Especially for senior one students, the environment can be said to be brand-new. New textbooks, new classmates, new teachers, new groups ... Students have an adaptation process from unfamiliar to familiar. In addition, after intense review of the senior high school entrance examination, some students will have the idea of "relaxation" after entering school, and have no sense of urgency. Some students are also afraid. Before entering school, they heard that high school mathematics was difficult to learn. At the beginning of high school math class, there are some abstract concepts that are really difficult to understand, such as mapping, set, straight lines in different planes and so on. This made them in a passive situation from the beginning. These factors seriously affect the learning quality of freshmen in senior high school. So how can we learn high school mathematics well?
First, recognize the state of learning ability.
1, psychological quality. Whether a student's sense of honor and success in a specific junior high school environment can be brought to senior high school depends on whether he or she has the ability to face setbacks, calmly analyze problems and find ways to overcome difficulties and get out of trouble. Students who can learn can get good grades because they learn well. Good grades can stimulate interest, enhance confidence and want to learn more. The further development of knowledge and ability has formed a virtuous circle. Students who can't learn can't learn well and get poor grades. If they can sum up their lessons in time and change their learning methods, they will not learn badly, but they can still catch up with them after some efforts. If left unchecked, they will not make progress, work hard, lack perseverance and confidence, and their grades will get worse and worse. Therefore, high school study is a test of students' psychological quality.
2. Reflection and understanding of learning methods and habits.
(1) Learning initiative. After entering high school, many students still have strong dependence psychology like junior high school. They follow the teacher's inertia and have no initiative in learning. They don't make plans, wait for classes, don't preview before classes, don't understand what the teacher is going to do in class, are busy taking notes in class, ignore the real class task, attend to one thing and lose sight of another, and learn passively.
(2) the organization of learning. Teachers usually explain the ins and outs of knowledge in class, analyze the connotation and extension of concepts, analyze key points and difficulties, and highlight thinking methods. But some students don't pay attention in class, don't hear the main points clearly or can't hear them completely, take a lot of notes and have a lot of problems. After class, I can't consolidate, summarize and find the connection between knowledge in time, but I am busy with homework and confused questions, and I know little about concepts, laws, formulas and theorems.
(3) ignoring 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 do it instead of calculating and writing carefully, but they are very interested in difficult problems to show their "level". Their goals are too high, and they pay more attention to "quantity" than "quality", and they fall into the sea of questions, either making mistakes in calculation or giving up their formal homework or exams halfway.
(4) Students' bad habits in practice and homework. Mainly answer, do not believe in their own conclusions, lack of confidence and determination to solve the problem; Discuss problems without thinking independently, and develop a psychological quality of dependence; Slow work, not talking about speed, can not train the agility of thinking; My thoughts are not concentrated, and my homework and practice are not efficient.
3. Cohesive ability of knowledge.
The content of junior high school mathematics textbooks is popular and concrete, mostly constant, and the questions are few and simple; However, the content of high school mathematics is abstract, and the study of variables and letters focuses on both calculation and theoretical analysis, which increases the difficulty compared with junior high school.
On the other hand, compared with junior high school, senior high school mathematics requires a qualitative leap in the depth, breadth and ability of knowledge, and requires students to master basic knowledge and skills to prepare for further study. Because of the low starting point of junior high school textbooks, the requirements for students' ability are also low. In recent years, due to the adjustment of the content of textbooks, although the difficulty of junior high school textbooks has been reduced, in contrast, the reduction of junior high school textbooks is relatively large, and some contents are not mentioned or talked about very shallowly to cope with the senior high school entrance examination (such as quadratic function and its application). This part of the content is not in high school textbooks, but it needs to be often mentioned or applied to solve other math problems. However, due to the limitation of the college entrance examination, high school teachers dare not reduce the difficulty, which leads to high school. Therefore, in a certain sense, the adjusted textbooks have not narrowed the difficulty gap between junior and senior high school textbooks, but have increased. If remedial measures are not taken, the differentiation of students' grades is inevitable. This involves the convergence of knowledge and ability in junior and senior high schools.
Second, strive to improve their ability.
1. Improve learning methods and cultivate good study habits.
Students with different learning abilities have different learning methods. Try to learn the learning methods of more successful students. Improving learning methods is a long-term systematic accumulation process. Only by constantly accepting new knowledge, constantly encountering setbacks and generating doubts, and constantly summing up, can one continuously improve. "Students who can't summarize will not improve their ability, and frustration experience is the cornerstone of success." The biological evolution process of survival of the fittest in nature is the best example. Learning should always sum up the rules, with the aim of further development. Through the usual contact and communication with teachers and classmates, the general learning steps are gradually summarized, including: making a plan, self-study before class, paying attention to class, reviewing in time, working independently, solving problems, systematically summarizing and extracurricular learning, which are simply summarized as four links (preview, class, sorting and homework) and one step (review summary). Each link has profound content, strong purpose and pertinence, and should be put in place.
