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How to explain math exercises in classroom teaching
This paper analyzes the exercises of experienced teachers and their own teaching practice, and tries to teach exercises well. It is found that if the following teaching procedures are adopted in the exercise class, it not only conforms to the law of students' understanding, but also achieves good results in laying a solid foundation and cultivating their abilities, which embodies the requirements of reducing students' burden and improving the quality of mathematics teaching. Below, briefly talk about the experience of implementing and exploring the math exercise class, and ask colleagues to criticize and correct the improper points.
First, the structure of math exercises class
The teaching methods of mathematical exercises are diverse and vivid, so don't stick to a certain model. In general, the following methods are adopted, that is, the classroom activities of mathematics exercises are divided into six links:
1, review preparations to facilitate migration.
2, inspire and guide to find ways
3. Focus on revealing the law.
4, skillfully set up practice skills.
5, inductive review left an impression
6. Check the effect of homework after class
This structure emphasizes the overall function of teacher-student interaction in the teaching process.
Second, the principle of combining teachers' leading role with students' dominant position.
invest
The leading role of teachers < = > the subjective position of students.
output
The questions explained by the teacher and the questions independently done by the students should be given in batches and summarized in time to improve the students' attention; The six links can be carried out alternately, so that they can be taught and practiced in the teaching process, but the teaching principle of "teacher-led, student-centered" should always be followed.
Third, the role and effect of each link in classroom teaching.
1, review preparations to facilitate migration.
Everything in mathematics is not isolated, but closely related. Comenius said: "All lessons should be subdivided into stages, so that those who learn first can clear the way for those who learn later and give explanations." This requires us to follow the teaching principle of "from shallow to deep, step by step" in the exercise class teaching. Therefore, in the first few minutes of the lecture, according to the needs of this section, the teacher will briefly review the basic knowledge and basic formulas used in this exercise class by asking questions, talking or telling by the teacher, and reveal the internal relationship between formulas or theorems, so as to consolidate the knowledge learned and prepare for the exercise class. For example, when reviewing the summation of series, first review the summation formula of arithmetic and proportional series, and the sum of squares and cubes of natural series. This review can not only lay the foundation for the following summary, but also consolidate this knowledge. In order to make this review play its due role, teachers are required to have a thorough understanding of the contents of this section before preparing lessons, so that the review is focused and targeted, and at the same time pay attention to reasonable arrangement of review time.
2, inspire and guide to find ways
German educator Dostoevsky once said, "A good teacher should teach people to discover the truth", which means that teachers should always insist on analyzing topics and help guide students to find ways in analysis. If it is known that sinα+cosα= 1/5, 0 < α < 3. 14, find the value of tgα. Teachers can ask the following questions: What do you get from the transformation of the condition sinα+cosα= 1/5? Students can draw the following deformations: conditional deformation 1: sinαcosα= 12/25 after the two sides are squared, and conditional deformation 2: sin2α=2tanα/ 1+tan2α. Conclusion Deformation: tanα=sinα/cosα. In this way, by developing conditions and transforming conclusions, the internal relationship between conditions and conclusions is found and the way to solve problems is found.
Teachers always say analytically, let students have fun from analysis, and fun will be transformed into the internal motivation of students to study hard.
3. Focus on revealing the law.
Dialectical materialism tells us that law is the inherent and essential inevitable connection between objective things. When talking about exercises, don't talk about topics, but talk about methods and laws, and explore the potential laws of exercises through explanation. Example 89 College Entrance Examination: Does the constant A, B and C make the equation 1.22+2.32+3.42+ ...+n (n+1) 2 = n (n+1) (AN2+BN+c)//. At first glance, this problem can't be solved, but after careful analysis, it is found that the key to solve this problem is that every term on the left in the formula (1) conforms to an=n(n+ 1)2, which is converted into the form of sum by dividing the terms: n (n+1) 2 = n3+2n2.
When teaching exercises, we should teach students the rules of solving problems. The law of solving problems can be divided into general law and special law. General law refers to the method of dealing with problems, that is, turning complex problems into simple problems and turning new problems into problems that have been solved through research. Therefore, we should grasp this law in the teaching process and teach students to do a good job of transformation. Such as sum sn =11+103+1005+... = (10+100+0000+..+10. In teaching, we should combine specific problems and repeatedly teach students some problems and laws in these three steps. In addition, when doing exercises, we should also teach students to master the special laws of solving problems, help them summarize the conventional solutions to some common problems, and constantly improve their problem-solving ability.
