Writing an essay using mathematics as a language

1. An essay about mathematics, 200 words

The mathematician Kolya once said, what is mathematics? Mathematics is about problem solving, which is about transforming unfamiliar problem types into familiar ones.

As a mathematics teacher, problem-solving ability is very important. Mathematics is a maze composed of mathematics, letters, symbols, and graphics.

Many people like to play maze games. Reverse thinking is the trick to find the right way out of the maze. Once you successfully get out of the maze, the joy of success will make you excited, and you will look forward to new and more complex mazes. Challenge, this is also the charm of mathematics, thinking is trained unconsciously. It can be said like this: Mathematics is a subject that teaches people wisdom.

However, if you don’t know the method in the maze and often hit the wall and fail, you will get tired of this kind of game. We attach great importance to the training of thinking in mathematics. The subtle influence of ideas and methods is more important than the transfer of knowledge.

We want students to always have a sense of success and study mathematics in happiness. If it’s gymnastics, you have to do it, and if it’s a maze, you have to walk.

If you do not use your hands and brain, you will not be able to achieve the purpose of training your thinking. Mathematics has become a universal language in the universe due to its own characteristics, strict system and logical reasoning, operation rules and rationality of operation properties. It does not require translation. As long as the identity transformation of mathematical formulas is used, mathematics Symbolic language and graphic language can convey our thoughts and achieve the purpose of communication, so mathematics is a language.

Mathematics is full of philosophy, and many mathematicians (such as Pythagoras) were also philosophers. In other words, many philosophical views have found empirical evidence and been reflected in mathematics.

Many philosophers also study mathematics, such as Engels, whose "Dialectics of Nature" is an outstanding mathematical treatise. Mathematical objects are not real existences in the material world, but the products of human abstract thinking. Culture, broadly speaking, 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 so-called In this sense, mathematics is a kind of culture. 2. An essay about junior high school mathematics

A "Tips" for Solving Problems - "Mathematics Essay" In total, I have been exposed to the subject of "mathematics" for eight years.

Talking about my thoughts and feelings about learning mathematics, it is very simple, one word - "method". Today, the era we live in is the era of lifelong education.

The so-called "lifelong education" means learning throughout your life and continuing to learn, otherwise you will fall behind. But "illiterates in the 21st century are not people who cannot read, but people who cannot learn."

What we are facing now is the entrance exam, and how can we quickly master a large amount of knowledge and become today's students? The most urgent problem we need to solve. How to use the most effective learning methods to gain the most knowledge in this era of information explosion... If you want to learn more knowledge in a limited life, in addition to unremitting efforts, the most important thing is to master a set of skills that are suitable for you. learning methods.

A complete set of learning methods can not only enhance self-confidence, but also achieve success in related learning fields. Some people say: "There is nothing impossible, only people who can't do it."

We can also say: "There is no knowledge that cannot be learned, only bad learning methods." So learn anything For a subject, the most important thing is to have a correct and scientific method.

Today, mathematics is a tool.

In people's production and life, mathematics exists "implicitly" in society as a special tool for people's thinking. Although it is not as "visible and tangible" as tangible tools, its role has always been In a sense, it is far more than those 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 , so it has its own set of languages ??(symbols), and this special language is recognized by everyone. People can use this special language to communicate ideas and methods, and achieve the goals of science and technology. *** develop together... This shows how widely the applications of mathematics are! As a second-year junior high school student, I also have some research on mathematics.

Some of the current mathematics tests and exercises are nothing more than multiple-choice questions and "popular" geometry proof questions. But we often lose points on these questions - so, here, I explore some common problem-solving methods in mathematics.

Multiple-choice questions are a kind of objective test questions. They have the characteristics of obvious answers, objective scoring, and wide coverage of examination content. In recent years, multiple-choice questions have been regarded as an important type of questions in the high school entrance examinations in various provinces and cities across the country and occupy a large proportion.

