As a new teacher, classroom teaching is one of the important tasks. New discoveries in teaching can be written in teaching reflection, so what problems should be paid attention to when writing teaching reflection? The following is my reflection on the teaching of quadratic function in junior high school mathematics (generally 5 articles), which is for reference only and I hope it will help you.
Reflection on the Teaching of Quadratic Function in Junior Middle School Mathematics 1 From the perspective of the textbook system, this lesson is obviously to let students understand what quadratic function is, distinguish the difference between quadratic function and other functions, deeply understand the general form of quadratic function, and initially understand the restrictions on the definition field in practical problems.
After this lesson, calm down and prepare to write a reflection on teaching. Reflecting on the writing intention of the textbook, it is found that most of these textbooks are about three practical problems, which leads to quadratic functions. I realized that the focus of this lesson should actually be "experiencing the process of exploring and expressing the relationship of quadratic functions, and gaining the experience of expressing the relationship between variables with quadratic functions, thus forming a definition". With this understanding, everything becomes simple!
For the choice of practical questions, I integrate the four questions in the same practical background. This design can not only arouse students' interest, but also minimize the time for students to examine questions, which is very hierarchical. These practical problems run through the whole class and make the whole class feel natural.
For the design of exercises, we still adopt the principle of non-repetition, try our best to summarize each question in time, and follow the principle of opening to closing, which has achieved good results.
As for the design and proposal of the final discussion topic, after preparing lessons in the whole chapter, I found that we don't actually talk about the maximum value of quadratic function, but it doesn't mean that it won't be involved at all. The thinking method used in it is still very important, and it also plays an important role in the observation of images. In addition, after answering the previous practical question, this question comes to the fore: multiple trees-want to increase production-multiple trees. So I designed this exploratory question: If you were the owner of the orchard, how many trees would you prepare? Note that I didn't ask the question of maximum and minimum here, but all the students can understand that this is the charm of mathematics. This problem is the climax and essence of the whole class, and it is students' thinking after learning the definition of quadratic function, using the basic knowledge of function, algebra knowledge and the knowledge of quadratic equation in one variable. So their ideas and statements, whether right or wrong, comprehensive or biased, all involve important mathematical thinking methods, and these are very important. Facts have proved that students' thinking is really active. You should give them enough space, they can always think and explain from all sides. I also saw the spark of their wisdom, which was very gratifying.
Reflection on the teaching of quadratic function in junior high school mathematics 2 This lesson is the first lesson of quadratic function arranged after learning a function, inverse ratio and quadratic equation of one variable. The learning goal is to make students understand the concept of quadratic function, distinguish the difference between quadratic function and other functions, understand the general form of quadratic function, and initially understand the limitations on the range of independent variables in practical problems. In my opinion, the focus of this lesson should be "going through the process of exploring and expressing the relationship of quadratic function, gaining the experience of expressing the relationship between variables with quadratic function, thus forming a definition". As soon as I finished this class, I realized something:
1, quadratic function is a common function and widely used. It is a very important mathematical model that objectively reflects the quantitative relationship and changing law between variables in the real world. Many practical problems can often be turned into quadratic functions to study.
2. Teaching should pay attention to the formation and construction of concepts. In the process of learning concepts, starting from the rich realistic background and the problems that students are interested in, through the exploratory activities of cooperation and exchange between students, we can guide the analysis of practical problems, such as the process of exploring the area, interests, observing and discovering the rules in the table and expressing these relationships with relationships, and lead to the concept of quadratic function, so that students can feel the close relationship between quadratic function and life.
3. In classroom teaching, teachers should not only fully prepare lessons, but also know how to deal with them flexibly according to students' feedback. When organizing students' discussion, put it away and take it away. They should make good use of the 45-minute classroom and return it to the students as much as possible.
I feel that in teaching, enthusiasm alone is not enough. Students' enthusiasm for learning has not been actively mobilized and their attraction is insufficient. When preparing lessons in the future, we should pay attention to creating rich and interesting languages to arouse students' enthusiasm. In short, in mathematics teaching, we should not only be good at setting doubts and difficulties, but also stimulate students' enthusiasm for learning, and at the same time strengthen the cultivation of students' autonomous learning ability and integrate theory with practice. Only in this way can we attract students' love for mathematics.
