As a math teacher, the ability to solve problems is very important. Mathematics is a maze of mathematics, letters, symbols and numbers.
Many people like to play maze games. Reverse thinking is the key to find the right way out of the maze. Once you get out of the maze smoothly, you will be excited by the pleasure of success and will challenge a new and more complicated maze. This is also the charm of mathematics, and your thinking has been trained unconsciously. It can be said that mathematics is a subject that teaches people to be smart and keen.
However, if you don't know how to walk in the maze and often fail, you will get tired of this game. We attach importance to the training of mathematical thinking, and the subtle influence of thinking methods is more important than the imparting of knowledge.
We should let students often feel successful and learn mathematics in happiness. You must do gymnastics, but you must walk into the maze.
You can't train your mind without using your hands and brains. Mathematics has become a common language because of its own characteristics, strict systematic and logical reasoning, reasonable operation rules and properties. Without translation, mathematical symbolic language and graphic language can convey our thoughts and achieve the purpose of communication only by using mathematical equivalent deformation. Therefore, mathematics is a language.
Mathematics is full of philosophy, and many mathematicians (such as Pythagoras) are also philosophers. In other words, many philosophical views have found evidence in mathematics and have been embodied.
Many philosophers also study mathematics, such as Engels, whose Dialectics of Nature is an outstanding mathematical treatise. Mathematical object is not the real existence in the material world, but the product of human abstract thinking, and culture, in a broad sense, refers to the sum of material wealth and spiritual wealth created by human beings in the process of social and historical practice. Therefore, in the sense mentioned, mathematics is a kind of culture.
2. About the "trick" of solving problems in junior high school mathematics writing-"Mathematics Thesis" has been in contact with the subject of "Mathematics" for eight years.
Speaking of my experience and feelings of learning mathematics, it is very simple, one word-"method". Today, we live in an era of lifelong education.
The so-called "lifelong education" means lifelong learning and continuous learning, otherwise it will fall behind. But "the illiterate in the 2 1 century are not illiterate people, but people who can't learn."
Now facing the entrance examination, how to master a lot of knowledge quickly has become the most urgent problem for students. In this era of information explosion, how to acquire the most knowledge with the most effective learning methods ... In order to learn more knowledge in a limited life, besides unremitting efforts, the most important thing is to master a set of learning methods that suit you.
A complete set of learning methods can not only enhance self-confidence, but also succeed in the field of learning. Some people say, "Nothing is impossible, only people who can't do it."
We can also say: "There is no knowledge that can't be learned, only bad learning methods." Therefore, the most important thing in learning any subject is to have a correct and scientific method.
Nowadays, mathematics has become a tool. In people's production and life, mathematics, as a special tool of people's thinking, exists "invisibly" in society. Although it is not "tangible" like a tangible tool, in a sense, its role far exceeds that of tangible tools, so it is said to be "an indispensable tool for people's life, labor and study". And it is also a wonderful language. Because mathematics has its own characteristics, it has its own set of languages (symbols), and this special language is recognized by everyone. People can use this special language to exchange ideas and methods and realize the * * * development of science and technology ... This shows how widely mathematics is used! As a junior two student, I also have some research on mathematics.
Some math exams and exercises now are nothing more than multiple-choice questions and "hot" geometric proof questions. But we lose points on these issues from time to time-so here, I explore some common methods of solving mathematical problems.
Multiple-choice questions are objective questions, which have the characteristics of obvious answers, objective scoring and wide coverage of investigation contents. In recent years, multiple-choice questions will be regarded as an important test item in the senior high school entrance examination in all provinces and cities in China and occupy a large proportion.
Therefore, mastering the solution of multiple-choice questions and improving the ability to solve multiple-choice questions is an aspect that our students should focus on in the math exam. To solve multiple-choice questions, we must first carefully examine the questions, adopt scientific and appropriate problem-solving methods according to the characteristics of the questions, and solve them quickly and accurately.
There are several common solutions to multiple-choice questions: 1. The direct method is a common method, which is based on the conditions given by the stem of the question, the definitions, theorems, formulas, axioms and laws learned, reasonable operation and reasoning are carried out, the correct results are obtained, and then the selected branches are used for checking, and then a judgment is made. 2. Some problems of special value method are difficult to judge under given conditions, and some special values can be used instead of verification judgment.
