New methods of mathematics teaching in primary schools
(A) the method of discovery
Discovery method is a teaching method advocated by Bruner, a famous contemporary American educator and cognitive psychologist, in the 1950s and 1960s.
1, the discovery method and characteristics of basic meaning
Discovering laws means that teachers are not directly close to students' ready-made knowledge, but the main material to guide students to discover problems and laws independently according to teachers and textbooks, active thinking and teaching methods.
The study found that compared with other teaching methods, it has the following characteristics:
(1) This law emphasizes the discoverer of students, students' self-discovery, and students know the answer to their own questions, rather than the teacher providing a ready-made conclusion, which makes students passively absorb.
(2) The law of discovery emphasizes students' intrinsic motivation. The best motivation of students is their inherent interest in the research process. The study found that this rule accords with children's psychological characteristics, such as fun, active, inquisitive and source-seeking. For example, if they encounter novel and complicated problems in tracking, they will actively explore. Teachers make full use of this function, novelty, difficulties and contradictions cause conflicts in students' thinking, encourage them to have a strong desire for knowledge, explore and solve problems, and change the traditional teaching methods to only use external stimuli to promote students' learning and practical activities.
(3) The discovery of laws makes teachers play a leading role potentially and indirectly. The purpose of this method is to let students make use of existing knowledge, and provide teachers with various learning materials and intuitive teaching AIDS, observe the analysis, synthesis, judgment and reasoning of the brain, and discover the essential laws of things, so in this potential indirect process, teachers play a leading role.
2. The main advantages and limitations of this method are found.
The discovery method of has the following main advantages.
(1), let students learn external motivation and internal motivation, and learn confidence.
(2) It helps to cultivate students' ability to solve problems. Because law often practices how to solve this problem, students can learn, explore and cultivate their problem-solving ability, attitude and enthusiasm for invention.
(3) Search methods that help to improve students' wisdom, potential and thinking quality of excellent students.
(4) It is conducive to the memory and consolidation of students' knowledge. Discover the internal reorganization of students' knowledge structure in the process of learning. This reorganization better combines the existing knowledge structure with learning new knowledge. This systematic and structured knowledge is helpful for students to understand, consolidate and apply.
It is found that this method also has some limitations.
(1) It takes more time to discover the purpose of teaching efficiency. Students' knowledge, because it is a process of rediscovery, all the truths must be discovered by students themselves or rediscovered, rather than simply spoken by teachers. Therefore, it is necessary to explore for a long time in the teaching process.
(2) The purpose is to adapt to a certain range of teaching content. Discovery method is suitable for some strict disciplines such as logic, physics and chemistry, but not for humanities. Applied discipline is a teaching concept and context that only applies to general knowledge, such as average method. The name, symbol and representation of the concept still need to be explained by the teacher.
(3) The teaching target is more suitable for middle and advanced students. Discover that learning must be the premise of having certain basic knowledge and experience. Therefore, the higher the level, the stronger the students' independent exploration ability. Therefore, it is not necessary to use discovery method to teach all teaching contents and teaching objects.
3. Find examples (except the two-digit teaching method)
Give a title, such as 39÷3. Students can get 39 articles, 3, and they are divided into 13. Do a few themes and you can make a set of 10 projects. For example, give a title: "Harry buys candy and uses 10 every time." He ate one and packed it for the students. When are the students? "
Students may have the following solutions:
(1)3 heaps, and then count the number of heaps occupied.
(2) One of the 3 10 students comes first, the rest arrive at 3 students from 9: 00, and then the rest are divided into groups of 3.
9 +9 +9 +3 +3 +3 +3 = 39 (block)
↓↓↓↓↓↓↓
3+3+3+1+1+1=13 (person)
(3) It is similar to (2), but it can be seen that 4.
9 +9 +9 +9 +3 = 39 (block)
↓↓↓↓↓
3 +3 +3 +3+1 = 13 (person)
(4) They saw that only three people with a score of 10 went to 10, and the rest were divided into groups of three.
30 +3 +3 +3 = 39 (block)
↓↓↓↓
10+ 1+ 1+ 1 = 13.
(5)(4), but they can see that there are only nine or three people left.
30 +9 = 39 (block)
↓↓
10 +3 = 13 (person)
After the students put forward the solution, the class discussed it. Teachers are evaluating different algorithms. Then a topic came out, and many students chose this topic instead of his first simpler method. Teachers further put forward guiding questions to urge students to find more effective calculation methods, thus forming a generally vertical calculation.
