First, the necessity and function of writing appropriate exercises in teaching.
It is a supplement and perfection to the teaching materials. Professor Su said: "First of all, we should deepen our understanding of basic concepts, definitions and theorems (including proof); The second is to train our arithmetic ability and logical thinking. " Because in the process of thinking and solving problems, we must use the concepts, definitions and theorems we have learned to reason, judge, associate and explore, so as to find a solution to the problem. In this process, we will deepen our understanding of knowledge and be proficient in problem-solving skills. However, the exercises selected in the textbook cannot meet the needs of all students at different levels. In particular, there are few examples and exercises in the current middle school mathematics textbooks, which cannot be applied to different regions, different schools and different students. At the same time, no textbook can cover all kinds of problems that the knowledge can solve. Therefore, under the premise of using the same textbook in an all-round way, it is necessary for teachers to compile appropriate exercises to meet different needs according to the actual teaching situation. On the other hand, we should see that the concepts, theorems, ideas and methods involved in the textbook have a process of gradually deepening understanding and consolidating proficiency, and this process is often realized by practicing calculus. In particular, some key concepts always need to be deepened, and there will be updated understanding in the new category of mathematical knowledge; On the contrary, this understanding will optimize the learning of new knowledge.
It can mobilize students' non-intellectual factors and stimulate their enthusiasm for learning.
In teaching practice, we all have this experience: the role played by a good math exercise is often not limited to a deeper understanding of knowledge and flexible mastery of methods; Sometimes, it will mobilize students' non-intelligence factors, stimulate students' interest and enthusiasm in learning mathematics, and play a role that other teaching links can't play. And such a good question often depends on the teacher to write purposefully according to the problems found in teaching and the actual needs of students. Such good questions can be the extension and exertion of examples and exercises in the book; It can be selected temporarily in combination with the difficult problems encountered by students in their study; It can be supplemented for students' weak links; It can also be a counterexample of the mistakes made by students. In short, such a topic can't be written in the textbook in advance.
Therefore, teachers often compile some exercises according to the actual situation of teaching, which can not only help students learn relevant knowledge, but also stimulate students' interest in learning mathematics. Compiling appropriate exercises is also the need to mobilize students' non-intellectual factors and stimulate their learning consciousness. Can better implement the principle of teaching students in accordance with their aptitude.
In the class teaching system, there is a weakness, that is, among dozens of students in a class, their acceptance is different; It is difficult to embody the principle of teaching students in accordance with their aptitude by using the same unified textbook. Because it is required by the unified model, in order to take care of the acceptance of most students, teachers can only teach at the intermediate level. This will certainly aggravate the polarization, especially for some students with higher level, and even dampen their learning enthusiasm. Faced with this key problem in the class teaching system, teachers must adopt different methods to remedy it according to the principle of teaching students in accordance with their aptitude. The most important method is to arrange exercises at different levels according to different needs, so that students can choose the appropriate exercises to calculate according to their own needs, so that they can improve at different levels. Therefore, writing appropriate exercises is the need to implement the principle of teaching students in accordance with their aptitude and accelerate the training of talents.
Since exercise plays such an important role in mathematics teaching, how can we give full play to its role? The key is to ensure the quality of the selected exercises. This requires: first, the selected exercises should not only help students understand and apply what they have learned, but also pay attention to the flexibility of conception skills and methods, which is conducive to cultivating the ability to analyze and solve problems; Secondly, the compilation of exercises must be closely combined with the needs of teaching and properly coordinated with the actual situation of students. In other words, compiling exercises must establish the concept of serving teaching and students and the concept of quality first. Therefore, we should pay attention to the following basic principles when compiling exercises: 1.
Editing exercises should have a clear purpose.
