Reflection on the Conceptual Teaching of Functions

Part 1: Reflection on the Conceptual Teaching of Functions

The function is one of the most important contents in high school mathematics. It runs through the whole middle school mathematics learning, and it is the lifelong mathematics learning process. Its importance is mainly reflected in: 1. The function itself is derived from a wide range of applications in real life, such as the natural sciences and even the social sciences. 2, the function itself is an important part of mathematics, is a bridge to communicate algebra, geometry, triangle and other content. It is also the basis and method for further study of advanced mathematics in the future. 3, the contents of the function contains a large number of important mathematical methods, such as the thinking of the function, the idea of ​​the equation, the idea of ​​classification discussion, the idea of ​​combining numbers and forms, the idea of ​​returning to the original, the method of changing the element, the method of the coefficient of the servant, the method of matching Wait. These thought methods are the basis for further study of mathematics and solving mathematics problems. It is the part of our teaching process that should focus on the key points of the students.
However, this part of the knowledge is a major difficulty in teaching. This is mainly because of the abstract nature of the concept. It is not easy for students to understand. It is more difficult to accept. This is due to the main ideological characteristics of this part of the function. Reflected in a "change" word. That is to say, the main research is the relationship between "variables" and "variables". It is necessary to use the perspective of variables, the point of change of movement to see the relevant issues of contact and contact, which is the thinking of learning from the static view of the middle school. The characteristics are quite different, so the function has become a roadblock for the first year of high school students entering high school. Some students graduated from high school and did not understand the concept of the function.
In fact, in the knowledge of learning the function, the concept of the function is the most important, that is, the most difficult place, it is easy to break through the learning behind it. The main content of the current mathematics textbooks is the technical form of mathematics knowledge. The concept of the function is also the same, whether it is the traditional definition or the modern definition, the expression is the abstract mathematical form. In the teaching of mathematics, the formal expression of learning is a basic requirement, but not only Limited to formal expression, we must emphasize the understanding of the nature of mathematics, otherwise it will drown the lively mathematical thinking activities in the formal ocean. The teaching of mathematics should be returned to the truth, and efforts should be made to reveal mathematical concepts, rules, conclusions, development processes and essence. The more abstract the mathematical concept, the more so. Therefore, the teaching of the concept of the function is more difficult to take care of the text, and we must pay attention to the reorganization of knowledge. Try to remind the essence of the concept of the function, so that the student truly understands it, feels it useful, and is willing to learn it.

Chapter 2: Reflection on the Conceptual Teaching of Functions

There are generally two methods for introducing the concept of a function. One method is to learn the mapping first and then learn the function. The other method is to realize a special correspondence between the sets, that is, the function, through a concrete example. In order to make full use of the existing cognitive foundation of students, in order to give sufficient abstract background to abstract concepts to help students understand the essence of the concept of function, I use the latter way, starting from three background examples, in the experience of two Based on the dependencies between variables, the students are guided to use the set and the corresponding language to describe the concept of the function. Then, through examples, the problems in thinking, inquiry, and practice understand the concept of the function from three levels: function definition, function symbol, and function three elements, and compare with the definition of the country.
Before learning to use the set and the corresponding language to describe the function, you can also let the students review the concept of the function that has been learned in the country, and use the courseware to conduct simulation experiments, draw an image of a specific function, and the image in the function. Take a point P from the previous position, measure the coordinates of the point P, and observe the variation law of the coordinate abscissa and the ordinate of the point P. Let the student see the function describing the dependency between the variables, that is, no matter where the point P is, the abscissa of the point P always corresponds to the unique ordinate. Thus, the student realizes that the change of the function value in the function always depends on the change of the self-variable, and is uniquely determined by the self-variable.