(B) experimental teaching methods
The teaching methods, teaching methods and teaching methods in primary schools have great influence. This is a teaching method with China characteristics. The earliest educational science teaching design in Qiu Xuehua was put forward by Changzhou Institute of Technology, and gradually extended to 10 years in some areas, which achieved good teaching effect and even had a certain influence internationally.
1, try teaching method
What is the attempt teaching method? The basic idea of trying teaching method is: in the teaching process, it is not the first time that the teacher speaks, but the first time that the students try on the basis of knowledge. In the process of trying, guide students to study textbooks independently and guide students to discuss and practice. On the basis of practice, the teacher gives a targeted explanation. The teaching plan of trial lecture is divided into five steps: making the topic of trial lecture; Self-compiled teaching materials, try to practice, students discuss and teachers explain.
The most fundamental difference is to try teaching methods and means, change the first practice talk of "practice" in the teaching process and say "as the main form of teaching".
Background of experimental teaching method: China's teaching reform has been on the right track. In the early 1980s, many experimental studies on teaching reform were launched. At the same time, there are many foreign experiences in teaching reform. In this case, people began to think about how to research and create experimental teaching reform with China characteristics in China, which not only meets the needs of modern educational technology reform, but also has strong operational teaching methods. Teacher Qiu Xuehua conducted a study. A survey before and after the Cultural Revolution shows that it is necessary to study a new primary school mathematics teaching in the reform and experiment of primary school mathematics teaching. Therefore, on the basis of analyzing and comparing the experience of teaching reform at home and abroad, he put forward the idea of de-teaching. He used the ancient heuristic teaching principles of China for reference and discovered this idea? Law and self-study tutoring teaching, comprehensively analyze and study the advantages and disadvantages of these teaching methods, and try to form a unique, operable and feasible teaching method.
2. Try teaching methods of teaching plan and teaching structure.
The basic teaching procedure of trying teaching method can be divided into five steps.
(1) Generate the title of the attempt.
Try the topic is roughly the same as the example in the textbook, and distort the problems in the textbook.
Examples in the book: 1/2+1/3.
Trial question: 1/4 5/6
The purpose of this question is to stimulate students' interest in learning and let them know their learning situation in this class.
(2) Self-study teaching materials
Students try to practice and have a certain interest in this issue, and teachers guide students to read books on how to speak on this issue. The teacher put forward some ideas to solve the problem: what should I do if the denominator is different for the problems related to the above questions? Why do * * * have something in common? "
By self-learning textbooks, students can know their own understanding problems, and teachers can also understand the difficulties students encounter in their studies.
(3) Try to practice
Through self-taught textbooks, students have a basic understanding of what they have learned, and most students have answers. Trying again at this time is a way for students to try. Generally speaking, good circuit board performance is allowed, there are differences among the three types of students, and other students do the same in practice.
(4) Students discuss
Try to practice, some students may make mistakes, and different methods may appear. Let the students solve problems and discuss them in their own way.
(5) Teachers
Just because a student does a problem doesn't mean that he has mastered what he has learned. Teachers can explain that students follow a certain logical system in learning. This shows that on the basis of the goal, students have a preliminary understanding of what they have learned, and have some learning ways or some research methods to explain the problem, which is relatively concentrated.
The above five steps, try new teaching methods. In the classroom, as a complete course, the classroom teaching structure of trying teaching methods includes the following six aspects:
(1) Basic training (5 minutes);
(2) Introduce a new lesson (2 minutes);
(3) New lesson (15 minutes);
(4) Consolidation exercise (6 minutes);
(5) Class assignments (10 minutes);
(6) Class summary (2 minutes).
The advantages of this teaching structure are: highlighting the teaching focus, increasing the practice time and changing the method of full-house irrigation.
3, the advantages and limitations of trying teaching,
Its advantages lie in the following aspects.
(1) is beneficial to students' exploration spirit and self-learning ability. In the process of learning, students want to try and solve this problem in their own way.
(2) It is beneficial to improve the efficiency of classroom teaching. You can make full use of the best time in teaching, so that students can integrate into new learning as soon as possible and have more time to try and consolidate exercises.
(3) It is beneficial to improve the teaching quality in a large area. This teaching method is easy to operate, and teachers can master it, which is more conducive to poor students' learning. Therefore, it can be applied to a wider range of occasions, thus improving the teaching quality in a large area.
Its limitations are as follows.