Therefore, mastering the solutions to multiple-choice questions and improving the ability to solve multiple-choice questions is an aspect that our students should focus on in the mathematics examination. To answer multiple-choice questions, you should first carefully review the question and use scientific and appropriate problem-solving methods to solve the problem quickly and accurately according to the characteristics of the question.

Commonly used methods to solve multiple-choice questions are as follows: 1. Direct method The direct method is a commonly used method. It starts from the conditions given in the question stem and based on the learned definitions, theorems, and formulas. , axioms, rules, etc. to perform reasonable calculations and reasoning to obtain the correct result, then check it with the alternative, and then make a judgment. 2. Special value method: For some questions, it is difficult to make judgments based on given conditions. You can use certain special values ??to verify and make judgments.

For example, if 0 (A) x^2 (C) x analysis: From the given condition 0, take x=1/2, then x^-1=(1/2)^-1= 2. x^2=(1/2)^2=1/4, so we have x^2 3. Elimination method The elimination method is to negate the untrue answers one by one through reasoning, so as to get the correct answer. For example, it is known that the graph of the quadratic function y=ax^2 bx c passes through the points (1, 6), (0, 5), and the axis of symmetry is x=1/3, then ( ) (A) a=1/ 2, b=2, c=-5 (B) a=3, b=-2, c=5 (C) a=3, b=2, c=5 (D) a=-3, b=- 2, c=6 Analysis: From the quadratic function graph through (0, 5), we know that c=5, so (A) and (D) can be excluded, and the symmetry axis is x=1/3, that is -b /2a=1/3, and (C) can be excluded, so (B) should be selected.

4. Verification method The verification method is to use the given conclusion and put it back into the original question to verify and make a judgment. If we can make good use of the above methods to do multiple-choice questions, then we can definitely show your "style" on it! There are also some special methods that are specifically aimed at current geometric proof problems.

Geometry is the mathematization of material space in life, taking material space as the source of mathematical activities. The objects of its research are mainly things that our students often come into contact with in their daily lives.

But it is much more difficult for us to learn geometry than algebra. During some exercises, when we encounter some unfamiliar geometry problems, we often feel unable to start.

At this time, we must master some methods of association so that geometry will not make us feel so abstract. 1. Associate basic figures: Many figures in geometry are often obtained by deforming some of the most basic figures in a certain way. If we can associate these figures with the changes in basic figures, and use these basic figures to If you study this problem in the context of the problem, then the ideas for solving the problem will naturally come out.

Example 1 In the trapezoid ABCD, as shown in Figure 1, AD∥BC, ∠BCD=90 degrees, BC=CD=12, ∠ABE=45 degrees, point E is on DC, BF⊥AE is at F, find the length of BF. G A D Analysis: From ∠BCD=90 degrees and H F two adjacent sides BC=DC, it can be thought that the basic E figure is a square, so the figure can be solved by completing the figure into a square.

B C (Figure 1) Draw BG⊥AD through point B, intersect the extension line of DA with G, extend DG to H, so that GH=CE, it is easy to prove that △BHG ≌ △BEC, so BH= BE, it can be proved that △ABH≌△ABE, ∴ ∠H=∠AEB, ∴∠BEC=∠H, ∴ ∠BEC=∠AEB, and it can be proved that △BDE≌△BFE, ∴BF=BC=12. 2. Associate common conclusions: There are many conclusions in mathematics. Although they do not appear in the form of theorems, they are often used during practice. For example, the area of ??an equilateral triangle with side length a is equal to square root 4/3. a?.The area of ??a quadrilateral with mutually perpendicular diagonals is equal to one-half mn (m.n are the lengths of the two diagonals respectively). The areas of two triangles with the same base (equal base) and equal height (same height) are equal wait. If we memorize these conclusions skillfully, it will not only facilitate the exploration of problem-solving ideas, but also greatly increase the speed of problem-solving.

Example 2 Uncle Zhang’s house has a quadrangular vegetable plot, as shown in Figure 2. 3. I want a mathematics composition

Classmate, what stage of mathematics composition do you need?

Children, if you can ask such a question, as long as you follow the following carefully, you will His mathematics must be "top" in the class.

