For a long time, people only devote themselves to the teaching and research of basic knowledge, basic skills and logical thinking in mathematics teaching, but are not good at discovering the unique beauty of mathematics itself. They do not pay attention to infecting and inducing students' thirst for knowledge with mathematical beauty, stimulating students' interest in learning, and guiding students to discover and appreciate mathematical beauty, let alone to create mathematical beauty, so that some students find mathematics abstract and boring and lose confidence in learning it well. So what is the beauty of mathematics? How to exert the aesthetic function of mathematics in primary school mathematics education? This is a question worthy of every primary school teacher's consideration. I studied the ways of aesthetic education infiltration in primary school mathematics teaching from the following aspects.
First, the perception of the beauty of teaching materials
It is often said that mathematics is a kaleidoscope and a colorful world. There are abundant aesthetic education factors in mathematics textbooks. The current mathematics textbooks correctly handle the relationship between the characteristics of mathematics and children's cognitive law, moral education and intellectual education, teaching and learning, and reducing the burden and improving the quality, and integrate the abstract beauty, symbolic beauty, magical beauty of numbers, harmonious beauty and generalization beauty of numbers, conjecture beauty, rich flavor of times life and open and flexible beauty of mathematics into it. In my opinion, it is an effective way to stimulate students' emotions and cultivate students' hearts by excavating and refining aesthetic education factors in teaching materials and making students feel the existence of mathematical beauty.
For example, in many geometric figures, it is full of endless beauty and flashing beautiful style. When teaching rectangles, squares and circles, as soon as I walked into the classroom, the eyes of all the students in the classroom gathered on my chest. ? Wow? Some students get carried away, called:? Miss Wang, you are so beautiful today! ? I asked:? Why does the teacher look so beautiful today? The students cried at once: there were all kinds of sticky papers on the teacher's clothes, rectangular, square and round. ? The students were attracted by my actions at once, so they worked very hard in the next study. Five minutes before the class is over, I arranged a program:? Let the children make postcards from the cards, combine the front with rectangular, square and round sticky paper, design beautiful pictures, and then give them to you, preferably friends. ? The students are so excited that they won't stop until class is over. In teaching, we should make mathematics become? Human mathematics? To make mathematics full of vitality, we must explore the inner beauty of mathematics and make students like mathematics.
Second, feel the beauty in the scene.
Situational teaching is needed in all subjects of primary school, especially in junior high school mathematics teaching. Junior students are young, naive, curious about things and suitable for studying in? Play? Learn mathematics in middle school. Teachers should create various situations and opportunities, encourage students to explore and practice, find the combination of knowledge, emotion and individual soul, integrate life and self into the classroom, and let students feel the beauty of mathematics.
Some teaching contents in mathematics textbooks can allow students to perform situational performances. Mathematics originates from life and must be integrated into certain life situations. Classroom performance is to create a certain living environment, give children a world of free development and free play, and let students create the beauty of behavior and language through virtual scene performance. Pupils have a strong desire to perform. Both junior and senior students are willing to participate and socialize. They like to reproduce the learning content in various situations and apply the knowledge in books to their lives. Like teaching? Know RMB? In one class, I asked the students to act as customers and salespeople. The students were so enthusiastic that they scrambled to raise their hands and asked to participate. I asked them to divide into groups, each group had goods with different prices, and each classmate was equipped with RMB with different face value. After the activity began, there was a constant noise of buying and selling in the classroom, just like in life. Another example is: In the first textbook "Statistics", the birthday scene of uncle elephant is created by using multimedia, so that students can count the guests from uncle elephant's house through group work and cooperation, thus gaining statistical knowledge, which animals come more and which animals come less. In this way, the selection and design of teaching content closely related to students' life, through multimedia processing, can effectively mobilize students' multiple senses to participate in learning activities and improve students' interest in learning. Transforming these abstract knowledge into visual content will bring students into a novel realm. Strange? Born? Fun? By who? Fun? Born? Confused? Questioning aroused students' thirst for knowledge, achieved the goal of optimizing classroom teaching, and made students feel the beauty of mathematics.