For example, if 0 (a) x 2 (c) x analysis: x= 1/2 is taken from the given condition 0, then x-1= (1/2)-1= 2, x 2 = (65438). For example, given that the symmetry axes of the image passing points (1, 6) and (0,5) of the quadratic function y = ax 2+bx+c are x= 1/3, then () (a) a = 1/2 and b = 2, c.
4. Verification method Verification method is to replace the original question with a given conclusion to verify and make a judgment. If you can make good use of the above methods to do multiple-choice questions, then you can definitely show your "demeanor" on it! There are also some special methods, which are specifically aimed at the current geometric proof problems.
Geometry is the mathematization of material space in life and is regarded as the source of mathematical activities. Its research object is mainly what we students often contact in our daily life.
But for us, learning geometry is much more difficult than learning algebra. In the process of some exercises, when we encounter some unfamiliar geometry problems, we often feel at a loss.
At this time, we should master some associative methods, so that geometry will not make us feel so abstract. 1. Associating basic graphics: Many graphics in geometry are often deformed by some basic graphics in some way. If we can relate these figures with which basic figures have been changed, and study this problem under these basic backgrounds, then the idea of solving the problem will naturally come out.
Example: 1 in trapezoidal ABCD, as shown in figure 1, ad∨BC, ∠BCD=90 degrees, BC=CD= 12, ∠ABE=45 degrees, point e is on DC, BF⊥ AE. Analysis of G A D: From the two adjacent sides of H F ∠BCD=90 degrees and BC=DC, we can think that the basic E graph is square, so we can fill the graph into a square to solve it.
B C (figure 1) crosses point B as BG⊥AD, and G crosses the extension line of DA to extend DG to H, so GH=CE, so it is easy to prove △ BHG △ BEC, so BH=BE, so it can be proved that △ ABH △ Abe, △ BEC. ∴BF=BC= 12.2. Common conclusions of Lenovo: There are many conclusions in mathematics. Although they do not appear in the form of theorems, they are often used in practice. For example, the area of an equilateral triangle with side length a is equal to 4 a of the root sign. The area of a quadrilateral with diagonal lines perpendicular to each other is equal to one-half mn (m.n is the length of two diagonal lines respectively), and the areas of two triangles with the same base (equal base) and the same height (same height) are equal. If we memorize these conclusions skillfully, it will not only help to explore the thinking of solving problems, but also greatly improve the speed of solving problems.
Example 2 Uncle Zhang's house has a quadrangular vegetable field, as shown in Figure 2.
I want a math composition. What stage does the math composition need?
Children, if you can ask such a question, as long as you do the following seriously, you will be the "best" in math in your class in the future.
In my opinion, to learn math well, you can simply say "understanding plus practice". Remember to learn math by rote. To fully understand its meaning, it is best to express it correctly in your own language. Specifically, the understanding of concepts requires four skills: correct narration, judgment, example and application. The understanding of laws, formulas, theorems and properties requires a clear understanding of conditions and conclusions, a mastery of reasoning ideas and methods, an understanding of reasoning processes, and flexible use of the conclusions drawn. To understand the example, you should try to understand the meaning of the question clearly, try to solve it yourself first, and then compare it with the answers in the book. Through reflection, you can sum up the rules and methods of answering such questions. Pay attention to the discovery of problem-solving ideas and the summary of problem-solving methods. Learning mathematics is to cultivate our abilities of calculation, thinking, logical reasoning, problem analysis and problem solving. However, "ability" is a skill, which cannot be formed without necessary training. An American mathematician said: The only way to learn mathematics is to "do mathematics". The so-called practice is to complete a considerable amount of practice. We know that Chen Jingrun, a famous mathematician in China, made a breakthrough in Goldbach's conjecture and shocked the world, but he used several sacks of draft paper! It can be seen how important practice is. Everyone must work hard to finish the exercises in the textbook independently. Students who have spare capacity should also read some extra-curricular books, such as Mathematics for Middle School Students and Mathematics Weekly, which can broaden their horizons and improve their mathematics level. In addition, students who have the opportunity and conditions should actively participate in various math competitions to exercise and cultivate themselves. When doing a problem, it's best to have multiple solutions to one problem, and one problem is changeable, sum up experience, master skills and techniques, draw inferences from others, and discover the "universal method", which will be useful for life.
