Independent inquiry learning-the key point is that students experience the learning process personally, and its value is not so much to let students find the conclusion, but to let students pay more attention to the inquiry process. Autonomous inquiry learning attaches importance to allowing each student to explore, discover and "re-create" related mathematical problems freely and openly through observation, experiment, guess, verification and reasoning according to his own physical examination. In this process, students not only acquire the necessary mathematical knowledge and skills, but also understand the formation process of mathematical knowledge, especially the thinking method and value of experiencing and learning mathematics.
Cooperative learning-a common form in primary school mathematics teaching. However, at present, the efficiency of group cooperative learning is less, and some are just a mere formality. Some researchers believe that there are several types of group learning, such as independence, competition, dependence and dependence. At present, we use more students to communicate with each other after studying independently, but seldom study or solve a problem together in the real sense.
"Practical activity" teaching method-through practical activities, cultivate students' innovative spirit and practical ability, explore students' potential and let students learn useful mathematics knowledge.
……
Whether it is "optimization" or "innovation", we should generally pay attention to the following four points: First, the choice or innovation of teaching methods must conform to the teaching laws and principles; Second, according to the teaching content and characteristics, to ensure the completion of teaching tasks; Thirdly, it must conform to students' age, psychological change characteristics and teachers' own teaching style; Fourth, it must conform to the existing teaching conditions and the prescribed teaching time. In addition, in guiding ideology, teachers should pay attention to examine various teaching methods from a dialectical point of view.
As the saying goes, "there is no fixed method for teaching."
Common teaching methods
Since the 1980s, with the deepening of the reform in the whole teaching field, the mathematics teaching methods in primary schools have also shown a vigorous development momentum. The majority of primary school mathematics teachers and teaching researchers, on the one hand, boldly improve and transform our traditional primary school mathematics teaching methods, on the other hand, introduce advanced foreign teaching methods in a polar region, so that new teaching methods have sprung up in China.
First, the introduction of new teaching methods of primary school mathematics
(A) the discovery method
Discovery method is a teaching method advocated by Bruner, a famous contemporary American educator and cognitive psychologist, in the 1950s and 1960s.
1, the basic meaning and characteristics of discovery method
Discovery method refers to a teaching method in which teachers do not directly impart ready-made knowledge to students, but guide students to think actively and discover corresponding problems and laws independently according to the topics and materials provided by teachers and textbooks.
Compared with other teaching methods, the discovery method has the following characteristics:
(1) The discovery method emphasizes that students are discoverers, so that students can independently discover, understand and work out the answers to their own questions, instead of teachers providing students with ready-made conclusions, so that students can become passive absorbers.
(2) The discovery method emphasizes the role of students' intrinsic learning motivation. For students, the best motivation is their innate interest in the courses they study. Discovery method accords with children's psychological characteristics of fun, activity, curiosity and root-seeking. When encountering novel and complicated problems, they will actively explore. Teachers make full use of this feature in teaching, using novelty, difficulty and contradiction to trigger students' thinking conflicts, prompting students to have a strong desire for knowledge, actively exploring and solving problems, and changing the traditional teaching method that only uses external stimuli to promote students' learning.
(3) The discovery method makes the leading role of teachers latent and indirect. Because this method allows students to observe, analyze, synthesize, judge and reason with their minds, and discover the essential laws of things by themselves, the leading role of teachers in this process is potential and indirect.
2. The main advantages and limitations of discovery method.
This discovery method has the following main advantages.
(1) can transform students' external motivation into internal motivation and enhance their learning confidence.
(2) It helps to cultivate students' ability to solve problems. Because the discovery method often practices how to solve problems, it can make students learn the method of inquiry, cultivate their ability to ask and solve problems, and be willing to create and invent.
(3) The application of discovery method is helpful to improve students' wisdom, develop their potential and cultivate their excellent thinking quality.