(1) requires students to have a certain mathematical foundation and self-learning ability. This teaching method is not suitable for young students.
(2) Don't use the principles of new teaching ideas, which are suitable for teaching successors.
(3) It is not applicable to the content with strong operability.
4. Try teaching application examples.
There are many experimental teaching methods in mathematics teaching. Suitable for a variety of teaching. The following is a teaching example of "Divided by Zero in Business". (abstract)
(1) Basic training (omitted)
Oral calculation:
Board game: 645÷3
(2) Introducing new courses
Change the exercise from 645 to 6 15 and continue your study.
(3) New courses
(1) generates an attempt title: 6 15÷3.
② Try to practice.
Try this question. It's a little different from the last one. Can you solve this problem?
(3) Self-study teaching materials
④ Students discuss.
Students who discuss three algorithms (only the second algorithm is correct):
25
?
25
?
The teacher is there.
(4) Consolidate exercises
(5) Class assignments
(6) Class summary
(3) Self-study tutoring method
1, the basic meaning of self-study counseling method
Lu Zhongxing, a professor of science at China Academy of Social Sciences, is a self-study tutoring method of experimental teaching method for middle school mathematics self-study tutoring sponsored by the Institute of Psychology. , has achieved great success in middle school mathematics teaching. The basic idea of? The teaching methods of primary school mathematics also have certain influence. Similar to experimental research primary school. In particular, the basic principles of primary school mathematics teaching reform are adopted.
The study of learning experiment was first put forward in 1958, and the experiment was carried out. At the beginning, it was to learn the planned teaching principle in the western region and implement the principle of small steps and feedback teaching. Later, the transformation and self-study counseling method were named.
Self-study tutoring method is a teaching method which focuses on tutoring students to learn independently under the guidance of teachers. Instructors of self-study counseling are used in primary school mathematics teaching, and students generally refer to the teaching method of acquiring knowledge and skills by reading textbooks.
2, the method of self-study tutoring lesson plans
Learning methods, using psychological principles, rewriting textbooks with appropriate steps and timely feedback principles, and implementing the comprehensive use of textbooks and exercise books are the answers to this question. Teach students to learn independently by means of self-study counseling, and provide 30 to 35 minutes for high school students in a class, including self-study, self-study and self-test self-study time. The teacher's explanation time is generally less than 15 minutes.
The basic steps of self-study tutoring teaching are divided into five steps.
(1) theme. Teachers can introduce the new curriculum directly, or they can ask questions after checking the relevant knowledge. The latter method is more suitable for students' learning characteristics. At the same time, high school students must also provide self-study programs for self-study, and strive to find solutions to problems while reading around the central theme.
(2) Cultivate students' self-study ability. This step is to let students read the textbook independently, and the teacher should give necessary guidance at the same time. From a practical point of view, teachers choose appropriate ways to guide the highlights of introspection according to different grades, different cognitive levels and the difficulty of textbooks, which is concise and clear.
(3)Q and problem-solving ability. Teachers' answers to students' self can also stimulate students to discuss and answer each other. In order to further improve students' autonomous learning ability after answering questions, students are also allowed to read textbooks and consolidate their knowledge.
(4) organize and summarize. Teachers should check students' learning results, and if they know the problems and remedy them in time, they should also learn to sum up the problems. This paper tries to make students summarize in accurate mathematical language, draw conclusions and gradually cultivate students' ability to express in mathematical language.
(5) Consolidation and application. The autonomous work of classroom teaching content arrangement aims to let students further understand and consolidate their knowledge and skills, and initially form them.
(3) Evaluation of self-study counseling method.
The main advantages of this method are: fully mobilizing students' learning enthusiasm, giving them more opportunities to think independently, and mastering knowledge through self-study is conducive to the cultivation of self-study ability. This kind of teaching can solve the basic problems in the classroom and greatly reduce the students' academic burden. Our students can correct their mistakes in time at work, free teachers from their work, and have more time to prepare lessons and study students' problems, which is conducive to improving teaching quality. In addition, students can look at other reference books after class to expand their knowledge, which is conducive to the all-round development of students.
Self-study guidance is not only the integration of teaching methods and teaching concepts, teaching contents and teaching methods. Especially the teaching method based on the selection and arrangement of teaching materials. Therefore, it can be regarded as a comprehensive teaching method.