Reflections on the teaching of quadratic function in junior high school mathematics 3 Quadratic function is an important content of middle school mathematics and a hot spot in senior high school entrance examination. Among them, the investigation mainly involves the definition, image, nature and application of quadratic function. In ninth grade teaching, teachers should base themselves on the classroom, aim at the senior high school entrance examination and study the examination questions. In recent years, the application of quadratic function has appeared in the senior high school entrance examination questions all over the country. It is particularly worth mentioning that some of them are examples or exercise prototypes and variants from textbooks. In daily teaching, paying attention to docking and paving the way for the senior high school entrance examination is my real way to solve this practical problem of quadratic function.
1, the expectation of practical exploration course
Generally speaking, the way to solve the problem is to establish a plane rectangular coordinate system, mark the coordinates of points on the image, find out the analytical formula of the image, and use the analytical formula and properties of the image to solve practical problems such as optimization. First of all, I guide students to recall three different analytical formulas of quadratic function, namely, general formula, vertex type and intersection type, and tell their respective properties, such as the opening direction of parabola, symmetry axis, vertex coordinates, maximum and minimum values, and the increase and decrease of functions on both sides of symmetry axis. Combined with the teaching content of the textbook published by Beijing Normal University, the exercises are presented, and students try to explore and solve problems in groups. Each group quickly worked out the analytical formula of parabola, of course, the speed was fast and slow. The second question, and few students raised their hands to show their completion, I am very happy, and I have not studied their situation in detail. Continue to organize student activities according to the scheduled plan and start to explore the second question. For this question, many students have a dignified expression, confused eyes and poor thinking, and don't know where to start. I repeatedly guided and reminded several times to consider the function from the image according to the example, but no one responded, and the inquiry almost came to a standstill, which surprised me beyond my imagination. Fortunately, I can handle it, so I asked Xiao Xiong, who is called "the headmaster". what do you think? Xiong said that he also knew how to set up a plane rectangular coordinate system and draw a sketch first, but he didn't know how the truck passed through bridge opening, whether by the middle or by the side. As soon as I heard it, I suddenly realized. It turns out that students' cognition is different from what the teacher imagined, and with little life experience, it is no wonder that students are silent. For the method of establishing coordinate system, students are often helpless in the face of many possible choices. The fundamental reason is that teachers do not pay attention to the study of students' thinking level, which leads to the substitution of teachers' thinking for students' thinking and the disconnection between students' thinking and practice. This requires teachers to proceed from students' reality, understand students' learning situation, and be good at enlightening and guiding, so as to better realize teaching objectives.
The original intention of this course is to let students perceive mathematical models from concrete life practice, abstract mathematical models from practical problems, solve problems with mathematical knowledge, and at the same time let students perceive and experience the changeable training of a problem, so as to increase their understanding of mathematical problem-solving ideas. However, in teaching, students' lack of some conventional knowledge is prominent. For example, it is difficult for students to solve three-dimensional linear equations by using three-point coordinates to solve the quadratic resolution function.
When I was ready to ask the next question with confidence, a classmate said, I haven't got the answer yet. I said, didn't your group show it? Why not? He said that my analytical formula is set to y=ax2+bx+c, so it cannot be substituted. The group leader and I have different settings. I told him, in fact, you can do it accurately with the general formula, but the speed is a little slower, and you need to strengthen your operation practice. After class, I have been thinking that the worse the students' foundation, the harder it is to master those good methods. Learning is very hard and tiring, which requires strengthening double-base training at ordinary times, and every student should master basic concepts and skills.
If teachers want to be flexible in the open classroom, they need to be considerate when preparing lessons, not only to prepare teaching materials, but also to prepare students. More importantly, teachers should have rich scientific and cultural knowledge, so that our students can find fun and interest in learning in a relaxed and active classroom.