4, skillfully set up practice skills.
Educational psychology believes that the formation of opinions and the mastery of skills should be accomplished by students' independent operation. This kind of autonomous performance cultivates their learning needs, stimulates their learning motivation, improves their interest in learning and arouses students' nervous attention. In exercise teaching, the first two steps can make students master methods and find rules, but they can't reach proficiency and form certain skills. The teaching task of this step is to require students to be proficient and skilled through practice on the basis of understanding and satisfaction.
Example: Given cotα=m(m is not 0), find cosα. Finish the method and law of solving this problem, and let an above-average student write "known sinα=m, | m |"
5, inductive review left an impression
Each teaching content has key points, difficulties and precautions. Use a few minutes before the end of the exercise class to summarize and review this section, so that students can leave a deep impression on the important contents of this section, which is very beneficial to students.
For example, before the conclusion, I will make a conclusion:
Total quantity (this section mainly includes:
(1) two formulas (arithmetic, geometric series)
(2) Two kinds of sums (the sum of squares and the sum of cubes of the first n terms in a natural sequence)
(3) Two methods (project splitting and project splitting)
6. Check the effect of homework after class
Math homework is an important part of a good exercise class. It is an effective way for students to consolidate their basic knowledge and skills through their own practical activities and gradually form creative talents. It is also a powerful means for teachers to understand students' learning situation, check teaching effect, adjust teaching ideas in time, accurately grasp teaching time and achieve the best teaching effect. This requires teachers to correct homework in time and obtain teaching feedback information through correction. Due to the different levels of students, the information appearing in the homework may be different. First of all, some students will make some mistakes in their homework. At this time, teachers should follow the principle of teaching students in accordance with their aptitude and face individual students. Second, students have different ideas, and the solutions to the same problem are often different, and some original solutions will appear in their homework. In this way, after correcting the homework, the teacher should do the following work: (1) release the standard answers, so that students can find their own shortcomings and learn their own strengths, which can play a demonstration role; (2) Organize job evaluation. Analyze the advantages and problems in students' homework by using the exercise class or before the start or end of each class, and point out what to carry forward and what to overcome; For those innovative solutions, we should organize students to follow suit and cultivate their thinking creativity; (3) job modification. Through review, one question can be solved in many ways, so that knowledge can be further understood and recognized, and knowledge can be learned vividly and firmly.
In a word, as long as these six links are handled flexibly, students' thirst for knowledge can be fully stimulated, and their ability to analyze and solve problems can be enhanced, so that math exercises can be really taught well.
How to teach exercises well? Monday, June 65438+March 65438 09: 065438+ 0: 00 p.m.
Exercise class is an important class in mathematics teaching. Optimizing exercise teaching can not only effectively enhance students' ability to solve problems, improve the quality of mathematics teaching, but also promote the formation of students' good mathematical concepts.
How to teach a high-quality exercise class? I think the key lies in the following three links:
First of all, a reasonable topic:
As a math teacher, I used to envy the rich possession of Chinese teachers: I can wander around the palace of literature with students, enjoy touching masterpieces and produce spiritual voices. In Chinese class, teachers and students create a realm of flying passion and flowing poetry in the enjoyment of literature. ...
In recent years, I have often thought about: What should I do to attract and infect students in math class? What should my students get in math class? What should mathematics teaching do? Is it for students to recite some formulas, concepts, properties and laws? Or teach students to do problems to cope with exams? Don't! Mathematics teaching should have a broader connotation.
Mathematics is science, mathematics is art, mathematics is language, and mathematics contains the beauty of human culture. Mathematics education is for all students, and different people will get different development. The math we give our children should be the math that those children can learn with their own personal experience. The math classroom we build together with our children should be a classroom full of vitality, promoting the generation of wisdom, full of life and showing smart colors. Such a classroom is also charming.
How the students' mathematics level is, in the final analysis, reflected in solving problems, so it is very important for students to have proper exercise training, and the quality of exercise selection directly affects the training efficiency, so teachers should carefully consider and reasonably choose topics when choosing exercises. Generally speaking, we should pay attention to the following five aspects:
1, exercise selection should be targeted.
