A good start is half the battle. High school mathematics classes are about to begin, which are related to junior high school knowledge, but are more systematic than junior high school mathematics knowledge.

In the first year of high school mathematics, we will learn functions. Functions are the focus of high school mathematics. They play an outline role in high school mathematics. They are integrated into the entire high school mathematics knowledge, among which are important functions in mathematics. Mathematical thinking methods;

For example: the idea of ??functions and equations, the idea of ??combining numbers and shapes, etc. It is also the focus of the college entrance examination. In recent years, the final questions of the college entrance examination have all used function questions as the examination method.

In the college entrance examination questions, exercises related to functional thinking methods account for more than 60% of the entire test questions.

1. Have good interest in learning

(1) Preview before class, raise questions about the knowledge learned, and generate curiosity.

(2) During the lecture, you must cooperate with the teacher to satisfy the excitement of the senses. When listening to the class, focus on solving the questions in the preview. Treat the teacher's questions, pauses, teaching aids and model demonstrations as music for appreciation. Answer the teacher's questions in class in a timely manner. Cultivate the synchronization of thinking with the teacher, improve your spirit, and understand the teacher's questions about you. Evaluation becomes the driving force for learning.

(3) When thinking about problems, pay attention to induction and tap your learning potential.

(4) During the lecture, pay attention to the teacher’s mathematical thoughts when explaining, and ask more questions about why you think this way and how this method came about?

(5) Return the concept to nature. All subjects are derived from practical problems, and mathematical concepts also return to real life. For example, the concept of angles, the creation of the azimuth coordinate system, and the polar coordinate system are all abstracted from real life. Only by returning to reality can the understanding of concepts be reliable and accurate when applying conceptual judgment and reasoning.

2. Good habits in high school mathematics should be: question more, think frequently, be hands-on, focus on induction, and pay attention to application.

In the process of learning mathematics, students must translate the knowledge taught by teachers into their own special language and remember it permanently in their minds.

In addition, you must ensure that you have a certain amount of self-study time every day in order to broaden your knowledge and cultivate your ability to re-learn.

3. Consciously cultivate your own abilities in all aspects

Mathematical abilities include: logical reasoning ability, abstract thinking ability, calculation ability, spatial imagination ability and analytical problem-solving ability*** ability.

These abilities are developed in different mathematical learning environments.

Activities such as Mathematics Second Classroom, Mathematics Competitions, and Intelligence Competitions.

Pay attention to observation in daily life. For example, spatial imagination ability is to purify thinking through examples, highly abstract entities in space in the brain, and conduct analysis and reasoning in the brain. The cultivation of other abilities must be developed through learning, understanding, training, and application.

In particular, in order to cultivate these abilities, teachers will carefully design "intellectual lessons" and "intellectual problems", such as answering exercises with multiple solutions, training and classification by drawing inferences from one example, and applying models and computers. Multimedia teaching, etc., are all good courses for cultivating mathematical abilities. In these courses, students must devote themselves wholeheartedly and participate intellectually in all aspects, so as to ultimately achieve the comprehensive development of their abilities in all aspects.

IV. Other matters needing attention

1. Pay attention to the study of transformation of thoughts. The learning process of people is to use the knowledge they have mastered to understand and solve unknown knowledge.

The mathematics learning process is all about using old knowledge to elicit and solve new problems. When new knowledge is mastered, it is then used to solve updated knowledge.

Junior high school knowledge is the foundation. If you can use old knowledge to answer new questions, you will have the idea of ??transformation.

It can be seen that learning means continuous transformation, continuous inheritance, development and updating of old knowledge.

2. Learn the mathematical thinking methods of mathematics textbooks.

Mathematics textbooks use implicit disclosure to dissolve mathematical ideas into the mathematical knowledge system. Therefore, it is very necessary to summarize and summarize mathematical ideas in a timely manner.

Summary of mathematical ideas can generally be divided into two steps:

The first is to reveal the content rules of mathematical ideas, that is, to extract the attributes or relationships of mathematical objects.

< p>The second is to clarify the connection between knowledge of mathematical thinking methods and extract a framework for solving the whole problem.

Measures to implement these two steps can be carried out during classroom lectures and extracurricular self-study.

