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A new model of mathematics teaching in rural primary schools
A new round of teaching reform is booming. As a math teacher in the first-line rural primary schools, the new curriculum concept guides me. In recent years, I have tried to change the inherent and outdated teaching concepts and methods in my own mathematics teaching. However, when the teaching concept of the new curriculum is gradually rooted in the hearts of the people, there are also some puzzles about the new curriculum from the actual teaching experience. The following points are my thoughts in teaching practice.

Confusion 1: the confusion of target positioning

In the course reform, some teachers think that because the teaching materials have changed, the form, content and difficulty of the test papers are changing, so our teaching should also change and adapt to the new situation. This thought reflects the teachers' lack of understanding: it is not to implement the new curriculum standards, embody new ideas and achieve new goals, but to adapt to textbooks and exams and change for a new round of exams. The new curriculum requires that everything be changed for the development of students. The reform is to change students' learning style, so that students can learn autonomous learning, cooperative learning and inquiry learning in learning, so that students can learn to plan and manage their own lives in choice, so that students can choose modules they are interested in after learning certain basic knowledge, so that their personality can be fully developed and their innovation consciousness and creativity can be effectively cultivated. Because there are still blind spots in teachers' understanding and misunderstandings in their actions, teachers are confused and wandering in teaching practice, and even stagnate and regress, so the current quality education is earth-shattering, and the exam-oriented education is firmly grasped; What you say is one thing, but what you do is another. No wonder some people say that if this continues, the curriculum reform will soon end in failure.

To solve this problem, I think it is necessary to study the new curriculum standard repeatedly and further understand the new concept. When we study and understand the new curriculum standards, the new ideas we first come into contact with are purely theoretical. These educational and teaching theories lack the support of teaching practice, which sounds reasonable. However, after entering the actual combat stage, because the actual conditions of schools and students (especially rural villages) are far from it, we find that many ideas are not feasible, some good ideas are greatly discounted in practice, and there are fewer effective new teaching methods. If we don't reflect on the failure effectively, the curriculum reform can't be deepened and it can't be successful. Therefore, the best way to solve the problem is to study the new curriculum standard again. At this time, because we have teaching materials and teaching practice, teachers have accumulated some successful experiences and failed lessons in teaching practice. Revisiting the new curriculum standard at this time will certainly give us a deeper understanding and apply new ideas and methods to teaching practice, thus pushing the curriculum reform deeper.

Puzzle 2: Can the polarization of students' growth be avoided under the new curriculum?

Under the guidance of the new curriculum concept, teachers' teaching behavior and students' learning methods are undergoing obvious changes. Equality between teachers and students and teaching democracy have become a trend, and the classroom situation of teacher-student interaction and equal participation has begun to take shape. However, with the deepening of the experiment, the polarization of students has also appeared. The new curriculum provides a broad development space for the vast majority of students, and the winners will be more prominent. Under the new curriculum situation, due to the changes of teaching content, teachers' teaching methods, students' learning methods and academic evaluation methods, the classroom is full of democratic and harmonious atmosphere, and autonomous learning, cooperative learning, inquiry learning and teacher-student interaction push the classroom to a brand-new realm. In terms of teaching content, the presentation of new curriculum information is diverse and selective, the problem-solving strategies are diverse, and the answers are not unique and open, which provides a brand-new learning space for most students to the greatest extent, activates most students' thinking and inspires them to find their own learning methods. Through several years of teaching practice, it is found that this new learning method is more suitable for students with better intelligence, faster response and stronger self-discipline ability. They have played an extraordinary role in cooperative discussion and practical operation. This is the advantage of the new curriculum, but also the reason for polarization! This differentiation is particularly obvious in mathematics teaching. At present, there are sixty or seventy students in our school, ranging from fifty to sixty. So how should our teachers grasp the hierarchical teaching under the background of large class size, so that all students can learn knowledge well and develop in an all-round way?