Part 3: Reflection on the Conceptual Teaching of Functions

The video provided by the training, combined with the lessons of this lesson, I reflect on the following:
First, prepare for the lesson, take classes in accordance with the lesson
Prepare more textbooks, study the topic setting of textbooks, and review the five-year college entrance examination questions in Hainan before preparing for the class, so as to be consistent with the authors of the book-makers. For example, after the new curriculum reform, the textbooks are mostly examples of introducing or drawing concepts, formulas, and theorems, and downsizing the logic proof. The college entrance examination is more about the basic routine questions, so when you prepare for the lesson, you should pay attention to applying and diluting the theory.
My personal problem is that the idea of ​​class is easy to be confused, I like to use the mantra, love to repeat the students, I am afraid that the students do not understand, and add some non-strict content. Then the solution is to introduce the core content directly through examples and fun life examples, and accept the key point "arbitrary x unique y" from the visual, simplify the explanation as much as possible, and make more concrete examples; spread the textbook and prepare the textbook during class Is it necessary to sweep your eyes and prohibit temporary additions? On the basis of preparing lessons, the content of the complete course can be taught in the class, and a simple connection between the contents is added.
Second, the students’ sleepers are reported to the Moral Education Department. There is no passion for the performance of the audience.
I think learning is a student's right, not me forced to learn, so before I go to sleep from the phone, regardless of the student's speech. However, I found out that there was a large slept, and I was very passionate. When I talked about it, I was sleepy. So I used the name of the squad leader to give me a name, and each class was handed over to me. At the end of the period, I summed up the method of handing over to the moral education department. On December 12, when the school raised the flag, an automatic dropout was issued. The students were afraid of expulsion. So, in each lesson, only the individual self-abandoned students slept. When I went to class, I sat down and sat upright. I had more desires for performance and a series of content that was continually strained.
Third, the class has more exaggerated expressions and tones to resist the tedium of mathematics.
Mathematics is difficult for Hainan students to affirm, so it is extremely easy to get tired. The teacher should be full of love to go to the funny, Jiao Yu play treasure dress to tell jokes, or exaggerated pronunciation, deliberately accented, sing and talk with the students, can bring students a smile. In the long run, the relationship between teachers and students will be harmonized and will be loved by students.
Fourth, the core is still focused on repeatedly stressing, difficult to make a technical breakthrough
For a teacher, no matter how lively your class is, this is just a form. The core is still not enough to streamline and memorize the knowledge points. The students who are difficult to understand are very easy to understand, or the vague heads are smashed. It’s all about the teacher’s effort in preparing for the lesson and class. It’s because the teacher’s own thoughts are gone, and the right teaching or analogy method is not found. Breakthrough is a simple truth in a moment, don't let the teachers and students go in.
After the end of each chapter, I will work with the students on the book cover to summarize the core knowledge points of this chapter for easy reading. Not important, no need to remember, I will tell the students directly.
Finally, summarize the core knowledge points highlighted in a textbook and college entrance examination into memorable numbers: for example, compulsory 1 is 7. For example, compulsory 2 is 71221k.

Part 4: Reflection on the Conceptual Teaching of Functions

The function is an important model for studying the law of change in the real world. The learning of functions has always been an important part of the middle school stage. The concept of the function is the most important basic content for learning the follow-up "function knowledge", and the concept of the function is a relatively abstract one. The understanding of it has always been a difficult teaching point. Students' exploration of these problems and research ideas They are all relatively unfamiliar. Therefore, in the process of teaching, pay attention to the review and reflection of the “relationship between variables” that we have learned before, and strive to provide vivid and interesting problem situations and stimulate students' interest in learning; In-depth problem design, guide students to observe, operate, communicate, summarize and other mathematical activities, summarize and summarize the concept of the function in the activity; and deepen the students' concept of the function through teacher-student exchange, student communication, identification and identification. understanding.
The function is an important part of the mathematics learning in the middle school. The students are the first contact function, taking into account the students' ability to accept, starting from the vivid and interesting problem scene, abstracting from the actual problem through the exploration process of the general law. The concept of a function and a proportional function is introduced. Through the example with rich realistic background, the concept of a function and a proportional function can be further understood, which lays a foundation for the next step of learning "one-time image". The functional perspective recognizes the capabilities and consciousness of the real world.
For the first time, students use the idea of ​​combining numbers and shapes to study the image of a function. It is normal to feel strange. In the process of teaching, teachers should stimulate students' interest in learning through context creation. The correspondence between functions and images should be allowed to be practiced by students. It is found that the image of a function is a straight line and should be drawn by the students themselves. . After drawing the conclusion, let the students use the "two points to determine a straight line" and quickly make a function image. In the consolidation exercise, students are encouraged to think positively and improve their ability to solve practical problems.
According to the student's situation, the instructional design should also be adjusted accordingly. For example, the first link: creating a situation to introduce a topic can certainly stimulate students' interest, but it may also make it easier for students to pay attention to the search for algebraic expressions, and even some students in the team form certain cognitive obstacles. Therefore, the link can also be straightforward and straightforward. The topic, such as asking questions: the algebraic form of a function is y=kx+b, then what is the characteristic of a graphic corresponding to a one-time function? Today we will study the graphical features of the function. This lesson is the first time that students use the idea of ​​combining numbers and shapes to study a functional image and nature. For them, observation objects, exploration ideas, and research methods are unfamiliar. Therefore, in the process of teaching, teachers should stimulate students' interest in learning through the creation of problem situations, and pay attention to the careful design of hierarchical problem strings to guide students to observe the image of a function and explore the simple nature of a function. Deepen students' understanding of a function and nature. In the exploration and practice activities of teacher-student interaction and interaction, promote students' construction and improvement of a functional knowledge structure; improve students' ability to solve problems in consolidating activities - The focus of this lesson is to require students to understand that the determination of a proportional function requires a condition. The determination of a function requires two conditions. The condition can be obtained by using the undetermined coefficient method to find some simple one-time expressions. Reality. The design of this lesson focuses on the development of students' methods of combining numbers and forms and the comprehensive analysis of problem-solving skills and the cultivation of application awareness, laying the foundation for subsequent learning.
The process of inquiry is from shallow to deep, and it utilizes a wealth of practical scenarios, which not only increases the interest of students, but also makes students deeply understand that a function is around us and is widely used. In the teaching, I noticed the use of the form of the problem string, step by step, and gradually let the students master the general method of seeking a function expression. The teaching also noticed respecting the individual differences of the students so that each student can learn something. According to the students and teaching conditions of the class, the following contents can be selected or supplemented during the teaching process, and can also be reserved for homework. The focus of this lesson is to require students to understand that the determination of a proportional function requires a condition. The determination of a function requires two conditions. The condition can be solved by using the undetermined coefficient method to solve some simple functional expressions. problem. The design of this lesson focuses on the development of students' methods of combining numbers and forms and the comprehensive analysis of problem-solving skills and the cultivation of application awareness, laying the foundation for subsequent learning. The course design focuses on the development of the students' method of combining numbers and forms and the comprehensive analysis of the ability to solve problems and the cultivation of application awareness, laying the foundation for subsequent learning. The process of inquiry is from shallow to deep, and the use of rich practical facts is focused on the students to understand the positive proportional function. The need to explore a process from shallow to deep, and to take advantage of the rich practical situation of the class is focused on To make students understand the determination of the proportional function requires a condition. The determination of a function requires two conditions. The condition can be obtained by using the undetermined coefficient method to solve some simple one-time expressions, and can solve the practical problems. The design of this lesson focuses on the development of students' methods of combining numbers and forms and the comprehensive analysis of problem-solving skills and the cultivation of application awareness, laying the foundation for subsequent learning.