I hope teachers can do the following:
First, be "clear"; Clear knowledge, clear methods, clear thinking, clear links and clear starting points. In a word, math class should be a "clear line", not a "fuzzy piece". This is not the proper feature of mathematics class, which should have a "mathematical taste". Second, be "new"; This kind of math class is novel in content and method, and it is more attractive and worth discussing. Third, we must "live"; In other words, a good math class should be flexible in methods, active in students' thinking, flexible in teachers and students, and open in class. Fourth, be "real"; Live and be real, live and not be chaotic, and the knowledge, methods, skills, emotional attitudes and other aspects of the implementation can be implemented. I always think that if a math teacher can make your class "vivid and practical", then you are a very good math teacher. Fifth, be "odd"; That is to say, math class should be as "unexpected and different" as possible. Of course, this is a very difficult thing, and there is no need to unilaterally pursue "being different", but as a seminar class and an observation class, everyone always wants to hear some innovative and thoughtful classes. If you take a class and design some links, everyone will be used to it for a long time, and others will do the same. He may think that you are nothing special, just like everyone else. Therefore, I have always adhered to the seminar's viewpoint of "not seeking perfection, but seeking discussion value". I don't really like some slow and mindless classes.
In a word, learning mathematics well requires not only a good teacher, but also one's love and interest in mathematics.
4. "Plain is also a kind of enjoyment? Wuhu candidates? Building a house is human, and there are no horses and chariots.
What can you do? The heart is far from being self-centered. Picking chrysanthemums under the east fence, you can see Nanshan leisurely.
The mountains are getting better and better, and the birds are back. This makes sense. I forgot to say it if I wanted to defend myself.
What a "Return to the Garden", what a Tao Yuanming who regards utility as dirt, and what a dull life. ? I don't like vigorous life. I haven't done anything earth-shattering
Friends, in this exciting year, I love a kind of dullness, because it is a kind of enjoyment. ? Taste a cup of fragrant tea and turn over a few pages. Every time you know something, you will be so happy that you forget to eat. Dull is a kind of enjoyment.
Looking at Li Qingzhao's Dongli wine after dusk, there is a faint fragrance and sleeves, which is a kind of sadness and dullness, but it is a sigh that "the west wind blinds people are thinner than yellow flowers", because she has an enviable first half of her life, and when she leads a dull life in the last years, she can't bear loneliness. ? Dull is a kind of enjoyment.
Peach Blossom Garden is the highest realm of Tao Yuanming's plain imagination. There, people have a sense of security for their old age and a sense of happiness for their young age, and people enjoy the dull family happiness.
Dull is a kind of enjoyment. Liu Yuxi's "Bashan Chujiang River is desolate, and he gave up on himself for twenty-three years".
Without fame and the emperor's favor, I finally understood that "Qian Fan is on the side of the sunken ship and Wan Muchun is in front of the sick tree". And whether he realized the plain truth in the enjoyment is a kind of enjoyment.
Wu Jun has told us in his book with Zhu. He is a person who likes to be plain, drifting from the stream in Fuchun River and doing everything.
Because he calmed his passion for fame and fortune, gave up his job in economic and trade affairs and lived a plain and chic life, and his happiness and joy were beyond words. ? Dull is a kind of enjoyment.
Although Ouyang Xiu was relegated, he enjoyed a dull happiness with Chu people in a dull life, without lamenting or being discouraged, which is why he only cares about mountains and rivers. ? Plain, I am a member of the universe, I don't like luxury, I don't like fame and fortune.
In the plain, you can read the hearts of the ancients; In the plain, you can see the beauty of nature; In the plain, you can understand things; In the plain, you can be deeply moved; In the plain, you can help the world; In the plain, you can have many. ? It's too cold up there.
Dance to find out what shadows look like on the earth. The ancients had the dullness of the ancients, and I also had mine.
Dull is life, dull is happiness, and happiness is enjoyment. Although I am still young and don't understand Tao Yuanming's "true meaning", I want to stop the noisy gears in my heart and let the dullness bring quiet joy. This is a kind of life, but also a kind of enjoyment.
Dull, but also a kind of enjoyment, from the depths of the soul. ? [Teacher's comment]? Although the title requires 500 words, this article has written more than 800 words, which meets the requirements of the college entrance examination.
But this article is more exciting. Deep thoughts.