(4) It helps students to remember and consolidate their knowledge. In the process of discovery learning, students can reorganize the existing knowledge structure internally, which can better link the existing knowledge structure with the new knowledge to be learned. This systematic and structured knowledge is more helpful for students to understand, consolidate and apply.
The discovery method also has some limitations.
(1) In terms of teaching efficiency, it takes more time to use the discovery method. Because the process of students acquiring knowledge is a process of rediscovery, all the truths must be acquired or rediscovered by students themselves, not simply taught by teachers. Therefore, the teaching process is bound to go through a long exploration process.
(2) As far as teaching content is concerned, its adaptation has a certain scope. Discovery method is more suitable for disciplines with strict logic such as mathematics, physics and chemistry, but not for humanities. As far as applicable disciplines are concerned, it is only applicable to the teaching of concepts and related common sense, such as finding the average value and algorithm. The name, symbol and representation of the concept still need to be explained by the teacher.
(3) As far as the teaching object is concerned, it is more suitable for middle and advanced students. Because discovery learning must be based on certain basic knowledge and experience, the higher the grade, the stronger the ability of independent exploration. Therefore, it is not necessary and possible for all teaching contents and teaching objects to adopt discovery teaching.
3. Discover teaching examples (one digit divided by two digits)
Give a question, such as 39÷3. Students can take 39 items first, one for every three items, and divide them into 13. After doing a few such questions, you can ask them to group 10 items. For example, give a question: "Harry bought four sweets, each 10." He ate 1 piece, wrapped the remaining three pieces in a bag and distributed them to his classmates and several classmates. "
Students may have the following solutions:
(1) Divide every three into a pile, and then count the piles.
(2) Take out 1 from each of the three 10, give the remaining nine to three students, and then divide the remaining three into a pile.
9+9+9+3+3+3+3=39 (block)
↓↓↓↓↓↓↓
3+3+3+1+1+1=13 (person)
(3) Similar to (2), but they see that there are four 9s.
9+9+9+9+3=39 (block)
↓↓↓↓↓
3+3+3+3+ 1= 13 (person)
(4) They saw that three 10 were just distributed to 10 people, and the rest were divided into three groups.
30+3+3+3=39 (block)
↓ ↓↓↓
10+ 1+ 1+ 1 = 13.
(5) It's similar to (4), but they see that the remaining 9 is only distributed to three people.
30+9=39 (block)
↓ ↓
10+3= 13 (person)
After the students put forward the solution, the class discussed it. Teachers don't evaluate different algorithms. There is another problem. Many students will choose a simpler method than the one he used for the first time. Teachers further put forward guiding questions to urge students to find more effective calculation methods and form general vertical calculation.
(B) Try teaching methods
Trying teaching method is one of the most influential teaching methods in primary school mathematics teaching. This is a teaching method with China characteristics. The attempt teaching method was first designed and put forward by Qiu Xuehua, a teacher from Changzhou Institute of Educational Science. After being gradually popularized in some regions and the whole country, it has been more than ten years now, and it has achieved good teaching effect, and even has certain influence in the world.
1, try the basic content of teaching method
What is the attempt teaching method? The basic idea of trying teaching method is: in the teaching process, let students try to practice on the basis of what they have learned, guide students to teach themselves and discuss the teaching materials, and then give targeted explanations on the basis of students' trying practice. The basic procedure of trying teaching method is divided into five steps: showing the trying questions; Self-study teaching materials; Try to practice; Student discussion; The teacher explained.
The fundamental difference between the trial teaching method and the general teaching method lies in changing the way of "speaking before practicing" in the teaching process, and taking the way of "practicing before speaking" as the main teaching form.