I think that to learn mathematics well, it can be simply said---"understanding and practice". Remember to memorize mathematical knowledge by rote and apply it mechanically. To fully understand its meaning, it is best to express it correctly in your own words. Specifically, the understanding of concepts requires the following four skills: the ability to describe correctly in language, the ability to judge, the ability to give examples, and the ability to apply. The understanding of rules, formulas, theorems and properties requires the ability to accurately clarify conditions and conclusions, master the ideas and methods of reasoning, understand the reasoning process, and be able to flexibly use the conclusions obtained. To understand the example questions, you must be able to clearly examine the meaning of the questions. You must first use your hands and brain to solve the problems, and then compare them with the solutions in the book. Through reflection, you can summarize the rules and methods for solving such problems. The emphasis is on the discovery of problem-solving ideas and the summary of problem-solving methods. Learning mathematics is to cultivate our computing ability, thinking ability, logical reasoning ability, problem analysis and problem-solving ability. However, "ability" is a skill that cannot be formed without necessary training. An American mathematician It has been said: The only way to learn mathematics is to "do mathematics". The so-called practice means completing a considerable amount of exercises. We know that the famous Chinese mathematician Chen Jingrun made a breakthrough in Goldbach's conjecture, which shocked the world, but he only used several sacks of draft paper! This shows how important practice is. Everyone must work hard to complete the exercises in the textbook independently. Students who have room for learning should also read some extracurricular readings, such as "Mathematics for Middle School Students", "Mathematics Weekly", etc. This can broaden our horizons and improve our mathematics level. In addition, students who have the opportunity and conditions should actively participate in various mathematics competitions to exercise and cultivate themselves. When doing exercises, it is best to be able to solve multiple questions and change multiple questions, summarize experience, master skills and techniques, draw inferences from one instance, draw parallels from analogies, and discover "general methods". This general method is something useful throughout your life. .

I hope that teachers can achieve the following aspects:

First, be "clear"; clear knowledge, clear methods, clear ideas, clear links, and clear penetration points. In short, mathematics class should be "a clear line" and must not be "a blurry expanse". This is not the characteristic of a mathematics class. Mathematics classes should have a "mathematical flavor". The second is to be "new"; with novel content and innovative methods, such mathematics classes are more attractive and have more value for discussion.

The third is to be "living"; that is, a good mathematics class should have flexible methods, active thinking of students, flexible teachers and students, and open classrooms. The fourth is to be "real"; lively and practical, lively but not chaotic, and the knowledge, methods, skills, emotional attitudes, etc. that should be implemented can be implemented. I always believe that if a math teacher can make your classes "live and practical", then you are a very good math teacher. The fifth is to be "surprising"; that is, mathematics classes should be as "unexpected and different" as possible. Of course, this is a very difficult thing, and there is no need to pursue "differentiation" one-sidedly. However, as seminars and observation classes, everyone always hopes to hear some innovative and thoughtful classes. If the classes you take and some of the links you design are already commonplace and others do the same, they may think that you are nothing special and that you are just like everyone else. Therefore, I always adhere to the point of view that seminars "do not seek perfection, but seek value for discussion." I don’t really like classes that are flat and without ideas.

In short, to learn mathematics well not only requires a good teacher, but also relies on one's own love and interest in mathematics. 4. "

Ordinariness is also a kind of enjoyment? Candidates from Wuhu? The house is in a human environment, without the noise of cars and horses.

How can I ask you? You are far away from home. Side. Picking chrysanthemums under the eastern fence, leisurely seeing the Nanshan Mountain. The scenery is beautiful day and night, and the birds are flying back and forth. There is a true meaning in this, and I have forgotten to explain it.

It is a good poem. "Returning to the Garden", Tao Yuanming, who regards utilitarianism as dirt, has such a dull life? I don't like the vigorous life, and I have never done any earth-shattering actions.

Friends, in this. In the exciting years, I love a kind of indifference, because it is a kind of enjoyment. When I sip a cup of tea and turn a few pages of a book, I happily forget to eat.