Third, experience beauty in activities.
Are you online? Feel beauty, appreciate beauty and experience beauty in mathematics activities? It is an important idea actively advocated by mathematics curriculum standards. Mathematics teaching should build a bridge between mathematics knowledge and teachers and students, so that the beautiful factors in mathematics can be reflected. As we all know, only relying on the perception of beautiful things, aesthetic feeling is only superficial, hidden and not profound. We must produce corresponding emotional experience in the process of perceiving beauty, so as to deepen our understanding and perception of the image of beauty and gain rich aesthetic experience through various aesthetic experiences and appreciation. Therefore, we should carefully organize real experience activities to let students experience the beauty of mathematics.
For example, in Understanding Objects, I designed? Touch and say? Games. Combine the operation activities with the expressions, and ask the students to touch an object and say its name. You can also say the name first and then touch the corresponding object. Let students learn to express and listen in activities, and develop their mathematical communication ability. Through this interesting math game, students' interest in learning can be stimulated and students can get a good emotional experience.
Fourthly, highlight the humanistic beauty of the subject in teaching evaluation.
"Mathematics Curriculum Standard" points out:? The evaluation of mathematics learning pays attention to the results of students' learning mathematics and their learning process; We should pay attention to students' mathematics learning level, and pay more attention to students' emotions and attitudes in mathematics activities, so as to help students know themselves and build up confidence. ? This kind? Human development? Paying attention to students' personality differences and protecting students' self-esteem and self-confidence are worthy of our reflection and research. Therefore, in our mathematics teaching, we should take the promotion of emotional experience as the guide, increase the diversification of evaluation objectives and methods, and promote the all-round development of students. Therefore, in our mathematics teaching, we should take the promotion of emotional experience as the guide, and appropriately use some encouraging comments in homework correction, so as to improve students' interest in learning, establish learning confidence and show the humanistic beauty of mathematics.
For example, in general teaching, we should evaluate students from a developmental perspective, pay attention to recording students' usual performance, and adopt democratic appraisal methods to let students evaluate students, students evaluate teachers, and teachers evaluate students, so that students can motivate themselves in an atmosphere of democratic appraisal. To test students' knowledge and ability, we should not only use a test paper to examine students, but also add some interview and oral examination links for students to operate and encourage them to put themselves in the most important position. Proud? Skills, enhance students' learning confidence, and promote students' all-round improvement. When students make mistakes, teachers should not rush to point them out, but give students enough time and opportunities to find and correct them, tolerate their mistakes and give them the opportunity to correct themselves. When students can't express themselves clearly and accurately, the teacher's words should try to make students consciously correct their mistakes between traces, highlight tolerance and reflect humanistic care.
I think that the infiltration of aesthetic education in mathematics classroom teaching can fully mobilize students' learning enthusiasm, make them form a good habit of being brave in exploration and innovation, experience and enjoy the fun of beauty in a beautiful atmosphere, develop actively and vividly in the cultivation of beauty, and achieve the harmony between rational perception and emotional activities. Is this the aesthetic function of mathematics? Sneak into the night with the wind, moisten things silently? Let us have the beauty of mathematics, create a stronger aesthetic education atmosphere, shape a generation of beautiful people and create a beautiful world.
The Beauty of Mathematics Classroom Part II Summary: Some senior three students report that the mathematics classroom in senior three is abstract and boring, and the mathematics homework is difficult and difficult to start. They spend too much time on mathematics, but there is no result, and they gradually lose confidence in mathematics learning. This paper expounds how teachers attract students' attention in class, how to memorize mathematical knowledge skillfully, how to explore and discuss, and how to acquire new knowledge and feel the joy of success. Explore how to arrange interesting homework so that students can use mathematical knowledge and skills to solve practical problems. Interesting classroom can promote the effectiveness of teaching, and effective teaching can improve students' intrinsic interest, so that students can fully feel the beauty of mathematics and face mathematics calmly.
