In senior one, we will learn functions, which is the focus of senior high school mathematics. It plays an outline role in senior high school mathematics, and it is integrated into the whole senior high school mathematics knowledge, including important mathematical thinking methods in mathematics.
For example, the idea of functions and equations, the idea of combining numbers and shapes, and so on. This is also the focus of the college entrance examination. In recent years, the final questions of college entrance examination are all entitled functional investigation methods.
The exercises related to function thinking methods in the college entrance examination account for more than 60% of the whole test questions.
1, has a good interest in learning.
(1) preview before class, and have doubts and curiosity about what you have learned.
(2) Cooperate with the teacher in class to satisfy the excitement of the senses. In class, we should focus on solving the problems in preview, regard the teacher's questions, pauses, teaching AIDS and model demonstrations as appreciating music, answer the teacher's questions in time in class, cultivate the synchronization of thinking and teachers, improve the spirit, and turn the teacher's evaluation of your questions into a driving force to spur learning.
(3) Think about problems, pay attention to induction, and tap your learning potential.
(4) Pay attention to the teacher's mathematical thinking when explaining in class and ask yourself why you think so. How did this method come about?
(5) Let the concept return to nature. All disciplines are summarized from practical problems, and mathematical concepts are also returned to real life, such as the concept of angle, the generation of polar coordinate system and the generation of polar coordinate system are all abstracted from real life. Only by returning to reality can the understanding of concepts be practical and reliable and accurate in the application of concept judgment and reasoning.
2. The good habits of high school mathematics should be: ask more questions, think hard, do easily, summarize again, and pay attention to application.
In the process of learning mathematics, students should translate the knowledge taught by teachers into their own unique language and keep it in their minds forever.
In addition, we should ensure that there is a certain amount of self-study time every day, so as to broaden our knowledge and cultivate our ability to learn again.
3. Consciously cultivate your abilities in all aspects.
Mathematical ability includes five abilities: logical reasoning ability, abstract thinking ability, calculation ability, spatial imagination ability and problem solving ability.
These abilities are cultivated in different mathematics learning environments.
Such as math second class, math contest, intelligence contest and other activities.
Usually pay attention to observation, such as the ability of spatial imagination is to purify thinking through examples, abstract the entities in space in the brain, and analyze and reason in the brain. The cultivation of other abilities must be developed through learning, understanding, training and application.
Especially in order to cultivate these abilities, teachers will carefully design "intelligent courses" and "intelligent questions", such as multi-media teaching such as solving one question, training classification by analogy, applying models and computers, which are all good courses to cultivate mathematical abilities. In these classes, students must devote themselves to all aspects of intelligence and finally realize the all-round development of their abilities.
Fourth, other matters needing attention
1, turn your attention to ideological learning. People's learning process is to understand and solve unknown knowledge with mastered knowledge.
In the process of mathematics learning, old knowledge is used to lead out and solve new problems, and new knowledge is used to solve new knowledge when mastered.
Junior high school knowledge is the foundation. If you can answer new knowledge with old knowledge, you will have the idea of transformation.
It can be seen that learning is constantly transforming, inheriting, developing and updating old knowledge.
2. Learn the mathematical thinking method of mathematics textbooks.
Mathematics textbooks melt mathematics thoughts into mathematics knowledge system by means of suggestion and revelation. Therefore, it is very necessary to sum up and summarize mathematical thoughts in time.
Summarizing mathematical thoughts can generally be divided into two steps:
One is to reveal the content law of mathematical thought, that is, to extract the attributes or relationships of mathematical objects,
The second is to clarify the relationship between mathematical thinking, methods and knowledge, and refine the framework to solve the whole problem.
The implementation of these two steps can be carried out in classroom listening and extracurricular self-study.
Classroom learning is the main battlefield of mathematics learning. In class, teachers explain and decompose mathematical ideas in textbooks, train mathematical skills, and enable high school students to acquire rich mathematical knowledge. Scientific research activities organized by teachers can make mathematical concepts, theorems and principles in textbooks be understood and excavated to the greatest extent.