Watching Li Qingzhao drink wine in Dongli after dusk, there is a faint fragrance filling her sleeves, a kind of poignant plainness, but it is a sigh of "the west wind blows behind the curtain, and people are thinner than yellow flowers", because she has an enviable first half of life, In the last years of my life, I can no longer bear the loneliness.

Peach Blossom Spring is the highest state of Tao Yuanming's unremarkable imagination. If you have something to support, you can have fun when you are young, and people can enjoy the happiness of ordinary family life.

Plain life is a kind of enjoyment. p>

Without fame and the favor of the emperor, he finally understood in the ordinary that "thousands of sails pass by the side of the sinking boat, and thousands of spring trees grow in front of the diseased trees." And whether he realizes the true meaning of ordinary while enjoying the ordinary is a matter of fact. A kind of enjoyment.

Wu Jun has already told us in his book that he is a person who enjoys ordinary things, drifting in the Fuchun River and doing whatever he wants. He calmed down his passion for fame and wealth and gave up his responsibilities in economic matters. He lived a plain and unrestrained life, with a kind of happiness and joy that was beyond words.

Although Ouyang Xiu was demoted, he lived a life of peace and tranquility. He enjoys the ordinary life with the people of Chu, without lamenting or getting discouraged, but enjoying a kind of ordinary happiness. That's why he has the feeling that "the drunkard's intention is not to drink, but to care about the mountains and rivers." Ordinary, I am. I am a member of the universe. I don’t like the luxury of life and fame.

In the ordinary, you can read the minds of the ancients; in the ordinary, you can see the beauty of nature; in the ordinary, you can understand things; In the ordinary, you can be moved and enlightened; in the ordinary, you can have a lot of things.

How can you dance to understand the shadows in the world? The plainness of the ancients, I also have my own plainness.

Blandness is life, happiness is happiness, and happiness is enjoyment. Although I am still young and do not understand Tao Yuanming's "true meaning", I want to let it go. The noisy gears stop in the heart, and let peace bring tranquil joy. This is a kind of life and a kind of enjoyment.

Ordinariness is also a kind of enjoyment, coming from the depths of the soul.

? [Comments from famous teachers]? Although the question requires only 500 words, this article has more than 800 words, which meets the requirements of the college entrance examination.

But there is more to this article than anything else. Deep intention.

It’s hard to imagine that a third-year junior high school student could choose to enjoy life in a “plain” way. Isn’t it a bit immature? The article quotes and comments on the ups and downs and pursuits of many famous figures in history. The examples are accurate, the comments are profound and insightful, and one cannot help but admire the depth of the author's thoughts.

Rigorous conception. Rigorous conception is a major feature of this article.

The article is introduced by Tao Yuanming's poem, and ends with Tao Yuanming's poem, echoing from beginning to end. In the second paragraph, I will again use the example of Li Qingzhao to demonstrate the opposite. The following will list the life experiences of Tao Yuanming, Liu Yuxi, Wu Jun, Ouyang Xiu and others to illustrate that plainness is a kind of enjoyment.

The writing is organized and neat. ? Soaring literary talent.

This article is full of literary talent and leaves a lingering flavor in your tongue. There are two reasons.

First of all, this article quotes a lot of poems, which makes the whole article full of poetic beauty. Being able to quote so many poems shows that I usually memorize it, so how can I not get high marks?

Secondly, be good at organizing dual sentences and parallel sentences. These couplets and parallel sentences not only increase the beauty of the language, but also add momentum to the article.

It can be seen that if you cannot quote poetry, it is good to make some neat sentences. Parting is also a kind of enjoyment? Candidates from Wuhu? It’s the third year of junior high school and I’m out of the mountains.

We, who have never been young but are already old, walked to the end of the third grade of junior high school in a daze with our cloudy eyes open in the sea of ??books. The sun is still bright, even bright, but our dark eyes seem to be gradually clearing, and behind the sobriety is the unpreparedness for parting.