Keywords: teaching effectiveness; Mathematics classroom; Create a situation; Return to life
Some high school students feel that math classes are abstract and boring, homework is difficult, and they have no confidence in math learning. They spend a lot of time on math, but they always fail. In my opinion, in addition to students' efforts, our math teachers should also enrich teaching methods, let our math class bloom beautiful flowers, show its lively and moving side again, and let our students smile at math. Specifically, in teaching practice, we can learn from the following points.
■ Create interesting classroom situations to stimulate students' interest in learning mathematics.
In mathematics classroom teaching, we should be good at creating interesting classroom situations, get rid of the boring explanations of mathematics teachers, enliven the classroom atmosphere in the situations, and stimulate students' interest in learning mathematics and enthusiasm for accepting knowledge actively in a pleasant atmosphere.
For example, when talking about the "two counting principles", the follow-up part of Smith was shown with animation: since the occurrence of Smith, the tiger has a grudge for being fooled by the fox, hates the fox, and gnashes his teeth in the forest. Hum! Fox, fox, unless you can't hide, I will eat you one day. We'll see. One day, the tiger was out foraging and happened to meet a fox on the grass. The tiger is very happy. It's really a breeze. Hahaha! Here's my chance for revenge! ? The tiger's eyes suddenly showed a fierce look. The fox was scared to death when he saw the tiger's momentum, thinking that he was going to run away quickly! Run for your life! The nearest island is across the grass. There are trees and holes on the island, so you can hide. At this time, the picture shows that there are three boats on the water leading to the island and four cars on the shore leading to the island. The teacher asked: How many ways can a fox reach the island by means of transportation in the picture? At this time, the students are still in an interesting scene, and the mentality of protecting the weak makes them eager to help the fox find a way to calculate the escape method. They first found out that the fox's escape route belongs to the principle of classification, not the principle of gradual progress, and finally worked out seven methods by addition. The interesting story has aroused students' strong interest in learning, and they are still curious about whether the fox can escape again.
Through a large number of interesting story situations collected from around us, they are moved to classroom teaching, so that students can experience common sense of mathematics in the sentiment situation, thus summing up important mathematical models, making boring mathematical concepts and knowledge lively and interesting, deepening their understanding, and letting students fully feel the charm of mathematics.
■ Enrich the classroom teaching language and memorize the basic knowledge of mathematics skillfully.
Throughout the mathematics textbooks, concepts, laws and rules are very concise and profound, and some are even abstract and difficult to understand. There are many knowledge points in high school mathematics, and the concepts are easily confused. In order to fully understand and remember them, in addition to creating some story situations and life situations to make the math class lively and interesting, teachers should also use rich teaching languages to touch students' heartstrings, so that students can understand the math knowledge in humorous and vivid language explanations and remember it for a long time.
For example, in order to memorize the definite integral formulas of several elementary functions, the author designed a language fairy tale: constant function and exponential function are good friends. They often play together. Today, they go shopping together I didn't expect the differential operator to be in the street. It is the bane of constant function. Constant functions are most afraid of encountering. Constant function sees the differential operator far away, and hurriedly pulls the exponential function away. Exponential function inexplicably asked: Why did you go back? Are you feeling sick? Didn't you see the differential operator, asked the constant function? Look, what happened to him? Exponential function is stranger. Constant function timidly said: If I meet it and be differentiated by it, I have nothing! ? Exponential function thought for a moment and said: Yes, you are different from me. I'm not afraid of it. It can't do anything to me, but I'd better go home with you. Who told us that we were good friends? After that, they hurried home. The students were deeply attracted by this interesting language fairy tale and listened to the teacher's story quietly. In the process of listening, they understood the relationship between constant function, exponential function and differential operator and the differences between them, and gave warm applause to the teacher's humorous speech. I didn't expect such a boring mathematical concept to be so vivid.
This effective teaching method not only makes the classroom interesting, allows students to insert the wings of imagination in the fairy tale world and feel the beauty of mathematical language, but also strengthens students' memory of basic mathematical knowledge.
