-Practice and experience of developing mathematics practice in our school.

Autonomy, cooperation and inquiry are the three basic dimensions of the new curriculum learning style. Carrying out mathematical practice activities in time and effectively can help students to be independent and complacent in practice, thus internalizing book knowledge into their own knowledge and skills, which is conducive to cultivating students' interest in learning mathematics, promoting the harmonious development of students' personalities and specialties, and thus comprehensively improving students' comprehensive quality. Let's talk about the practice and experience of developing mathematics practice in our school.

(A) the choice of content should be in line with the age characteristics of students, with strong operability.

Mathematics practice is a practical activity that combines teachers' life experience with students' knowledge background. Learning activities that guide students to explore independently and cooperate and communicate. This activity must be based on students' original knowledge, which is of interest to their age group and can be done. Only in this way can students better accumulate experience in activities and feel and understand the connotation of mathematical knowledge. Formulate problem-solving strategies, experience the connection between learning and real life, mobilize learning emotions, and lay a good foundation for more effective learning in the future.

This semester, the "problem bank" activity was carried out among the first-year students, providing students with inquiry learning places that dare to ask questions, are good at asking questions, and understand and answer questions in different ways. Through the cooperation between students, ask parents, grandparents and find extracurricular books, so that students can jump out of the strange circle of "what teachers say" in the past and develop good qualities of positive thinking and daring to explore from an early age. During the activity, students * * * put forward more than 100 different questions, and Yue Huang, a student in Class 4 a year, put forward 8 questions, which showed good problem awareness and innovative thinking ability. In the second grade, the activity of "My Family's Numbers" was carried out, and the students' understanding of the length units introduced in the book changed from abstract to intuitive through repeated measurements. And through computer synthesis, handwritten newspapers and other forms to show their talents.

In the third grade, "Looking for the perimeter of home"; Fourth grade birthday party plan; My Design in Grade Five; The activities such as "out of the classroom and into the bank" in the sixth grade are in line with the age characteristics of students and are the extension and expansion of classroom learning. Furthermore, it has brought positive, vivid and interactive effects to classroom teaching, made classroom teaching move from "mastery" to "innovation", and opened up a broad world for students' autonomous learning and inquiry learning.

During the activity, communicate in time, inspire each other and gradually improve.

Mathematical practice is a comprehensive activity process. No small activity can be completed at once. It is necessary to go through the process of determining the objectives and contents of the activity-drawing up the activity plan-organizing concrete implementation-exchanging feedback and evaluation. In the process of activities, we should not only let students experience and create, but also give timely feedback and guidance, and also have a certain time guarantee. For example, after learning the understanding of the circle, in order to enable students to draw a circle flexibly and correctly, and to further understand the terms such as center, diameter and radius, students are encouraged to draw a plan with the circle as the mainstream. After students hand in their homework, there are stick figures, watercolors, imaginary paintings, cartoons and so on. , colorful. But the concept is relatively simple, the theme is not clear, and it is just a combination of large and small circles with profound implications. In this case, the teacher is not in a hurry to comment, but organizes students to group, group and exchange creative ideas, creative processes and creative experiences in a timely manner. So as to feel the different thinking of others. Inspire each other and gradually improve their works. In the end, a number of works with distinctive themes, novel ideas and strong sense of the times stand out. In this way, activities let students experience failure, try methods and experience the process, which is the harvest! More importantly, repeated practical activities have brought about changes in students' learning methods and improved and developed their knowledge and ability.

Pay attention to process and method, pay attention to emotion and attitude, not just results.

Comprehensive practical activities are cooperative learning activities carried out by students themselves under the guidance of teachers. The development of practical activities is to let students understand and pay attention through their own personal experiences, and try to analyze and solve their concerns. These problems may seem naive and meaningless to us, and some problems can't be solved by them. But we know more clearly that the fundamental purpose of comprehensive practical activities is not only to let students really solve a practical problem, but more importantly, to find a perfect solution. It focuses on how students find problems, how to think and try to solve problems, and what changes have taken place in their bodies, minds, emotions, thinking and attitudes in the process of paying attention to this problem. Knowing oneself, caring for life and developing oneself through practical activities are the goals of carrying out practical activities. "Mathematics Curriculum Standard" points out: "Teachers should make full use of students' existing life experience, guide students to apply what they have learned, and realize the application value of mathematics in current life. "When studying the collation and review of statistical charts, we organize students to obtain information through the Internet, investigation and interview, reading books, newspapers and magazines in groups, extracurricular books, etc., and skillfully make statistical charts or statistical tables. In this activity, mathematical knowledge is no longer a variety of exercises divorced from life, but a re-creation that fully reflects practical activities. Emotional experience is always accompanied by activities.