There is an old saying: "It is a joy to have friends from far away." Another saying: "I advise you to drink another glass of wine. There will be no old friends when you leave Yangguan in the west."

People We are always keen on the joy when we get together but feel desolate when we part. In fact, parting can be regarded as a kind of enjoyment, because it can reappear the warmth that has been missed inadvertently.

The kind math teacher struggled to move his fat body. In the last few classes before graduation, everything slowed down for some reason. There is no more writing and whispering, and there is only the solemnity before departure, which is a little less solemn and a little more helpless.

The white chalk dust slowly falls along the sunlight, and the teacher’s sweat flashes in the summer sun like a frozen frame. He asked us over and over again: "Do you understand?" Then erased and started again.

Another burst of ashes from the fading sunset, carrying three years of dedicated love, are flying in the air full of emotion. What accompanied *** after class was his somewhat hoarse helplessness.

I wish this lesson had no end. He, who was not good at words, gave us undoubtedly the most touching inspiration - parting is a moving enjoyment.

Although the old class banned it, the classmate records were still spread "underground" at lightning speed, just to let the memory move on the paper with the simplest words in the last days. In the classmate list that I accidentally browsed, some of them just shed their past flashy appearance and expressed their true feelings. Everyone tried hard to leave their own shadow on the small manuscript paper, and spent three years of getting along with each other to instill their sincere thoughts and hearts. .

Here, there is no ridicule and sarcasm, no inferiority and arrogance, only true friends who are reluctant to leave one after another - parting is a sincere enjoyment. ? The old classmate who had been cruel to us for three years finally couldn't hold back the tears in her eyes. Only then did we understand that she, who looked tough on the outside, also had the softest place in her heart. In that place lived sixty crystal-pure and happy children.

She was still busy arranging class duties, but she was a little more reluctant to leave - parting is a cherished enjoyment. ? The love and excitement that were once scattered in the corner came quietly during parting. 5. Can mathematics be considered a language?

Yes.

Language has always been an indispensable "excellent example of human intelligence" in human society. Language has the potential to enhance memory and the ability to explain concepts. Mathematical language is a scientific language, which refers to the expression of mathematical concepts, calculations, formulas, operating laws, rules, problem-solving ideas, and derivation processes. Mathematical language has the characteristics of accuracy, abstraction, conciseness and symbolization. Its accuracy can cultivate students' honest and upright character. Its abstractness is conducive to the cultivation of students' ability to reveal the essence of things. Its conciseness and symbolic characteristics can help Students can better summarize the laws of things, which is also conducive to thinking.

The "New Curriculum Standards" require in the overall goal: learn to cooperate with others, and be able to communicate with others the process and results of thinking, and be able to explain one's own opinions in an organized and clear manner, and do what they say. Reasonable, in the process of communicating with others, you can use mathematical language to discuss and question logically, and the "Standards" in various fields at different academic levels have different requirements for mathematical language. In the classroom, we found that some students wanted to say something but couldn't, some students were afraid or dare not speak, and some couldn't speak at all. There was an obvious gap between students' use and expression of mathematical language and the requirements of the "Standards" distance.

Based on the above situation, the author analyzed the reasons and believed that: ① Mathematics classroom teaching is limited by the traditional educational tendencies of "only focusing on results and ignoring the process" and "just being able to do it, not having to speak it" Influenced by exam-oriented education, students lack opportunities for language practice, thus restricting the display of students' thinking. ② Teachers lack understanding of the role of mathematical language and do not pay attention to cultivating students' mathematical language, resulting in students' mathematical language being inaccurate, irregular, and loose, thus hindering the development of students' thinking. ③ Due to the limited number of students in the class, there are too many students. Some introverted students cannot speak clearly what they want to say, and some good students often have no patience to listen. Over time, these students will no longer be able to express mathematical language accurately and standardizedly. ④The reasons for the students themselves are mainly the influence of non-intellectual factors.

In summary, in today's primary school mathematics classroom teaching, it is imperative to strengthen the cultivation of students' mathematical language abilities.

