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Mathematical research paper
Cooperation-the symbol of success of discussion teaching

Cooperation is a more important ability than knowledge and an important content of quality education. Today is the era of scientific and technological competition, and the success or failure of competition often depends on the cooperation of people. A person's ability is limited. If he is not good at cooperating with others, communicating, synthesizing, improving and applying different knowledge, he can't adapt to the development requirements of the times. Therefore, the implementation of group cooperation teaching in research discussion teaching is an important content in the experimental subject of research discussion teaching. Mathematics group cooperative learning is the application of collective teaching mode in primary school mathematics. It is designed according to the principle of group dynamics, aiming at changing the past that classes only serve as a "static collective background" to restrain students' classroom behavior, and making classes, groups and other student groups become "dynamic collective forces" to help students learn in class. Therefore, "group cooperative learning" is a good teaching mode. This model is beneficial for students to participate in the whole learning process. Students' learning is lively and everyone is willing to try to succeed. It can not only explore the internal potential of individuals, but also cultivate the spirit of cooperation between the collective and the group.

First, a reasonable formation, improve the efficiency of cooperative learning

According to students' personality and psychological characteristics, it is an important beginning to form a reasonable study group. When forming a study group, we should first make a comprehensive evaluation based on students' knowledge base, hobbies, learning ability, psychological quality and personality characteristics, and then match them into several study groups, with 4-6 people as the group leader and 1 as the group leader. Group leaders are generally students who have a good learning foundation, are helpful, have a certain sense of cooperation and innovation, and have strong oral expression and organizational skills. There is no obvious difference between each group, and strive for balance, which is conducive to fair competition. After the establishment, members of each group are required to help each other, be frank, democratic and equal. In order to improve the efficiency of cooperative learning.

Second, let the cooperative team actively participate in the teaching process.

1. Create an atmosphere and stimulate interest.

Mentality directly affects the learning effect. In contrast, according to the characteristics of teaching materials, teachers should give full play to audio-visual teaching methods and create a relaxed and pleasant cooperative learning atmosphere, so that students can give full play to their wisdom and stimulate their interest in cooperative learning. For example, in the review teaching of One Column Volume, we should grasp the connection between old and new knowledge, fully respect and trust students, create an equal, democratic and harmonious cooperative atmosphere, and use media and physical means to show a picture of a "little doctor" and explain the review method, that is, we can ask ourselves and answer related knowledge when we see a picture, and I will ask you and answer you. Then show the graphics and cuboids one by one. Let each group say what they know in groups, and then ask a question to the next group of students to answer, in turn. In this way, the team members actively cooperated and successfully reviewed what they had learned to prepare for the new classroom teaching.

2. Create an environment to improve efficiency

In cooperative learning, teachers should aim at teaching objectives, teaching contents and teaching materials, and combine the actual situation of class students to create a situation that can not only stimulate students' learning motivation effect, but also give full play to the cognitive function of group cooperative learning, so as to improve the efficiency of peer cooperation.

For example, when teaching "Basic Quantitative Relationship", we can design a prize purchase plan for class activities, let students choose their favorite prizes, make a favorite purchase plan, stimulate students' interest in learning, and master the basic quantitative relationship in cooperative research. When teaching "Tourism Route Design", we can contact students' travel experience, talk about their feelings and experiences in tourism, stimulate students' interest in learning to choose reasonable tourism routes, and master the knowledge of optimization strategies.

3. Pay attention to guidance and reasonable organization.

Effective guidance and reasonable organization are the guarantee of successful cooperative learning. In classroom teaching, students are encouraged to explore and think about new problems by various methods, such as reading, operation, trying, migration, analogy and classification. Teachers should do a good job of patrol guidance, especially for students with difficulties. Conducive to all-round teaching. Therefore, students' independent exploration and successful cooperation cannot be separated from teachers' encouragement and guidance. When students are confused about new knowledge and have problems, they should seize the opportunity and dispel doubts. The purpose of cooperative discussion is to encourage students to actively participate in learning, to mobilize all students to think, speak and do things, to participate in the whole teaching process from beginning to end, and to actively learn.

From the perspective of information theory, the interaction and information exchange among students, teachers and teaching materials in classroom teaching can optimize the classroom teaching structure and improve the classroom teaching effect. Therefore, it is beneficial to the interaction and information exchange between students to let students talk and discuss more in class. However, there are many links in the 40-minute class, and finally, students must be guaranteed time to practice. There are so many students now that it is impossible for every student to speak. Therefore, it is very important to organize various forms of discussion reasonably in group cooperative discussion. These forms include two-person discussion at the same table, four-person group discussion, large group discussion and teacher-student discussion, which gives some students who don't usually talk much a chance to speak. In the process of organizing students to discuss in groups, we should also pay attention to cultivating them how to discuss around the center and grasp the key points. For example, in the process of discussion, students below the average level use their imperfect knowledge to gradually develop problems, while students above the average level use the transfer of knowledge to try their best to sum up new knowledge and inspire students in the group to understand. In this way, the enthusiasm of students at different levels can be mobilized, and their ideas can be broadened to express and discuss different views from different angles.

For example, when discussing why the calculation formula of trapezoid area is (upper bottom+lower bottom) × height ÷2, most students can make a parallelogram with two identical trapeziums, but some students demonstrate a trapezoid by cutting, which cultivates their openness of thinking, grasps the learning method and knows why they should do this.

Another example is "trapezoid" teaching, and the following group learning questions can be designed:

(1) What is a trapezoid? Which of the following figures is trapezoidal? Which ones are not? Why?

(2) What is the bottom of the trapezoid? Point out the bottom of the upper trapezoid?