For example, in the teaching of the concept of reciprocal in junior high school, teachers often have the following understanding in classroom teaching:
(1) from the definition point of view to find the reciprocal of 3 and -5, the number of reciprocal is _ _ _ _.
② Understanding from the angle of number axis: Which two points indicate that numbers are opposite? (a point symmetrical about the origin)
③ In terms of absolute value, the two numbers of absolute value _ _ _ _ _ are opposite.
④ Are the two numbers that add up to zero opposite? These different angles of teaching will broaden students' thinking and improve their thinking quality.
Five, some suggestions about learning mathematics.
1, take math notes, especially the different aspects of concept understanding and mathematical laws, as well as the extra-curricular knowledge added by the teacher to prepare for the college entrance examination.
2. Establish a mathematical error correction book. Write down error-prone knowledge or reasoning in case it happens again.
Try to find the wrong mistakes, analyze them, correct them and prevent them.
Understanding: being able to deeply understand the right things from the opposite side;
Guo Shuo can get to the root of the error, so as to prescribe the right medicine;
Answer questions completely and reason strictly.
3. Memorize mathematical laws and conclusions.
4. Establish a good relationship with classmates, strive to be a "little teacher" and form a "mutual aid group" for math learning.
5. Try to do extra-curricular math problems and increase self-study.
6. Repeatedly consolidate and eliminate forgetting before school.
7. Learn to summarize and classify. Ke: ① Classification from mathematical thoughts, ② Classification from problem-solving methods and ③ Classification from knowledge application.
Physics is a natural science course that is difficult to learn. You can't learn by rote. Even if you recite it verbatim, you can't solve the problem. Physics is a difficult subject in senior high school science subjects. Most students who have studied physics in senior high school, especially those who have poor grades in physics, always have such questions: they can understand and listen clearly in class, but they can't do problems after class. This is a common problem, which deserves serious consideration by physics teachers and students. Let's talk about some learning methods of high school physics to help students learn.
First, correct learning attitude.
First, analyze the questions that students generally ask, that is, why can you understand in class and not do it after class? Everyone has such personal feelings, such as reading a literary work, describing the natural scenery in the article and describing the inner activities of the characters, which are amazing, you know, but if you let yourself start writing, you may not be able to write others' level. There is absolutely no problem listening to others and reading other people's articles, but it is not so easy to write them yourself and become your own things. Therefore, if we want to change from understanding to doing, we should practice more on the basis of understanding, so as to master the laws and mysteries and truly become our own things, which is exactly where we should study physics in senior high school hard.
If you want to learn physics well, the first thing is to cherish time and study persistently. Establish confidence, firmly believe that you can learn any course well, and firmly believe that you can pay a little and gain a little. In this regard, please see the following three quotations:
1, I never believe in any innate or acquired talent. Without firm and long-term efforts, I can succeed. -Dickens (English writer)
Some people can go far beyond others. The main reason is not so much genius as his indomitable spirit of concentrating on his studies and not giving up until he reaches his goal. -Dalton (British chemist)
3. The fastest and the slowest, the longest and the shortest, the commonest and the most precious, the most easily overlooked and the most regrettable thing is time.
-Gorky (Soviet writer)
Second, we should pay attention to eight links in learning: making plans → preview before class → concentrate in class → review in time → work independently → solve problems → system summary → extracurricular learning.
The most important thing here is: concentrate in class → review in time → work independently → solve problems → summarize systematically. In the above eight links, there are many learning methods. According to the characteristics of physics and how to learn physics well, some specific learning methods are introduced below.
(1) Sanji. Basic concepts should be clear, basic laws should be familiar, and basic methods should be skilled.
About basic concepts, such as speed, there are two meanings: one is to express speed; The second is the ratio of distance to time (such as in uniform circular motion), and the speed is the ratio of displacement to time (in uniform linear motion).
