting some highly targeted topics for intensive training, so that review can be effective.
Understand the knowledge network and build a cognitive system.
The knowledge module of mathematics is not isolated. Students should find the connection points between knowledge under the guidance of teachers, some of which are conceptual extension connections and some are application connections. When choosing exercises, it should not be too difficult. We should focus on basic exercises, fully experience and reflect on the existing knowledge and experience, and realize the construction of knowledge on this basis. This requires careful memory, pondering and reflection after class. Looking back on some typical examples, we can further deepen our cognitive impression through reflection. Over time, you can quickly draw inferences and improve your thinking ability and problem-solving ability. For typical questions, we should take the method of rolling review and review the contents of the previous days every few days. When doing your own questions, consciously find out the best way, try not to jump too much in thinking, and you can also target wonderful or wrong questions. The process of checking and filling gaps is the process of reflection. In addition to understanding different problems, we should also learn to "draw inferences from others" and summarize them in time.
Do a good job in every class and mobilize the organs.
Chen said that students must concentrate on their ears, eyes, heart, mouth and hands in class. Listening means listening attentively to the teacher's analysis of the problem, and what kind of inspiration do you get from it? Note: In class, you should not only read the paper, but also read the teacher's blackboard. We must take both into account organically, learn the layout of the teacher's blackboard writing, and improve the standardization of our own problem solving. Heart is to think hard, keep up with the teacher's thinking of solving problems, and seriously understand how the teacher grasps the key points, the essence and the direction of solving problems. Speaking is thinking positively and preparing to answer the teacher's questions. On the basis of listening, watching, thinking and speaking, we should draw the key points and difficulties of knowledge, record the key points and points of the teacher's lecture, and memorize the teacher's methods and skills of analyzing problems so as to review after class, and at the same time do the homework assigned by the teacher carefully. The goal of understanding is the most taboo in class. It is best to extract the teacher's explanation steps and even recite some key steps when necessary.
[Expert reminder]
Reminder 1 Attach great importance to the review of new courses and new contents.
The new contents of liberal arts in senior high schools in Shanghai are: simple logic, plane vector and projection drawing are the highlights of outline revision and examination reform, which are all involved in the college entrance examination. Compared with the past, the present teaching situation has a short review time and a tight review time. However, the requirements for new content inspection are increasing year by year, and the scores are also increasing. For example, vectors have become an indispensable tool for analyzing and solving problems. In the new curriculum test questions, some topics belong to the combination of old and new textbooks, and the college entrance examination proposition adopts the method of combining old and new. For example, the problem of solid geometry can be solved by both traditional methods and vector methods. As long as you practice this kind of exercises more, you can make perfect, improve your ability and speed of solving problems, improve the accuracy of solving problems and the success rate of exams. Only by attaching importance to and strengthening the review of new content can we keep up with the pace of education reform and college entrance examination reform.
Reminder 2 Review the research of test questions and turn passive into active.
Students should be right.
Teachers should carefully study the exercises involved in the review, especially the college entrance examination questions in recent years, draw lessons from the examination knowledge points and examine the thinking methods, form their own understanding, review some typical exercises, and further deepen their cognitive impression through reflection. Over time, we can draw inferences from others. Only the knowledge that can be recalled can be internalized into your own knowledge. The most important point, which is easily overlooked by everyone, is that teachers or classmates will put aside the topics they don't understand after explaining them. If you take them out in a few days, you will find that you don't understand them. Therefore, for typical exercises, we should take the method of rolling review and review the contents of the previous days every few days. According to different knowledge points, carefully design various questions with different difficulties and form your own learning question bank, so that you can spend more time in the examination room while preparing for the exam.
Reminder 3 When doing math problems, don't "chew on words".
Mathematics is often the "short board" and weakness of liberal arts students. Cheng Lihai reminded that, first of all, students should pay attention to their own advantages in understanding the meaning of the question. This is the advantage of liberal arts students. Some writing questions are "around". If you don't read the topic carefully and don't understand the meaning of the topic, you may understand and make mistakes, and "speaking like a book" is the specialty of liberal arts students. In this respect, liberal arts students must highlight their own specialties, which is also crucial for learning mathematics, but it has been ignored by many students. Don't take it lightly.
Secondly, highlight the advantages in carefulness. Liberal arts students, especially girls, are careful and patient. They are meticulous in learning new knowledge and doing problems, and will not make "careless" mistakes more or less. However, the study, consolidation and problem-solving of many mathematics contents require care and patience-it is often not that the knowledge points of mathematics are not mastered, but that carelessness leads to the loss of points, which requires attention.