Some people describe mathematics as "gymnastics of thinking, sparks of wisdom". In today's era of knowledge economy, mathematics is moving from behind the scenes to the front. Its combination with computer technology has directly created various values for the society and promoted the development of social productive forces. Mathematics is an important part of human culture and has become a basic quality that citizens must possess. Mathematics plays a unique and irreplaceable role in the formation of human rational thinking. As an important subject to measure a person's ability, most students from primary school to high school have a special liking for it and have invested a lot of time and energy. However, not everyone is a success. Many excellent math students in primary and junior high schools fall into math when they enter high school. In the summer vacation of 2002, when the author participated in the training of senior high school math teachers in Xinjiang, several liberal arts experts and scholars who had taught us talked about their poor math scores and their fear of meeting senior high school math teachers. This phenomenon of "fear" of high school mathematics is relatively common at present, which should be paid attention to. Of course, there are many reasons for this phenomenon. This paper only discusses the following points from the aspects of students' learning situation:
In the face of many successful students in junior high school becoming losers in senior high school, the author has conducted research and investigation on their learning situation. The results show that the main reasons for the decline in grades are as follows.
1. Passive learning. After entering high school, many students, like junior high school, have a strong dependence, follow the teacher's inertia and can't grasp the initiative of learning. It is manifested in the uncertain plan, waiting for class, not previewing before class, not knowing the teacher's class content, being busy taking notes in class and not hearing the "doorway". I didn't really understand what I learned.
You can't learn law. Teachers usually explain the ins and outs of knowledge in class, analyze the connotation of concepts, analyze key and difficult points, and highlight thinking methods. However, some students didn't concentrate in class, didn't catch the main points or didn't catch them at all. They took a lot of notes and met many problems. After class, they can't consolidate, summarize and discover the connection between knowledge in time. They just do their homework in a hurry, confuse the questions, have little knowledge of concepts, laws, formulas and theorems, imitate them mechanically and memorize them by rote. Some people work overtime at night, are listless during the day, or don't listen at all in class, so they have another set. The result is half the effort, with little effect.
3. Do not pay attention to the foundation. Some students who "feel good about themselves" often despise the study and training of basic knowledge, basic skills and basic methods, and often only know how to do it, but they are very interested in difficult problems to show their "level". They are too ambitious, pay more attention to "quantity" than "quality" and fall into the sea of questions. In regular homework or exams, either calculus is wrong or "stuck" in the middle.
4. Do not have the conditions for further study. Compared with junior high school mathematics, senior high school mathematics is a leap in depth, breadth and ability requirements. This requires you to master basic knowledge and skills to prepare for further study. High school mathematics is difficult in many places, with new methods and high analytical ability. Such as the maximum value of quadratic function in closed interval, the solution of function value domain, the distribution of real roots and parametric equation, the deformation and flexible application of trigonometric formula, the formation of spatial concept, the application of permutation and combination and practical application problems. Objectively, these viewpoints are the points of differentiation, and some contents are still out of touch in the textbooks of high school and junior high school. If remedial measures are not taken, differentiation is inevitable.
It is not enough for high school students to just want to study. They must also "learn", pay attention to scientific learning methods, improve learning efficiency, and thus turn passivity into initiative. In view of the above-mentioned situation in students' learning, teachers should take measures to strengthen the guidance of learning methods, supplemented by solving differences:
1. Strengthen the guidance of learning methods and cultivate good study habits.
Good study habits include making plans, self-study before class, paying attention to class, reviewing in time, working independently, solving problems, systematically summarizing and studying after class.
Making a plan to make the learning purpose clear, the time arrangement reasonable, unhurried and steady, is the internal motivation to promote students' active learning and overcome difficulties. But the plan must be practical, with both long-term plans and short-term arrangements. In the process of implementation, we must be strict with ourselves and temper our learning will.
Self-study before class is the basis for students to learn new lessons well and achieve better learning results. Self-study before class can not only cultivate self-study ability, but also improve interest in learning new lessons and master the initiative in learning. Don't go through the motions in self-study, pay attention to quality, try to understand the teaching materials before class, pay attention to the teacher's ideas in class, grasp the key points, break through the difficulties and solve the problems in class as much as possible.
