1, the position and function of teaching materials

Quadratic function is learned on the basis that students systematically learn the concept of function and basically master the properties of function. The images and properties of quadratic function have been given in junior middle school, and students have basically mastered the images and properties of quadratic function, but the methods of learning function are all carried out according to the method of analytic function-domain-image-property. Based on this situation, I think the role of this class is to let students. It can further deepen students' understanding of the concept and properties of functions, enable students to acquire more systematic knowledge of functions and methods of studying functions, and study the properties and images of functions at a new height. Therefore, the content of this lesson is very important.

2. Emphasis and difficulty of teaching.

Teaching emphasis: make students master the concept, nature and image of quadratic function; The method of inferring images from the properties of functions.

Teaching difficulty: master the method of inferring images from function properties.

Second, the target analysis

According to the three-dimensional goal pointed out in the new curriculum standard and the actual situation of the students in the teaching class, I have determined the teaching goal of this class as follows:

1, knowledge and skills: master the properties and images of quadratic functions, and with the help of specific quadratic functions, understand and master the method of inferring images from the properties of functions.

2. Process and method: Through the guidance and teaching of teachers, students can master the method of understanding and studying functions from the perspective of decomposition functions and properties in an atmosphere of group cooperation and active exploration.

3. Emotion, attitude and values: let students feel the beauty and importance of mathematical thinking methods; Cultivate students' awareness of active learning, cooperation and communication.

Third, the analysis of teaching rules

Follow the "teaching law of the unity of teachers' leading role and students' dominant position", highlight the role of teachers as designers, organizers, guides and collaborators, and implement the whole teaching process with problems as the carrier through teachers' analysis and understanding of teaching materials. As for students, through a series of activities such as independent exploration, cooperation and exchange, and inductive methods, they can feel the formation process of knowledge, expand and improve their cognitive structure, and then reflect the dual roles of teachers and students in the teaching process.

Fourthly, the analysis of teaching process.

According to the concept of new curriculum standards, I divide the whole teaching process into six stages, namely, creating situations and asking questions.

Teacher-student interaction and exploration of new knowledge

Independent investigation and merger method

Strengthen training and deepen understanding

Summarize, expand and deepen.

Arrange homework and improve sublimation

Link 1 At the beginning of this class, I asked students to directly summarize the properties and image shapes of quadratic functions. Is it necessary for students to repeat after answering? Editorial error? Or is there another intention? Ask questions to stimulate students' thirst for knowledge. When students are confused, they will immediately go to link 2: try to make a quadratic function.

Image of. The purpose is to fully expose the mistakes or deviations caused by students' inability to combine the properties of functions well in drawing, and highlight the importance of this lesson. On the basis of students' summary and communication, teachers point out students' mistakes by asking questions, and put forward the goal of this lesson: how to use the study of function properties to infer more accurate function images, and then guide students into the stage of teacher-student interaction and exploration of new knowledge.

At this stage, I quoted the example 1 given in the textbook and asked the students to try to finish it in the study group and make a concluding speech. The purpose is to let students fully participate in cooperative inquiry, so that students can break through the goal or expose the analysis obstacles to the maximum extent in the process of trying to learn, that is, they can't grasp the influence of the nature of the function on the image well, and can't integrate the abstract nature with the intuitive image, so that teachers can accurately grasp the difficulties and break them one by one in the process of interacting with students, and finally form the transfer of knowledge. After the students discuss, the teacher chooses group representatives to make concluding remarks, and other groups make supplements. Teachers gradually guide the analysis of the nature of functions. Among them, students may have difficulties in determining the symmetry axis, analyzing and expounding monotonous interval and monotonicity. At this time, teachers can use the analysis of analytical expressions combined with multimedia demonstrations to guide students to get analytical ideas and solutions, and improve the nature of functions in the process of teacher-student interaction. Then enter the link 3: let students infer the image of quadratic function by using the properties of quadratic function again, and strengthen the key to infer the image by using the properties of quadratic function. Then break through the teaching difficulties. Let students truly realize the transfer of knowledge, complete the whole inquiry process and form a relatively complete new cognitive system. Of course, in this process, some students may ask questions such as why the image is a curve instead of a straight line. In order to eliminate students' doubts, enter the fourth link: teachers should briefly explain that this is an important property to be considered in learning functions, and it is the concavity and convexity of functions. It will be introduced to you later, and students can look at the textbook number 165438. This will also leave room for students to think and explore, cultivate students' ability of extracurricular reading and independent research, and improve students' enthusiasm for learning mathematics.

After the completion of the above links, enter the fifth link: let the students sort out, abstract and summarize the research process of inferring the function image through analytical analysis, and get the specific operation process of the research function, so as to sublimate the problem, broaden the students' thinking, internalize new knowledge into their own cognitive structure, and finally find a solution to the problem.

The ultimate goal of teaching should be the internalization and development of each student, so as to guide students to enter the stage of independent exploration and consolidation of methods. Example 2 Changing the opening direction of quadratic function in the topic setting aims at deepening students' understanding of knowledge and perfecting the knowledge structure, and on the other hand, making students change from simple imitation and acceptance to active knowledge, thus further improving their ability of analysis, analogy and synthesis. On the basis of the example 1, students clearly learn the function properties, and then infer more accurate function images, so that new knowledge can be effectively consolidated.

Through the first three stages of study, students should basically master the relevant knowledge of this lesson. However, the influence of coefficients A, B and C in quadratic function needs to be improved. So I adapted Example 3 in the textbook to guide students into the stage of intensive training and deepening understanding. On the one hand, it can solve students' doubts about parity, on the other hand, it can also raise students' understanding of quadratic function to a new height.

The fifth stage: summary, expansion and deepening. In order to let students understand quadratic function from a higher angle and master the general research methods of function, teachers guide students to summarize from two aspects. The teacher should guide and expand your understanding of the relationship between function images and properties, and make it clear that the method you learn today is actually a general method to learn function images. For some unfamiliar or complex functions, we can infer the function image with the help of appropriate methods, so that students' cognitive level can be fixed at a new height to understand and understand the function problem.

The last stage is to arrange homework and improve sublimation. Jobs are set in different levels. Consolidate the questions, let the students review the problem-solving ideas and use them accurately, so as to draw inferences. The inquiry questions are adapted from the examples in the textbook, so that students with spare capacity can explore independently and improve their ability to analyze and solve problems.

The above six stages are interlocking at different levels, which fully embodies the communication and interaction between teachers and students. Under the general control of teachers, students have personally experienced the formation and development of knowledge through hands-on operation, eye observation and brain thinking, and have been able to migrate and internalize. The final inquiry assignment will stimulate students' interest and guide them to further think and study quadratic function, so as to reach the extension of knowledge outside the classroom. In short, this lesson is designed with the idea of "teaching people to fish" rather than "teaching people to fish".