There are two formulas for calculating basic laws, such as average speed. The commonly used formulas are V=s/t and V=(vo+vt)/2. The former is a definition formula, which is applicable to any situation, and the latter is a derivation formula, which is only applicable to linear motion with uniform change.
As for basic methods, such as studying middle school problems, holistic method and isolated method are often used, which are typical complementary methods.
Finally, let me talk about another problem, which goes beyond the "three basics". In the process of learning physics, we sum up some concise and practical inferences or conclusions, which are very useful for solving problems and learning physics well. For example, the potential decreases along the electric field line; The tension on the same rope is equal; When the acceleration is zero, the speed is the maximum; Lorentz force does not do work and so on.
(2) Do the problem independently. Do some problems independently with good quality and quantity (meaning not relying on others). There must be a certain number of topics, not too few, but also a certain quality, that is to say, there must be some difficulty. Anyone who studies mathematics and physics can't learn this level well. Solving problems independently may sometimes be slow, sometimes you have to take detours, and sometimes you can't even solve them, but these are normal and the only way for any beginner to succeed.
(3) Physical process. To clarify the physical process, the physical process is not clear, and there must be hidden dangers in solving problems. No matter how difficult the topic is, try to draw as much as possible, some can draw sketches, and some need to draw accurate pictures, using compasses, triangles, protractors and so on. To represent geometric relationships.
Drawing can turn abstract thinking into image thinking and master physical process more accurately. With this diagram, we can make state analysis and dynamic analysis. State analysis is fixed, dead and discontinuous, while dynamic analysis is alive and continuous.
(4) attending classes. Listen carefully in class and learn from the teacher with an open mind. Don't give up listening just because the teacher speaks simply. If this happens, it can be regarded as review and consolidation. Try to be consistent and synchronized with the teacher, and you can't do it yourself, otherwise it will be self-study. After getting started, with a certain foundation, you are allowed to have your own activity space, that is, you are allowed to have something of your own. The more you learn, the more things you accumulate.
(5) notebook. Class is mainly based on listening, and there are notebooks, and some things should be written down. Knowledge structure, good problem-solving methods, good examples, places you don't understand, and so on. , should be recorded. You should sort out your notes after class, on the one hand, for digestion, and on the other hand, for supplementary notes. Notebook is not only to remember what the teacher said in class, but also to make some reading notes. Good problems found in homework and good solutions should also be recorded in a notebook, which is what students often call a "good problem book". It's best to number your hard-earned notebooks and read them often in the future, so as to review the old and learn the new.
(6) learning materials. Learning materials should be well preserved, classified and marked. The classification of learning materials includes exercises, papers, experimental reports and so on. Marking refers to marking good questions, valuable questions and error-prone questions separately for future review. Marking can save a lot of time.
(7) time. Time is precious. Without time, there is no time to do anything, so pay attention to make full use of time. Using time is a superb art, for example, using the method of remembering to save time, using the scattered time before going to bed, waiting for the bus, and recess activities to recall the lessons spoken that day, and learning again and again to achieve the purpose of strengthening.
(8) learn from others. Learn from others with an open mind, learn from classmates, learn from people around you, see how others learn, and often have academic exchanges with them, teach each other and improve together. Don't be self-righteous, tell others when you have a good method, so that others will tell you when you have a good method, and learn from each other's strengths.
(9) Knowledge structure. We should attach importance to and systematically master the knowledge structure and organically link scattered knowledge. From the whole knowledge structure of physics to the knowledge structure of mechanics, even to chapters, such as the knowledge structure of statics and so on.
(10) Mathematics. The calculation of physics depends on mathematics, which is too important for learning physics. Without mathematics, it is difficult to learn physics well. We should learn math well and make good use of this powerful tool.
(1 1) Sports activities. Healthy body is the foundation of learning, and vigorous energy is the guarantee of learning efficiency. Often participate in sports activities, know several exercise methods, and be conscious. To ensure adequate sleep, it is not advisable to reduce sleep time and increase study time. You can't get some good results at the expense of overdraft health. You can't always talk about the so-called sprint and struggle, and you should also pay attention to regularity in your study, that is to say, you should always work hard, but don't make sudden attacks.
