How to break through the conceptual constraints and establish a new educational philosophy to lay the foundation for students' sustainable development

With the development of the times, people's values of mathematics education have undergone profound changes, and mathematics education has changed from taking the acquisition of knowledge as the primary goal to focusing on the development of human beings first and foremost, and people's demands on mathematics education will become higher and higher. In order to adapt our math classroom teaching to the learning needs of today's students. Teachers should first update their concepts, and update our concepts of education and teaching by studying the Mathematics Curriculum Standards for Full-time Compulsory Education. Bring new ideas into the classroom to optimize the learning process of students.

A new concept of the role of elementary school mathematics teachers

1, the depth of the curriculum reform requires teachers to have a new concept of education

Education is not only productive and other economic functions and values, and this value and function to be coordinated with the enrichment of the spiritual world of human beings, the improvement of moral qualities, the harmony of human beings and nature, and the cultivation of the spirit of humanity. And some of our original educational methods are incompatible with the development of students' personality and psychology, as well as the cultivation of innovative qualities. In view of this objective fact, the teacher's function should make corresponding changes, from closed teaching to guide students "open learning," the teacher should establish the "student development-oriented" concept of education. The establishment of a completely equal new teacher-student relationship.

Additionally, the "double base" is our specialty, but "double base" is changing with the times, "mathematical operation of proficiency and logical reasoning rigorous" although the two basic points of the double base, but induction, conjecture, innovative way of thinking, broad mathematical vision, information technology means of use, should be "new double base" organic part of the elementary school mathematics teachers must be conscious of this.

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2, the curriculum of the new content, requiring teachers to have the spirit of innovation

The new curriculum, the addition of "mathematical activities, exploratory questions, mathematical culture," the three modular content. The main purpose of these additions is to develop students' mathematical qualities. These contents require teachers to use a new teaching mode to teach, therefore, teachers are required to have an innovative spirit, to be able to promote innovation, to pursue innovation and be proud of innovation, and to be good at discovering problems and raising questions. To be good at breaking the routine, break through the traditional concepts, with keen insight and rich imagination. Make thinking ahead of time and originality. Teachers themselves should have broad basic knowledge and modern information quality, the formation of multi-level, diversified knowledge structure; have a broad vision, good at analyzing and synthesizing information, innovative mathematical model, innovative teaching methods, flexible teaching content selection, innovative thinking training as the core of the evaluation criteria. They are good at creating a "free space for innovation", providing students with a broader learning space, and guiding them to improve their learning styles.

3. Lifelong education requires teachers to have a sustainable personality

First of all, the introduction of lifelong education requires teachers to regard the updating of their own knowledge as a responsibility, so that "lifelong learning" can be transformed into the conscious behavior of teachers.

Secondly, students are in the period of personality shaping and customization, and the values, ideals and beliefs, moral sentiments, and aesthetic tastes of the social culture will be reflected from the teacher's role in the culture. And through his "reflection" in the students' personality in the world, as a mathematics teacher's teaching by example, determines the formation of his personality on the students' personality has a "silent" effect. This requires elementary school mathematics teachers to mold themselves according to the moral principles and norms of society, to realize the "superego".

Second, elementary school mathematics teachers should renew their concepts

1, the renewal of teachers' ideological concepts

First of all, to recognize the necessity and importance of curriculum reform. Teachers should get rid of the shackles of the old concept of education. Update the concept of education, set up a correct view of talent, quality and students. Secondly, teachers should recognize their role and position in the curriculum reform. They can devote themselves to the curriculum reform with full enthusiasm. Thirdly, teachers should realize that the proposal of "quality education in mathematics" requires teachers to pay attention to the physical and mental development of each student. The proposal of "cultivating the spirit of innovation and practical ability" requires teachers to promote the development of students' personality. Teachers should truly understand: "Everyone learns valuable mathematics, everyone can obtain the necessary mathematics, and different people get different development in mathematics." This is the basic concept of the mathematics curriculum for the new century. Fourth, teachers should realize that in the future society, the ability to acquire knowledge is more important than acquiring knowledge itself, and the method of acquiring information is more crucial than acquiring information itself. What teachers give to students should be a library of methods, a library of tools. Teaching mode should be: knowledge, quality, innovation ability of three-dimensional teaching mode.

2. Updating of teachers' knowledge structure

The knowledge structure of teachers is composed of ontological knowledge, conditional knowledge, practical knowledge and cultural knowledge.

The knowledge structure of the future society should be: informatization plate structure, intensive basic structure, and true-line cutting-edge structure. Teachers, as socialized human beings, must update their knowledge in order to adapt to the requirements of society.