Therefore, they have a keen sense of news, a solid basic knowledge of mathematics and a good aesthetic concept. To show the imagination and creativity of modern children's superman, and to reflect students' innovative consciousness and quality. In addition, in every activity, we are very concerned about the individual differences of students. Pay attention to protecting each child's self-esteem and self-confidence, let students communicate with each other in activities, ignite the spark of thinking in evaluation, broaden the horizon of knowledge, understand the colorful world and enjoy the joy of success.

(B) teacher-student interaction to help teachers update their ideas.

In the comprehensive practical activities, teachers' condescending dignity is impacted. After all, comprehensive practice is a brand-new subject, not only for students, but also for a wider life world. In a complex world, students are students and teachers are students. In some ways, students are more imaginative and creative than teachers. This means that teachers should learn from students and make the relationship between teachers and students truly equal. Make teachers seriously reflect on their teaching and adjust themselves to adapt to the new situation. The statistics of sixth-grade students on the driving situation around the central road of the city and the statistics on the number of ships and planes dispatched by China search pilot Wang Wei show that modern children are concerned about society. They are no longer just learning from teachers about addition, subtraction, multiplication, division and Divison, but caring about a member of the social family.

In the comprehensive practical activities, the greatest role of teachers is to create a good atmosphere and provide a broad space for students to freely display in a free space. Give students confidence, believe that they are capable and can do well. Teachers should be open-minded, not preconceived, impartial, put themselves in the shoes and think about students' lifelong development. Respecting students' personalities and differences between people will improve and develop each student on the original basis, instead of insisting on sameness and favoritism, and establishing a truly equal teacher-student relationship. Students have a strong interest in learning mathematics around them.

Mathematical practice is the teaching of mathematical activities, and it is a process of interactive development between teachers and students and between students. In this process, we should attach importance to the emotional experience of students' participation, let students feel mathematics in activities, experience the role of mathematics, cultivate students' consciousness and attitude of consciously applying mathematics to practice, make mathematics truly become a tool in students' hands and realize its great application value. After learning the length units of centimeter, decimeter and meter in the second grade, we can cultivate students' sense of number and improve their knowledge application ability by measuring the height of family members and the length and width of household appliances. The third grade "Looking for the Perimeter of Home" and the fifth grade "My Design" turn practical problems in real life into mathematical problems, so that students' practical application ability can be improved. In this way, students can not only connect the knowledge in books with practice to realize the social value of mathematics, but also learn knowledge that books can't learn, so that knowledge can be improved in practice. Students feel that today's study and life are closely related, and truly realize the willingness, fun and ability to learn.

Thirdly, the comprehensive utilization of knowledge helps to improve students' comprehensive ability.

"Mathematics Curriculum Standard" points out: "Effective mathematics activities can't rely solely on imitation and memory, and hands-on practice, independent exploration and cooperative communication are important ways for students to learn mathematics." Students understand the extensive relationship between mathematics and life through mathematical practice activities, learn to solve simple practical problems by comprehensively applying the knowledge and methods they have learned, deepen their understanding of the knowledge they have learned, and acquire the thinking method of solving problems by using mathematics. Put them together. It can cultivate students' abilities in these aspects: first, the ability to collect and sort out information; The second is the ability to cooperate and communicate with others; The third is the ability to solve practical problems by using what you have learned. More importantly, students experience observation, operation, experiment, investigation, reasoning and other activities in mathematics practice, and gain a good emotional experience, feel the interconnection of mathematical knowledge and appreciate the role of mathematics in the process of cooperation and communication. Promote students' all-round, sustained and harmonious development. This is an essential quality for top-notch talents in 2 1 century, and it is also a new learning method advocated by mathematics curriculum standards. As a new learning content and way, subject practice is a brand-new subject for us. In practice and exploration, we realize that students' learning is not only the accumulation of knowledge, but also the consciousness of flexible application in knowledge application; Let students not only actively acquire knowledge, but also find and study problems. We should not only let students use knowledge to solve practical problems, but also stimulate students' innovative potential and realize learning ideas and methods in the process of seeking problem solving.

