In junior high school mathematics, quadratic function occupies a large proportion. Quadratic function is both difficult and important for students. The difficulty in teaching is that students don't understand many concepts of quadratic function, and various problems in solving problems will also affect students' learning enthusiasm. In view of these problems in teaching, this paper systematically annotates the definition of quadratic function, and discusses the teaching methods that are more suitable for junior middle school students in the teaching process.
Junior high school mathematics; Quadratic function; Teaching strategy
Junior high school mathematics occupies a large proportion in the senior high school entrance examination, and it is also a very important basic subject in students' learning process. In daily life, the application of mathematics will also bring many benefits. The study of quadratic function can not only enhance students' sensitivity to numbers, but also enhance students' logical thinking, improve students' learning attitude and methods, thus improving their academic performance. Therefore, we should seriously improve the teaching method of quadratic function.
Concepts of linear and quadratic functions
The concept of quadratic function is a "formal" concept. In teaching, teachers can't give the concept directly, but should focus on explaining the formation process of the concept of quadratic function. So I used several problem situations to introduce students into the concept step by step.
Situation 1: When a stone is thrown into the water, the ripples keep expanding outward. What is the relationship between the expanded circle area y and the radius x?
Case 2: Use the 16m fence to form a rectangular biological park for raising rabbits. (1) If the rectangle is y meters long and x meters wide, what is the relationship between y and x? (2) If the rectangle has an area of Y square meters and a width of X meters, what is the relationship between Y and X?
Scene 3: The athlete runs 5 kilometers. A walks x kilometers per hour, B walks more than A 1 kilometer, and A spends y hours more than B at the end of the game. What is the relationship between Y and X?
Case 4: Floor a square room with a side length of x meters. It is known that the price of a floor is 240 yuan per square meter and the price of the skirting line is 30 yuan per meter. If other expenses are 1000 yuan and the door is 0.8 meters wide, what is the total cost y?
The above problem situations are all about the centralization of functions, especially the last two questions are to find two variables from practical problems and determine the resolution function, so as to prepare for the formation of the concept of quadratic function. Therefore, in the teaching of quadratic function, teachers should explain the basic concept of quadratic function to students in detail, so that students can have a deeper understanding of the concept of quadratic function.
Discussion on Quadratic Function and Quadratic Function Teaching Activities
(A) the diversification of classroom teaching
In actual teaching, a single classroom will make students' learning activities show fatigue, while diversified classroom teaching will enhance students' interest in learning, and at the same time strengthen students' mastery of knowledge points, especially the teaching activities of quadratic function, which originally require students to have great interest, constantly raise doubts in their hearts, and verify and divergent thinking under the guidance of teachers. Therefore, teachers should constantly improve in practical teaching. For example, when learning the general formula and other deformed forms of quadratic function, we can teach the similarities and differences between vertex y=a(x+m)2+n and general formula Y = MX2+NX+C. Besides the external differences, there are also great differences in solving problems. We can deduce the same deformation in two forms to help students better.
(B) the combination of numbers and shapes, looking for the law of the function in the image
Compared with ordinary function, the image change of quadratic function is more complicated. Taking vertex function as an example, the change of different parameters will have a great influence on the image of quadratic function. With the increasingly heavy teaching activities, it is difficult for junior high school math teachers to have time and energy to lead students to draw images of quadratic functions. This makes it difficult for students to study quadratic function seriously and understand the corresponding relationship between quadratic function and its coordinates. Therefore, it is very useful to draw the image of quadratic function in junior high school mathematics teaching. At the same time, due to the limited class hours, in order to ensure the teaching quality, teachers should use drawing paper to guide students to draw images, fully ensure the teaching quality, and ensure that students can skillfully draw the corresponding quadratic function images. For example, in teaching activities, teachers can focus on y=3x2, y=3x2+5 and y=3x2-5. Guide the students to observe the position change between the three images and think about the reasons for the change. Then, guide the students to draw the images of y=-x2, y=-(x-5)2 and y=-(x+5)2, and then let the students observe the changes of the images and find out the rules. Finally, guide students to sum up the laws found, and let them combine numbers and shapes to enhance their ability in this respect.
(C) to stimulate students' interest and improve learning efficiency
Compared with other subjects, the study of mathematics, especially the study of quadratic function, is very boring and abstract. Even when drawing an image, a lot of calculations are needed. These mechanical studies make students not interested in learning mathematics and quadratic functions. In order to improve students' interest in learning, teachers should take the initiative to carry out interesting teaching, such as using the increasingly popular network system and multimedia equipment for teaching. Interesting teaching through videos and pictures. For example, FLASH animation technology is used to show the image changes of different parameters, so that students can be more proficient in the inner meaning of quadratic function. These activities will greatly enhance students' interest in quadratic functions. If teachers find that students are tired of learning in teaching activities, they should relax the requirements for students according to their actual situation in order to improve students' weariness. Avoid further discouraging students from learning mathematics. In junior high school, students are in adolescence. According to the characteristics of students in this period, students' enthusiasm for learning mathematics should not be affected by the study of quadratic function. We should fully guide students to learn, pay attention to their psychological changes, and enhance their enthusiasm for learning mathematics.
Third, summary.
Because quadratic function plays an important role in junior middle school mathematics teaching, teachers should pay full attention to strengthening students' understanding of quadratic function in teaching activities. In order to ensure the quality of teaching, teachers should think carefully about teaching activities according to the actual situation of students and the characteristics of quadratic function, and carry out teaching activities in a targeted manner. Through the combination of numbers and shapes, students can deepen their understanding of quadratic function images. Reduce students' weariness of learning due to poor learning, fully protect students' thirst for knowledge, and at the same time strengthen teaching for the parts that students are difficult to understand and easy to confuse, effectively improve teaching quality and help students learn happily and effectively in the process of junior high school learning.
refer to
[1] Wang. Research on the Teaching Strategy of "Quadratic Function" in Junior Middle School Mathematics [J]. Academic Weekly, 20 14 (22): 47.
[2] Jia. Research on Strategies of Math Function Teaching in Junior High School under Information Environment [J]. China Educational Technology Equipment, 20 1 1 (5): 85-86.
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