In recent years, in order to improve the quality of primary school mathematics teaching, more and more attention has been paid to the reform of teaching methods at home and abroad. Not only have many new teaching methods appeared, but they have also been discussed in depth from the teaching theory. So a series of questions are put forward: which teaching methods are good? How to distinguish from modern teaching theory? From the development trend of modern teaching theory, what is the reform direction of mathematics teaching methods in primary schools? This paper wants to introduce some situations around these problems and talk about some superficial views.
The guiding ideology of the reform of mathematics teaching methods in primary schools
We cannot study the reform of mathematics teaching methods in primary schools in isolation. Teaching method is an important part of teaching theory. Primary school mathematics teaching method is the concrete application of general teaching method in primary school mathematics teaching, which should be guided by the principles of general teaching theory; But it must also reflect the characteristics of mathematics.
Teaching theory is not static. Especially in the last twenty years, with the rapid development of science and technology and the constant change of society, on the one hand, new requirements are constantly put forward for education and teaching, on the other hand, people's understanding of the objective laws of teaching is deepening, and the research on teaching theories, including teaching methods, has also made great progress, which has had a positive impact on the reform of primary school mathematics teaching methods. Therefore, primary school mathematics teaching methods must be constantly reformed with the development of modern teaching theory.
According to the viewpoint of teaching theory, teaching methods are closely related to teaching purposes, teaching contents, psychological characteristics of teaching objects, teaching means and teaching organization forms. To study the reform of primary school mathematics teaching methods, we must closely combine the teaching purpose and content of primary school mathematics, adapt to the age characteristics of primary school students, and contact the reform of primary school mathematics teaching methods and teaching organization forms in order to achieve good results.
Second, the development trend of modern teaching theory and its influence on the reform of mathematics teaching methods in primary schools
(1) In terms of teaching purposes and tasks, it has changed the traditional simple knowledge transmission and paid more attention to developing intelligence and cultivating ability.
For example, when talking about the overall goal of education, Bruner in the United States pointed out that "not only should we educate students with excellent grades, but we should also help each student get the best intellectual development." Volkov of the Soviet Union pointed out that in the past, the education system provided "executors", but now "the education system is required to provide creators" ... The education system should become a "workshop" for cultivating smart people with unique ideas. zankov pointed out more clearly that teaching is not simply imparting knowledge, and the core of teaching theory is that the teaching process should make students' general development achieve results. He criticized the past teaching theory and regarded the development of students' intelligence and logical thinking as a "by-product". For example, learning arithmetic naturally becomes a logical exercise. Sidgenschein also stressed that students should not only master scientific knowledge, but also cultivate their independent thinking and judgment ability. In recent years, China needs to train talents to realize the four modernizations, and the importance of developing intellectual training ability is also emphasized in teaching.
Due to the change of teaching purpose, the traditional teaching method based on imparting knowledge obviously cannot meet the new requirements. Therefore, some new teaching methods have appeared one after another, such as discovery, inquiry, discussion and independent operation. Some educational psychologists have also done comparative experiments with traditional teaching methods, and the results show that inquiry learning is very beneficial to inspire thinking and promote the transfer of learning. Because these methods give full play to students' initiative in learning, and at the same time learn the methods of acquiring knowledge to varying degrees, they are conducive to developing students' intelligence and cultivating students' ability to acquire knowledge independently, which has attracted the attention of educators.
After the emergence of new teaching methods, should we abandon the traditional teaching methods? In foreign countries, there was a time when traditional teaching methods were completely denied, but some changes have taken place in recent years. On the one hand, people see that the new teaching methods are not perfect and cannot be used everywhere. For example, even Bruner himself said that "it may take too much time". "Some people easily accept this idea of' discovery', as if one should even find the names of a group of stars!" On the other hand, traditional teaching methods are not without advantages. When talking about teaching methods, Kenneth Hansen of the United States said, "Although it has been criticized by many contemporary educators, it has survived for so many years, which proves that teaching methods have some unique advantages." He believes that this method "can effectively introduce and summarize the main concepts mentioned in the class", but it is difficult to stimulate interest and improve creativity. Therefore, it is necessary to use it less, especially in classes or lower grades with poor learning ability, and the speech time is short. It is suggested to combine discussion to achieve better results. It can be seen that the traditional teaching methods tend to be reserved and used conditionally.
