We have studied the positive and negative proportions, the properties and images of the linear function, and now we have to learn the images and properties of the quadratic function after learning the quadratic equation of one variable. From the perspective of teaching materials and syllabus system, quadratic function is the most important thing in junior high school mathematics. How to make students learn quadratic function well. Master the image and nature of quadratic function? Let students know what quadratic function is, which can be distinguished from other functions, deeply understand the general form of quadratic function, and initially understand the restrictions on the definition domain in practical problems.
To this end, our third-grade math group invited Li Jinyou and President Li to the math group. President Li said that if we want to teach quadratic function well, we should let students draw pictures in different situations at the beginning, and let them observe, understand and master what they have learned through drawing, and sum up the similarities and differences of each image. Under the guidance of President Li, when we study the image and properties of y=a(x-h)2, first let the students draw y=x2, y=(x-2)2 and y=(x+2)2. By comparison, they get y=(x-2)2 and y=(x+2)2 by translating y=x2 to the left or right, but many students still don't understand why the figure plus 2 is translated to the left. Finally, when studying the relationship between the image of quadratic function y=a(x-h)2 and the image of quadratic function y=ax2, students solved the problem of addition and subtraction caused by translation to the left or right, and solved the difficulty that students are easily confused here, so that students can clearly see that if H is added after X, it will be translated to the left by H units, and vice versa. Secondly, when looking at how to translate, the key is to look at the translation of vertices and images. First, get the vertex membership from the analytical formula, and then look at the translation problem.
Through the explanation of this lesson, I think that if we want to teach mathematics well, we should make students move, which can not only arouse students' interest, but also deepen their impression of the knowledge of quadratic function learned earlier and adapt to the recent development area of students. In the future, we should reflect on the shortcomings in our teaching in time, fully anticipate every detail of the classroom before each class, think about corresponding measures, and constantly improve our teaching level.
The second experience of function teaching;
Entering the third grade, not only students are nervous because all subjects are main courses, but also teachers in all subjects are nervously grabbing their own subject study time.
This chapter is one of the important contents of junior high school algebra. The finale of Henan is indispensable. It can be linked with some difficult knowledge in junior high school, such as quadratic equation, linear function, inverse proportional function, similar triangles and so on. Moreover, the application problems involved require high calculation requirements in the process of solving. Therefore, learning this chapter well can improve students' ability to solve problems by combining numbers and shapes, and also lay a good foundation for future comprehensive problems.
The formation of students' mathematical thinking is not a day's work, and teachers need to infiltrate it in their usual teaching. In the first class of quadratic function, I compared the learning methods of linear function that students are familiar with, so that students can not only review what they have learned, but also have a macro understanding of new knowledge.
When learning the nature of functions, I put special emphasis on drawing, requiring every student to draw images correctly and accurately. On this basis, each category emphasizes four properties of parabola: opening direction, vertex coordinates, symmetry axis and increase and decrease. And tell students that the quadratic function contains a lot of contents, but it can be summarized into three knowledge points: 1. The image is a parabola; 2. Opening direction, vertex coordinates, symmetry axis and maximum value (the maximum value is the ordinate of the vertex); 3. Increase or decrease, discuss up and down after separation. And these three points can be seen from the function image, so I repeatedly stressed that the key to learning the properties of quadratic functions is drawing, and the process of analyzing the properties of functions by using images is the combination of numbers and shapes.
When learning the application of quadratic function, I also ask students to draw a sketch when solving problems, and analyze the pictures to get the maximum value, instead of memorizing the properties to do the problems. Let students realize the simplicity and importance of studying mathematical problems by combining numbers with shapes.
In the teaching of solving quadratic decomposition function, another important and difficult point in this chapter, I summarized some skills for students to solve analytical formulas by undetermined coefficient method. For the three commonly used analytical formulas: general formula, vertex and intersection, no matter which form, it involves the determination of three constants, that is, it takes three conditions to find, and the analytical formula of the function is set according to the known conditions: the general formula is used when the known image passes through any three points; The image vertex coordinates are known, and the vertex type is applied; Given the intersection of the image and the x axis, it is simpler to use the two-point formula. At the same time, we can also choose the appropriate form according to the position of the image: if the coordinates of the intersection point between the image and the Y axis are known, the general formula is set, and the process is simple; It is known that the image is symmetrical about Y axis, and it is easy to calculate by setting vertices or intersections.
The third experience of function teaching;
Function teaching is the key and difficult point of junior high school mathematics. How to improve the understanding of the integrity and coherence of function teaching? I think we must grasp it from the following aspects.
First, fully understand the concept. (1) has two variables during a certain change. (cannot be 1, 3,4 & hellip variable). (2) One of the variables takes a value within a certain range (pay attention to the range of independent variables). (3) Another variable always has a unique value corresponding to it (the corresponding value cannot be 2, 3, 4&; hellipa)。 In order to understand the concept of function, the textbook gives positive examples, and we can give some counterexamples to better explain it. The relationship between (1) rectangular area s and length x and width Y = XY has several variables. (2) In the relationship between distance s and time t in uniform motion, can't t t t t be negative? (3) Is the value of y negative for every value of x in the graph?
Second, make full use of the thinking method of combining numbers and shapes. Every time you talk about a function, students are required to have its image in their minds, so as to think of its nature.
Third, pay attention to comparative study, and deepen memory through comparison. When you talk about a function, compare the resolution function with the image in time to find out their similarities and differences. Similarly, when talking about inverse proportional function and quadratic function, we should also compare several functions we have learned before.
Fourth, pay attention to the relationship between univariate function and binary linear equation, univariate linear inequality, quadratic function and univariate quadratic equation. Students are required to solve equations (or inequalities) by image method and find the intersection of function images and coordinate axes by equations (groups).
Fifth, pay attention to the organic combination of function and real life. For example, many images of linear functions in life are not straight lines, but line segments or rays, and many images of inverse ratio and quadratic functions in life are only one branch or part of them.
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