Exercise class is different from new teaching. It regards training as the main part of classroom teaching. Therefore, in order to achieve an efficient training goal, teachers should examine the knowledge points and students' learning status according to the teaching goal when choosing related exercises. Students who have a good foundation can do less or even nothing, and those who have mastered it on the spot can do less or even nothing. However, for students who are generally flawed and often commit crimes, they should be appropriately and repeatedly strengthened, and they should not be arbitrary and blind.
2, exercise selection should pay attention to the feasibility.
Teachers should choose students' "zone of proximal development" exercises. Too simple exercises will affect the quality of students' thinking, thinking activities have not been fully developed, and they lack due motivation. Too difficult exercises can easily dampen students' enthusiasm for learning and make it difficult for them to gain the joy of success. In the long run, students will lose self-confidence. Therefore, the choice of exercises should grasp the "degree".
3. The choice of exercises should be typical.
The choice of mathematical exercises should overcome greed, and sometimes it is good to see which topic is good. Everyone wants students to do it, resulting in a lot of problems. Therefore, the choice of exercises must be typical, not only pay attention to the coverage of knowledge points, but also let students master the law through training to achieve the goal of "taking one as ten".
4. The choice of exercises should be research-oriented.
First of all, the choice of exercises should be accurate and rich in connotation. In addition to the results, teachers should pay more attention to the way and quality of composition questions, so that "practice makes perfect"; Multi-solution unification, excavating the same essence of * * *; Unify multiple questions and sum up the laws of thinking. "Third, try to design prototypes selected from real life, compile exercises from questions that students are interested in, cultivate students' autonomy and exploration, and let students experience the application of mathematics in practice. Only when they pay attention to the research process in the process of collecting information can they apply mathematical knowledge and improve their ability to solve practical problems.
5, exercise selection should pay attention to the mining of textbook exercises.
Textbook exercises are excellent topics selected by experts many times. Teachers should give priority to the examples and exercises in textbooks when choosing topics, and deepen and evolve them appropriately, so that they come from textbooks, not just textbooks. You can't "throw away watermelons and pick up sesame seeds" and ignore textbook exercises to do a lot of extracurricular exercises.
In practice, we should carefully design and excavate the exercises in teaching materials, and write exercises with multiple solutions, changeable questions, multi-purpose questions and one method to improve students' ability to use knowledge flexibly.
Second, have an efficient class.
The classroom is a mirror, and the teacher's every move in the classroom reflects his teaching philosophy. A vibrant classroom is a people-oriented classroom. Respecting human values is the starting point of humanistic spirit. When people are respected and get their own "dignity right", they will have a sense of responsibility and stimulate their enthusiasm and initiative in learning. Once learning awakens students' subjective life consciousness, the classroom will be full of vitality. The development of potential, the awakening of spirit and the opening of heart are the manifestation of unique personality and the promotion of subjectivity. The life course of teachers and students in the classroom is the fusion of vision, the enjoyment of experience and the singing of soul, which also makes teachers and students enjoy the happiness of education.
"How to make every student develop to the maximum extent on the original basis is the wisdom of all education." In mathematics classroom, teachers' wisdom lies in creating an open situation, giving students a space to think and an opportunity to express themselves, allowing colorful thinking to meet in the classroom, opening the door to creation with novel and unique thinking, and letting the thoughts shining with wisdom gallop in the classroom. The most important thing for teachers is to listen carefully, give guidance in time, and give students enough inquiry materials, so that students can truly become the main body of learning.
The wisdom in the classroom shines on the creation of the theme. Mathematics can really enter students' hearts only if it fits students' experience system. Mathematics is realistic, interesting, useful and challenging for primary school students. Mathematics full of life breath and mathematics to solve practical problems can make students feel the value of mathematics and produce positive and happy emotions. The connection between mathematics knowledge and life makes mathematics learning more practical.
For example, combined with the teaching of statistical charts, before students go on a spring outing, I ask students to count the number of people, estimate the number of vehicles, make statistical charts, and then design a reasonable car rental scheme to solve practical problems.
Introducing vivid life themes into the classroom, activating the classroom with life problems, skillfully applying students' life experiences to the classroom, and applying vivid examples of life mathematics to the classroom, the mathematics classroom has been nourished by the water of life and is more interesting and charming.