At present, foreign primary school mathematics teaching methods have the same trend, that is, while advocating the use of new teaching methods, the traditional teaching methods are conditionally retained. For example, after advocating the use of guided discovery in primary school mathematics teaching, Andrew Hill in the United States also pointed out that teachers also need to tell students the names of concepts, how to establish equations, how to solve problems vertically, and so on. After students discover the concept and make a general summary, they should also use explanations appropriately to point out its characteristics and explore its details. Morrow and others in the Soviet Union also emphasized in the "Primary Mathematics Teaching Method" that "we should pay more attention to the teaching methods that can promote and mobilize the enthusiasm of students' cognitive activities, and at the same time, we should also pay attention to the role of those methods (oral explanation, etc.). It is related to teachers imparting knowledge in a ready-made form and should be evaluated reasonably. " The author also improved the explanation method to stimulate students' enthusiasm for thinking.
In recent years, many teachers in our country have clearly realized the teaching purpose of primary school mathematics, carried out corresponding reforms in teaching methods, and paid attention to adopting inspiring teaching methods that are helpful to develop students' intelligence, and achieved good results. However, some teachers lack a clear understanding of the purpose of primary school mathematics teaching, are not good at using teaching methods to promote intellectual development, and still adopt the teaching method of indoctrination and memorization of some terms and formulas to a certain extent. This situation needs to be changed urgently. On the other hand, in primary school mathematics teaching, in order to develop students' intelligence, we can't completely exclude the opposite teaching method. We can use less simple explanation methods and combine them with other methods such as demonstration, question and answer, and practice. When explaining, we should pay attention to asking enlightening questions and guide students to think, so that primary school students can not only acquire clear mathematical concepts, but also develop their intelligence.
(2) Emphasize that students are the main body of learning, and the leading role of teachers must be combined with the main role of students.
Traditional teaching theory emphasizes the leading role of teachers and ignores the main role of students in learning. In line with this, we advocate teaching methods. For example, in Pedagogy edited by Kailov, it is clearly stated that "teaching plays a leading role in the teaching process." Great changes have taken place in modern teaching theory, which emphasizes that students are the main body of learning. For example, Bruner regards children as "people who actively participate in the process of knowledge acquisition" and teachers as "main tutors". Soviet pedagogy also clearly put forward that "children are the main body of education" and "children will always be active participants in the educational process; "Students' cognitive activities are the main ones", "Teachers' task is to create conditions for improving students' general cognitive enthusiasm, form a positive learning attitude, and cultivate independence and working ability". Teachers' leading role no longer lies in their teaching level, but more importantly, whether they can give full play to students' main role in the teaching process, stimulate students' enthusiasm for learning, guide students to think, and guide students to gradually learn how to acquire knowledge independently. This view accords with materialist dialectics' view on the relationship between internal cause and external cause. From this basic point of view, the study of teaching methods is no longer just the study of teachers' teaching methods, but more importantly, the study of methods to stimulate students' learning enthusiasm and guide students to learn and explore. The disadvantage of teaching method is that it does not give full play to students' initiative, nor can it effectively enable students to master learning methods and cultivate their ability to acquire knowledge independently. The advantage of some new teaching methods is that they can promote students' active learning and cultivate their ability to acquire knowledge independently. Of course, we should also see that some new methods fully display students' initiative, but they are not enough to play the leading role of teachers. The discovery method is an example. This is also an important reason why some foreign educators and psychologists have raised objections. For example, Gagne, an American psychologist, stressed that students should be given the most adequate guidance so that they can study according to carefully prescribed learning procedures; Some people also put forward the guided discovery method in view of the shortcomings of pure discovery method. Teachers can act as promoters, give appropriate hints and help, effectively control students' learning activities and ensure the expected goals are achieved.
In our country, some primary school mathematics teachers have also begun to try some new teaching methods to arouse students' enthusiasm and initiative in learning and cultivate students' ability to explore and acquire knowledge independently, and have received certain results. However, there are still some teachers who don't know enough about the combination of teachers' leading role and students' main role, or although they know something, they lack methods. In order to solve this problem well, we should pay attention to the following points in the reform of mathematics teaching methods in primary schools:
1. Teachers should be good at explaining the meaning of learning, creating problem situations, revealing contradictions and stimulating students' learning motivation. Let students feel the need and interest of learning and exploration, and they will take the initiative to learn.
2. Teachers should strive to create conditions for active thinking and guide students to think. Only when students actively think about problems can their enthusiasm and initiative be truly brought into play. Some problems (such as calculating the result of a formula) can have the nature of seeking common ground, and some problems can have the nature of seeking differences (such as coming up with different solutions to a problem), which can stimulate students to think positively and develop the flexibility and creativity of thinking. Students should also be encouraged to ask questions, but the whole class should solve them together to promote each student to think independently.