Classroom is the key link to understand and master basic knowledge, skills and methods. "Learning is not enough", students who have taught themselves before class can concentrate more, and they know where to be detailed and where to omit; Where to carve carefully, where to pass by and where to record, instead of copying all the records, pay attention to one thing and lose another.
Timely review is an important part of efficient learning. By reading textbooks repeatedly and consulting relevant materials in multiple ways, we can strengthen our understanding and memory of the basic conceptual knowledge system, link the new knowledge we have learned with the old knowledge, make analysis and comparison, and arrange the review results in our notes at the same time, so that the new knowledge we have learned can be changed from "understanding" to "knowing".
Independent homework is a process in which students can analyze and solve problems flexibly through their own independent thinking, further deepen their understanding of new knowledge and master new skills. This process is a test of students' will and perseverance. Through application, students can change from "knowledge" to "familiarity".
Problem-solving refers to the process of understanding the exposed knowledge errors or missing answers due to blocked thinking in the process of completing homework independently, and making the thinking smooth and supplementing the answers through inspiration. You must be persistent in solving problems, and do your homework if you do it wrong. If you don't understand the mistakes clearly, you should think again and again. If you can't solve them, you should consult your teachers and classmates. You should review frequently, strengthen mistakes, do appropriate repetitive exercises, digest the knowledge that you let your teacher let your classmates enter, and persist in changing your knowledge from "familiar" to "alive" for a long time.
Systematic summarization is an important link for students to master knowledge comprehensively, systematically and profoundly and develop their cognitive ability through positive thinking. The summary should be based on systematic review, teaching materials, notes and related materials, and reveal the internal relationship between knowledge through analysis, synthesis, analogy and generalization. In order to achieve the purpose of mastering the knowledge learned. Frequent multi-level summary can change knowledge from "living" to "understanding".
Extracurricular learning includes reading extracurricular books and newspapers, participating in academic competitions and lectures, and visiting senior students or teachers to exchange learning experiences. Extracurricular learning is a supplement and continuation of in-class learning. It can not only enrich students' cultural and scientific knowledge, deepen and consolidate what they have learned in class, but also satisfy and develop students' hobbies, cultivate students' autonomous learning and working ability, and stimulate students' thirst for knowledge and enthusiasm for learning.
Step by step to prevent impatience
Because students are young and have limited experience, many high school students are prone to impatience. Some students are greedy for more and quick, swallowing dates, some students want to "sprint" in a few days, some students are complacent when they get a little achievement, and they will never recover when they encounter setbacks. In view of these situations, teachers should let students know that learning is a long-term accumulation process of consolidating old knowledge and discovering new knowledge, which can never be achieved overnight. Why does high school take three years instead of three? A very important reason why many excellent students can get good grades is that their basic skills are solid, and their reading, writing and computing abilities have reached the level of automation or semi-automation.
3. Study the characteristics of the subject and find the best learning method.
Mathematics is responsible for cultivating students' computing ability, logical thinking ability, spatial imagination ability, and the ability to analyze and solve problems by using what they have learned. It is characterized by a high degree of abstraction, logic and wide applicability, and requires high ability. Learning mathematics must pay attention to "living", not only reading books without doing problems, but also burying oneself in doing problems without summarizing and accumulating. We must be able to learn from textbooks and find the best learning method according to our own characteristics. This is the truth in the learning process of "from thin to thick" and "from thick to thin" advocated by Mr. Hua Methods vary from person to person, but four steps (preview, class, arrangement and homework) and one step (review and summary) are indispensable.
4. Strengthen counseling and resolve differentiation points.
As mentioned above, there are many easily differentiated places in senior high school mathematics, which are generally characterized by new methods, great difficulty and strong flexibility. For local teachers who are prone to division, we should take repeated measures to strengthen counseling, set up special lectures and guide reading reference books. Put forward mistakes for students to discuss, fully display their thinking process, improve their appreciation ability through variant exercises, and achieve the purpose of mastering and applying knowledge flexibly.