It's hard to imagine that a third-year student can choose "plain" enjoyment, isn't it a bit premature? The article quotes and comments on the ups and downs and pursuits of many famous artists in history. Full and accurate examples and profound and insightful comments make people have to admire the profundity of the author's thoughts.
Rigorous conception. Strict conception is a major feature of this paper.
The article starts with Tao Yuanming's poems and ends with Tao Yuanming's poems, echoing from beginning to end. In the second paragraph, I will take Li Qingzhao's example as a negative argument. Next, I will list the life experiences of Tao Yuanming, Liu Yuxi, Wu Yun and Ouyang Xiu in turn to illustrate that dullness is a kind of enjoyment.
The article is well organized. ? Flying literary talent.
This article is full of literary talent, which makes people stay fragrant after reading it. There are two reasons.
First of all, this paper quotes a large number of poems, which makes the full text full of poetic meaning. Can quote so many poems, it can be seen that it is generally hard work, how can it be not high.
Secondly, he is good at organizing antithesis and parallelism. These antithesis and parallelism sentences not only add beauty to the language, but also add momentum to the article.
It can be seen that if you can't quote a poem, it is good to make a neat sentence. Parting is also a kind of enjoyment? Wuhu candidates? It's the third grade, and it's already out of the mountain.
We are old before we are young, and we have come to the end of the third grade with our muddy eyes open in the sea of books. The sun is still shining, even * * *, and our black eyes seem to be gradually clear. Behind our sobriety, we are caught off guard.
As the old saying goes, "It's a pleasure to have friends coming from afar." Another cloud said, "There's no reason to go out to the Western Heaven."
People are always keen on the joy when they get together, but they feel sad when they leave. In fact, parting is also a kind of enjoyment, because it can reproduce the warmth that you missed inadvertently.
The kind math teacher struggled to move his chubby body, and in the last few classes before graduation, everything somehow slowed down. There is nothing but writing and whispering, only the solemnity before parting, less solemnity and more helplessness.
White chalk dust slowly falls along the sunshine, and the teacher's sweat flashes like a freeze in the summer sunshine. He asked us again and again, "Do you understand?" Then erase it and start over.
It is also a dust of the sunset, bearing the love of three years' dedication, and the air is full of emotion. With the class * * *, his voice is hoarse and helpless.
I hope this course has no end. Inexplicable, he undoubtedly gave us the most touching revelation-parting is a touching enjoyment.
Although the old class banned it, the classmate record was circulated in the "underground" with lightning speed, just to let the memory move on the paper with the simplest words in the last days. Some of the student records I have inadvertently browsed only shed the true feelings of the flashy appearance of the past. Everyone tries to leave his own shadow on a small piece of manuscript paper, and instills sincere thoughts and hearts with three years of getting along.
Here, there is no ridicule and sarcasm, no inferiority and arrogance, only a real friend who never leaves-parting is a sincere enjoyment. ? After killing our old class for three years, I finally couldn't hold back my tears. Only then can I understand that she has the softest place in her heart, which is inhabited by sixty crystal-pure and happy children.
She is still rushing to arrange class affairs, but she is a little reluctant-parting is a cherished enjoyment. ? Love and beauty that once scattered in the corner came quietly in parting.
5. Can mathematics be considered as a language? Yes
Language has always been an indispensable "excellent example of human wisdom" in human society. Language has the potential to enhance the ability to remember and explain concepts. Mathematical language is a scientific language, which refers to the expression of mathematical concepts, formulas, formulas, arithmetic rules, rules, problem-solving ideas and derivation processes. Mathematical language has the characteristics of accuracy, abstraction, conciseness and symbolism. Its accuracy can cultivate students' honesty and integrity, its abstraction is conducive to cultivating students' ability to reveal the essence of things, and its conciseness and symbolism can help students better summarize the laws of things and help them think.
The overall goal of the new curriculum standard requires: learn to cooperate with people, and be able to communicate with people about the process and results of thinking, clearly explain their own views and make sense, and use mathematical language to discuss and ask questions logically in the process of communicating with people. The standard has different requirements for mathematical languages in different fields. In class, we find that some students want to speak but can't, some students dare not speak, and some don't speak at all. The use and expression of students' mathematical language is still far from the requirements of the Standard.
