Reflection on the teaching of quadratic functions

Part 1: Reflection on the teaching of the quadratic function

We have learned the properties and images of positive and negative proportions, one-time functions, and after learning the quadratic equations, we now need to learn the images and properties of the quadratic functions, from the textbook and syllabus system. The quadratic function is the weight of the middle school mathematics. How do you let the students learn the secondary function? Master the image and nature of the quadratic function? Let the students understand what is a quadratic function and distinguish the binary function. Different from other functions, it can deeply understand the general form of the quadratic function and can initially understand the limitations of the domain in the actual problem.
To this end, our third-grade mathematics team invited Li Jinyou, the principal of Li, to the mathematics group. President Li said that if you want to teach the second function, you must let the students draw pictures, draw different situations, and draw students through drawing. Observe, understand, grasp the content of the learning, and can summarize the similarities and differences of each image. Through the guidance of President Li, when we study the image and nature of y=a2, we first let the students start to draw y= X2, y=2, and y=2. By contrast, it is observed that they are shifted to the left or right by y=x2 to get y=2 and y=2, but many students still don’t understand the graphics. 2 Why is it panning to the left? ? At this time, I thought that President Li said that I should not be afraid to spend time. I must let my classmates draw pictures. I asked my classmates to draw a group. Finally, the students were learning the image of the quadratic function y=a2 and the quadratic function y=ax2. When the relationship of images is solved, the leftward or rightward translation solves the problem of addition and subtraction, which solves the difficulty that students are confused here. It is very clear for students to combine images with x. If it is followed by x, it is left. Translate h units, otherwise it is to shift h units to the right, and secondly, when looking at how to translate, the key is to see the translation of the vertices, how the vertices translate and how the image is translated. First, the vertices are obtained from the analytic formula, and then the translation problem is observed.
Through the explanation of this lesson, I feel that if I want to teach mathematics well, I must let my classmates move. It can not only arouse students' interest, but also deepen the impression of the knowledge of the second function learned in the past, and adapt to the student's recent development zone. In the future, we should reflect on the shortcomings in our teaching in a timely manner, fully anticipate every detail of the class before each class, think about the corresponding measures, and constantly improve our teaching level.

Part 2: Reflection on the teaching of the quadratic function

In the teaching of the quadratic function, according to its position in the teaching of mathematics in the country, carefully prepare the teaching of the "secondary function". The teaching focus is on the image nature and application of the quadratic function. The difficulty of teaching is The relationship between a, b, c and the image of the quadratic function. According to the reflection of the preparation process and the effect of the lecture, the experience is quite deep, rewarding, and insufficient.
The teaching of this chapter is that I have a better understanding of the topic, and to reflect the teaching objectives, it must have practical significance. To reflect the students' "developed area" is conducive to student analysis. For example, in order to help students establish the concept of a quadratic function, starting from the study of the area of ​​the square that the students are very familiar with, the function of the analytic expression is summarized by establishing the analytical expression of the function, and the definition of the quadratic function is given. After the concept of the quadratic function is established, through the analysis and solution of the three examples, students can understand and construct the concept of the quadratic function. In the process of constructing the concept, let the student experience from the problem to the column quadratic function. Analytical process. Experience the use of functional ideas to describe and study the significance of the law of variation between variables.
Next, the teaching is mainly from the "parabola opening direction, symmetry axis, vertex coordinates, increase and decrease" step by step, from special to general learning the nature of the quadratic function, and help students to sum up the memory. In the learning process, the training method is used to generalize the vertices of the quadratic function, determine the parabolic symmetry axis, and increase or decrease the image analysis function. This part of the content is easy to confuse students in the lower middle, but also need to master the method, strengthen the memory, emphasizing the need to use graphics to analyze. Through teaching, students have a clear understanding of modeling ideas, graphic combination ideas and classification discussion ideas, and learned the initial method of analyzing problems.
The translation of the quadratic function in this chapter is a part of the more successful one. It mainly uses multimedia to dynamically display the translation process of the quadratic function, allowing students to summarize the rules themselves, which is very image and easy to remember.
The quadratic function contains three letter coefficients, so it is determined that the analytical expression requires three independent conditions, which are solved by the undetermined coefficient method. Learning to determine the general form of the quadratic function, that is, the form, in this respect, the student's learning situation is still ideal, but the method is no problem, the computing power needs to be strengthened.
After learning the knowledge of the quadratic function, we try to solve three practical problems. Question 1 is to establish a functional analytic formula based on actual problems and learn how to determine the domain of the function; the second problem is to analyze the properties of the quadratic function according to the analytic formula of the quadratic function, and make a visual image test. The analysis and judgment of whether or not; the third problem is to comprehensively apply the function of one function, the function of the quadratic function to determine the analytic and domain of the function, and try to solve the problem of the biggest profit in the sales problem; through the analysis of these three problems and Solve, let the students initially understand the use of the second function in real life, and once again realize that mathematics originates from life and serves life. Although some students are still not proficient in solving related application problems, they will be supplemented and improved in the following study.
However, in teaching, I think that there is not enough enthusiasm. I have not actively mobilized the language of students to learn enthusiasm, and the infection is not enough. In the future, when preparing lessons, we must pay attention to creating rich and interesting language to mobilize the enthusiasm of students.
In short, in mathematics teaching, not only should we be good at setting doubts, but also to connect theory with practice. Only in this way can we attract students' love of mathematics.