Because this course is the application of quadratic function, it focuses on summing up the application of problem-solving methods and mathematical ideas through learning, so this course takes "inspiring inquiry" as the main line to carry out teaching activities, pays attention to students' cooperation and exchange, and guides them when necessary, fully mobilizes students' learning enthusiasm and initiative, highlights students' main position, and achieves the goal of "letting students learn both". After the teaching of quadratic function application, the effect is better than I expected, and several points are thought-provoking:
2. Carefully design questions to arouse students' thinking about establishing mathematical models.
This section takes the comprehensive application of quadratic function as an opportunity to cultivate students' ability to analyze and solve problems. This lesson focuses on analyzing problems, transforming practical problems into mathematical problems, and establishing mathematical models to solve problems. Therefore, in teaching, teachers should consciously train students to start reading problems, analyze the meaning of problems, find mathematical knowledge related to problems, and use knowledge and skills to solve problems. In preparing lessons, I found it difficult for students to understand examples. We designed small problems and set up small steps to guide students to explore, break through teaching difficulties and lead students to find solutions. The problems I encountered when making the paving plan are as follows:
(1) Read questions and retrieve useful information;
(2) Analyze the known, what do they mean? Draw a picture according to the meaning of the question;
(3) What do we want by analyzing what we want? What knowledge can be transformed into solving practical problems?
(4) How to find the maximum value of quadratic function?
According to the teacher's questions, students discuss in groups, and students communicate with each other and complement each other. Under the guidance of the teacher, they found that this problem was transformed into the problem of finding the maximum value of quadratic function, gradually breaking through the difficulties and helping students to establish mathematical models to solve problems. On the basis of hands-on drawing and discussion, students find solutions and steps. They first find the analytic expression of quadratic function, and then find the maximum value of quadratic function. Students draw pictures after understanding the meaning of the topic, which deepens their understanding of the topic, lays the foundation for solving problems, further understands the problem of solving quadratic functions by using the thinking method of combining numbers and shapes, and permeates the mathematical thinking method into the whole teaching process.
3. Provide students with space for thinking, and pay attention to multiple solutions to one question.
After the students establish the plane rectangular coordinate system, according to the meaning of the question, the symmetry axis is the coordinates of x= 1, point A (0,2), point B (0,0) and point C (0,2). When determining the quadratic resolution function, an episode appeared. After students use the general formula to determine the solution of quadratic function, some students want to solve their own ideas in other ways. I immediately encourage students to find new methods. Some students are active in thinking. A student wants to find an analytical formula with two formulas, so that the student can express his ideas and other students can help him analyze and supplement them. The student brought the three coordinates of A, B and C into the two-formula solution, and found that the analytical formula was different from the general formula. He is confused and wants to know what the problem is. I didn't deny this classmate's method, but asked other students to help me correct it. In everyone's analysis diagram, I found that the coordinates of point B are not on the parabola and cannot be brought in.
When there are differences in teaching, students should be given room to think, find out the causes of the problems, and then determine the solutions to avoid similar mistakes in the future. Students are good at thinking. When using two formulas to find the analytical formula, I designed a small trap to deliberately guide students to choose three points A, B and C to find the analytical formula. Through calculation and observation, the students also found this problem: the coordinates of point B are not on the parabola, so they cannot be brought into the solution. In this case, Q: How to determine the analytical formula with two formulas? The students are very enthusiastic. Discuss in groups. Students can find another intersection point D (-0) between parabola and X axis according to its symmetry. 5, 0), the three points A, D and C are brought into the analytic formula for finding quadratic function. In teaching, we should pay attention to the flexibility of problem-solving methods, broaden students' thinking and improve students' ability to find and solve problems. In the process of teaching, asking questions at different levels stimulates students' curiosity and actively participates in teaching activities, which greatly improves classroom efficiency.
4. Mathematics comes from life and is applied to life.
Examples have a strong sense of reality, and the choice of examples increases the authenticity of mathematics teaching, allowing students to experience the close connection between mathematics knowledge and daily life, thus cultivating students' feelings of loving mathematics and learning mathematics well. In the classroom, students realize that mathematics comes from life and is applied to life in the process of solving mathematical situation problems, which stimulates students' interest in learning mathematics. In class, students are active in thinking and have a strong desire to explore because the problems come from around them, so as to give full play to students' learning enthusiasm and improve the quality of classroom teaching.
5. Disadvantages:
"Mathematics Curriculum Standards" proposes that teachers are not only the guides of students, but also the collaborators of students. In teaching, students should be allowed to explore the problems and difficulties encountered in learning through independent discussion and communication, and teachers should guide them and study and discuss with students. In the teaching of this course, teachers are more about guiding students, rather than completely letting students explore and learn independently and acquire new knowledge; Students still have a strong dependence on mathematics learning, and teachers should consciously cultivate students' autonomous learning ability.