Teaching examples of self-study counseling method (the significance and basic nature of proportion)
Specific teaching process:
(1) teacher talking
(2) Prepare for practice
(3) New courses
(1) This example and self-test questions
For example, a car travels 80 kilometers in the first two hours and 200 kilometers in the Twelfth Five-Year Plan.
Time (hours)
? 2
? five
?
Distance (km)
? 80
? 200
?
As can be seen from the table, this car:
The ratio of the first travel distance to the time;
The ratio of distance to time on the second trip.
What is the ratio of these two? They what?
Q: What is proportion? What do I need to do to make up for it? Can these conditions be extended? If the proportion is written as a point, what is it? What is the nature of proportion?
② Guide self-study and summarize the rules.
Guide students to observe the meaning of two proportions.
Conditions for guiding students to participate in group discussions.
Proportion of students who have arrived.
Guide students to practice thinking: the difference between ratio and proportion.
Let the students know the proportion of each part of the name.
Guide students to use addition, subtraction, multiplication and division to explore the basic properties of the ratio between different methods.
③ Think more, question and ask difficult questions, be concise and guide.
According to the students' questions, the teacher explained the basic nature of proportion: the proportion of two off-site items is the inner product of two identical quantities, which is the so-called basic nature proportion.
(4) classroom teaching
(D) "inquiry-discussion" method
Questioning-A Seminar for Teaching Experts, Professor Lambenda's Lambenda. Have a certain influence in the United States. Introduced to China in the early 1980s. Science teaching and mathematics teaching are widely used.
1, the basic content law of "exploration-theory"
The basic idea of? "Inquiry-discussion" teaching is divided into "inquiry" and "discussion".
The first step of "exploration" is to explore your own students under the guidance of the teacher. Teachers provide students with certain questions and necessary operating materials, so that students can operate by themselves, fiddle with the influence of various factors and study the quantitative relationship of questions. Teachers should give appropriate guidance in the process of teaching activities.
In the process of investigation, the material structure provided for students is an important factor. Teachers should combine teaching, learning and research materials for students to choose reading. Such as the color of wood, geometric puzzles.
The second link "seminar" is to give students an opportunity to fully express their opinions. Students in this early stage have a certain understanding of the research problems. At this stage, teachers organize students to watch and think about their opinions, and make full use of language communication to let students know more information. Moreover, in the process of discussion, we can inspire each other and have a more comprehensive and profound understanding and research on the problem. A learning problem in which rules or conclusions are decided by teachers and students.
In the teaching process, it is not limited by these two links, and it is flexibly organized and used.
2, "explore-on" the main characteristics of the law
"Inquiry-discussion" has the following main features.
First, we can give full play to students' initiative and creativity.
Teachers' leading role is reflected in problem cases, helping students choose suitable materials and design surveys.
The third is to form a more communicative classroom teaching atmosphere.
3, explore the applicable law-seminar ",for example (average).
The first category is divided into several groups, each with 4 people.
Measure the height of each student and cut out a piece of paper according to the measured height. The teacher asked, "How do I know how many people are put together?" "How high, four people on average?"
And the average level of teachers. And put forward how to find the average height of the class. "How to behave, what is the average height?" The students said that you can add such things to the height and then remove the total. Then the height of a piece of paper per student is the average of the places where a piece of paper is nailed to the wall and underlined and connected to the wall. Find some online below and some online above. , and indicated by "-"and "+". The high part was cut off, which just filled the low part of the students. The students are very excited.
Next, the students put forward a simple method to calculate the average. Identify tall and short students. This number is higher than the numerical value, and so on, together, divided by the total number of students in the class, plus the average height of short students.
Find a few students at random and come up with a standard and relatively simple method to calculate the standard line of average height.
Reform of mathematics teaching methods in primary schools
In the past, most people thought that the factual indicators of students' mathematics learning in class (such as concepts, formulas, rules, operator management, etc. ), but with the development of subject education theory, the deepening of mathematical education knowledge research, and the in-depth reflection on the humanity of school mathematics education, mathematical theory and practitioners have realized: using a kind of mathematics "in activity" instead of formal mathematical operation. "Students should have experienced mathematics, not mathematical abstraction, not abstraction; Step, not step, not formal algorithm, not algorithm, language expression, mathematics learning process, not language. " Therefore, learning to understand mathematics in class includes not only mathematical facts, but also mathematical activity experience. The new teaching language should not be a one-way teaching mode of teachers' system based on the content of textbooks, but an interactive mathematics teaching between teachers and students, which should be closely related to students' life and development process. In reality, students begin to create interesting situations based on their own life experience and existing knowledge, and guide students to observe, operate, guess, reason and communicate. Therefore, students master basic mathematical knowledge and skills through mathematical activities, initially learn to observe things and think about problems from a mathematical point of view, stimulate their interest in mathematics, and learn the desire of mathematics teachers to organize, guide and cooperate with students' mathematical activities; According to the specific situation of students, we should pay attention to the processing of materials and the teaching process designed by creators, correctly understand the individual differences of students, and teach students in accordance with their aptitude, so that students can gain successful experience and establish self-confidence in learning mathematics on the basis of the original development of each student. "With the development of the concept, the new mathematics curriculum reform in philosophy, politics, science and technology, culture and so on. Develop modern teaching methods and put forward new features.
