(B) choose the appropriate teaching organization form
As mentioned above, classroom teaching is the basic organizational form of teaching. But it is not the only form of teaching organization. Mathematics teaching in primary schools is mostly carried out in the classroom. However, some teaching contents, such as measurement, want to receive good teaching results, and students should go to the playground or outside the school for actual observation and measurement activities. There are also some teaching contents, such as the calculation of interest and insurance. Some teachers organize students to visit banks, credit cooperatives and insurance companies. Socializing mathematics teaching activities will take more time, but it will get good educational results.
Even in classroom teaching, the form of teaching organization should not be static. At present, the class teaching system is widely used in classroom teaching, which is characterized by rapid progress and unified progress, and it is easy to ignore the individual differences of students, so that each student can not be fully developed. In order to overcome this shortcoming, modern teaching theory proposes to strengthen group teaching and individual teaching. The primary school mathematics teaching method in the former Soviet Union emphasizes the close combination of classroom teaching, group teaching and individual teaching. In the book "Mathematics Teaching in Primary Schools", Andrew Hill of the United States also designed a teaching schematic diagram combining large groups (the whole class), groups and individuals (as shown below).
In recent years, some teachers in our country have adopted appropriate group teaching according to the specific situation of their own classes. For example, some teachers divide the whole class into three groups according to the math level: A, B and C, and encourage students in Group A to study independently and do some comprehensive and thoughtful topics on the basis of meeting the requirements of the syllabus. Group B students are required to master the basic knowledge and skills stipulated in the syllabus and give appropriate help to those who have difficulties. Group C students give more guidance and gradually meet the basic requirements stipulated in the syllabus. As a result of this teaching, the math level of the whole class has improved. Therefore, improving teaching organization plays an important role in improving teaching efficiency.
Fourth, choose appropriate teaching methods.
Choosing appropriate teaching methods also plays a very important role in improving classroom teaching efficiency. Babanski believes that "choosing the most effective teaching method for a certain class is one of the core issues in the optimization of teaching process." In recent years, many new teaching methods have been studied at home and abroad. How to choose? Here are some points.
(1) Choose teaching methods that help to mobilize students' enthusiasm for cognitive activities and develop their abilities.
Morrow of the former Soviet Union emphasized in his book "Primary School Mathematics Teaching Methods" that "more attention should be paid to teaching methods that promote students' enthusiasm for cognitive activities. "Modern teaching theory holds that students are the main body of learning, and teachers should play a leading role, not imparting knowledge to students, but creating conditions to improve students' enthusiasm for cognitive activities and cultivate their ability to work independently. Specifically, teachers should pay attention to creating problem situations, organizing the learning process, mastering the learning direction and helping students explore. To achieve these points, we must carefully choose teaching methods. For example, in primary school math class, if you choose methods such as explanation and explanation, teachers will have more activities and students will have less activities, so it is better to adopt methods such as question and answer, discussion, inquiry and guiding discovery. The latter method increases students' activities to a certain extent, which can better mobilize students' learning enthusiasm and promote the development of students' thinking. However, the use of methods such as explanation and explanation cannot be ruled out. For example, it can be used when teaching the method of making statistical charts in senior grades. Modern teaching theory holds that any teaching method is not omnipotent, and appropriate teaching methods should be selected according to different contents, grades and conditions. The Mathematics Teaching Syllabus for Compulsory Primary Schools (for Trial Implementation) also emphasizes that "teaching methods should be applied flexibly according to the teaching content and students' specific conditions, and cannot be applied mechanically." Even with the same teaching content, the teaching methods may not be exactly the same because of the different situations of students in the class. For example, students can explore more freely in classes with strong autonomous activities; Teachers need to give more inspiration and guidance in classes where students' autonomous activities are poor. Sometimes several teaching methods can be combined in a class to make up for the deficiency of a single teaching method. For example, the calculation of teaching rectangular area can be guided by operation and discovery, supplemented by the teacher's summary and explanation.
(2) No matter which teaching method is adopted, we should pay attention to stimulating students' learning motivation.
This is an important condition to promote students' learning and improve teaching effect. As mentioned above, some teaching methods can easily arouse students' learning enthusiasm, but there are also problems of stimulating learning motivation. Some teaching methods, such as explanation, are poor in mobilizing students' enthusiasm for learning, so we need to pay more attention to this problem. In addition, in the case that junior students' learning consciousness is still relatively poor, we should also pay attention to constantly stimulating students' learning motivation. Many teachers have accumulated a lot of experience in this field. For example, explain the purpose of learning new knowledge, intuitively stimulate students' interest in learning, create situations to arouse students' thinking, and carefully set doubts to urge students to explore.
