Reflections on the Primary Function Teaching of Grade Eight Mathematics (1)
? Function and image? This chapter focuses on the concept, images and properties of linear functions. On the one hand, when students are new to the related content of a function, they must learn with specific functions. Therefore, the main content of the whole chapter focuses on the description of specific functions. On the other hand, among several specific functions specified in the syllabus, linear function is the most basic, and the discussion of linear function in the textbook is also comprehensive. Through the study of a function, students have a preliminary understanding of the research methods of the function, so as to better master the learning methods of learning quadratic functions and inverse proportional functions. After teaching, I have a deeper understanding of the new textbook.
Prepare lessons carefully
The process of preparing lessons is a hard and complicated mental labor process. With the development of knowledge, the change of educational objects and the improvement of teaching efficiency, preparing lessons as an artistic creation and re-creation is endless, and the design and selection of an optimal teaching scheme is often difficult to satisfy people completely.
One: The textbook schedule is too tight. There is not enough teaching time for textbooks in senior two. There are two classes in the first section, the second section and the third section of the function, and the class hours are too few. This section should be supplemented with a review class.
Second, the teaching content is not easy to handle.
? What are the properties of linear functions? B has no effect on the image of the function, but there is one problem that needs to be supplemented.
Link 2: Summarize the properties of linear function images.
The linear function y=kx+b has the following properties:
(1) When k >: 0 and y _ _ _ _ increases with X, then the image of the function goes from left to right _ _ _ _ _;
(2) When k < 0 and y _ _ _ _ _ increases with X, then the image of the function goes from left to right _ _ _.
(3) when b>0, when the intersection of the function image and the y axis is:
(4) When b>0, when the intersection of the function image and the y axis is:
How to introduce undetermined coefficient method? The length of the spring y (cm)? It's too difficult to tell. Do you want to talk about it in the book first? Do: The image passing point (-1, 1) and point (1, -5) of the linear function y=kx+b are known.
Third, the difficulty is not easy to deal with:
For example, when we are talking about the definition of function (the first category), we add an example: When the function y= is known, when the value of m is taken, is y a linear function of X? When m takes what value, y is a proportional function of x?
It is difficult for students to understand. Personally, I think it is too difficult, which is beyond the students' understanding ability. On the contrary, in a specific linear function y=-2x+3, there is not much emphasis on the number of k and b.
The pen of satisfaction
The linear function satisfies the following conditions:
First, combined with life examples, fully mobilize students' enthusiasm for learning, make appropriate transition, and ignite the desire for knowledge.
In the introduction part of this class, use the real person in the class (using the concrete example of the school sports meeting)? How much money is involved in this operation? Assuming that every player is moving in a straight line at a uniform speed, what is the relationship between speed, time and distance? Transitional questions such as distance is a function of time not only review the knowledge of last class, but also pave the way for the concept of function image.
2. Boldly adjust and modify the teaching materials.
Complete the integrity of knowledge content.
(Image knowledge point of linear function: geometric shape of linear function: a straight line; Drawing method of linear function image; The coordinates of the intersection between the linear function image and the coordinate axis. ) The textbook is correct? Drawing function images? The explanation is incomplete and not detailed. Learning the image of function needs to cultivate students' idea of combining numbers with shapes. The image of primary function is the simplest of all function images, and it is also the basis for learning other complex functions in the future. Therefore, studying the image of elementary function in an all-round way can provide students with a sample of ideas and save their later study time. Although in the exercises and exercise books after class, how to draw the image of the function when the independent variables of the function are limited in a certain range is involved, it seems that such problems are not involved in the teaching materials. For the students in Class B, this kind of problem needs the teacher to demonstrate and solve. (1) Find the functional relationship of y 1 about the range of x and the independent variable x; (2) Draw the image of the above function. Is the image still straight? This topic is called expanding knowledge points: when the independent variables of a linear function are limited in a certain range, the image of a linear function is specially designed as a ray or a line segment. As for how to draw a ray or line segment quickly, let the students discuss and summarize: for a ray, draw a ray at any point different from the starting point and another point; For a line segment, take two endpoints of the line segment and connect them.
disadvantage?
First, the time is not accurate. Because I have broadened the scope and depth of knowledge points on the basis of the original textbook, individual links need group activities or individual students to operate on stage. I want to finish all this in one class, which seems to overestimate my ability and that of students. So I think so much content can be taught in two classes.
Second, there are some mistakes in the content processing: when I first explored the drawing method of function y=x, I directly forced to take five points first: (-2, -2), (-1,-1), (0,0), (1, 65438+.
In the future teaching work, I will make persistent efforts to better reflect the effectiveness of mathematics classroom teaching.
Reflections on the teaching of linear function in eighth grade mathematics (part two)
After learning the concept of proportional function, students are more confident to learn the concept of function at one time.
According to the arrangement of teaching materials, the teaching plan leads to an analytic function process from practical problems through design experience to realize the connection between mathematics and real life; By thinking about problems and constantly refining teaching materials, we can achieve the goal of paving the way step by step.
1. Understand the concepts of linear function and proportional function; Learn functions once by analogy, and realize the diversity of mathematical research methods.
2. List the expressions of simple linear functions according to practical problems. Finding out the variables in the problem and expressing them in letters is the first step to explore the relationship between functions.
3. This lesson focuses on using relational expressions of functions to express practical problems. Through guiding analysis, I feel that students have gained a lot.
In addition, the relationship between functions is difficult for students to write, and this course can be continuously improved and perfected.
Reflections on the teaching of the first function of mathematics in the eighth grade (3)
The analytical function is usually solved by undetermined system method. For students, how to understand this method is the key to solve this problem.
In order to solve this problem, let me give an example: Given the point (1, 2) and the point (-2, 3) where the straight line y=kx+b passes, try to find this functional relationship. It is easy for students to think of solving this problem with equations, but I put forward a relatively simple problem. Why choose equations to solve this problem? What's your purpose? The students in the class I taught were silent for a long time. Yes, for students, they are used to how to do problems, but they have never thought about why they should adopt this method. What is the starting point of this method? After a period of thinking, some students finally answered this question: they said that this is to determine the values of K and B. As long as the values of K and B are determined, the resolution function will be determined once. In fact, what they answered is precisely the essence of the undetermined coefficient method. Only when students understand this point can they understand the essence of the undetermined coefficient method. Furthermore, I come to the conclusion that if we know a point on the function image once, we can determine its analytical formula. The above example is two obvious points.
Then I'll give another example: We know that the image crossing point (1, -2) of a linear function intersects with the straight line y=3x+2 at the same point, and try to find the analytical formula of the function. One point of this problem is obvious, and the other point is implicit. Students began to find a bright line and another dark line through analysis. Finally, everyone agreed that two points determine a straight line. To find the analytical expression of the function, only the coordinates of two points are required.