2. What kind of math paper is a good one? There are many standards, but I think a good math paper must have the following three characteristics-novelty, truth and beauty. "New" means that the topic should have a unique perspective, and the content written is not simply repeating other people's things or simply downloading a paragraph. Words, it is best to be original, at least to have their own creation, their own views, their own ideas; "Truth" means that the content should be true and reasonable, not empty and tasteless, nor lengthy. The article should stick to the theme, strive to be accurate and concise, and embody the rigor and scientificity of mathematics as much as possible; "Beauty" refers to the fluency of language and writing, and articles should give people the enjoyment of beauty. Of course, judging from the name of the second Mathematics Learning "Star of the Times" Practice and Innovation Thesis Competition, papers with both practice and innovation are definitely more likely to win the favor of the judges. Therefore, I hope that students will be closer to life, pay attention to observation, discovery and discovery, connect life with mathematics, and take writing papers and trying to write them well as evaluation, supplement and innovation for their mathematics learning.

"Plum blossoms come from bitter cold". As long as you are willing to make great efforts, as long as you are willing to endure hardships, keep thinking, guessing and learning, good math papers will be born in your hands. In a word, learning to write papers and trying to write good papers will always be an excellent way for each of our students to exercise themselves and improve their abilities. I believe that the students of Grade One and Grade Two in our school will actively participate in the activities and exchanges of the second "Time Mathematics Learning" and "Time Star" practical innovation thesis competition under the organization and guidance of teachers, and get good results. I wish more and better math papers will be born in the hands of students in the future. I hope that more students will take off from learning to write math papers in the future and write more high-level and high-quality papers.

This is to strengthen training and improve math ability (it should be for teachers)

"Without training, there is no ability", which is Mr. Ma Xinlan's profound experience in the practice of mathematics teaching reform. By training, we mean the bilateral activities between teachers and students in the classroom. This kind of activity requires teachers to do two things well before class: one is to go deep into the whole set of teaching materials and put the training content of each class into the overall structure of knowledge; The second is to fully understand the knowledge level of each student in the class, and on this basis, design training content according to the teaching progress. Therefore, the training course has the following characteristics:

First, there must be new breakthroughs.

Training is to reproduce students' existing knowledge in many directions and angles with the most primitive basic concepts in knowledge as the soul and the internal connection of knowledge as the line. In the process of knowledge reproduction, students should be required to update and have a new understanding of old knowledge. This "newness" contains students' new learning ability.

Second, we must grasp the key.

In the process of training, the teacher's role is to give students just the right "tips". This "hint" is by no means to point out new knowledge and content to students, nor is it a lecture; Instead, it inspires students' thinking and guides them to actively explore, discover, understand and improve in the direction suggested by teachers.

Third, we must do a good job in design.

In the classroom, teachers should consciously design the situation of problems, provide students with more opportunities for exploration and discovery, and have sufficient time to think, explore and study, so that they can all think positively and give full play to their wisdom and creativity.

Fourth, we should mobilize the enthusiasm of all students.

In the process of training, teachers should urge students at different levels to put forward different thinking methods and viewpoints, understand students' existing problems, different ideas, and what flash things or profound understanding they have, so that teachers can get accurate feedback and determine the contents and methods of the next training.

Fifth, create a harmonious classroom atmosphere.

In the process of training, teachers should pay attention to creating more opportunities for students to think and debate, give full play to their inherent potential, and urge them to have an endless desire to create. In the process of continuous exploration and discovery, students not only have the joy of success, but also have some wrong or imperfect ideas. Teachers strive to keep them in active thinking, the sparks of wisdom are constantly flashing, the enthusiasm for learning is constantly growing, and the mathematical ability is gradually improved.

The following is just a lesson to illustrate.

Applied problem training

First, the teaching content: the application of addition and subtraction in "Sum and Surplus" (Beijing Experimental Textbook for the next semester)

Second, the class type: training (systematic arrangement, divergent)

Third, the teaching purpose:

1. Deepen the understanding of the concept of "harmony", master the quantitative relationship between addition and subtraction application problems, and seek solutions from a global perspective with the concept of "harmony" as the core.