■ Organize interesting inquiry activities to deepen the understanding of mathematical knowledge.
Scholar Shi Ningzhong once said: We must be clear that there are many things in the world that cannot be passed on, and we can only rely on personal experience. Wisdom does not depend entirely on the amount of knowledge, but on the use of knowledge and experience. Teachers can only let students hone in practical operation. Mathematics teaching is more important than process teaching. Teachers should give students enough time and space to experience mathematics, feel mathematics, and accumulate mathematical experience in inquiry, so as to understand mathematics knowledge more deeply.
For example, in the teaching of the first n sums of geometric series, set up a questioning situation: It is said that Big Wolf wants to start a company in the forest and suffers from limited funds, so he went to Pleasant Goat to invest, and Pleasant Goat agreed: OK, I will inject capital into your company for 60 consecutive days from today. Invest 10000 yuan on the first day, and then invest 10000 yuan more every day than the previous day. But in return, you must return me 1 yuan from the first day of investment, and the amount returned every day after returning my 2 yuan money the next day will be twice that of the previous day. After 60 days, the two of us. Grey wolf listened, and his eyes turned, and the more he thought, the more beautiful he became. Did Big Wolf take advantage? Through the introduction of question situation, the topic is introduced and the students' interest is stimulated, their learning enthusiasm is effectively mobilized, and their desire for inquiry is also stimulated. The students first thought that to answer this question, they need to calculate the money paid by Pleasant Goat and Big Big Wolf respectively, and then compare the sizes. For Pleasant Goat, students will simplify and sum according to the sum formula of arithmetic sequence they have learned before, but for Big Wolf, students all know that it is. At this point, the teacher promptly guides the students to recall: The method we used to learn arithmetic progression's summation was inverse addition, the essence of which was to get n identical sums, to turn the general arithmetic progression summation problem into a constant series summation, to simplify complex problems by using the idea of equations, and to turn the problems that are not easy to sum into problems that are easy to sum, so the essence of summation is to reduce terms. Is this method ok now? If not, how to simplify the operation? Can we construct a formula according to the characteristics of geometric series terms by analogy with the essence of reverse addition and solve the problem through the operation of two formulas? Under the guidance of the teacher, students explore step by step, make full use of what they have learned before, and answer questions perfectly. In challenging inquiry activities, students have deepened their understanding of old and new knowledge, and at the same time gained happiness after conquering difficulties.
Interesting inquiry activities can stimulate students' interest in learning, make them diligent in thinking, dare to explore, experience the process of inquiry, feel the difficulty and success of inquiry, effectively cultivate their dialectical thinking ability and innovative thinking ability, fully improve their perseverance and endurance, and make them firmly believe that they will climb the peak of mathematics and appreciate its elegance.
■ Create a life-oriented mathematics classroom and experience the fun of using mathematics flexibly.
In senior high school, there are many, difficult and boring math problems, which affect students' self-confidence in learning math well. Faced with this common phenomenon, we math teachers have the responsibility to resolve students' negative emotions, create some life-like classroom scenes in the teaching process, let students learn math in their familiar life fields, and find that math knowledge is not only in textbooks, but also everywhere in life. We live in the world of mathematics, and then apply what we have learned to our lives.
Like after studying? Probability? After knowledge, the author creates a familiar life scene for students: sending letters is what students have done in their daily lives. Now the teacher has n letters and wants you to put them in m mailboxes for me. How many voting methods do you have? For seemingly simple life questions, students can't answer them clearly at once, so the author inspires them to use them flexibly? Probability? Although knowledge has wavered between and, and some even verified it with examples, students generally feel that their thinking is simple and clear after using probabilistic thinking. As long as they analyze it step by step, the first letter has M voting methods, and the second letter also has M voting methods. After that, there are m voting methods for each letter, so the total voting method is mn. A classmate also summed up a memory mouth after analyzing the solution. The letter power of the mailbox? In this way, if you encounter similar problems in the future, you just need to know about it? Whose mailbox is it and whose letter is it? You can sit in the right place. This method has been unanimously recognized by everyone, and students are happily exchanging and sharing other people's successful experiences.