The background of the attempt teaching method is that in the early 1980s, the teaching reform in China has been on the right track, and there are many experimental studies on teaching reform in China. At the same time, a large number of foreign teaching reform experiences have been introduced. In this case, people began to think about how to research and create a teaching method with China characteristics that not only meets the needs of modern education reform, but also has strong operability. Over the years, Mr. Qiu Xuehua has studied mathematics teaching in primary schools, conducted many investigations and experiments on the reform of mathematics teaching in primary schools before and after the Cultural Revolution, and deeply felt the necessity of studying a new mathematics teaching method in primary schools. Therefore, on the basis of analyzing and comparing the experience of teaching reform at home and abroad, he put forward the idea of trying teaching methods. He drew lessons from the "heuristic teaching" principle, discovery method and self-study guidance method in ancient China, comprehensively analyzed and studied the advantages and disadvantages of these teaching methods, and tried to form a unique, operable and feasible teaching method.
2. Try the teaching procedure and classroom teaching structure of the teaching method.
The basic teaching procedure of trying teaching method can be divided into five steps.
(1) Show the test questions
The examination of questions is generally similar to the examples in textbooks, which is the deformation of the questions in textbooks.
For example: 1/2+ 1/3.
Number of attempts: 1/4+5/6
The purpose of putting forward trial questions is to stimulate students' interest in learning and let them know what they have learned in this class.
(2) Self-study teaching materials
After the students try to practice and have a certain interest in this problem, the teacher guides the students to see how to talk about this topic in the book. The teacher asked some questions related to the way of solving problems: As mentioned above, "What if the denominator is different?" "Why do you want to divide it?"
By teaching materials by themselves, students can know their own understanding of this problem, and teachers can also know what difficulties students have encountered in their studies.
(3) Try to practice
Students have a basic understanding of what they have learned through self-taught textbooks, and most students have methods to solve the problem. At this time, they will give students another try. Generally speaking, let good, medium and poor students perform on the board, while other students do it in the exercise book at the same time.
(4) Students discuss
When trying to practice, some students may make mistakes or do things differently. Students can discuss with their own problem-solving methods.
(5) Teachers explain
Students who do problems do not mean that they have mastered knowledge. At this time, the teacher can explain what he has learned to the students according to a certain logical system. This explanation is targeted. On the basis of students' preliminary understanding of what they have learned, we can highlight the key points when students have learned or partially learned problem-solving methods in some ways.
The above five steps are all used in the trial teaching method in the new curriculum. As a complete course, the classroom teaching structure of the trial teaching method includes the following six links:
(1) Basic training (5 minutes);
(2) Introduce a new lesson (2 minutes);
(3) Conduct a 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; Increase practice time; Changed the practice of full house irrigation.
3. Advantages and limitations of trying teaching method.
Its advantages are shown in the following aspects.
(1) is conducive to cultivating students' exploration spirit and self-learning ability. In the process of learning, students want to try to solve problems in their own way.
(2) It is beneficial to improve the efficiency of classroom teaching. We can make full use of the best time in teaching, so that students can learn new content as soon as possible and spend more time on exploratory and consolidated exercises.
(3) It is beneficial to improve the teaching quality in a large area. This teaching method is easy to operate, and teachers can generally 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 shown in the following aspects.
(1) Students need to have a certain mathematical foundation and self-study ability. This teaching method is not suitable for younger students.
(2) It is suitable for the teaching of subsequent courses, but not for the teaching of new concepts and principles.
(3) For content with strong operability, it is not suitable for use.
4. Try to illustrate teaching methods with examples.
Attempt teaching method is widely used in mathematics teaching. It is suitable for the teaching of many contents. The following is a teaching example of "division with zero quotient". (outline)
(1) Basic training (omitted)
Oral calculation:
Motherboard performance: 645÷3
(2) Introducing new courses
Change 645 in the exercise to 6 15 to continue learning.
(3) Implementing new courses
① Presentation of test questions: 6 15÷3
② Try to practice.
Just try it. This question is a little different from the last one. Can you work it out?
③ Self-study teaching materials
④ Students discuss.