Teachers should let students practice properly. This is still the weak link of mathematics teaching in primary schools in China. Since students are the main body of learning, we should organize more activities in a planned way, so that students can observe, operate, experiment, think and practice independently, understand and master mathematical knowledge in various activities, gradually master learning methods, and cultivate students' ability to acquire knowledge independently. This is also in line with the cognitive law of psychology from action, perception to representation to abstract symbols. Students have fully accumulated perceptual experience in practical activities, which is convenient for correctly abstracting the essential characteristics of mathematical concepts and summarizing complete calculation rules, which is impressive and easy to maintain.
4. Teachers should change the form of math homework appropriately. On the one hand, it can stimulate students' interest in mathematics and constantly improve their enthusiasm for learning, on the other hand, it can deepen their understanding of the mathematics knowledge they have learned.
5. Teachers should be good at using the feedback information of learning, do a good job of inspection and evaluation, and strengthen the effect of feedback. Feedback information is very important for both students and teachers. Positive feedback information can strengthen students' correct understanding and teachers' good teaching methods, while negative feedback information can correct students' wrong understanding and teachers' improper teaching methods. If teachers only pay attention to teaching and ignore students' reaction, or only pay attention to correcting homework after class and ignore the inspection of classroom homework, students will not be able to see their progress in time and correct their mistakes in calculation in time, which is not conducive to giving full play to students' learning enthusiasm. Moreover, because teachers can't find and solve problems in class in time, it may also cause a vicious circle of insufficient extracurricular supplements, which is not conducive to reducing students' learning burden. This is worthy of our attention. Of course, strengthening the information feedback in the classroom does not mean that all homework is corrected in the classroom. There is still a difference between the two, which should be handled properly.
To achieve the above points, the key is to understand students, their age characteristics, learning foundation and learning potential, so that teachers can organize students' cognitive activities on a reliable scientific basis.
(3) In terms of teaching methods, it emphasizes the cross-use and mutual cooperation of various methods.
Traditional teaching often adopts fixed teaching methods and forms a set of models. Great changes have taken place in modern teaching theory. Due to the increasing number of teaching methods and the in-depth study of the nature of teaching methods, educators are increasingly aware that teaching methods are diverse and there is no one-size-fits-all teaching method. As babanski of the Soviet Union pointed out, there is no "treasure chest in teaching methods". Frank Kerr, an American educator, also said, "There is no' best method' that is effective for any student under any circumstances." The absolutization of a certain teaching method does not conform to the principle of materialist dialectics that concrete things are analyzed and different contradictions are solved by different methods. Therefore, modern teaching theory tends to choose different methods and use several teaching methods together according to the teaching purpose, content and students.
This new teaching theory is also reflected in the primary school mathematics teaching methods. For example, the Soviet Union's Primary School Mathematics Teaching Method emphasizes that teaching methods are closely related to teaching purposes, contents, means and organizational forms, and it is these relationships that determine the choice of methods used in each individual situation; "There can be no ready-made prescription to solve the structure of any class." American C. Rideser also emphasized in the book "Mathematics Teaching in Primary Schools" that the teaching methods are different because of different mathematics topics, different children and different teachers' styles. Teaching methods are not single, and there can be different combinations.
Our research on primary school mathematics teaching methods is in line with modern teaching theory. For example, some comrades put forward that "there are methods for teaching, but there is no fixed method" and stressed that different methods should be adopted according to different situations. Even if experienced teachers teach different classes in the same grade, the teaching methods are not exactly the same. However, contrary to the above principles, some comrades want to develop a universally applicable teaching method, and some comrades want to popularize a certain teaching method or a certain classroom teaching structure in all grades, so that every class is taught according to the same model. This does not conform to materialist dialectics, and it is easy to bind teachers' hands and feet and limit their creativity, which is not conducive to better improving the quality of primary school mathematics teaching.
(D) in the form of teaching organization, flexible use of various forms to adapt to the differences of students.
For centuries, the widely used teaching organization form is the class teaching system. It is characterized by uniformity. Its advantage is that a teacher can teach more students at the same time, but its disadvantage is that it can't adapt to individual differences. In particular, the teaching purpose has changed, emphasizing the development of each student, and the disadvantages of the class teaching system have become more and more prominent. Over the years, there have been endless criticisms, and some even want to cancel the class teaching system. However, from various experimental results, it tends to combine class teaching, group teaching and individual teaching, so as to face the whole and pay attention to individual differences.