Based on the above situation, the author analyzes the reasons, and holds that: ① Mathematics classroom teaching is limited by the traditional educational tendency of "focusing only on results, ignoring process" and "only knowing how to do without dictation", and is infringed by exam-oriented education, which makes students lack opportunities for language practice, thus restricting the display of students' thinking. (2) Teachers don't know enough about the function of mathematical language and neglect the cultivation of students' mathematical language, which leads to the inaccuracy, nonstandard and imprecision of students' mathematical language and hinders the development of students' thinking. (3) Limited by the number of classes, there are too many students, some introverted students want to talk but can't speak clearly, and some good students often have no patience to listen. Over time, these students can't express mathematical language accurately and standard. ④ Students' own reasons are mainly influenced by non-intelligence factors.
To sum up, in today's primary school mathematics classroom teaching, it is imperative to strengthen the cultivation of students' mathematical language ability.
First, teachers' accurate and standardized mathematical language has a subtle influence on students.
Teachers' words and deeds have a subtle influence on students, so we should cultivate students' mathematical language expression ability, standardize teachers' language and set an example for students. Mathematics teachers should accurately describe concepts, laws and terms, and don't let students have doubts and misunderstandings. To this end, teachers should do the following two things: First, they should have a thorough understanding of the essence of concepts and the meaning of terms. For example, if we confuse "divide" with "divide", "number" with "number", and "number" with "number", we violate the law of identity. Some teachers instruct students to draw pictures, saying that "these two straight lines are not parallel enough" and "this right angle is not drawn at 90", which violates the law of contradiction. However, languages such as "the figure composed of three sides is a triangle" and "leap year is a multiple of 4 in the Gregorian calendar year" lack accuracy. Second, it must be explained in scientific terms. For example, we can't say "vertical line" as "vertical downward line" or "simplest fraction" as "simplest fraction". In addition to accuracy, rigidity should also have normative requirements. For example, speak clearly, read sentences clearly, and insist on using Mandarin. Conciseness means that the teaching language should be clean, important words should not be lengthy, focus on the key points, be simple and targeted; According to the age characteristics of primary school students, say what they are easy to accept and understand; Be accurate, don't beat around the bush, and deliver more information in a shorter time.
Second, let students train their mathematical language expression ability in oral expression.
In order to train all students' mathematical language, teachers can flexibly use the training mode of "deskmate communication, group discussion, classroom evaluation and student summary", and implement the teaching idea of "language training as the main line and thinking training as the main body" in classroom teaching, so that students at different levels can have something to say, stimulate students' enthusiasm for speaking and improve their speaking ability in positive evaluation.
6. The math composition is short. I like all the courses in school, especially math.
A few weeks ago, I learned "Numbers and Information". When I got home that night, I began to number the houses in our community. There are two villages in our community, 3 buildings horizontally, 7 buildings vertically and 2 1 vertically. So I named the first building "2. 1" and the second building "2.2".
A few days ago, my father gave me a difficult problem. The topic is this: there are 43 students, and the amount of money ranges from 8 cents to 5 cents. Each student bought a painting with his own money. There are only two kinds of graphs: one with 3 points and the other with 5 points. Everyone should buy as many pictures as possible with 5 cents. What is the total number of three-point pictures they bought? "I've thought for a long time and listed many formulas, but I still can't think of one. I'm helpless. Then the father said, "Let me analyze it for you. The number of people is 43, and the amount of money ranges from 8 to 50. There are exactly 43 kinds, that is, there are just one classmate with an amount of 8 points and one classmate with an amount of 9 points. Everyone bought the pictures separately, which means everyone has spent all their money. But everyone's money is used separately and they don't put it together. " This made me suddenly realize: "Oh, I see, if these 43 students are divided into five groups according to the amount of money from less to more, but there are still three people left." "According to the analysis, each of the first eight groups bought (1+2+0+2+4) 10 three-pointer pictures, so eight groups * * * bought 80 three-pointer pictures. In addition, 48 clubs will buy 1 3-point chart, 49 clubs will buy 3 3-point charts, and 50 clubs will not buy 3-point charts, so the remaining three people * * * bought (1+3)4 3-point charts. In this way, we can find that 43 people bought (40+4)84 3-point graphs. Am I right? " Dad touched my head and said, "Exactly."
Actually, counting is also wonderful. For example: 432-234= 198, 654-456= 198, 987-789= 198, etc. Students, have you found the pattern? )
Math is really interesting!