From the point of view of curriculum reform, many new knowledge contents will be added in the new elementary school mathematics curriculum standard. Some of the content is what teachers have learned, and some content is what teachers have not learned. In order to adapt to the teaching, elementary school mathematics teachers should firstly improve their professional theoretical level through self-study, attending continuing education study or some training courses. Secondly, they should collect relevant educational and teaching materials through newspapers, magazines, information technology and so on, so as to fully utilize their practical knowledge. The opening of mathematics culture classes and comprehensive courses requires elementary school mathematics teachers to understand the history of mathematics, the educational value of mathematics culture, and the application of mathematics in other related subjects. That is to say, mathematics teachers are not only proficient in their own professional knowledge, but also to expand their knowledge and have an understanding of interdisciplinary knowledge.

With the development of society, the students we face will also become more complex, which requires teachers must continue to learn psychology and pedagogy, and be able to support their teaching work with new educational theories.

Three, the teachers teaching ability to improve

1, teachers to improve the ability to grasp the new curriculum

The new curriculum standards to ensure that the teaching of basic knowledge, basic skills training, the basic ability to cultivate the premise of the deletion of the not very useful, and students to accept a certain degree of difficulty in the content. At the same time, added some for further study to lay the foundation for a wide range of applications, but also students can accept the new knowledge. As an elementary school math teacher, we must first understand what has been subtracted and what has been added. Secondly, they should try to understand the new contents and requirements of the new teaching material system. The distribution of knowledge points and their requirements are different. Teaching should grasp the degree of each place when it appears, to prevent the knowledge reached in the textbook in several times as a one-time treatment because of not understanding the overall arrangement. Advancement. For new content, you should analyze why and how much is introduced. How to teach can reflect the intention of the new textbook to prevent the scope and difficulty from getting out of control. Full attention should be paid to the application and practical requirements. It should not be discarded because of the need to take the test. The deletion of the content should also be analyzed, some of the knowledge is deleted, but the idea may still be reflected.

2, teachers to improve the ability to use modern educational technology

With the continuous development of modern educational technology, the new curriculum standards, the application of the calculator has been introduced into the textbook, multimedia computer-assisted teaching will enter the classroom. This requires teachers to master computer tools, in terms of teaching aids: the ability to come up with good scripts, the ability to use common math teaching software to solve the teaching of the key points, the ability to evaluate the good and bad courseware, the ability to choose good courseware. They are capable of obtaining information materials needed in teaching on the Internet. In the aspect of assisting learning: teachers are able to organize and guide students to participate in mathematical experiments. For example, the use of animation technology to demonstrate the changing law of geometric shapes, create animated situations, and so on. Through practical exploration, students experience the thinking process of mathematics. Teachers should be able to provide colorful educational environments and powerful learning tools for cultivating students' spirit of exploration and sense of creativity. Teachers should also be able to guide students to use calculators for complicated calculations to save calculation time and improve learning efficiency.

Fourth, reflect the new concept in lesson planning

1. Select realistic and meaningful materials.

Because the preparation of teaching materials has the nature of the times, limited to the social background at the time, according to the conditions of the students in that era and the different requirements of society at the time of the need for talents in all aspects, the content and requirements of the preparation of teaching materials only meet the use of a certain period. With the rapid development of society and science and technology, even the best textbooks will lag behind after a number of years. Therefore, some of the order of the textbook in our hands, the preparation of questions, examples, presentation and the context of the examples can not be adapted to our students learning today. This requires us to prepare for the lesson, while basically not changing the intention of the arrangement of the textbook, according to the characteristics of the physical and mental development of the students, choose the students around the familiar, like, interested in the things or content as learning materials. Stimulate students' desire for knowledge, so that they feel that mathematics is around them, and closely linked to the reality of daily life. In this way, students will be happy to participate in the learning process, they will be interested in learning mathematics. For example, to change the narrative plot of the example problem, the summing up of the application problem on page 43 of the seventh book of the provincial compulsory textbook is to summarize the quantitative relationship formula of "working efficiency × working time = total amount of work" through the preparatory questions, and then show the example problem. This kind of lesson is indisputable from the perspective of the past, and the logical thinking is also very good nowadays. But the children we teach are different, they may not be interested in 3 hours to pump 420 tons of water, 5 hours to pump how many tons of water. I think it would be a good idea to change it to "Teacher wants to know how many questions 55 people in my class did in a minute **** last night"? Make up a math problem based on your own work. Students discussed the question in groups of four or two for a few moments and scrambled for answers. Some students say, "I did 20 problems a minute. At that rate, it is estimated that 55 people in the class can do 1,100 problems." Some say, "I did 30 problems in two minutes. Estimating the class of 55 people, you might do 825 problems." Again, ask them to tell you how they did their calculations. Since this problem is constructed by the students from their own personal experience with the facts, they have a much better grasp of the structure and quantitative relationships of the example problem than if you were to go in and deliberately teach it. Students easily grasp the idea of solving these kinds of problems.

