Secondly, we should pay attention to efficiency. Don't do "repetitive work", each preview should have a clear purpose. Here, I want to make it clear that too many reference books are unnecessary. Reading one reference book is often better than reading two, but not reading it. The famous mathematician Hua said: "When reading, the more you read, the thinner you get." In other words, we should grasp the basic clues and spiritual essence of the commander-in-chief book.
This reminds me that every student is weaving a knowledge network for himself while learning knowledge. Its main function is to link what he has learned and improve learning efficiency. Knowledge networks should be properly woven. Too sparse, can not let their thinking extend in all directions, free; Too dense, it will affect the clarity of the main line, not worth the loss. Let's take an example here: a classmate usually studies hard and does a lot of math problems, but he doesn't understand the main idea. In order to "leak-proof", he takes almost every sentence in every reference book as the focus. What is more sad is that in the process of repeated work, he never arranges his long thoughts in an orderly way, and some questions asked by teachers and classmates are often "low-level"-just turn his head a little! Because he doesn't pay attention to the sense of solving problems, his grades have not improved, which is the consequence of the book "getting thicker and thicker". Mathematics problem-solving is often very flexible, and everyone has their own problem-solving ideas to improve learning efficiency.
Many math problems are intriguing. Solid geometry allows us to understand the art of space, and mathematical induction allows us to appreciate the skills of proof ... China football team coach milunovic advocates "happy football", so we might as well enjoy mathematics and experience the fun it brings. Think more, enjoy more and gain more. This is my third point. In the usual study, you must leave a considerable number of topics for yourself to fully think about, especially the more difficult ones, even if you think for an hour or even longer. To solve a difficult problem, as long as it is fully considered, even if it is not done, the whole thinking process is valuable. Because difficult problems are often comprehensive and have strong ability, and require high continuous divergent thinking, solvers often have a long exploration process. In the whole process of exploration, problem solvers keep looking for breakthroughs, constantly hitting a wall, constantly adjusting their thinking power and making progress. At the same time, the problem solver tried a lot of knowledge and skills he had learned, which had a good review effect. Problem solvers also test their mastery of relevant knowledge by doing problems, so as to set appropriate goals for their future study. I remember that there is an inequality proof problem in the magazine "Middle School Mathematics", which is quite difficult. I thought hard for four hours and finally came up with a better plan than the reference plan. This makes me ecstatic, and of course it also gives me a deeper understanding of this inequality. By the way, thinking more is a good way to cultivate a person's comprehensive ability in mathematics, but some students often ignore the calculation ability and practice. Although calculators can be used in exams (not in competitions), calculators cannot perform algebra, analysis and trigonometry. Unfortunately, sometimes the students' thinking of solving problems is right, but the calculation is wrong, which leads to the final mistake. One of the reasons why I am not good at analytic geometry is that it requires a lot of calculation. If the method used is not good, the calculation will be more complicated and error-prone. I hope readers will work together with me to make themselves have excellent computing ability.
In addition to the above three points, I think, whether in the learning process or in the review stage, we should pay attention to the adjustment of mentality. There are many reasons for failing an exam. It may be that the knowledge is not firm, that the problem-solving feeling is not in place, that the calculation mentioned above is wrong, that the conditions are not good, that it may be a special reason, or that the mentality is unbalanced because I want to do well in the exam. I think a person's mentality should not be excessively influenced by test scores. Always remember that sufficient accumulation is the guarantee of stability. Study hard at ordinary times, and take time out to do a certain amount of exercises with moderate difficulty when reviewing before the exam, so as to improve the proficiency in solving problems and enhance confidence. Stay calm and excited during the exam, which may burst into endless energy. Of course, at any moment, we should also remember one sentence; "Be content only with progress, not with success."
Some students are knowledgeable, but their divergent thinking ability is poor. In this regard, you can buy some divergent thinking synchronization counseling books. (Note: I don't know much about the book market. I think students might as well think backwards, adapt or even make up some questions and answer them themselves. First, you can review the topics you have done so that you can solve similar problems more skillfully; Secondly, we can explore whether or how subtle changes in conditions affect the process of solving problems. In addition, you can also get a preliminary understanding of the proposition ideas, thus broadening the ideas and deepening the problem-solving ideas.
Making up a topic makes it easier for you to draw inferences. Although compiling a new problem is often several times more difficult than solving an exercise, the gains gained through divergent thinking in the process of compiling the problem are often greater than doing ten problems. Spending a small amount of time sorting out and solving problems is also a good way to explore and learn.