At present, this form of teaching organization is also advocated in foreign primary school mathematics teaching. For example, the Soviet Union's "Primary School Mathematics Teaching Method" emphasizes the combination of collective homework, group homework and individual homework in various forms. To adapt to this form, print several sets of homework questions of the same type with different difficulties. Ender Hill of the United States also designed a teaching mode combining large groups, small groups and individuals in Mathematics Teaching in Primary Schools. According to the understanding and mastery of the situation, enrich, practice or supplement the teaching respectively, so that the top students can get greater development and improvement, and the poor students can meet the basic teaching requirements.
In mathematics teaching in primary schools in China, some teachers have noticed that they should face the whole and teach students in accordance with their aptitude, and have also taken corresponding measures; However, there are still many teachers who do not pay attention to meeting different levels of needs and adopt a "one size fits all" approach. Some teachers also pay attention to hello students in class, but not enough guidance to poor students. In order to improve the scientific and cultural level of all the people and lay a good foundation for every student in primary school, we must improve the teaching organization form as soon as possible and sum up the experience of teachers who have done well in this field. How to provide different assignments for teachers to choose from is also worth studying.
(5) Optimize the teaching process and improve the teaching efficiency.
In recent years, due to the introduction of system theory, information theory and cybernetics into the study of teaching theory, some people regard the teaching process as an information transmission and exchange system composed of teachers and students, and study the best control of the teaching process to achieve good teaching results. Babanski of the Soviet Union is a representative. He put forward the basic criteria for the optimization of teaching process, the first is the effect, and the second is the time. He emphasized that it takes less time and energy to achieve the maximum teaching effect. Therefore, we should make the best and reasonable choice in teaching tasks, teaching structure, teaching content, teaching methods, teaching forms, teaching means, teaching progress and homework. He thinks this is one of the most important requirements of modern classroom teaching.
At present, foreign primary school mathematics teaching also emphasizes this requirement. The Soviet Union's "Primary School Mathematics Teaching Method" emphasizes the need to choose the teaching method that is most suitable for specific teaching conditions. It is believed that in the teaching methods of the Soviet Union, the method of avoiding children's excessive schoolwork burden is still the primary problem, and the main potential of improving teaching effect should basically be found in improving the quality of each class. The National Federation of Mathematics Teachers in the United States also proposed that mathematics teaching must have strict standards of effectiveness and efficiency.
In recent years, some primary school mathematics teachers in China have begun to pay attention to improving teaching efficiency. For example, some teachers put forward the idea of "improving quality in 40 minutes" and "making full use of every minute" and took some measures. There are also a few teachers who propose to make the best teaching plan. But on the whole, there is not much experience in this reform and it needs to be further strengthened. For example, first, how to determine the purpose requirements, highlight the key points, and use the limited teaching time on the cutting edge; Second, how to fully estimate students' learning foundation and potential, and try to guide students to make analogies on the basis of what they have learned, which not only mobilizes students' enthusiasm, cultivates students' ability, but also saves time; Third, how to properly determine the quality and quantity of homework according to the requirements of the purpose, the difficulty of knowledge and the foundation of students, so as to be targeted; Fourth, how to organize all students to carry out various activities and exercises as much as possible; Fifth, how to strengthen the understanding and inspection of students, make full use of the role of teaching feedback information in the teaching process, and timely regulate the teaching process in order to carry out effective teaching in the most appropriate way and speed; Sixth, how to choose the best teaching plan from the comparison of different teaching plans according to the topics and students taught, and avoid using the teaching plans in reference materials in teaching. These problems are worth studying and summing up experience.
Three-point concluding remarks
More and more practice shows that in order to improve the quality of primary school mathematics teaching, besides textbooks, teaching methods must be reformed. To do this work well, we must first study, take dialectical materialism as the basic guiding ideology, make clear the direction of reform from the perspective of modern teaching theory, contact the main problems in our teaching, give play to teachers' initiative and creativity, keep experimenting and sum up experience, so as to quickly promote the reform of primary school mathematics teaching methods.
In fact, it is also empty talk. . . . . . In short, there is not too difficult knowledge in primary schools. The key is to teach the basics. I suggest not to be too strict, but not too loose. It is very effective to establish proper authority and encourage students to learn more Olympic Mathematics. . . O(∩_∩)O haha ~