The essence and essence of exercise class is whether teachers can play the role of exercises in dealing with exercise materials, fully mobilize students' participation, "externalize" what students have learned and strengthen the "internalization" of knowledge through "externalization", which is the key to the success of an exercise class.
Good teaching effect is the ultimate goal of teaching activities. How to teach an efficient class well is very important to every teacher. To measure the teaching efficiency of a class, we mainly look at the effective teaching time, that is, the time for students to learn knowledge, master skills, form abilities and raise awareness in the process of teaching activities. Therefore, teachers must do everything possible to improve the efficiency of class for 40 minutes.
Therefore, the teaching design of exercise class should pay attention to the following three points:
1, the design of the topic should have a certain gradient, create appropriate situations, and stimulate students' interest in learning.
There are some differences in the basic knowledge, intelligence level and learning methods of students in each class. In the teaching of exercises, exercises should be designed in layers according to the actual situation of students. We should not only create a stage for outstanding students to perform and develop their personalities, but also pay attention to providing opportunities for underachievers to participate and let them get the joy of success. Otherwise, a large number of students will be "left out" and lose confidence in learning mathematics well. The arrangement of topics can be from easy to difficult, forming a gradient. Although the starting point is low, the final requirement is higher, which conforms to the cognitive law of students, so that the underachievers will not "sit still" and the top students will "eat their fill" and they will all be improved to varying degrees.
2. The teaching methods of exercises should be diversified.
The so-called teaching includes two aspects, one is the teacher's "teaching" and the other is the student's "learning". For a long time, the traditional teaching mode in China is "teachers teach students to learn", and students are used to learning only by accepting knowledge. In the current wave of new curriculum reform, as a teacher, we must not let the simple "spoon-feeding" teaching method continue. Because it is contrary to the "students are the main body of learning, cognition and development" in the "new curriculum".
The new curriculum emphasizes that teachers are organizers, participants, directors and appreciators in the teaching process, which shows that the fundamental task of teachers in teaching activities is to "guide", that is, to arouse students' desire for knowledge, create a good learning environment for students, and improve and sublimate their learning ability. At the same time can accumulate knowledge.
Therefore, the starting point of "teaching method makes way for learning method" is based on the status of students and teachers in the teaching process. The task of teachers is not only to guide students to learn and improve their learning ability through various teaching methods, but also to create an atmosphere for students to learn knowledge, stimulate students' interest in exploring knowledge, and enable students to master the fundamental methods of understanding the world from known to knowledge and from phenomenon to essence. It will benefit students for life.
The knowledge density of exercise teaching is high, and there are many questions, so students are easy to get tired. If the teaching organization is simple, students will feel bored and lose their enthusiasm for learning. In order to overcome this phenomenon, teachers' teaching and students' learning activities must be reflected in exercise teaching, and teaching, practice and thinking should be organically combined to create conditions through "solving doubts, focusing on lectures and discussing difficult points".
3. Cultivate a good teacher-student relationship and give full play to students' initiative.
The process of mathematics classroom learning should be a complex process including guessing, making mistakes and trying, proving and refuting, testing and improving.
Mathematics teaching is the result of living, dynamic and possibly wrong mathematics activities, rather than static and closed results.
Friedenthal said: The best way to learn mathematics is to let students discover this knowledge by themselves. Mathematics classroom teaching is to guide students to concentrate on experience. At first, people explored this knowledge.
The teacher's lesson plan is just a preset in the classroom. Every student is a different thinking subject, and children with different understanding abilities always have their own discovery from their own perspective. In the classroom atmosphere full of joy, friendship, cooperation and longing, teachers let children inspire and compete with each other, making re-creation colorful again and again. Teachers should explore these valuable dynamic generation resources, so that the classroom can be generated in the preset, and the beauty of agility can be transformed in the dynamic generation.
I have heard many successful math classes and practiced them in my own class. I gradually like math class. Although not as emotional as Chinese class, I am delighted and moved by the students' spirituality in listening, wisdom in thinking, emotion in experience and brilliant flower of life blooming in mutual respect. Let's experience the interaction with children and taste the charm of math class!
Good teacher-student relationship is one of the indispensable factors in teaching activities.