Cultivate the habit of attending classes in classroom teaching. Listening is the main thing. Listening can make you concentrate, understand and listen to the key parts of the teacher's speech, and pay attention to thinking and analyzing problems while listening. But if you just listen and don't remember, or just remember and don't listen, you will not see one thing and the classroom efficiency will be low. So you should take notes properly and understand the main spirit and intention of the teacher in class. Coordinating activities with the five senses is the best habit. To cultivate homework habits in classroom and extracurricular exercises, we should not only do it neatly, but also cultivate aesthetic feeling and organization. This is to cultivate logical ability and must be done independently. Can cultivate a sense of responsibility for independent thinking and correct problem solving. When doing homework, we should advocate efficiency, and do not put off homework that should be completed in ten minutes for half an hour. Tired homework habits make our thinking loose and our energy unfocused, which is harmful to the cultivation of mathematical ability. We should grasp the study habits of mathematics from the first grade, and guide them from the psychological characteristics of age growth and the requirements of different learning stages.
2. Strengthen the benefits of four 5-minute classes.
To improve mathematics ability, of course, through the classroom, we should make full use of this position.
(1) Grasp the teaching materials. The process of learning mathematics is alive, so is the object of teachers' teaching, which changes with the development of teaching process, especially when teachers pay attention to ability teaching, and the teaching materials cannot be reflected. Mathematical ability is formed simultaneously with the occurrence of knowledge. Whether forming a concept, mastering a law or doing an exercise, we should cultivate and improve it from different ability angles. Through the teacher's teaching, we can understand the position of what we have learned in the textbook and make clear the relationship with the previous knowledge. Only by mastering the teaching materials can we master the initiative in learning.
(2) Grasp the formation of knowledge. A concept, definition, formula, rule and theorem of mathematics are all basic knowledge of mathematics, and the formation process of these knowledge is easily ignored. The forming process of this knowledge is actually the training process of mathematical ability. The proof of theorems is often the process of discovering new knowledge. Cultivate the development of mathematical ability in the process of mastering knowledge. Therefore, in order to change the teaching method of emphasizing conclusion over process, we should regard the process of knowledge formation as the process of cultivating mathematical ability.
(3) Grasp the learning rhythm. Mathematics class is ineffective without a certain speed. Slow learning can't train thinking speed, thinking agility and mathematical ability, which requires that mathematics learning must have rhythm. Over time, the agility of thinking and mathematical ability will gradually improve.
(4) Grasp the problem and expose it. In math class, teachers usually ask questions and rehearse, sometimes accompanied by discussions, so they can hear a lot of information. These problems are all spent now. For those typical problems, problems with universality must be solved in time, and problems cannot be left behind or even settled. It is necessary to seize the problems existing in the current expenses in time, make up for the remaining problems in a targeted manner, and pay attention to actual results.
(5) Grasp the classroom exercises and do a good job in the teaching of practice class, review class and test analysis class. The classroom practice time in math class accounts for about 1/4- 1/3 of each class, and sometimes exceeds 1/3. This is an important means to remember, understand and master mathematical knowledge. It is not only a speed training, but also a test of ability. Students are not interested in doing problems, but the examples that teachers find are intentional. What knowledge needs to be made up, consolidated and improved, and what knowledge and ability need to be cultivated and strengthened. Class should be targeted.
(6) Grasp the problem-solving guidance. Reasonable choice of simple operation path is not only the need of fast operation, but also the need of accuracy. The more operation steps, the greater the complexity and the greater the possibility of errors. Therefore, according to the conditions and requirements of the problem, it is not only the key to improve the operational ability, but also an effective way to improve other mathematical abilities.
(7) Grasp the training of mathematical thinking methods. Mathematics is responsible for cultivating computing ability, logical thinking ability, spatial imagination, and the ability to analyze and solve problems by using what you have learned. Its characteristics are high abstraction, strong logic, wide applicability and high requirement for ability. Mathematical ability can only be cultivated and improved through the continuous application of mathematical thinking methods.
3. Experience success and cultivate interest in learning.
"Interest is the best teacher", and the interest in learning is always closely linked with the joy of success. If you understand a lesson, master a math method, solve a math problem, get good grades in the exam, and the teacher encourages and appreciates you at ordinary times, you can experience the joy of success from these "successes" and stimulate higher learning enthusiasm. Therefore, in the usual study, we should learn more, sum up more, and constantly get pleasure from success (even if it is a trivial achievement), thus stimulating the enthusiasm for learning and improving the interest in learning.
Third, pay attention.
1, the process of improving students' mathematical ability is a step-by-step process. To prevent impatience, some students are eager for quick results, gulping down dates, some students want to sprint in a few days, some students are complacent about their achievements, and they will be devastated when they encounter setbacks. Therefore, targeted teaching should be carried out to solve these practical problems.
2. The accumulation of knowledge and the cultivation of ability is a long-term process, just as the learning process of "from thin to thick" and "from thick to thin" advocated by Mr. Hua is the truth. At the same time, in recent years, the appearance of applied questions in college entrance examination questions has posed a more severe challenge to students' ability to apply their learned mathematical knowledge to real life. We should strengthen the cultivation and training of applied mathematics consciousness and creative thinking methods and abilities.
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