Third, pay attention to the cultivation of self-study ability.
Memory: In the study of high school physics, we should memorize the basic concepts, laws and some basic conclusions, which is what we often call the most basic knowledge. Students often ignore the memory of these basic concepts, thinking that learning physics does not need to memorize these literal things. As a result, when reviewing physics concepts in senior three, few students can say them accurately. I can't absolutely say that the incompleteness of physical concepts has a great influence on your study in a certain exam or at a certain stage, but I can definitely say that it will have an inherent adverse effect on your understanding of physical problems and the formation of the knowledge of the whole physical system. I can't tell which exam will lose points because of your inaccurate concept. Therefore, learning Chinese requires memorizing famous sayings and epigrams, learning mathematics requires memorizing basic formulas, and learning physics also requires memorizing basic concepts and laws. This is the most basic requirement for learning physics well. Without this step, the following study is impossible.
Accumulation: it is the work after memory in the process of learning physics. On the basis of memory, I constantly collect a lot of information about physics knowledge from textbooks and reference materials, some of which come from a topic, some from an illustration, and some may come from a short reading material. In the process of collecting and sorting out, we should be good at analyzing and classifying different knowledge points, and find out similarities and differences in the process of sorting out, so as to facilitate memory. The process of accumulation is a process of struggle between memory and forgetting. However, it is necessary to make knowledge more comprehensive and systematic through repeated memory, and the relationship between formulas, theorems and laws is closer, so as to achieve the purpose of accumulation. Never repeat your homework like a bear breaking a stick and memorize it mechanically without thinking. The result can only be that you remember more and forget less.
Synthesis: Physical knowledge is divided into chapters and sections, and the contents required by the physical examination outline are also piece by piece. They are both interrelated and different. Therefore, in the process of physics learning, we should constantly carry out small synthesis, and wait until the third grade knowledge is learned before systematically synthesizing. This process requires students' ability, and the chapters are interrelated. Different chapters can be compared with each other, and the knowledge before and after can be truly integrated, and the internal relationship of knowledge can be gradually found from the synthesis.
Improvement: through the memory and accumulation of previous knowledge and careful synthesis, the ability to solve problems can be improved. To improve one's ability is to improve one's ability to solve and analyze problems. For a topic, we should first look at what the problem is-mechanics, heat, electromagnetism, optics or atomic physics, and then make clear the research object, combine the conditions given in the topic, apply relevant physical concepts and laws, and also use some physical first-and second-level conclusions to get a smooth result. It can be imagined that if the basic concepts of physics are not clear, the given conditions or implied conditions in the topic are not clear, or the formula used in solving the problem is wrong, or the original formula is used to replace the first and second conclusions, the speed and correctness of solving the problem will be affected.
Improvement is to solve the problem first, then the solution is flexible, and then the solution is innovative. This includes multiple solutions to a problem, that is, the simplest method can be selected from multiple solutions; It also includes a method to solve many problems and solve many similar problems smoothly, and truly achieve dexterity and handy degree.
To sum up, there are roughly six levels in learning physics, that is, understanding first, remembering later, practicing and using, gradually mastering, practice makes perfect, and being brave in innovation. From the initial goal of basic knowledge to the highest realm of learning physics.
In the process of physics learning, according to the cognitive process from simple to complex, and comparing with six learning levels, we gradually find out our own position and level, find out our own shortcomings, and then determine our own improvement direction and efforts. High school study is to prepare for university study, which puts forward higher requirements for students' self-study ability. The basic process of physics learning mentioned above-memory, accumulation, synthesis and improvement-is the process of cultivating their self-learning ability. They learned the learning methods, became interested in physics, and mastered the characteristics of physics as an experimental subject. Through their efforts, they will certainly learn high school physics well.