Classroom learning is the main battlefield for mathematics learning. In the classroom, teachers explain and decompose mathematical ideas in textbooks and train mathematical skills so that high school students can acquire rich mathematical knowledge. The scientific research activities organized by teachers maximize the mathematical concepts, theorems, and principles in textbooks. Understand and dig.

For example, in the teaching of the concept of opposite numbers in junior high schools, teachers often have the following understandings in classroom teaching:

① Find the opposite numbers of 3 and -5 from the definition point of view. The opposite numbers are The number is _____.

②Understand from the perspective of the number axis: What two points indicate that the numbers are opposite to each other. (A point that is symmetrical about the origin)

③Understand from the perspective of absolute value: The two numbers with absolute value _______ are opposites of each other.

④Are two numbers that add to zero the opposite of each other? Teaching from these different angles will broaden students' thinking and improve their thinking quality.

5. Some suggestions for learning mathematics.

1. Take notes on mathematics, especially on different aspects of conceptual understanding and mathematical rules, and extracurricular knowledge added by teachers to prepare for the college entrance examination.

2. Create a mathematics correction book. Write down knowledge or reasoning that is prone to errors in daily life to prevent it from happening again.

Strive to: find errors, analyze errors, correct errors, and prevent errors.

Achieve: being able to understand the correct thing deeply from the negative side;

being able to use Guo Shuoyin to get to the bottom of the reasons for errors so as to prescribe the right medicine;

answer the question completely , rigorous reasoning.

3. Memorize mathematical rules and small mathematical conclusions.

4. Establish good relationships with classmates, strive to be a "little teacher", and form a "mutual aid group" for mathematics learning.

5. Strive to solve extracurricular mathematics problems and increase self-study efforts.

6. Consolidate repeatedly and eliminate forgetting what you have learned before.

7. Learn to summarize and classify. Can be: ① Classification based on mathematical ideas ② Classification based on problem-solving methods ③ Classification based on knowledge application

Physics is a natural science course that is relatively difficult to learn. You cannot learn it by rote memorization, even if it is a word. Even if I memorize it correctly, I still can't do it when asked a question. Among the various subjects in high school science, physics is a relatively difficult subject to learn. Most students who have studied high school physics, especially students with poor grades in physics, always have this question: can they understand in class? Yes, I just don’t know how to do it after class. This is a common problem that deserves serious consideration by physics teachers and students. The following is a brief discussion of some high school physics learning methods to help students learn.

1. Correct learning attitude

First analyze the common questions raised by students, that is, why can they understand things in class but not do them after class? Everyone has this personal experience. For example, when reading a certain literary work, the description of the natural scenery and the description of the characters' inner activities are all amazing, and they know it is so, but if they remind themselves If you use a pen to write, you may not be able to write at the level of others. There is absolutely no problem in listening to other people talking or reading other people's articles, but it is not so easy to write it yourself and make it your own. Therefore, in order to change from understanding to being able to do, you must practice a lot on the basis of understanding, so that you can master the laws and secrets and truly make it your own. This is where you should work hard when studying high school physics. .

If you want to learn physics well, the first thing is to cherish your time and study relentlessly. Build up confidence, firmly believe that you can learn any course well, and firmly believe that how much you put in, you should gain something. Regarding this point, please see the following three quotations:

1. I absolutely do not believe that any innate or acquired talent can be successful without a firm quality of long-term hard work. -- Dickens (British litterateur)

2. The main reason why some people can far surpass others is not so much genius, but rather that they are dedicated to learning and will never give up until they achieve their goals. tenacious spirit. --Dalton (British chemist)

3. The fastest and slowest, the longest and shortest, the most ordinary and precious, the most easily ignored, and the most surprising in the world What I regret is time.

--Gorky (Soviet writer)

2. Pay attention to the eight links in learning: Make a plan → Preview before class → Concentrate on class → Review in time → Independent homework → Solve Difficulties → System Summary → Extracurricular Learning.

The most important thing here is: concentrate on class → review in time → work independently → solve problems → system summary, these five links. In the above eight links, there are many learning methods. The following is based on the characteristics of physics and puts forward some specific learning methods on how to learn physics well.

(1) Three basics. The basic concepts must be clear, the basic rules must be familiar, and the basic methods must be proficient.