In view of this confusion, according to my current feeling, I think we should start with the following points: First, we must admit that there are differences between children. In fact, not all children can learn math well. Some students, no matter how confident they are, will never be top students in mathematics. Teachers must look at this difference objectively, and can't evaluate students with the same ruler, let alone compare them horizontally. They must see that different children have different starting points. Every student should be affirmed and admitted that he can do it as long as he makes progress on his original basis. Some students got 60 points through hard work, but I was as happy and praised as some students got 100. Only when teachers look at students from a developmental perspective can they see a little progress in children's learning mathematics and really encourage children to say "I can do it"! To this end, I first pay special attention to "students with learning difficulties" in class. For these students, it is not enough to rely on verbal encouragement to help them build their self-confidence. Because of their poor foundation, they will lower the starting point of knowledge in class, just like listening to "heavenly books"! In fact, it is impossible for teachers to lower the starting point of knowledge for these students in class. So in class, I often leave some simple questions for them to answer, intentionally or unintentionally, so that they feel that they still have something to understand, thus enhancing their thirst for knowledge. In feedback exercises, I often have two kinds of questions, which require most students to finish all the questions, while "students with learning difficulties" only need to do one group. In this way, different standards are required for different students, so that "students with learning difficulties" can accept and basically follow the work rhythm. When I patrol students to do problems, I mainly pay attention to "students with learning difficulties", give timely guidance, help solve the difficulties encountered in the process of doing problems, and let them gain something after the last class. In the long run, they will also establish the self-confidence that "I can learn math well". Secondly, the deeper problems are left to the gifted students, so that they can perform when it is time to perform, so that students with learning difficulties can admire the gifted students and stimulate all students' interest in learning. Once again, I don't hesitate to praise talented students and students with learning difficulties. Mathematics teachers in primary schools usually teach mathematics in two classes. Facing more than 100 students, it is unrealistic to praise every child in every class. So, I made full use of my exercise book to have a "private chat" with my students: "You have made great progress in math recently, which is really good"; "The question you answered in class yesterday is very complete, go on!" ; "You made rapid progress in this test, come on!" ..... In this way, a small comment has built a bridge of love between teachers and students. As a teacher, don't be stingy with praise. According to different children, convey their feelings and love to their children's hearts in time, so that children can ignite the spark of progress in the care of teachers and enhance their confidence in winning! Let children learn mathematics in a confident and successful experience.

Puzzle 3: Puzzlement in carrying out inquiry activities.

(A) the contradiction between carrying out activities and completing teaching tasks

In teaching, teachers often have such confusion: when we carry out a lot of activities in the classroom, the teaching tasks are often not completed on time; Instead of carrying out classroom activities, it is contrary to the spirit of the new curriculum reform. How to deal with these two contradictions? In thinking about this problem, we must first make clear what classroom activities should be advocated in the new curriculum reform. In the requirements of the new curriculum reform, we should advocate our teachers to introduce mathematics knowledge from students' existing common sense of life, activities and games. But at the same time, it also advocates students to feel the process of knowledge acquisition in inquiry, cooperation and communication. At the same time, it should be clear that any classroom activities serve the teaching tasks and objectives, and it is very important to accurately locate the teaching tasks and objectives of each class for reasonable arrangement of classroom activities. In a class of "addition and arrangement of numbers within ten", a teacher spent 30 minutes asking students to arrange their own addition formulas within ten, 10 minutes to sum up, which made the class monotonous. Although the students study independently, they deviate from the real teaching task of the class. In the same class, another teacher spent 10 minutes sorting out the addition formulas in groups and parts, and spent 25 minutes for students to observe all the formulas, explore the rules and exchange summaries. The whole class has a lively atmosphere, and the students have also learned useful methods and rules in this class. Therefore, accurately positioning the tasks and objectives of classroom teaching will play a directional role in the arrangement of classroom activities.

In my opinion, in math class, activities should be in various forms, not only games but also students' observation, communication, cooperation and exploration. Moreover, activities should serve the completion of teaching tasks and the realization of teaching objectives, and the theme should not be diluted. Such activities are effective and beneficial classroom activities.

(B) classroom activities and the problem of too many students

In the standard, the process objectives such as "experience (feeling)", "experience (experience)" and "exploration" are particularly emphasized. In order to achieve the above process objectives, students must be involved in mathematics activities in the teaching process. In the process of students' learning activities such as "experience (feeling)", "experience (experience)" and "exploration", teachers play the role of organizers, guides and collaborators in students' learning activities. At present, it is time to run a school on a large scale. Most schools far exceed the rated class size, and the class size is basically around 65 students. There are too many students in the class, which brings difficulties to the implementation of the new standard. Teachers can't play his role successfully, especially it is difficult to play the role of a good guide and collaborator in students' learning activities, to make every student develop, and to realize the new standard of "everyone learns valuable mathematics"; Everyone can get the necessary mathematics; Different people get different development in mathematics. "

Lack of classroom activities and teaching tools.

The standard points out: "The development of modern information technology has a great influence on the value, goal, content and the way of learning and teaching of mathematics. The design and implementation of mathematics curriculum should attach importance to the application of modern information technology, vigorously promote the application of information technology in the teaching process, promote the integration of information technology and disciplines, gradually realize the changes in teaching presentation mode, students' learning mode, teachers' teaching mode and teacher-student interaction mode, and give full play to the advantages of information technology in students' learning. However, in our rural areas, although most schools have computer rooms and even networks, it still takes some time for each class to take math lessons with computers.