(3) What is a trapezoidal waist? Point out the upper trapezoidal waist?

(4) What is the height of the trapezoid? How many heights does a trapezoid have?

(5) In a ladder diagram sent in advance, mark its upper bottom, lower bottom and waist respectively, and make its height?

Some math problems are difficult. Solving them is like taking students to a higher level. In this kind of questions, eugenics is like a student with good jumping ability, who can jump in place; For middle school students, you can also take a few steps back and leap forward with the help of running power; What about students with learning difficulties? We used a group study called "Setting Steps and Lowering Slope". After group study, all students can master learning.

Communicate the results of the exploration between groups. Teachers will listen carefully or participate in discussions. It provides more opportunities for all students, especially those with learning difficulties, and transforms the achievements of individual independent thinking into the cognitive achievements of the whole group, thus cultivating group consciousness and activity ability. In the new curriculum teaching, we should pay attention to encouraging students to explore and discuss deeply on the basis of independent thinking, so that group members can express their opinions and teachers can guide them in time, so as to realize the multi-directional exchange of information between groups and let students try the fun of cooperative learning.

When teaching "cuboid and cube features", first show the physical model cuboid and cube bracket model, and let the students observe and discuss in groups to see which group of students find the most complete features and record them. At this time, the students are very enthusiastic. Through the discussion and cooperation within the group and the mutual communication between the groups, the characteristics of faces, edges and vertices can be quickly obtained. The learning effect is very good. Let students taste the happiness of successful cooperation.

5, exchange reports, in-depth induction.

The group sent representatives to report the discussion results to the whole class, and the teacher guided each group to put forward different ideas and encouraged divergent thinking. On the one hand, this kind of report creates opportunities for more students to "represent the collective" and carry out competition and cooperation; On the other hand, by transforming the cognitive achievements of the group into the cognitive achievements of the whole class, we can stimulate innovation and expand our thinking.

Group discussion fully mobilized the enthusiasm of all students. On this basis, representatives of each group are allowed to exchange and discuss their ideas and viewpoints, so that students can find out the regular things and methods to solve problems from concrete to general and from concrete to essence, and at the same time train them to discuss in standardized mathematical language and draw scientific conclusions.

After the students have a preliminary understanding of new knowledge and problem-solving methods through group discussion, each group sends representatives to speak, discuss and analyze the problems in the group, and sum up an idea. At first, the students' speeches were unclear and missed the point. At this time, teachers should guide them to master the method of analyzing problems step by step. They can start from the conditions and gradually find problems, or they can walk out of the problems and seek the conditions that the problems must know. At first, they all used this language in their own lives. Later, they gradually paid attention to the use of mathematical language and the accuracy of words, which improved students' ability of induction and generalization. Some students are not satisfied with what they have learned and oral discussion. Teachers can guide them to learn to write small papers and cultivate their thinking creativity. For example, a student is not satisfied with the method of "judging whether a number is divisible by 3" taught by the teacher in class, and writes a learning essay by using his usual calculation experience. After classroom demonstration, students' interest in learning mathematics is greatly enhanced. Received very good results.

Students can exchange the process, results and methods of solving problems in groups, analyze the causes of mistakes and exchange experience in solving problems, so that students can learn more from others' mistakes and solving problems. Let the students speak freely and summarize the opinions of the class. Teachers create an appropriate atmosphere for students to debate consciously and freely, which fully embodies the learning spirit of democracy, equality and independent innovation. At the same time, students are encouraged to use their own methods to verify the conclusion and cultivate the rigor of thinking and the attitude of seeking truth from facts.

Third, let the cooperative team evaluate the learning accurately.

Learning evaluation is an intensive way for both teachers and students to affirm or deny the learning process, results and attitudes, which has the function of encouragement and guidance. The main purpose of evaluation is to promote the development of students' subjectivity. The main task of experience evaluation is to enhance students' initiative development motivation and improve their initiative development ability. Group cooperative learning brings many opportunities for students' performance, and reasonable evaluation can fully affirm students' learning effect and further stimulate students' learning enthusiasm. Therefore, in classroom teaching, teachers should pay attention to the evaluation of students' subjective spirit and quality such as autonomy, initiative and originality in independent inquiry, cooperative discovery and practical application, so that students can gain emotional experience of actively exploring and acquiring knowledge and enhance their confidence and motivation in learning. At the same time, you can also use group self-assessment. Students review their knowledge and skills in groups and check their goals; Reflect on your own learning methods and problem-solving ideas, so as to improve the level of metacognitive ability such as self-monitoring and self-regulation in learning.

Sometimes students' encouragement and help are more effective than teachers'. For example, in order to promote students' self-study, sometimes several questions will be compiled for students to test, and then the group leader will grade each student according to the standard, and then evaluate according to the total score of the group. Students with good grades feel that they have not studied enough, while students with poor grades feel that they have affected their group's grades and are under pressure, which makes the pressure become a collective and individual motivation. After identification, the students with learning difficulties in the group will be urged and helped by their classmates every day, and their academic performance will be significantly improved. Therefore, carrying out learning evaluation activities in groups is conducive to enhancing students' sense of cooperation and improving their overall quality. Finally, don't ignore the importance of questioning and asking questions. At the end of the learning process, guide students to extend and popularize the math problems in this class, and extend the process of exploring and solving problems to extracurricular and subsequent learning.

Group cooperative learning mode is committed to meeting students' comprehensive social needs, changing inefficient learning mode, improving the relationship between teachers and students, giving full play to the collective role in learning, strengthening students' awareness of interaction with the environment, effectively promoting the development of students' psychological function and social communication ability, and cultivating students' ability to cooperate in research and explore practice. It is an indispensable and important means in the process of discussion teaching.