Part V: Reflection on the Conceptual Teaching of Functions

For teachers, 'reflective teaching' is a comprehensive and in-depth calm thinking and summarization of teachers' consciously taking their own classroom teaching practice as a target of understanding. It is a learning method used to improve their own business and improve teaching practice. Constantly reflect on their own educational practices and actively explore and solve a series of problems in educational practice. Further enrich yourself, optimize teaching, and gradually grow into a named human soul engineer. The following is a reflection of my concept after the function:
This classroom atmosphere is more active. Students can not only speak in the classroom, but also dare to question and be able to make sense, but also actively participate in group discussions and exchanges, share the results of teamwork, and basically complete the teaching objectives.
This lesson is the concept of studying functions. This lesson mainly uses the teaching process of exploration, discovery, induction and feedback, and has reached the teaching of the concept of the function.
The study of the nature of the function is an important part of the mathematics learning in high school. Therefore, the study of the concept of the function is an important aspect that should be examined when studying the nature of the function, and it should be applied in the follow-up study. It is useful in calculating function values, discussing the monotonicity of functions, and drawing function images. This is a new concept for students. The process of introducing new concepts is also a process of cultivating students to explore problems, discover patterns, and make inductions. Therefore, when teaching, there is no blunt question, but the introduction of life examples, and then the new concept of numerical values ​​in the Cartesian coordinate system is derived, which is not only natural but also buried for the geometric meaning of the function parity. Under the pen.
One of the highlights of this class is the process of giving thoughts, speeches, disputes, discussions, and even the correct answers to the students after giving a few examples in the feedback process. The teachers have promptly and appropriately prompted. The students' courage to question makes the classroom show a dynamic scene. The enthusiasm and initiative of learning are fully mobilized, which makes students' concept of seemingly simple functions not to be underestimated, but also develops their abilities. Generally speaking, students will feel boring when they learn some simple knowledge points. They should fully consider these shallow and plain knowledge and some places to think and pay attention when organizing teaching. It really shows that "there is new meaning in the shallow, and there is always in the plain."
The biggest style of my class is to focus on the new concept and to develop students' ability to explore and highly summarize in the process of teacher-student interaction, and to make students inferior. It is commendable that there are conclusions that students can summarize, so it can be used as a introduction to the parity of functions in the next lesson.
In general, this class is a good course for students to complete the process of “causing attention----inspiring enthusiasm---participating in experience” in their studies.
It is a pity that the number of speakers and the length of the speeches are not ideal due to time constraints.
The concept of a function seems to be relatively simple, and students often feel boring when they study. Therefore, in organizing teaching, we must consider how to make students feel these shallow, plain knowledge and some places to think and pay attention to.
According to the student's ability to accept, the content can be taught in two classes.