The so-called "close to his teacher and believe in his way" is this truth. People say that "interest is the best teacher". If students are not interested in subject knowledge, then if the relationship between teachers and students is good, they will be regarded as equal subjects with themselves through the persuasion of teachers. Then students' study will become easier. Imagine a student who has no "feelings" for math class and doesn't "catch a cold" when facing the math teacher. The result can be imagined. This is also a kind of "love me, love my dog". If teachers can handle the teacher-student relationship well, supplemented by encouragement and encouragement, students' "interest can be cultivated" and students will be willing to accept the teacher's education. Only in this way can the teaching efficiency reach the best state. Quality-oriented education requires teachers to respect students' subjective status and initiative, and regard students' learning process as an active exploration process for the subject to meet internal needs. Students' learning is a dynamic process, and the whole learning process should be composed of participation desire, participation process and experience success. In the teaching of exercises, teachers must change the habit of "cramming" and "talking in one word", give students more opportunities to use their brains, talk and do things, leave enough thinking space for students to ask questions, and let them solve problems through active exploration and discussion.
Third, do a good job in after-class consolidation exercises and feedback processing.
The design principle of high school math homework: The purpose of students' homework is to consolidate and digest what they have learned, turn knowledge into skills and develop their abilities.
Correctly organizing students' homework is of great significance for cultivating students' ability and habit of independent homework and developing their intelligence and creativity. Therefore, teachers should pay attention to the design of homework.
However, the design assignment is not as simple as imagined. In order to maximize the benefit of homework, teachers should pay attention to certain methods in teaching.
The following principles should be paid attention to when designing surgery.
1, the purpose of the job
That is, homework should reflect the general goal of senior high school mathematics curriculum, the goal of teaching unit and the teaching goal to be achieved in classroom teaching. Students can further consolidate their knowledge and develop their thinking ability through practice.
To put it simply, teachers should know what to practice in their homework. For the content that is difficult to learn, teachers should focus on the key points and break through the difficulties when designing homework. For the content that is easy for students to accept and has strong knowledge coherence, properly design homework about developing intelligence and improving thinking ability. This will not only ensure that students finish their homework on time, but also enable them to develop their intelligence while experiencing the joy of success.
2. Target operation
That is, homework can reflect the level of teaching content and is suitable for students with different levels of thinking ability.
Teachers should carefully choose and design homework questions according to the teaching materials and students' reality. The designed homework does not meet the actual ability and needs of students, or it is too difficult or too deep. Students can't do it, their interests and emotions will be affected, and there is no result. Under the premise of mastering the "two basics", difficult homework should make students competent and consider the adaptability of most students.
3. Differences in homework
Under the class teaching system, the differences between students' intelligence and non-intelligence factors will lead to different learning levels of students. Teaching students in accordance with their aptitude and treating them differently can narrow this gap. Of course, it needs to run through every link of teaching work. Homework design is no exception.
Students can be divided into two or three groups according to their level, and their homework can be arranged in categories. You can also arrange an appropriate number of multiple-choice questions while assigning homework. Teaching students in accordance with their aptitude is obviously effective, but we must pay attention to the misunderstanding of lowering teaching standards.
4. Reproducibility of operation
Representative, typical and critical homework should not be thought that students can pass the exam after doing it, but must arrange a certain degree of repetitive homework purposefully and planned to ensure that students acquire solid knowledge and skilled skills. However, it should be noted that repetition is not the same as mechanical repetition. The amount of homework is appropriate and the difficulty is moderate, so students can finish it.
5. Openness of homework
Homework should be open and students should have room for self-development. According to students' mathematical knowledge, skills and abilities, some exploratory homework can be designed appropriately in combination with teaching materials, so as to guide and encourage students to ask questions and find partners to complete the research homework.
How to teach math exercises well?
Exercise class is an important class in mathematics teaching. It not only consolidates, deepens and corrects what students have learned, but also combs and integrates what they have learned. So how should we have a good exercise class? First, the topic "Jing"
It is very important to choose typical topics as examples in exercise class, but it is not necessarily the most difficult to pay attention to typical topics. This topic should be selected according to the characteristics of this part of knowledge and the basic level of students. Generally speaking, a typical topic contains rich connotations, and its knowledge, skills, thinking and methods will be fully reflected after the teacher's excavation. In the important process of evaluation, we should organically link what we have learned and let students think freely, which is of great benefit to the consolidation of students' basic knowledge, the establishment of mathematical thinking and the improvement of their ability to analyze and solve problems.