Students are full of sense of accomplishment, and they can solve practical problems in life by using mathematics flexibly and experience the happiness of success. Mathematics in their eyes is no longer boring, and the originally boring mathematics problems suddenly become interesting.
Lively and interesting math classes can attract students' attention, make them study happily and improve the effectiveness of teaching. On the other hand, effective teaching can make students really master knowledge, improve their grades and experience a sense of accomplishment, thus maintaining their inherent interest in learning. Therefore, teachers should promote the effectiveness of teaching with interesting classes, improve students' ability to solve problems with effective teaching, ensure students' inner interest and enthusiasm in learning mathematics, and let students fully feel the beauty of mathematics and laugh.
The Beauty of Mathematics Classroom The third chapter of Mathematics Curriculum Standard (20 1 1 Edition) points out that mathematics is a tool of human life; Mathematics is the language used by human beings to communicate; Mathematics can give people creativity; Mathematics is a human culture. Then: Mathematics classroom should be a process for students to experience and explore knowledge from the personal practice of mathematics activities. Today's mathematics classroom no longer pursues flashy classrooms, but reproduces more simple and smart real classrooms. In fact, simple math class is equally wonderful, it can express rich connotations and ideas in simple math language, and students can study easily and happily! I think that in the research of primary school mathematics classroom teaching, we should try our best to find a new teaching and research method, that is, mathematics classroom teaching should be simple, solid and flexible.
First, simple but not simple.
Mathematics classroom should present a highly concise simplicity, but simplicity does not mean simplicity. Instead, there is too much behind it? Not simple? .
1, situational creation, refined? Jane? Interesting.
? Situation creation? It is a common strategy in mathematics teaching, which helps to solve the contradiction between the high abstraction of mathematics and the concrete visualization of primary school students' thinking. But when creating a situation, we don't have to pursue superficial prosperity and ignore internal thinking and efficiency. Therefore, the pursuit of situation creation is simple and efficient. For example, in the teaching of Hands-on (1), I created a situation in which students' favorite good friends were laughing and naughty and wise old people led them to swim in the wisdom palace. At the beginning of the class, the students were very enthusiastic about learning, eager to explore secrets and seek mathematical knowledge in the palace. At this time, the king's three stick figures are presented again, so that students can review the plane figures they have learned, which will not only help students develop their imagination, but also pave the way for Protestant hands-on puzzles and make them easy and interesting to learn.
2, teaching methods, spirit? Live broadcast? Orderly.
Curriculum standard points out: Mathematics teaching is the teaching of mathematics activities? . For this reason, when teaching the course "Knowledge in Collocation", my design conforms to students' cognitive law, from shallow to deep, from easy to difficult, with hierarchy. During the whole activity, students discover the diversity of collocation methods through group cooperation and independent inquiry, and at the same time feel the fun of cooperation, which can inspire and improve each other. First of all, let students use school uniforms, match them by hand, discuss writing and find diversified solutions to problems. The preliminary understanding is that in order to avoid repetition and omission of collocation methods, orderly thinking is needed. Through the collocation of routes, it is found that the method of expressing collocation routes by letters has advantages. So that students' thinking can be transformed from concrete to abstract, and their thinking ability can be improved. Finally, through the combination of the price and figures of entertainment items, let students try and talk independently, so that each student has the opportunity to try and succeed independently, so as to further understand the benefits of orderly collocation. Enable students to transfer and apply knowledge on the basis of independently seeking solutions to problems.
Second, solid and not messy.
Classroom teaching should pay attention to practical results, which is a fine tradition of mathematics education in China. However, in the process of paying attention to practical results, students should acquire solid knowledge instead of being confused and disorderly.
1, explore independently and develop thinking.