(3) No matter which teaching method is adopted, children's cognitive rules should be followed.
In the previous research on teaching objectives, we talked about children's cognitive laws. This problem should also be seriously considered when choosing teaching methods. This is an important aspect to improve the teaching effect. According to this rule, students should be organized to perform appropriate operations when teaching certain contents. Especially when mathematical knowledge is abstract and students lack perceptual experience, we should pay more attention to establishing representations for students, stimulating students' thinking and promoting students' understanding of abstract concepts and laws through operation. For example, to teach carry addition within 20 minutes, students should master the method of rounding off ten through operation. When teaching the understanding of rectangles and squares, we should actually measure their side lengths, measure their angles with the right angles of triangular plates, and do some spelling and swinging activities to understand their characteristics. When teaching simple application problems, you can also analyze the quantitative relationship through operation. For example, in the picture below, students can understand that there are more white disks than black disks by putting learning tools. White disks can be divided into two parts, one is as many as black disks, and the other is more than black disks. Remove five of the eight white disks as many as black disks, and the remaining three are more than black disks, which should be calculated by subtraction. Lower grades should not only pay attention to operation, but also teach some abstract and difficult knowledge in higher grades, such as prime number, composite number, factorization prime factor, greatest common divisor, least common multiple and so on. In order to improve the teaching effect, we should pay attention to the following points in operation:
1. Choose learning tools that can easily reveal the essential characteristics of the concepts or laws learned, so that students can operate easily and save time. Design operation steps before class.
2. Operation should be closely combined with thinking and language expression. For example, in the teaching of 34+2 and 34+20, students should be guided to think by putting sticks. From the addition of the whole beam and the whole beam, the addition of a single root and a single root, it is abstractly summarized as ten and how much ten adds, and how much one and one add. If only the calculation is used to verify whether the calculation result is correct, then the meaning of the operation will be lost. However, it should also be clear that operation and intuition are the means to understand concepts and laws, and attention should be paid to gradually separating from operation and intuition in teaching, so as to help develop students' abstract thinking ability.
3. Attaching importance to operation and intuition does not mean that any content of teaching begins with operation and intuition. Some students with new knowledge can make analogy on the basis of what they have learned, so they should be guided to apply the analogy of knowledge transfer they have learned.
(d) No matter which teaching method is adopted, we should pay attention to inspiring students to think and cultivate students' logical thinking ability in a planned and step-by-step way.
This is an important goal of effective teaching. In addition, by properly handling the relationship between knowledge and ability in teaching, students' thinking is developed and they learn to think, which creates favorable conditions for further learning new knowledge smoothly. Choosing a good teaching method can promote the development of students' thinking, but teachers need to work hard to develop students' thinking step by step. In order to develop students' thinking smoothly and effectively, the following points are worth noting:
1. Developing thinking and cultivating ability should run through the whole teaching process. The Mathematics Teaching Syllabus for Compulsory Primary Schools (Trial) emphasizes "teaching in all grades". In other words, how to develop students' thinking should be considered in every class and every link.
2. Closely combine the teaching content and cultivate the thinking ability. Therefore, when teaching every concept, law and application problem, we should analyze the favorable factors of developing thinking and focus on developing some aspects of thinking according to its characteristics. For example, combined with the teaching of numbers within 100, the significance of addition, subtraction, multiplication and division can focus on cultivating students' preliminary abstract and generalization ability; Combining the oral calculation of adding and subtracting two digits to one digit, the written calculation of two-digit multiplication and the teaching of application problems, we can focus on cultivating students' preliminary analytical reasoning ability; Combined with the teaching of operational research, we can focus on cultivating students' ability of preliminary judgment, induction and deductive reasoning. You can also combine some contents to teach students some common thinking methods. For example, combining the division of divisor into decimal can teach the thinking method of transformation, that is, transforming new knowledge into learned old knowledge; Combine calculation with the solution of application problems and teach students the method of testing.