Second, explain "through"
For the exercise class, you can't just talk about the topic, nor can you just talk about how to do it. On the basis of examples, we should extend the practice of letting students master this kind of topic, and we can draw inferences from others through practice. Teachers should sum up and popularize knowledge in time, and apply rigorous reasoning to solve problems according to certain causal relationship and logical order.
Through the evaluation of exercise class, students can consolidate basic knowledge, train basic skills, further broaden their horizons and improve their problem-solving ability.
How to teach exercises or test papers well?
1, pay attention to the three basics and cultivate the rigor of thinking.
① Consolidate the basic concepts, summarize the problem-solving methods and summarize the knowledge points used in the problem-solving process.
② Pay attention to the analysis of problem-solving process, and make up for the lack of students' knowledge.
2. Develop problem-solving thinking and cultivate the broadness of thinking.
(1) How to solve a problem and cultivate thinking ability.
(2) Learn to ask more questions and conduct self-training.
③ Seek the law of solving problems and highlight the thinking process of solving problems.
3. Show typical mistakes and cultivate critical thinking.
① Guide students to correctly understand the meaning of the question.
② Guide students to evaluate the problem-solving process.
③ Analyze the causes of errors and explore the correct methods.
(4) Guide students to test and cultivate their self-evaluation and judgment ability.
4. Explore openness and improve the enthusiasm of thinking.
(1) guided observation, and found that it has similar characteristics to the previous topics. When solving problems, we can learn from each other's strengths and cultivate students' observation ability.
(2) Encourage students to make bold analogies and conjectures, decisively choose the breakthrough point to solve problems, and cultivate students' exploration spirit.
5, strike while the iron is hot for variant training to cultivate the profundity of thinking.
① Change conditions and conclusions to cultivate students' reverse thinking.
② Strengthen the transformation consciousness and improve the computing ability.
6. Reflect after the question and cultivate the persistence of thinking.
① Reflect on the problem-solving process and clarify the problem-solving ideas.
(2) Summarize the problem-solving methods to systematize the knowledge and methods.
Teaching and Design of Math Exercises Course
Rugao Teachers College Wu
This paper mainly discusses the structure, design principles and content selection of exercises in normal universities. Talk about my own views on how to teach exercises well, and discuss the design principles, correction and feedback methods of homework after class.
Keywords: exercise class assignment design
It is very important to solve the mathematical problems of students in normal universities. For teaching, proper sports training is essential, and sports class is a common and important training class. Optimizing exercise design and exercise class teaching can not only effectively enhance students' ability to solve problems and improve the quality of mathematics teaching, but also promote students to form good mathematical concepts. How to teach a high-quality exercise class? I personally think the key lies in the following points:
First, the topic should be reasonable.
The choice of exercises directly affects the training efficiency. When choosing exercises, we should pay attention to scrutiny, which can be considered from the aspects of pertinence, feasibility, typicality, inquiry and the mining of exercises in teaching materials. Pay special attention to the excavation of textbook exercises. Textbook exercises are excellent products screened by experts many times. In the choice of exercises, we should give priority to the examples and exercises in textbooks, deepen and evolve them appropriately, and compile exercises with multiple solutions to one problem, changeable problems, multi-purpose problems and one method, so as to improve students' ability to use knowledge flexibly and make them come from textbooks without being bound by textbooks. We should not "throw away watermelons and pick up sesame seeds" and ignore textbook exercises to engage in a large number of essentially repetitive extracurricular exercises.
For example, according to the chapter on algorithm, we made a topic (compulsory 3P20 exercise in mathematics experiment of senior high school Jiangsu Education Edition 1):
Expressed by conditional statement: input two numbers and output the larger number.
This question is not difficult for students, but we can change the topic slightly and derive a series of questions:
(1) Enter two numbers, how to output the smaller number?
(2) If three numbers are input, how to output the maximum number? How to output the minimum number?
(3) Draw the flow chart of the above problem (2),
(4) Can you write basic algorithm statements (input and output statements, conditional statements, loop statements) in combination with the flow chart?
(5) If a sentence is randomly generated by the computer without your input, can you write this sentence?
In this way, students can not only be interested in solving problems, but also solve problems by their ability. In fact, they have reviewed the structure of the three algorithms, the basic statements of the algorithms, the generation of random numbers and other knowledge. If conditions permit, it can even be verified by VB on the computer. I believe this will be good for students' progress in all aspects.
(2)
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