First, contact with real life, create a situation of teaching problems
"All the learning of mathematics knowledge is aimed at starting from the reality of students, introducing learning topics with questions they are familiar with or interested in, and launching mathematical inquiry." (Excerpted from the editor of the new textbook). According to this guiding ideology, in the actual teaching process, we should make full use of the rich practical situations created in the new textbooks, and stimulate students' perceptual interest in the practice, exploration and cooperation of new knowledge through concrete and real data, pictures and life examples around students, so as to stimulate students' potential to actively acquire knowledge through these rich and vivid materials. For example, when teaching "divisor and effective number", by setting a situation similar to real life, we can open the boundary between the book world and the life world, entertain and entertain, write a paragraph to describe a story or event close to real life, and include the problems to be solved by this story or event. This story or event actually sets a situation for students to solve math problems around them, which makes the relationship between study and life closer.
(1) The following is a conversation in the museum. Manager: Miss, this fossil is 800,002 years old. Visitor: How do you know so clearly? Librarian: Two years ago, an archaeologist came here. He said this fossil is 800,000 years old. Now two years have passed, so it is 800002 years old. Is the administrator's inference correct? Why? (2) Both Xiao Ming and Xiao Bin are about 1.6 meters tall, but Xiao Ming said: I am 9 centimeters taller than Xiao Cong. May I ask? (3) The workshop accepts the task of processing two shafts, and the workshop director gives it to Xiao Fang to complete. Xiao Fang looked at the drawings and found that the length of the shaft was 2.60 meters. It took him three days to finish the task, but he can give the shaft to the director for acceptance. The director was very unhappy and said with a straight face, "The length is unqualified and can only be scrapped!" Xiaofang didn't believe me, and together with the director, he measured the length of the two shafts. There is no doubt that one shaft is 2.56 meters long and the other shaft is 2.62 meters long. Xiao Fang said that these two lengths should be qualified. Please tell me if Xiao Fang is wrong. Through the above three practical problems in life, students' strong interest in learning is stimulated, and at the same time, students have a preliminary understanding of the concept and application of divisor. For another example, when teaching "rational number addition", I created the following situations: The following is the situation of the winning football team playing football. Can you imagine all possible situations from the perspective of winning or losing with the knowledge you have learned and life experience? The winning football team scored 2 goals in the first game and 3 goals in the second game. The team scored two goals in two games. On the basis of positive and negative numbers, students get that they will win one ball or five balls, lose one ball or five balls. We got: (+2)+(+3) =+5, (-2)+(+3) =+ 1, (+2)+(-3) =- 1, (-2)+(-3) =-5. By guiding the students to get other information: the team will not lose or win: "The first game won 2 goals, and the second game lost 2 goals," (+2)+(-2)=0. Students actively use their brains to imagine all possible situations of winning or losing the team, and list the corresponding addition formulas, which paves the way for learning the addition law of rational numbers. On the basis of students' understanding of quantities with opposite meanings in life and their ability to express quantities with opposite meanings with positive and negative numbers, this example understands the law of addition and subtraction of rational numbers from specific examples. Because we start with familiar examples in life, we have a good feeling about numbers and can easily understand the law of rational number addition.
Second, change the teaching methods and guide students to become the main body.
Facing the new curriculum, teachers should first change their roles and confirm their new teaching identity. Dole, an American curriculum scientist, believes that in modern curriculum, teachers are "the chief among equals". As "the best among equals", teachers should be the organizers, guides and participants of students' learning activities. Let students truly become the main body of the classroom. (1) Teachers should be the organizers of students' learning. As the organizer of students' learning, a very important task of teachers is to provide students with space and time for cooperation and exchange, which is the most important learning resource. In teaching, individual learning, deskmate communication, group cooperation, inter-group communication and class communication are all common forms of classroom teaching organization in the new curriculum. These organizational forms create time for students to cooperate and communicate, and teachers must also provide enough time for students to study independently. (2) Teachers should be the guides of students' learning. When a student gets lost, the teacher does not tell him the direction easily, but guides him to identify the direction; When students are afraid of climbing mountains, the teacher does not drag them to climb together, but lights up his inner spiritual strength and encourages him to keep climbing. For example, when teaching "Comparison of Line Length", my initial design was to ask students how to compare their heights at ordinary times, and invited two students to demonstrate. Then let students compare the lengths of two pens by imitating the height comparison method, so as to guide students to find a way to compare the lengths of two line segments. In this way, students can easily understand the problem. When learning the comparison of angles, students no longer need my guidance, and find the comparison method of angles from the comparison of line segments. (3) Teachers should be participants in students' learning. Teachers participate in students' learning activities in the following ways: observing, listening and communicating. The teacher observes the students' learning status and listens to their voices. The communication between teachers and students is not only cognitive communication, but also emotional communication, which can be realized through language, expression and action. For example, when teaching "three-dimensional graphics", I asked the students to make the expansion diagram of polyhedron in groups. When students do it, I observe the production process of each group and participate in their production process. In the communication with them, I learned their ideas when making. Individual problems are solved individually. When talking about how to judge the expansion diagram of a cube, I first listen to the students' methods, and then let several representative students with good thinking methods explain. In this way, we have also learned a lot of knowledge in teaching and shortened the distance between students and teachers. Students regard me as a study partner and are willing to discuss and communicate with me.