The above is my learning experience, for reference only. One thing needs to be explained, because of their different situations, everyone has gradually formed a learning method suitable for them, which only needs to be properly adjusted and does not need to be deliberately changed. In fact, learning mathematics and other subjects can learn from each other. Bottom line: things can be done well if you are willing to use your head.
After entering high school, many students often can't adapt to mathematics learning, which in turn affects their enthusiasm for learning and even their grades plummet. There are many reasons for this. But it is mainly caused by students' ignorance of the characteristics of high school mathematics teaching content and their own learning methods. According to the characteristics of high school mathematics teaching content, this paper talks about learning methods of high school mathematics for students' reference.
First, changes in the characteristics of high school mathematics and junior high school mathematics
1, mathematical language is abrupt in abstraction.
There are significant differences in mathematics language between junior high school and senior high school. Junior high school mathematics is mainly expressed in vivid and popular language. Mathematics in senior one involves very abstract set language, logical operation language, function language, image language and so on.
2. Transition of thinking method to rational level.
Another reason why senior one students have obstacles in mathematics learning is that the thinking method of mathematics in senior high school is very different from that in junior high school. In junior high school, many teachers have established a unified thinking mode for students to solve various problems, such as how many steps to solve the fractional equation, what to look at first and then what to look at in factorization, and so on. Therefore, junior high school students are used to this mechanical and easy-to-operate stereotype, while senior high school mathematics has undergone great changes in the form of thinking, and the abstraction of mathematical language puts forward high requirements for thinking ability. This sudden change in ability requirements has made many freshmen feel uncomfortable, leading to a decline in their grades.
3. The total amount of knowledge content has increased dramatically.
Another obvious difference between high school mathematics and junior high school mathematics is the sharp increase in knowledge content. Compared with junior high school mathematics, the amount of knowledge and information received per unit time has increased a lot, and the class hours for assisting exercises and digestion have decreased accordingly.
4. Knowledge is very independent.
The systematicness of junior high school knowledge is more rigorous, which brings great convenience to our study. Because it is easy to remember and suitable for the extraction and use of knowledge. However, high school mathematics is different. It consists of several relatively independent pieces of knowledge (such as a set, propositions, inequalities, properties of functions, exponential and logarithmic functions, exponential and logarithmic equations, trigonometric ratios, trigonometric functions, series, etc.). ). Often, as soon as a knowledge point is learned, new knowledge appears immediately. Therefore, paying attention to their internal small systems and their connections has become the focus of learning.
Second, how to learn high school mathematics well
1, form a good habit of learning mathematics.
Establishing a good habit of learning mathematics will make you feel orderly and relaxed in your study. The good habits of high school mathematics should be: asking more questions, thinking hard, doing easily, summarizing again and paying 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. Good habits of learning mathematics include self-study before class, paying attention to class, reviewing in time, working independently, solving problems, systematically summarizing and studying after class.
2, timely understand and master the commonly used mathematical ideas and methods.
To learn high school mathematics well, we need to master it from the height of mathematical thinking methods. Mathematics thoughts that should be mastered in middle school mathematics learning include: set and correspondence thoughts, classified discussion thoughts, combination of numbers and shapes, movement thoughts, transformation thoughts and transformation thoughts. With mathematical ideas, we should master specific methods, such as method of substitution, undetermined coefficient method, mathematical induction, analysis, synthesis and induction. In terms of specific methods, commonly used are: observation and experiment, association and analogy, comparison and classification, analysis and synthesis, induction and deduction, general and special, finite and infinite, abstraction and generalization.
When solving mathematical problems, we should also pay attention to solving the problem of thinking strategy, and often think about what angle to choose and what principles to follow. The commonly used mathematical thinking strategies in senior high school mathematics include: controlling complexity with simplicity, combining numbers with shapes, advancing forward and backward with each other, turning life into familiarity, turning difficulties into difficulties, turning retreat into progress, turning static into dynamic, and separating and combining.
3. Gradually form a "self-centered" learning model.
Mathematics is not taught by teachers, but acquired through active thinking activities under the guidance of teachers. To learn mathematics, we must actively participate in the learning process, develop a scientific attitude of seeking truth from facts, and have the innovative spirit of independent thinking and bold exploration; Correctly treat difficulties and setbacks in learning, persevere in failure, be neither arrogant nor impetuous in victory, and develop good psychological qualities of initiative, perseverance and resistance to setbacks; In the process of learning, we should follow the cognitive law, be good at using our brains, actively find problems, pay attention to the internal relationship between old and new knowledge, not be satisfied with the ready-made ideas and conclusions, and often think about the problem from many aspects and angles and explore the essence of the problem. When learning mathematics, we must pay attention to "living". You can't just read books without doing problems, and you can't just bury your head in doing problems without summing up the accumulation. We should be able to learn from textbooks and find the best learning method according to our own characteristics.