3. Adapt to the age characteristics of students' thinking development and attach importance to the thinking process. Pupils are in the stage of gradual transition from concrete image thinking to abstract logical thinking. Students of different ages have different thinking characteristics. In order to achieve good results, we should cultivate students' thinking ability consciously and systematically according to the characteristics of students' thinking development in teaching. For example, junior students are young, have little life experience, have the advantage of concrete thinking in images, and their abstract thinking ability is still very weak, so they often can't distinguish the essential characteristics of things, and often can't tell what they think when solving application problems, or can't fully express their own problem-solving ideas. When teaching, we should combine operation with intuition, ask enlightening questions, guide students to analyze and compare step by step, and find out regular knowledge or methods to solve problems. Students sometimes express incorrectly, so teachers should give appropriate help and teach students how to analyze and solve problems when solving application problems. Students should be given more opportunities to describe their thinking process in class. You can also organize students to speak in groups. By communicating with your classmates, it is easy to cultivate students' ability to check and adjust their own thinking, so that their thinking and language expression skills can develop rapidly. With the increase of grades and the development of students' abstract thinking, students can think independently, evaluate each other, express different opinions, activate their thinking and pay attention to cultivating students' organized and grounded thinking. For example, in middle-grade teaching, X+5 = 12. After students work out "x= 12-5, x=7", they can ask "What is the basis of your calculation?" Teaching 25× 13×4 requires students not only to talk about simple algorithms, but also to talk about basics. Also pay attention to the logical rigor of students' judgment. For example, when teaching divisors and multiples in senior grades, you can ask, "12 is divisible by 3, so we say that 12 is a multiple and 3 is a divisor. Is this judgment right? " Students should explain the reasons after answering. In short, we should attach importance to students' thinking process in teaching, but we should put forward different requirements according to students' age characteristics to gradually improve students' thinking ability.
4. Pay attention to the cultivation of thinking quality. This is also an important aspect of developing students' thinking ability. Babanski's research proves that there is a high correlation between thinking quality and thinking ability. Good thinking quality plays an important role in laying a good foundation for cultivating creative talents. The agility and flexibility of students' thinking is also an important symbol of efficient classroom teaching. "Compulsory primary school mathematics syllabus (Trial)" clearly put forward this requirement.
The agility of thinking should be cultivated from the lower grades. For example, when teaching oral arithmetic, we should gradually put forward appropriate speed requirements. Teach students a calculation method, and after some practice, guide students to simplify the thinking process and further improve the calculation speed. For example, after teaching 9 plus a few and 8 plus a few, students can be guided to observe and compare, find out the changing law of numbers with the second addend, and then think about how to calculate numbers quickly. To cultivate the agility of thinking, we should pay attention to the appropriate requirements, give students time to think when asking questions, and don't make students too nervous.
The flexibility of thinking should also be consciously cultivated from the lower grades. You can do the following: (1) For some related and different knowledge, you can strengthen contrast exercises and mixed exercises. For example, strengthen the comparative practice of adding and subtracting two digits to one digit and integer ten digits, so that students can quickly determine the direction of solving problems with the help of the changes of numbers and operation symbols. (2) Strengthening variant exercises can not only deepen students' correct understanding of concepts and laws, but also help to cultivate students' thinking flexibility. For example, in the understanding of teaching rectangles in lower grades, rectangles in different positions should appear; The initial understanding of middle school students' teaching scores should be divided into several parts on average, and there should be uneven scores. (3) The practice of guiding students to explore laws, such as asking students to find out the arrangement rules of addition tables, subtraction tables and tables with numbers within 100 in lower grades, is helpful to cultivate students' ability to quickly turn from one angle to another to observe and analyze problems. (4) Encourage students to think of different ways to solve problems. For example, when teaching abdication subtraction within 20 years, the teacher teaches a certain calculation method, and encourages students to say or use algorithms themselves. Some application problems encourage students to come up with different solutions and compare which one is simpler. Some questions also allow students to find multiple answers, such as 5+() < 9. These exercises all contain divergent thinking to varying degrees, which not only helps to cultivate students' thinking flexibility, but also cultivates students' creativity. But in teaching, we should pay attention to the proper combination of divergent thinking and concentrated thinking. We don't need to ask students to do everything, but we should understand and master basic and simple methods, otherwise we will waste time and get no good teaching effect.
(E) The choice of teaching methods should pay attention to meet the different needs of the whole and teaching students in accordance with their aptitude.
Babanski pointed out that the primary criterion for optimizing teaching effect is that every student can reach the practical level in terms of student achievement, education and development during this period. In other words, every student should be fully developed. However, there are differences among students. In order to meet the above requirements, besides setting appropriate teaching objectives and choosing appropriate teaching organization forms, we should also consider choosing appropriate teaching methods. Because there are many differences between students, not only in life experience and mathematical foundation, but also in intelligence, cognitive style and personality, the teaching methods can't be the same. When teaching for the whole people, we should choose teaching methods according to the level of most students, and when teaching students in accordance with their aptitude, we should choose appropriate teaching methods according to the characteristics of different students. For underachievers, we should use more operation and intuition to help them understand new knowledge, but generally we can't adopt independent teaching methods. You should also check and coach more when practicing. However, for dependent students with poor independent thinking ability, we should also pay attention to properly guiding students to learn independent thinking and avoid directly telling students what to think and how to do it, so as to gradually improve their learning ability. For students with good math foundation and strong thinking ability, they should let go more and constantly improve their independent thinking and learning ability.