The standard pays more attention to the process evaluation of students' learning, and there are many learning contents that need students to practice and operate, so corresponding teaching AIDS are especially needed. Although some teaching AIDS can be made by students themselves, some teaching AIDS are difficult to make by themselves or self-made teaching AIDS are difficult to achieve the expected results, which brings great inconvenience to teaching.

It is difficult for students to finish extracurricular exercises. How is the quality?

The traditional teaching concept holds that the quality of teaching can only be guaranteed if you can understand the class and do extracurricular problems, otherwise it is an armchair strategist. The current textbook is shallow, which cancels the classification of knowledge in the original textbook and emphasizes the integration of knowledge and discipline, especially solving practical problems (that is, the original application problems). Because there is no typed application problem teaching, students have no rules to follow when solving practical problems. Students understand this topic, but they can't do another kind of problem, so they feel helpless when solving it. In order to help students solve learning problems, it is necessary to increase class hours, but every knowledge needs to increase class hours. In fact, it is impossible to have so much time. So students will only do a small part of extracurricular problems, and the other part will be guided by teachers or parents. Without guidance, it can't be completed. Teachers, students and parents are all worried about how to cope with the exam and how to ensure "quality"!

After the lecture, students still can't do the questions: first, students' knowledge can't be connected or the questions are too comprehensive; Second, students don't have a deep understanding of basic knowledge, can't master basic methods, and don't form good thinking consciousness and habits; Thirdly, teachers are only satisfied with the teaching of book knowledge, ignoring the broadening of dialogue knowledge and the cultivation of students' ability; Fourthly, teachers use traditional concepts and standards to understand this problem, and we should clearly realize that extracurricular exercises are only the auxiliary role of teaching materials; Fifth, the curriculum concept has changed, but the extracurricular exercises have not matched the textbooks and new curriculum standards, or the coordination is not enough. It is suggested that teachers should write some exercises themselves in such a special period according to the spirit of the new curriculum standard, avoid copying the whole page, and correct new textbooks with old questions.

Puzzle 4: Can the living and situational teaching of mathematics receive obvious teaching effect?

As the saying goes, "seeing is believing". Simple mathematics knowledge is often boring, and students have no interest and passion in learning. In the new curriculum, we usually combine mathematics teaching with students' real life, or create certain story scenarios or problem scenarios to arouse their original experiences with their favorite materials. This is easy to stimulate students' interest, and it must be kind, practical, interesting and easy to understand. Front-line teachers are indeed gradually infiltrating fresh blood into their own teaching ideas, striving to realize the concept of "mathematics living", so that students can discover, master and use mathematics from their familiar life background as much as possible, and experience the connection between mathematics knowledge and the surrounding world, as well as the role and significance of mathematics knowledge in social life, feel success, cultivate interest and enhance self-confidence in this process. However, there are still some problems in the teaching process ... When I was teaching the sixth grade mathematics interest and organizing the study of the application problems of principal, interest rate, interest tax, according to my previous experience, I think this is a kind of practical activity that students like best, and every student will finish this kind of problem with great interest. Otherwise, students can't get inspiration from practice. After inquiry, we know that the area where our school is located actually belongs to a remote mountainous area. Many children have never tried to deposit their money in the bank and have no idea what interest tax is. From this point of view, this time I assigned an assignment that is not in line with the reality of most students.

In this teaching example, there is no doubt that the new curriculum concept embodies the highest spiritual realm that everyone pursues unanimously, and everyone is trying to advocate and publicize it! So how far is it from our students' lives? Should students solve math problems in real life or tell them that math and life are two different things? How should students correctly grasp the scale between the two? As a teacher, how should we communicate the gap between this realm and the reality of students' lives? This is really worth exploring by colleagues.

Conclusion: Faced with many puzzles in teaching, front-line teachers also know that the curriculum reform can't be smooth sailing. There are downstream, countercurrent, rapids and reefs ... as long as we in Qi Xin work together to face up to the confusion and meet the challenge, through our constant attempts, explorations and even "hitting a wall" ... as long as we face up to the problem and then study ways to solve it, we will finally overcome the difficulties and solve the problem. Facing the new curriculum, I believe that as long as we really devote ourselves wholeheartedly, the math teachers in rural primary schools will become excellent surfers and gallop in the new wave of curriculum reform. Only in this way can the curriculum reform in China be successful.