As for the basic concepts, let’s take an example, such as speed. It has two meanings: one is to express the magnitude of the speed; the other is to express the ratio of distance to time (such as in uniform circular motion), and Speed ??is the ratio of displacement to time (in uniform linear motion).

Regarding basic rules, for example, there are two calculation formulas for average speed. V=s/t and V=(vo+vt)/2 are often used. The former is a definition formula and applies to any situation, the latter is a derived formula and is only applicable to the case of linear motion with uniform speed.

As for the basic methods, for example, when studying middle school issues, the holistic method and the isolation method are often used, which is a typical complementary method.

Finally, let’s talk about one more issue, which is outside the “three basics”. In the process of learning physics, we have summarized some concise, easy-to-remember and practical inferences or conclusions, which are very useful to help solve problems and learn physics well. For example, the electric potential decreases along the direction of the electric field line; the tension on the same rope is equal; the speed is maximum when the acceleration is zero; the Lorentz force does no work, etc.

(2) Solve the questions independently. You should do some questions independently (meaning not relying on others) and with high quality and quantity. There must be a certain number of questions, not too few, and they must be of a certain quality, which means they must be of a certain degree of difficulty. Anyone who learns mathematics, physics and chemistry without going through this level will not be able to learn well. Solving problems independently may sometimes be slower, sometimes take detours, and sometimes cannot even be solved, but these are normal and are the only way for any beginner to succeed.

(3) Physical process. It is necessary to have a clear understanding of the physical process. If the physical process is unclear, there will inevitably be hidden dangers in solving problems. No matter how difficult the question is, you must draw as many pictures as possible. Some sketches are enough, and some require precise drawings, using compasses, set squares, protractors, etc. to show geometric relationships.

Drawing can transform abstract thinking into visual thinking and grasp physical processes more accurately. With diagrams, you can perform state analysis and dynamic analysis. State analysis is fixed, dead, and intermittent, while dynamic analysis is living and continuous.

(4) Attend class. You must listen carefully in class and learn from the teacher humbly. Don't give up listening because the teacher makes it easy. If this happens, it can be regarded as review and consolidation. Try to be consistent and synchronized with the teacher, and cannot do your own thing, otherwise it will be equivalent to completely self-study. After getting started, with a certain foundation, you are allowed to have a certain space for your own activities, which means you are allowed to have some of your own things. The more you learn, the more your own things will accumulate.

(5) Notebook. Classes are mainly about listening to lectures, and you also need to have a notebook to write down some things. The knowledge structure, good problem-solving methods, good examples, parts that you don’t understand well, etc. should all be written down. After class, I have to organize my notes, on the one hand for digestion, and on the other hand, I need to supplement the notes. The notebook should not only record what the teacher said in class, but also make some reading excerpts. You should also write down the good questions and solutions you found in your homework in the notebook, which is what students often call a "good question book." It is best to number the notebooks you have accumulated so hard, and read them frequently in the future, so as to review the past and learn the new.

(6) Study materials. Study materials must be well preserved, classified, and marked. The classification of learning materials includes exercises, test papers, experimental reports, etc. Marking means 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. If you don’t have time, you won’t have time to do anything, so make full use of your time.

Utilizing time is a very superb art. For example, you can use the memory learning method to save time. You can use scattered time before going to bed, waiting for the bus, and recess activities to recall the lessons taught that day, and repeat them again and again. Learning it once can achieve the purpose of strengthening.

(8) Learn from others. We must learn from others humbly, learn from our classmates, learn from the people around us, see how others learn, and often have academic exchanges with them, teach and learn from each other, and improve together. Never be self-righteous. If you know a good method, you should also tell others, so that others will tell you if they have a good method, so that you can complement each other in learning.

(9) Knowledge structure. We must pay attention to and systematically master the knowledge structure, so that scattered knowledge can be organically connected. It ranges from the knowledge structure of the entire physics to the knowledge structure of mechanics, and even specific chapters and sections, such as the knowledge structure of statics and so on.

(10) Mathematics. The calculation of physics depends on mathematics. Mathematics is very important for learning physics. Without mathematics as a calculation tool, it is difficult to learn physics well. You must learn mathematics well and make good use of this powerful tool.