Third, give play to group cooperation and stimulate students to participate.
A very important role of cooperative learning is to turn two-way communication between teachers and students into multi-directional communication between teachers and students. This teaching mode reduces the one-way information exchange mode told by teachers, and increases the two-way and multi-way information exchange mode of students' autonomous cooperative learning, so that students can learn to check themselves in the process of mutual inspection, learn to evaluate themselves in the process of mutual evaluation, learn to cooperate and respect others in the horizontal information exchange, and cultivate and exercise their autonomy in the organization process of participating in classroom teaching. For example, in the teaching of "letters represent numbers", I ask students to bring a match stick for the group at the front and back tables in advance, and then ask them to solve the problems by themselves in groups. How many matchsticks does it take to build two squares and how many matchsticks does it take to build three squares? Take 10? Take 100? How many people does it take to build X? Students complete with questions, and the purpose is clear. After two people's discussion, the whole class found five different methods. Facing their achievements, they smiled happily. When students are eager for new knowledge. Students' cognitive needs often come from seemingly similar, but unclear, new knowledge and skills that students can't understand immediately, or practical problems that can't be solved immediately. For example, when teaching inequality, an interesting question was raised: "One day a group of monkeys stole peaches together. When splitting peaches, if each monkey gets 3 points, there are 59 points left; If each monkey is divided into five parts, you can get peaches, but the remaining monkeys get less than five peaches. Can you find out how many monkeys and peaches there are? " Faced with problems, students are curious. Under the influence of this mentality, students often have doubts about their own ideas, hoping to be verified by others' ideas or their own evaluations, and even more hoping to be inspired by others' speeches. So it's best to organize the discussion properly at this time. It is worth emphasizing that many classrooms are the stage for "top students" to show their elegance, ignoring the participation of all students. Even in group communication, there are few opportunities for "poor students" to show and participate. Therefore, when designing cooperative teaching, teachers should consider the actual situation of each group of students and put forward clear questions so that every student, especially the "poor students", can participate, discuss and perform. In the process of discussion, teachers should go deep into the group to understand the effect of cooperation and the discussion. Different students often find different conclusions in the discussion. The communication between classmates solved this difference well. Students can freely express their opinions and problem-solving strategies in group communication, listen to their peers' opinions, inspire each other, learn from each other's strengths and make progress together. In this process, students can be promoted to communicate knowledge and give full play to their divergent thinking ability.
Fourth, strengthen emotional communication and realize the common development of teachers and students.
In traditional teaching, teachers are responsible for teaching and students are responsible for learning, and teaching is a one-way "training" activity for teachers and students. The new curriculum emphasizes that teaching is the communication and interaction between teaching and learning, and both teachers and students communicate with each other. In this process, teachers and students share their thoughts, experiences and knowledge, and exchange their feelings, thus realizing the common development of teaching and learning. In teaching, I pay attention to respecting and caring for students and make teaching democratic and emotional. I tell students through classics: "The classroom is yours, the math class is yours, the learning tools such as the triangle and protractor are yours, and the task of this class is yours. Teachers and classmates are all your assistants. If you want to learn better knowledge, you must rely on yourself. " When students answer questions correctly, I often use "What you said is very reasonable and the analysis is well-founded". "Can you tell me your reasons?" "Do you think what he said is good?" These statements praised them; When students answer a little trouble, it is not criticism, but starting from protecting students' enthusiasm, asking other students to help correct it and saying, "How to modify the example of XX students?" Under such emotional communication, students think that learning mathematics is a happy thing. Curriculum reform has brought us new teaching ideas. The function of teachers is no longer just to convey, discipline and educate, but more to encourage, help and advise. The relationship between teachers and students is no longer linked by knowledge transmission, but by emotional communication.