First of all, fully mobilize students' learning motivation and give full play to the basic characteristics of teachers' leading role, and strive for the best combination of teaching and learning. JFHerbert's traditional "center" emphasizes that the absolute authority of teachers and the strict discipline of students are the containers of knowledge; On behalf of J. Dewey's "new center", compared with students, teachers are the planet in the sun, and children who study independently may absolutely deny the leading role of teachers. In order to avoid these two extremes, our teaching method combines the main role of students with the leading role of teachers as a dynamic level of transformation, development and unity of opposites, which is the main contradiction of this kind of teaching. In the teaching process, teachers can guide students to think independently and communicate cooperatively. For situational problems, teachers and students have different cognitive preparations and different ideas. Through the life and communication between teachers and students, they can promote each other. Class-group cooperative learning enables teachers to effectively combine and encourage students' groups, explain their own ideas and exchanges, learn mathematics through mathematical exchanges and exchanges between groups or class exchange associations, and cultivate students' mathematical thinking, language expression ability, thinking and learning responsibility for themselves.
Vivid and interesting learning situations stimulate students' learning motivation, stimulate students' brains, tongues and hands, and guide students to explore and discover. Teachers need to make full use of students' life experience, knowledge, background and realistic modeling. Students are interested in the learning environment. Students can understand the generation, formation and development of mathematical knowledge, feel the power of mathematics, appreciate the beauty of mathematics and master the necessary basic knowledge and skills through observation, operation, speculation, communication and reflection. Learn math by doing it.
Third, we should pay attention to students' individual differences and encourage diversified learning methods and problem-solving strategies. Effective methods to encourage diversification and individualization of problem solving strategies. For example, in computing teaching, students are encouraged to use existing knowledge and background calculation results. Teachers should not demonstrate and explain the written calculation rules first, and the operators should manage them to limit students' thinking. In the case of some practical problems, the teacher asked the students to make a preliminary estimate and then calculate independently? On this basis, communicate in groups and feel the diversity and flexibility of problem-solving strategies.
Fourth, pay attention to students' learning, especially the research and guidance of learning methods, so that students can learn in the process of going to society and gradually achieve it. Learning students' ability to acquire knowledge, the formation process, the basic movement patterns and laws, and the basic methods of research guidance are the necessary components to ensure the realization of modern teaching methods and the key to improve teaching quality.
Fifth, in order to make students adapt to the future social life and further development, we should pay more attention to cultivating students' attitudes, emotions and values. Attitudes, emotions, values? As the internal motivation of learning, it plays an important role in learning. Fully consider the teaching methods of modern primary school mathematics, pay attention to students' learning interest culture and learning motivation, emphasize the emotional communication between teachers and students, and make full use of the role of emotion to open the door to students' cognitive structure.
Sixth, pay attention to the cross-use and coordination of various teaching methods. Attach importance to the application of modern teaching methods. Traditional teaching methods are often formed by fixed teaching methods. With the development of the times, the development of modern teaching theories and methods, and the in-depth study of teaching methods, educators realize that there are various teaching methods, and no one size is suitable for all teaching methods. The mathematics theme of teaching methods, the teaching styles of children and teachers, and whether different teaching methods are "single" can have different combinations. In addition, modern teaching methods are emphasized, and vivid, infectious and abstract mathematical concepts and principles are used to explain clearly with screen images to attract students' attention and improve their interest in learning. Deepen our understanding and memory of materials. Micro-teaching CAI is carried out in China. It is the application of direct products and the development of modern scientific and technological means and modern teaching means. The role and position of modern educational technology must be considered. It is a teaching method that affects and changes traditional teaching methods, takes into account the introduction of modern technology and equipment, and finds the combination point and development direction.