4. Take some concrete measures according to your own learning situation.
Take math notes, especially about different aspects of concept understanding and mathematical laws. The teacher is in class.
Expand extracurricular knowledge. Write down the most valuable thinking methods or examples in this chapter, as well as your unsolved problems, so as to make up for them in the future.
Establish a mathematical error correction book. Write down the knowledge or reasoning that is easy to make mistakes at ordinary times to prevent it from happening again.
Submit. 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 closely.
Recite some mathematical rules and small conclusions to automate your usual operation skills.
Or semi-automated proficiency.
Knowledge structure is often combed into plate structure, and "full container" is implemented, such as tabular,
Make the knowledge structure clear at a glance; Often classify exercises, from a case to a class, from a class to multiple classes, from multiple classes to unity; Several kinds of problems boil down to the same knowledge method.
Read math extracurricular books and newspapers, participate in math extracurricular activities and lectures, and take more math classes.
Foreign topics, increase self-study and expand knowledge.
Review in time, strengthen the understanding and memory of the basic concept knowledge system, and repeat it appropriately.
Solid, eliminate forgetting before school.
Learn to summarize and classify from multiple angles and levels. Such as: ① classification from mathematical thought ② solution.
Classification of questions and methods (3) Classification from knowledge application and other aspects. Make the knowledge learned systematic, organized, thematic and networked.
Often do some "reflection" after doing the problem, think about the basic knowledge used in this problem, mathematics.
What is the way of thinking, why do you think so, whether there are other ideas and solutions, and whether the analytical methods and solutions of this problem are used to solve other problems.
Whether it's homework or exams, we should put accuracy first, general methods first, and
Instead of blindly pursuing speed or skill, learning math well is the important issue.
Problem: n times is 2N- 1, 6 times is 1 1, 10 times is 19.
(1) Cut a square piece of paper into four small squares with the same size and shape, then cut a small square into four small squares in the same way, then cut a small square into four small squares, and so on.
The tangent is 1 2 3 4 5. ....
Number of squares 4 8 12 16 20 ....
If you cut n times * * * and cut out _ _ _ small squares.
If you cut it 100 times, * * * will cut out _ _ _ small squares.
What other rules can you draw by observing the graph? Please write them on the horizontal line _ _ _ _ _ _ _ _ _ _.
Answer: 4n
100*4=400
(2)2x4=3？ - 1 3x5=4？ - 1 4x6=5？ - 1 ... 10x 12 = 1 1？ - 1
Use a formula containing only one letter to express the rule you guessed: _ _ _ _ _ _ _ _ _ _
Answer: (n- 1)(n+ 1)=n? - 1
(3) There are several figures, the first one has a square, the second one has three squares, the third one has six squares, and the fourth one has ten squares. How many squares does the fifth one have? What about the sixth one? Where is the nth one?
Answer: the fifth: 15, the sixth: 2 1, and the nth: n(n+ 1)/2.
(4)1* 2 * 3 * 4+1= 25 = 5 2 2 * 3 * 4 * 5+1=1=/kloc-0.
Answer: n (n+1) (n+2) (n+3)+1.
=[n(n+3)][(n+ 1)(n+2)]+ 1
=(n？ +3n)[(n？ +3n)+2]+ 1
=(n？ +3n)？ +2(n？ +3n)+ 1
=(n？ +3n+ 1)？
That is, n (n+1) (n+2) (n+3)+1= (n? +3n+ 1)？
(5) 1-2+3-4+5-6+......+99- 100 (2) 1+2-3+4-5+6-......-99+ 100 (3)0-|72/7 1-7 1/72|+|7 1/72-72/7 1|
Answer:-1*50=-50
(6) Observe the following numbers:11,-1/2,-2/1/3,2/2,3/1,-1/0.
Answer: Look at the law:
The denominator is 1, 2 1, 32 1, 432 1, ....
The number of numbers is 1.2340% arithmetic progression, so 1.2345 is already 15, so the next one should be 6, so the denominator should be 6.
The molecular range is from 1,-1 -2, 123,-1 -2 -3 -4, .....
The number of numbers is 1 2 3 4 5 ..., so by 5, the number has reached 16, so the next number should be-1 -2 -3 -4 -5 -6, because even numbers are negative. So the number 16 is:-1/6.
Look at the law again:
1 2 3 4 5 6 7 is 28 at this time, and the number after 5 is the 33rd number. So the denominator should be
8。 The fifth from the bottom, so the denominator should be 4.
Now look at the numerator: when it reaches 8, it is the fifth number, and because the even number is negative, it should be -5, so the 33rd number is -5/4.