This is the emergence and development of the concept of "number" (a certain discussion)

Humans are the product of animal evolution, and there was no concept of quantity at first. However, the developed brain's understanding of the objective world has reached a more rational and abstract level. In this way, in the long life practice, out of the need to record and distribute daily necessities, the concept of number has gradually emerged. For example, a wild animal is captured, which is represented by 1 stone. If you catch three heads, put three stones. "Knotting knots" is also something that many close ancient humans have done. There is a record of "tying the knot to govern the country" in the book of changes. Legend has it that the ancient Persian kings tied knots with ropes to count the days of war. It is also a common method used by the ancients to carve or hide the bark with sharp tools or count it on the ground with small sticks. When these methods are used much more, the concept of number and the symbol of counting are gradually formed. At first, the concept of numbers began with natural numbers, such as 1, 2, 3, 4 ... No matter where they are located, the symbols used for counting are the same size. The figures in ancient Rome were quite advanced, and now many old wall clocks are often used. In fact, Roman numerals have only seven symbols: I (for 1), V (for 5), X (for 10), L (for 50), C (for 100), D (for 500) and M (for 65438). No matter how the positions of these seven symbols change, the numbers they represent are the same. When they are combined according to the following rules, they can represent any number: 1 Number of repetitions: A Roman numeral symbol is repeated several times, indicating several times of this number. For example, "three" means "3"; "XXX" means "30" 2. Add right and subtract left: add a symbol representing big numbers to the right of the symbol representing small numbers, indicating that big numbers are added with small numbers, such as "VI" for "6" and "DC" for "600". A symbol representing a small number is attached to the left of the symbol representing a large number, indicating a number in which a large number is subtracted from a small number, such as "IV" for "4", "XL" for "40" and "VD" for "495". 3. Add a horizontal line: add a horizontal line to the Roman numeral, indicating that it is 1000 times that number. For example, ""means "15000" and "165000". In ancient China, notation was also very important. The oldest notation is found in Oracle Bone Inscriptions and Zhong Ding, but it is difficult to write and identify, so it is not used by future generations. In the Spring and Autumn Period and the Warring States Period, production developed rapidly. In order to meet this need, our ancestors created a very important calculation method-calculation. The computing chip used for calculation is made of bamboo sticks and bones. Arranged according to the specified length order, which can be used for counting and calculation. With the popularization of calculation, the arrangement of calculation and preparation has become the symbol of calculation. There are two types of calculation and arrangement, horizontal and vertical, both of which can represent the same number. It is clear from the absence of "10" in the calculation code that the calculation strictly follows the decimal system from the beginning. Numbers exceeding 9 digits will enter one digit. The same number, a hundred in a hundred, Wan Li has ten thousand. This calculation method was very advanced at that time. Because the decimal system was really used in other parts of the world at the end of the 6th century. But there is no "zero" in digital calculation, and there is a vacancy when it meets "zero". For example, "6708" can be expressed as "┴ ╥". There is no "zero" in the number, so it is easy to make mistakes. So later, some people put copper coins in the blank to avoid mistakes, which may be related to the emergence of "zero" However, most people believe that the invention of the mathematical symbol "0" should be attributed to Indians in the 6th century. They first used a black dot () to represent zero, and then gradually became "0". Speaking of the appearance of "zero", it should be pointed out that the word "zero" appeared very early in ancient Chinese characters. But at that time, it didn't mean "nothing", just "bits and pieces" and "not much". Such as "odd", "sporadic" and "odd". "105" means that there is a score of 100. With the introduction of Arabic numerals. "105" is pronounced as "105", and the word "zero" corresponds to "0", so "zero" means "0". If you look closely, you will find that there is no "0" in Roman numerals. In fact, in the 5th century, "0" was introduced to Rome. But the Pope is cruel and old-fashioned. He doesn't allow anyone to use "0". A Roman scholar recorded some benefits and explanations about the usage of "0" in his notes, so he was summoned by the Pope and executed the punishment of "Zn" so that he could no longer hold a pen and write. But no one can stop the appearance of "0". Now, "0" has become the most meaningful digital symbol. "0" can mean "No" or "Yes". For example, a temperature of 0℃ does not mean that there is no temperature; "0" is the only neutral number between positive and negative numbers; The power of 0 of any number (except 0) is equal to1; 0! = 1 (factorial of zero is equal to 1). In addition to decimal system, in the early stage of the germination of mathematics, there were many numerical decimal systems, such as five, binary, ternary, seven, eight, decimal, hexadecimal, twenty, hexadecimal and so on. In the long-term practical application, decimal has finally gained the upper hand. At present, the internationally used numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 and 0 are called Arabic numerals. In fact, they were first used by ancient Indians. Later, Arabs