2. Change the way the textbook is presented.

The use of different expressions to present teaching content to meet diverse learning needs. Educator Mr. Ye Shengtao once said, "Textbooks can only be used as the basis for teaching lessons; to teach well and to benefit students, it also depends on teachers to use them well." This sentence reveals us that the textbook is not a holy book, it only provides the most basic teaching content. In order to reflect the new concept of teaching, when preparing lessons, we have to recombine the teaching content and arrange the best form of presentation according to the specific situation of students and from a practical point of view. Because, the preparation of textbooks is often based on the structure of knowledge to show the sequence of its occurrence, formation and development. But our students in the learning process of the way of thinking is not necessarily adapted to the order of presentation and presentation of the textbook. I teach "the meaning of fractions" in this lesson, according to the students' original knowledge, life experience and the distance between the problems to be discussed in this lesson, change the presentation of the content of the textbook. With a physical object, a figure, a unit of measurement expressed in the unit "1" as opposed to a number of objects as a whole expressed in the unit "1" of the content, and at the same time allow students to use their own hands according to their own ability to participate in small groups with the assistance of active problem solving. Students experience the process of actively exploring the meaning of fractions in specific practical activities to establish the concept of fractions. And understand the meaning of the unit "1", in the learning process, let the students experience and feel cooperation, communication, success, happy emotional experience.

3. Change the way of introducing new lessons.

The preparation questions in the current textbook is to pave the way for new knowledge learning. Its content is generally closely related to the old knowledge of the new knowledge of the lesson, the purpose is to make students' thinking quickly into the realm of new knowledge. However, from the perspective of the new teaching concept, it precisely restricts students' autonomy and narrows the space for exploration. Coupled with the fact that the example problems in the textbook provide the answer as well as the thinking process, and how to think while presenting the example problems, it restricts the teachers' thinking and stifles the students' innovative spirit. With the value orientation of mathematics teaching from knowledge transfer to the development of personality and talent, the goal of the introduction stage should also be followed by the preparation for knowledge learning to the emotional induction of the main; from the focus on knowledge and skills to the focus on the development of the field of change. Therefore, to strengthen the function of creating scenarios, so that students experience today's math is around, the formation of the desire to explore,

is the direction of the introduction stage. When we prepare the lesson, we pay attention to the way to introduce the new lesson, but also pay more attention to the students' emotional attitude. According to different teaching content to create a closely related to the students' living environment, knowledge background, but also students are interested in the learning situation. Although the content of mathematics is abstract, but most can be found in the life of primary school students to accept the prototype. For example, in the teaching of "positive proportion", we can take students outdoors on a sunny day to measure the height of trees, flagpoles and surrounding objects by using the relationship between the height of the pole and the length of the shadow. When teaching "scale", students can draw their own houses on paper and design their favorite buildings according to the scale. In short, in the teaching, teachers should try to design students familiar with the life situation into the new class, so as to meet the psychological needs of students to actively explore.

V. Embodying new ideas in the classroom

1. Creating a learning environment without mental depression.

Students' mathematical learning activities should be a lively, active and personalized process. To enable students to actively participate in this process, the teacher's main task is to create a safe learning environment for this process.

(1) Transform the role of the teacher.

The teacher participates in the process of student learning and exploration as a friend. Realize the change from preaching, teaching, and solving problems to the activities of the organizer, guide, and collaborator. It is often said that "pro-teacher, faith", a good teacher-student relationship can create a democratic, equal, relaxed, friendly learning environment for students, so that students in the psychological ease of the situation to form an unrestrained thinking space, can promote students to actively, actively explore, produce a pleasant desire to know, no scruples, to fully express Their own creativity. For example, in the student discussion, controversy, we can say: "can let the teacher to express their views?" To "amiable" attitude, "discuss" tone, to "participants", "collaborators" identity with the Students *** with the discussion. Both play a "guide" role, but also for the students to create a kind of no mental depression, people-oriented learning environment. So that students in the exploration of mathematical knowledge at the same time experience a rich emotional experience.