If teachers want to be flexible in the open classroom, they need to be considerate when preparing lessons, not only to prepare teaching materials, but also to prepare students. More importantly, teachers should have rich scientific and cultural knowledge, so that our students can find fun and interest in learning in a relaxed and active classroom.
Reflections on the teaching of quadratic function in junior high school mathematics. Quadratic function is an important link in the spiral development of function knowledge after students learn direct proportional function, linear function and inverse proportional function. Quadratic function is an important mathematical model to describe the relationship between variables. It is not only one of the important methods used in other disciplines, but also a mathematical model of some simple variable optimization problems. Like linear function and inverse proportional function, it is also a very basic elementary function. The study of quadratic function will lay a foundation for students to further study functions, understand their ideas and accumulate experience.
The specific content of this lesson is to let students understand the concept of quadratic function, judge whether a function is quadratic or not, and solve some problems with the general form of quadratic function. To this end, I first led students to review what a linear function is, and then designed a specific problem situation, so that students can "deduce" a quadratic function by themselves, and observe and summarize its difference from a linear function. On this basis, the general analytical formula of quadratic function is gradually summarized: y=ax+bx+c(a, b, c are constants, a≠0). Finally, the concept of quadratic function is consolidated through in-class exercises to solve some simple mathematical problems.
Personally, I think the success of this course lies in:
In teaching, the concept of quadratic function is introduced through examples, which makes students know that quadratic function is a common function and widely used. It is a very important mathematical model that objectively reflects the quantitative relationship and changing law between variables in the real world. By learning to find the analytic formula of quadratic function in some simple practical problems, most students attach importance to the formation and construction of the concept of quadratic function. In the process of learning concepts, let students experience the process from problems to quadratic decomposition functions and experience the use of functions. Thinking methods that can benefit students for life can improve their thinking level. This not only improves students' ability to find and solve problems independently, but also avoids falling into a stylized mode of learning, and also allows students to experience the happiness of success.
Reflections on the teaching of quadratic function in junior high school mathematics 5 Quadratic function is a concrete and important function learned in junior high school, which occupies a large score in the examination questions over the years. Quadratic function is not only closely related to the unary quadratic equation that students learn in the early stage, but also plays an important role in cultivating students' mathematical thought of "combination of numbers and shapes" The concept of quadratic function is the basis of studying quadratic function in the later period, which plays a connecting role in the whole teaching material system.
The content of this lesson is to let students understand the concept of quadratic function, judge whether a function is quadratic or not, and solve practical problems with the general form of quadratic function. Therefore, let students review the related contents of function and linear function, and then design specific problem situations for students to deduce a quadratic function by themselves, and observe and summarize the differences between it and linear function. On this basis, gradually summarize the general expression of quadratic function, and finally consolidate the concept of quadratic function through exercises to solve some simple mathematical problems.
Personally, I think the success of this course lies in: First, the teaching design is "step by step" and the students' thinking ability is "improved layer by layer". In teaching design, I design targeted questions reasonably according to the needs of the content, and start teaching with the help of students' existing knowledge. By solving problems, I can fully stimulate students' thirst for knowledge and arouse their enthusiasm and initiative in learning.
Second, in the process of learning, we should not only pay attention to teaching students knowledge, but also pay attention to teaching students the methods of learning and thinking, improve students' ability to find and solve problems independently, and let students experience the happiness of success from time to time.
Third, in the whole teaching process, we pay attention to the development of students at different levels, the individual differences of different students, and the limitations of teaching purposes, which leads to the phenomenon that some students who have spare capacity feel underfed. Therefore, in the later exercise design, there are also targeted exercises, which are also very helpful for the improvement of these students.
Disadvantages are as follows:
1, because the students forgot the first function, so the review took up too much time, which led to the unfinished exercises after class.
2. The requirements for students' self-study are not detailed enough, and students' learning is not deep enough. They just read the textbook and didn't dig anything out of it.
3. Due to time constraints, the summary is not complete enough.
In short, the teaching of this class has achieved certain results. But it also exposes many problems. In the future, I will learn a lesson, try to correct my own shortcomings and improve my teaching level.
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