The selection of each question should have a certain purpose, some for deepening the understanding of the mathematical concepts learned, some for the mathematical methods to be mastered, some for the necessary skilled skills, some for the mistakes made by students, and so on. In this way, students can get the expected effect after calculation. To ensure the quality of exercise questions, the key is to choose the questions purposefully, based on the needs of both the teaching materials and the students, otherwise it will only cause extra burden to the students and have the opposite effect. 2.
The exercises written should be difficult, appropriate and appropriate in number.
The role of exercises should be brought into full play within the scope that students can do and complete through hard work. In order to ensure the feasibility of the exercise questions to play this role, it largely depends on the difficulty and quantity of the selected exercise questions.
Proper difficulty is the key to ensure feasibility. The topic is easy, which wastes students' energy and even easily dampens students' interest and enthusiasm in learning; The topic is difficult and deep, which is not desirable. Such a topic discouraged students with poor foundation and had to be put aside and not done at all. For students with good foundation, it is easy to deviate from the direction and ignore the solid mastery of basic knowledge and skills. Therefore, I want to emphasize that the difficulty is appropriate, and the difficulty standard should be based on the new curriculum standards and teaching materials and the actual level of students as the starting point. In order to let students master the key knowledge and typical problem-solving methods in textbooks, the difficulty of exercises should not stay at the level of general understanding. We should deliberately select some problems that can be solved after careful thinking, so that students can get inspiration and deepen their understanding. The arrangement of exercises should also be arranged in the order from easy to difficult, so that students can learn from the shallow to the deep step by step, and achieve the effect of drawing inferences from others.
Proper amount is also an important condition to ensure the feasibility of practice. Some important concepts, theorems, thinking methods and skills in mathematics can not be understood and mastered by doing a problem once; It often takes some practice and proper circulation and spiral rise to understand the mystery. Therefore, practice must be based on a certain amount in order to achieve the expected purpose. However, it is impossible to engage in sea tactics with generations of elites. Therefore, the number of exercises must be appropriate.
The appropriate number is reflected in "the choice of topics should be precise", that is to say, the selected exercises must be conducive to students' learning; ; There should be more important contents, important methods and typical problems to ensure the purpose of practice. The appropriate number is also reflected in the planned arrangement of exercises, which cannot be compiled and distributed to students at will.
Third, some problems that should be paid attention to in compiling exercises 1. Attention should be paid to the potential role of examples and exercises in teaching materials. In fact, quite a few exercises can be found in textbooks. Therefore, based on the textbook, it is one of the problems that should be paid attention to in writing exercises to tap and play the potential functions and guiding values of examples and exercises in the textbook. Many examples and exercises in the textbook contain some "mysteries" that students have not yet discovered, and these are the keys for students to expand and extend their knowledge. Therefore, teachers should be good at compiling exercises as crutches for students to explore these "mysteries", guide students to summarize and evolve knowledge in a wider range, and make knowledge form a more complete network; To make the methods in examples and exercises more flexible mathematical methods, we can draw inferences from one example to another. 2. When compiling exercises, we should give full play to the role of "mistakes". In students' homework and exams, some typical mistakes often appear. These mistakes reflect the weak links in students' study. Generally speaking, it is also the key, difficult and important point in the textbook, or the place where there are loopholes in teaching. Therefore, teachers should be good at compiling some corresponding exercises, correcting students' mistakes, filling in gaps and achieving the purpose of enriching and improving. 3. Editing exercises should ensure the scientific nature of the topic. When compiling exercises, people often pay more attention to the knowledge, ideas and skills of solving problems, but often ignore the overall scientific nature of the questions, so that "wrong questions" have played a negative role. 4. Be good at collecting information and updating questions. In recent years, many excellent questions have appeared in various examinations and materials, which are not only diverse in form, but also novel and flexible in conception, and are well received and valued. Therefore, the compilation of exercises should be widely understood, information from different angles should be collected, excellent questions and topics should be absorbed into teaching in a planned and purposeful way, and the quality should be constantly updated and improved, and the quantity should be controlled, so as to further improve mathematics teaching.