(2) Teachers should infect students with their enthusiasm.

"There is nothing like emotion to touch people's hearts." In classroom teaching, we should be sincere in the heart and act outside, should be full of enthusiasm, full of spirit to appear in the whole teaching process, and with their own work attitude and emotion to infect and influence students, properly organized teaching. Teachers should be flexible in choosing teaching methods, through an introduction to a problem, a link to the arrangement, a sentence of sincere words, to stimulate students' emotions, so that students feel the teacher's love for their own, so that students are interested in math class.

2. Create an open teaching process.

Because the open teaching process can provide each student with more opportunities for participation and success, so that each student can develop in the active exploration. To realize that everyone learns valuable mathematics; everyone has access to essential mathematics; different people develop differently in mathematics.

The open-ended teaching process is the process of letting students discover and solve problems by themselves. In the teaching process, in order to stimulate students' learning enthusiasm, to provide students with full opportunities to engage in mathematical activities, teachers should try to design exploratory and open teaching process, to give students the opportunity to actively explore and more space for thinking.

For example, I in the "meaning of fractions" teaching, designed such a teaching process: before the class let the students prepare their own learning materials (the students prepare materials are particularly full, some of the self-painted 10 small red flags, some paintings of 6 small animals, some paintings of 12 triangles, paintings of 8 small pieces of the circle, paintings of 9 small square, some of the cut a large circle, the longest one, the largest one. some cut out a large circle, rectangular and square paper, pencils, cakes, sticks, small squares and so on), by letting the students prepare their own learning materials, so that the students are mentally prepared for the new learning content. The materials chosen for the hands-on activities were again familiar and favorite to them. The lesson begins with two or three minutes of getting to know the students, "What do you already know about fractions?" "What else would you like to know?" "Can you get a fraction by dividing the materials you have in your hands?" Ask each student to divide at least one material and share your results with the group, stating the thought process of the operation in the exchange. After the cooperative group exchange (about 5 minutes), each group elects one student to come to the front to share with the class. In the exchange students ask each other questions and solve problems in the exchange and dispute. For example, if one student is demonstrating that 6 pencils are viewed as a whole and divided equally into 3 parts, and that each part is and can be, another student stands up and questions, "Why is and can be?" Another student immediately stepped up and said, "Because the number of equal parts is different; divided equally into 3 parts, each part is and is 2 pencils, and divided equally into 6 parts, 2 parts is and is 2 pencils." When exchanging, students on the stage speak and students off the stage scramble to add and correct from time to time. In the exchange, students learn to cooperate. In the exchange, students experience that there can be many ways to find the same result. Students in this open-ended exploratory activities to experience a rich (communication and cooperation, success, interest, pleasure) emotional experience.

3. Design open-ended practice problems at different levels.

In order to meet the different learning requirements of students, so that all students can get the appropriate development, teaching, teachers should make full use of the textbook practice problems or choose to closely linked to the real life of the students material, the use of students concerned and interested in the example of the design of each student have the opportunity to participate in the open practice problems, stimulate the students' desire for knowledge, so that students feel that mathematics is in their own surroundings and closely linked with the real world. The world is closely linked.

For example, when I was teaching "Preliminary Knowledge of Statistics", I designed this exercise according to the needs of students at different levels: "Please design a statistical table according to what you know about things around you." At this time, the students actively moved, some independent design; some two or three people cooperate, some collect information, some organize data. Some of them designed the "Class 4(1) Property Statistical Table", some designed the "Class 4(1) Teaching Aid Statistical Table", and some designed the "Class Number Statistical Table of Grade 4". "Fourth (1) class groups statistical table" "Zhongshan Road Elementary School grades statistical table" "a group of home address statistical table" "the number of people in a neighborhood statistical table" "four (1) class math scores statistical table" "recent week weather changes statistical table" and so on. This design of open-ended exercises, so that all students are actively involved in math learning activities. Another example is, please use an iron plate with a length of 24cm and a width of 12cm to design a lidless iron box with a height of 3cm for a customer. Students used different ways of thinking to design different sizes of iron boxes. Tell their design intention in the exchange.

Through this open-ended exploratory activity, students' interest in applying their knowledge was increased. Mathematical knowledge originates from life and ultimately serves life, especially elementary school mathematics, which can almost always find its prototype in life. As long as we teachers pay attention, we can design many realistic, meaningful and challenging open-ended practice problems using problems in life. So that students gain an understanding of mathematics at the same time, in thinking ability, emotional attitude and value and other aspects of progress and development.