(11) Sports activities. A healthy body is the foundation for learning, and strong energy is the guarantee for efficient learning. You should regularly participate in physical activities, know several ways to exercise, and exercise consciously and consciously. To ensure adequate sleep, it is not advisable to reduce the time to sleep and increase the time to study. You cannot exchange your health for some good results, and you cannot always talk about sprinting and hard work. You must also pay attention to regularity in learning, that is to say, always work hard, but do not engage in surprise.

3. Pay attention to the cultivation of self-study ability

Memory: In the study of high school physics, you should memorize basic concepts, rules and some of the most basic conclusions, which are the so-called things we often mention. The most basic knowledge. Students often ignore the memory of these basic concepts and think that learning physics does not require rote memorization of these literal things. As a result, when students are asked about physics concepts during the general review of senior high school, very few students can accurately explain them. I can’t say for sure how much impact incomplete memorization of physics concepts will have on your study in a certain exam or at a certain stage, but I can say with certainty that it will improve your understanding of physical problems and the formation of knowledge about the entire physical system. , all have inherent adverse effects. You may lose points in any exam because of your inaccurate concepts. Therefore, learning Chinese requires memorizing famous sayings, learning mathematics requires memorizing basic formulas, and learning physics requires memorizing basic concepts and laws. This is the most basic requirement for learning physics well. Without this step, the following learning is impossible.

Accumulation: It is the work after memorization in the process of learning physics. On the basis of memory, we continue to collect a lot of relevant information about physics knowledge from textbooks and reference materials. Some of this information comes from a question, some from an illustration, or a short paragraph of reading material, etc. In the process of collecting and sorting, one must be good at analyzing and classifying different knowledge points. During the sorting process, one should find similarities and differences to facilitate memory. The accumulation process is a process of struggle between memory and forgetting. However, through repeated memorization, knowledge must be made more comprehensive and systematic, and formulas, theorems, and laws must be more closely connected. Only in this way can the purpose of accumulation be achieved. It must not be like a bear breaking a stick. Repeated work and mechanical memorization without thinking will only result in remembering more than forgetting.

Synthesis: Physics knowledge is divided into chapters and sections, and the content required by the physics syllabus is also piece by piece. They are both related to each other and different from each other, so in the process of physics learning, small synthesis must be continuously carried out, etc. After completing the knowledge study in the third grade of high school, a systematic synthesis will be conducted. This process has high requirements on students' ability. Chapter contents are interconnected, and different chapters can be compared with each other to truly integrate and connect the previous and previous knowledge into one. In this way, the internal connection of knowledge can be gradually found from the synthesis.

Improvement: With the memory and accumulation of previous knowledge, and then careful synthesis, you can improve your problem-solving ability. The so-called improvement of ability, to put it bluntly, is to improve the ability to solve and analyze problems. For a topic, we must first find out what the problem is - mechanics, heat, electromagnetism, optics or atomic physics, and then clarify the research object and combine it with the topics in the topic. Only by providing conditions and applying relevant physical concepts and laws, as well as some first-level and second-level physics conclusions, can the results be obtained smoothly.

It is conceivable that if the basic concepts of physics are not clear, the given conditions or implicit conditions in the question cannot be seen, or the formula used to solve the problem is wrong, or the first or second level conclusion should be used instead of the original formula, it will all be wrong. The speed and accuracy of problem solving are affected.

Improvement first involves solving problems, then being flexible in solving problems, and then being innovative in problem-solving methods. This includes multiple solutions for one question, which means you can choose the simplest method from multiple solutions; it also includes one solution for multiple questions, one method to successfully solve multiple similar questions, so that you can truly use them dexterously and at your fingertips. .

To sum up, there are roughly six levels of learning physics, that is, first understand, then remember, practice to use, gradually become proficient, practice makes perfect, innovation, etc., starting from the initial goal of basic knowledge, Reach the highest level of learning physics.

In the process of physics learning, according to the cognitive process from simple to complex, compare the six levels of learning, gradually discover your own position and level, identify your own shortcomings, and then determine your own improvement and improvement direction of effort. Studying in high school is to prepare for university study, which puts forward higher requirements for students' self-learning ability. The basic process of physics learning mentioned above - memory, accumulation, synthesis and improvement is the process of cultivating one's own self-learning ability. , learned how to study, became interested in physics, and mastered the characteristics of physics as an experimental subject. Through hard work, I will definitely master high school physics.