1. Teachers’ accurate and standardized mathematical language has a subtle influence on students

Teachers’ words and deeds have a subtle effect on students, so it is necessary to cultivate students’ mathematical language expression ability , first of all, teachers are required to standardize their language and set an example for students. Mathematics teachers should describe concepts, rules, and terminology accurately and avoid causing doubts and misunderstandings among students. To this end, teachers must do the following two things: First, they must have a thorough understanding of the essence of the concept and the meaning of the terms. For example, "divide" and "divide by", "digits" and "digits", "numbers" and "digits", etc., if they are confused, it violates the law of identity; some teachers guide students to draw pictures and say: "These two "The straight lines are not parallel enough", "The right angle is not drawn at 90°", etc., which violates the law of contradiction; and "A figure composed of three sides is a triangle", "A year in the Gregorian calendar is a multiple of 4 is a leap year" and so on Language lacks accuracy. Second, it must be explained in scientific terms. For example, you cannot say "perpendicular line" as "vertical downward line", you cannot say "simplest fraction" as "simplest fraction", etc. Rigorousness, in addition to accuracy, should also have normative requirements. For example, you should speak clearly, read the question sentences clearly, and stick to Mandarin. Simplicity means that the teaching language should be clean and concise, important words should not be lengthy, focus on the key points, be concise and summarized, and be to the point; it should be based on the age characteristics of primary school students, and speak words that are easy for them to accept and understand; it should be accurate, do not go around in circles, and use shorter sentences. Time conveys more information.

2. Let students train their mathematical language expression skills in oral presentations

In order to enable all students to train their mathematical language, teachers can flexibly use "deskmates" in the classroom Communication, group discussion, whole class evaluation, student summary" training model, implement the teaching idea of ??"language training as the main line, thinking training as the main body" in classroom teaching, so that students at different levels have something to say and have something to say. It can be said, and in the positive evaluation, students' enthusiasm for speaking can be stimulated and their speaking ability can be improved. 6. Keep your mathematics essay shorter

I like all the courses in school, especially mathematics.

In the past few weeks, I learned about "numbers and information". When I got home that night, I began to number the houses in our community. The second village of our community has 3 buildings horizontally, 7 buildings vertically, and 21 buildings in the middle. Therefore, I called the first building "2.1" and the second building "2.2"``````

A few days ago, my father gave me a difficult problem. The title is this: There are 43 students, and the money they carry with them varies from 8 cents to 50 cents. Each classmate bought a picture with the money he brought with him. There are only two types of pictures: 3 cents a piece and 5 cents a piece. Everyone should try to buy as many 5 cents a piece of pictures as possible. What is the total number of 3-point pictures they bought? "I thought about it for a long time and made a lot of calculations, but I still couldn't figure it out. I was helpless. At this time, my father said: "Let me analyze it for you. The number of people is 43, and the money amounts vary from 8 cents to 50 cents, and there are exactly 43 types. That is, there is exactly one classmate whose money amount is 8 cents, and there happens to be one classmate whose money amount is 9 cents, etc. Everyone has spent all their money to buy pictures, indicating that everyone's money has been used up. But everyone used their money individually and did not pool the money together. "This is when I suddenly realized: "Oh, next I understand, if these 43 students are divided into groups of 5 people in order from least to most money, but there are still three people left. Analysis shows that each of the first 8 groups had to buy (1 2 0 2 4) 10 3-point pictures, so the 8 groups bought 80 3-point pictures. In addition, those with 48 points need to buy 1 3-point picture, those with 49 points need to buy 3 3-point pictures, and those with 50 points do not need to buy 3-point pictures, so the remaining three people *** bought (1 3) 4 pictures 3 points picture. In this way, we can find out that 43 people bought (40 4) 84 3-point pictures in one ***. Am I right? "Dad touched my head and said, "That's right. ”

In fact, arithmetic is also very strange. For example: 432-234=198, 654-456=198, 987-789=198, etc. (Students, have you found the pattern?)

Mathematics is so interesting!