integrated ancient Greek mathematics into their own mathematics, and this simple and easy-to-remember decimal notation spread all over Europe, gradually evolving into today's Arabic numerals. The concept of numbers, the writing of numbers and the formation of decimal system are all the results of human long-term practical activities. With the needs of production and life, people find that it is not enough to express it only by natural numbers. If five people share four things when distributing prey, how much should each person get? So the score is generated. China's academic score is earlier than that of Europe 1400 years! Natural numbers, fractions and zeros are usually called arithmetic numbers. Natural numbers are also called positive integers. With the development of society, people find that many quantities have opposite meanings, such as increase and decrease, advance and retreat, rise and fall, east and west. To represent such a quantity, a negative number is generated. Positive integers, negative integers and zero are collectively called integers. If you add a positive score and a negative score, they are collectively called rational numbers. With these digital representations, people find it much more convenient to calculate. However, in the process of digital development, an unpleasant thing happened. Let's go back to Greece 2500 years ago, where there was a Pythagorean school, a group that studied mathematics, science and philosophy. They believe that "number" is the origin of all things and dominates the whole nature and human society. So everything in the world can be summed up as a number or a ratio of numbers, which is the source of world harmony. When they say numbers, they mean integers. The appearance of scores makes "number" less complete. But the score can be written as the ratio of two integers, so their faith has not wavered. However, a student named hippasus in the school, when studying the median term in the ratio of 1 2, found that no number written in integer ratio can represent it. Let this number be x, because the result of deduction is x2=2. He drew a square with a side length of 1 and set the diagonal as X. According to Pythagorean theorem x2= 12+ 12=2, we can see that the diagonal length of a square with a side length of 1 is the required number, and this number must exist. But how much is it? How to express it? Hippasus and others were puzzled and finally decided that this was a new number that they had never seen before. The appearance of this new number shocked the Pythagorean school and shook the core of their philosophical thought. In order to keep the math building that supports the world from collapsing, they stipulated that the discovery of new figures should be kept strictly confidential. And hippasus still can't help letting the cat out of the bag. It is said that he was later thrown into the sea to feed sharks. However, the truth cannot be hidden. People later found many numbers that can't be written by the ratio of two integers, such as pi, which is the most important one. People write them as π, and so on, and call them irrational numbers. Rational numbers and irrational numbers are collectively called real numbers. The study of various numbers in the real number range makes the mathematical theory reach a quite advanced and rich level. At this time, human history has entered the19th century. Many people think that the achievements in mathematics have reached the peak, and there will be no new discoveries in digital form. But when solving the equation, you often need to make a square. If the square number is negative, is there any solution to this problem? If there is no solution, then mathematical operation is like walking into a dead end. So mathematicians stipulated that the symbol "I" was used to represent the square root of "-1", that is, I =, and the imaginary number was born. "I" became a fictional unit. Later generations combined the real number with the imaginary number and wrote it in the form of a+bi (A and B are both real numbers), which is a complex number. For a long time, people can't find quantities expressed by imaginary numbers and complex numbers in real life, so imaginary numbers always give people an illusory feeling. With the development of science, imaginary numbers have been widely used in hydraulics, cartography and aviation. In the eyes of scientists who master and use imaginary numbers, imaginary numbers are not "virtual" at all. After the concept of number developed to imaginary number and complex number, for a long time, even mathematicians thought that the concept of number was perfect and all the members of the mathematical family had arrived. However, in June 1843+16 10, British mathematician Hamilton put forward the concept of "quaternion". The so-called quaternion is a number. It consists of a scalar (real number) and a vector (where x, y and z are real numbers). Quaternions are widely used in number theory, group theory, quantum theory and relativity. At the same time, people have also studied the theory of "multivariate number". Multivariate number has gone beyond the category of complex number, and people call it hypercomplex number. Due to the development of science and technology, concepts such as vector, tensor, matrix, group, ring and domain are constantly produced, which pushes mathematical research to a new peak. These concepts should also belong to the category of numerical calculation, but it is not appropriate to classify them into super complex numbers. Therefore, people call complex numbers and hypercomplex numbers as narrow numbers, and concepts such as vectors, tensors and moments as generalized numbers. Although people still have some differences on the classification of numbers, they all agree that the concept of recognized numbers will continue to develop. Up to now, several families have developed greatly.