Part 3: Reflection on the teaching of the quadratic function

In this lesson, I first asked the students to think about the practical problems of the three functional relations. Then, based on the students' exploration of these three practical problems, I thought about and summarized the definition of the quadratic function and discussed the quadratic function. The judgment finally consolidates the definition of the quadratic function and the relationship between the variables that can be expressed by the quadratic function. Through the rich realistic background, this lesson enables students to feel the meaning of the quadratic function and feel the extensive connection and application value of mathematics. Through the student's inquiry activities, cooperation and communication with the students, through the analysis of practical problems, the concept of the quadratic function is introduced, so that students feel the close relationship between the secondary function and life. In the consolidation of the new knowledge, I The problems of different types of questions have been carefully designed, and the new knowledge of this section has been well consolidated, and the classroom has achieved a good teaching effect. Through this lesson, I also really realized that the teaching of each lesson can't be designed by experience alone. Be sure to make careful pre-sets before each class. In the classroom, at the same time, it is necessary to combine the actual effect of the classroom and the situation of the students to pay attention to the flexible processing of classroom generation. In the classroom teaching, the teaching time is preset in advance, and in each class, it is necessary to open and at the same time pay attention to recovering at the appropriate time to ensure the completion of the basic tasks of each session.

Part 4: Reflection on the teaching of the second function

This lesson is the first lesson of the quadratic function after learning the positive, inverse proportion, and one function, and knowing the quadratic equation. From the perspective of the textbook system, this lesson is obviously to let the students understand what It is a quadratic function that can distinguish the difference between a quadratic function and other functions. It can deeply understand the general form of a quadratic function and can initially understand the limitations of the domain in practical problems.
However, if you take this lesson from these knowledge points, it is actually very simple. Students can easily migrate and accept this knowledge based on the original knowledge reserve. So what better design is this lesson?
Rethinking the intent of writing the textbook, I found that most of the text in this part of the textbook is about three practical problems, which led to the second function. I realized that the focus of this lesson should actually be placed on "experiencing exploration and The process of representing a quadratic function relationship obtains the experience of expressing the relationship between variables using a quadratic function, thereby forming a definition. With this understanding, everything becomes simple!
The whole lesson's process can be summarized as follows: the simple practical problem that students are interested in – the one that has been learned – the form of all the functions that have been learned – asks: Is there a new form of function? - Exploring new problems - forming relationships - is it a function? - Is it a learned function? - Exploring a new form of function - summarizing the characteristics of the new form of the form - formulating the characteristics - forming a quadratic function definition - having exercises to consolidate the definition of features - returning to the actual question to discuss the actual problem with the argument Restrictions - Asking new questions, in-depth discussions - the summary of the class, so that the design is in one go, there is no slap in the face, the most important thing is that I think this is in line with the students' basic cognitive rules, which is easy for students to understand and accept. .
For the choice of practical problems, I will integrate the four questions into the same practical background. This design can not only attract students' interest, but also minimize the time for students to examine the questions. It is very hierarchical. These practical problems are throughout the classroom. To make the whole classroom feel like a natural one.
For the design of the exercise, the principle of non-repetition is still adopted. Try to solve each problem for each question, and make a timely summary, and follow the principle of opening to closing, and achieve good results.
For the design and presentation of the last discussion, I found out after the preparation of the entire chapter of the unit, we actually do not talk about the maximum value of the quadratic function, but not speaking does not mean that it will not involve The idea method used in it is still very important, and it also has an important position in the observation of the image. In addition, this problem is echoed after the previous practical questions are answered: a variety of trees - Want to increase production - how many kinds of good? So I designed this exploratory question: If you are the owner of an orchard, how many trees do you prepare? Note that I have not raised the issue of maximum and minimum here, but all students can understand that this is the charm of mathematics. This question is raised as a climax and essence of the whole lesson. After the students learn the definition of the quadratic function, they use the basic knowledge of the function, the algebraic knowledge and the knowledge of the quadratic equation, so they Ideas and arguments, whether right or wrong, comprehensive or biased, involve important methods of mathematical thinking, and these are very important. It turns out that students' thinking is really very active. You want to give you enough space. They can always think and explain from all sides.

Part V: Reflection on the teaching of the second function

After class, I reviewed the requirements for the quadratic function in the mathematics curriculum standards:
1. Determine the expression of the quadratic function by analyzing the actual problem situation and understand the meaning of the quadratic function.
2. The image of the quadratic function is drawn by the point method, and the nature of the quadratic function can be recognized from the image.
3. The vertices, opening directions and symmetry axes of the image are determined according to the formula, and simple practical problems can be solved.
4. The approximate solution of a quadratic equation is obtained by using the image of the quadratic function.
The discovery does not mention the use of vertex to find the analytical expression of the quadratic function, and in the following lessons, there is no requirement to use the vertex to find the analytical expression of the quadratic function. However, I believe that the requirements set out in the new curriculum standard should be the minimum requirements for students. It does not object to the teacher's actual reprocessing of the textbooks in combination with the students. And from the feedback of teaching, plus the three practice students can better understand the teaching objectives of this lesson, but also can deepen the impression of the knowledge of the vertices of the second function learned earlier. Adapt to the student's recent development area. Why not do it.