Friedenthal, a mathematics educator, stressed that the only correct way to learn mathematics is to recreate it, that is, students discover and create what they have learned. Teachers only need to guide and help students create, rather than instill ready-made knowledge into students. Therefore, in the teaching process of cognitive scoring, I let students understand the formation process of knowledge with their hands, brains and mouths. For example, in teaching, I asked students to fold 1/2 with rectangular paper, and found a variety of folding methods, so that students could introduce his folding methods and get a preliminary understanding of the score. Then ask the students to fold out 1/4 and feel a few quarters. On this basis, let students create their own scores, which provides students with a certain space for creation and exploration. Students discover in inquiry, innovate in discovery, seek knowledge in innovation and improve their thinking ability.
2. Exercise moderately and expand your thinking.
It is pointed out in the standard that students' learning contents should be realistic, meaningful and challenging, and these contents are mathematical activities that are conducive to students' active observation, guessing, reasoning and communication. Therefore, in the process of improving the application of cognitive score, I have carefully designed pictures of French flag, five-pointed star and chocolate in my life, so that students can spread their imagination wings and expand their thinking space, and let them experience observing objects from different angles and associate them with different scores. Finally, by estimating the proportion of "scientific world" and "art garden" in the blackboard newspaper, students can further feel that there is mathematics everywhere in their lives. The designed exercises are lively, interesting and challenging, so that students can experience the learning experience of application-expansion-promotion-deepening in consolidation.
3. Clever questions and innovative thinking.
? Learning is expensive and doubtful. ? Scientist Einstein said: I don't have any special talent, but I like to get to the bottom of it. Questioning is the key to innovation. Therefore, teachers should encourage students to find problems and question them boldly, and let students ask more why in teaching. For example, when teaching the drawing method of a circle in Understanding the Circle, some students suddenly pointed out: If the required circle is relatively large and the compass is too small, how should this circle be drawn? Another example: teaching? The significance of comparison? At that time, some students pointed out that the latter term of the ratio could not be 0, but in sports competitions, why do 3: 0 and 4: 0 often occur? For students' doubts, teachers should first praise their spirit of being good at thinking and daring to question, then let students discuss and express their opinions, and then dispel doubts and doubts in the appropriate choice of teachers. In this way, students can not only solve doubts through cooperation, but also deepen their understanding of the depth and breadth of new knowledge in the process of questioning and solving doubts, and develop the habit of thinking bravely and the spirit of bold innovation.
Third, smart but not rigid.
Traditional mathematics teaching is too mechanical and boring, lacking vitality, interest and curiosity. This kind of injected mathematics method is abandoned by us. It requires teachers to choose materials reasonably, create conditions, guide students to think, study, imagine and practice actively, and make the dull classroom lively and full of personality.
1. Make good use of teaching materials and choose them reasonably.
? Teaching with textbooks, not teaching textbooks? It has become a teacher's knowledge. However, teaching with textbooks does not mean that you can use textbooks at will. The premise of teaching with textbooks is to fully respect textbooks. Of course, after understanding the intention of compiling teaching materials, combining students' life experience and actual situation, it is sometimes icing on the cake to tailor and choose teaching materials appropriately. For example, in the class of "Comparative Application", I abandoned the original examples in the textbook and used a lot of local materials in my life to design a realistic and interesting learning activity to stimulate students' desire to explore and draw a conclusion. Only when the volume ratio of yellow and blue used in each group is the same can each group match exactly the same green? This conclusion makes students have a deeper understanding and feeling of the practical significance of proportional distribution. In this way, on the basis of correctly grasping the teaching materials, adapting measures to local conditions and teaching students in accordance with their aptitude, our mathematics classroom will be more flexible and vivid.
2, hands-on operation, intuitive image.
The Standard points out that hands-on operation, independent exploration and cooperative communication are important ways for students to learn mathematics. ? Therefore, teaching should give students enough practical operation space, so that every student has the opportunity to participate in activities and let students think by doing. For example, in the teaching of observing objects-building a building, I arranged two activities: building one independently and building one at the same table, and then drawing shapes seen from three directions on grid paper to guide students to describe them in language, thus enriching their appearances, perceiving the relationship between three-dimensional graphics and plane graphics, and developing their spatial concepts in full hands-on operation.