Three algorithms are discussed for students (obviously only the second algorithm is correct):
2 5
25
three
⑤ The teacher's explanation
(4) Consolidate exercises
(5) Class assignments
(6) Class summary
(C) self-study counseling method
1, the basic meaning of self-study counseling method
Self-study tutoring method is a teaching method adopted in the "Middle School Mathematics Self-study Tutoring Experiment" hosted by Professor Lu Zhongheng from Institute of Psychology, Chinese Academy of Sciences. It has achieved great success in middle school mathematics teaching. The basic idea of this method also has a certain influence on mathematics teaching in primary schools. Some people have done similar experimental research in primary schools. In particular, the reform of mathematics teaching in primary schools is carried out by using the basic principles of self-study tutoring teaching.
The experimental study of self-study counseling was first put forward and experimented in 1958. First of all, learn from the western procedural teaching principles and implement the teaching principles of small steps and multi-feedback. Later, after reform, it was named the self-study counseling method.
Self-study tutoring method is a teaching method based on students' self-study under the guidance and guidance of teachers. The application of self-study guidance in primary school mathematics teaching generally refers to the teaching method that students acquire knowledge and skills by reading textbooks under the guidance of teachers.
2. Teaching procedures of self-study counseling method
Self-study counseling method uses psychological principles, rewrites textbooks by taking appropriate steps and timely feedback, and implements the comprehensive use of textbooks, exercise books and answer books. Using the method of self-study guidance, students are mainly taught by themselves in teaching, and the self-study time of a class is 30~35 minutes, including self-study, self-practice and self-examination. The teacher's explanation time generally does not exceed 15 minutes.
The basic steps of self-study counseling in teaching are divided into five steps.
(1) Propose a topic. Teachers can directly introduce new lessons, or review relevant knowledge and raise topics. The latter method is more suitable for the learning characteristics of primary school students. At the same time, provide a self-study outline for senior students, let them study by themselves with questions, read and think around the central problem of the topic, and get the solution to the problem.
(2) Students teach themselves. This step is mainly to let students read the teaching materials independently, and the teacher gives necessary guidance at the same time. Teachers should proceed from reality, choose corresponding methods to guide self-study according to different grades, different cognitive levels and the difficulty of teaching materials, and the guidance of test questions should be concise and to the point.
(3) Answer questions. In view of the problems in students' self-study, teachers can answer them pertinently, and can also inspire students to discuss and answer each other. In order to further improve students' self-study ability, after answering questions, students should be required to read textbooks and consolidate what they have learned.
(4) organize and summarize. The teacher gave questions to check the students' learning effect. Problems in understanding should be remedied in time, and what you have learned should be summarized. When summing up, try to let students summarize and draw conclusions with accurate mathematical language, and gradually cultivate students' ability to express in mathematical language.
(5) Consolidation and application. Arrange independent homework in class according to the teaching content, in order to make students further understand and consolidate what they have learned and initially form skills.
3. Self-study counseling evaluation.
The main advantages of this method are: it can fully mobilize students' learning initiative, give students more opportunities to think independently, and master knowledge through self-study, which is conducive to the cultivation of self-study ability. This teaching method can basically solve the problems in the classroom and greatly reduce the students' academic burden. Because students can correct mistakes in homework in time in class, teachers can get rid of homework and have more time to prepare lessons and study students' problems, which is conducive to improving teaching quality. In addition, students can read more reference books after class to expand their knowledge, which is conducive to the all-round development of students.
Self-study guidance is not only a teaching method, but also a synthesis of teaching ideas, 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.
4. Teaching examples of self-study tutoring method (the significance and basic nature of proportion)
Specific teaching process:
(1) teacher talking
(2) Prepare for practice
(3) Implementing new courses
① Show examples and self-study thinking questions.
For example, a car travels 80 kilometers in two hours for the first time and 200 kilometers in five hours for the second time.
Time (hours)
2
five
Distance (km)
80
200
As can be seen from the table, this car:
The ratio of the distance and time of the first trip;
The ratio of distance to time for the second trip is.
What is the ratio of these two? What must they do?
Thinking: What is proportion? What are the conditions of composition ratio? Can we get the proportion from these conditions? What if the proportion is written as a fraction? What is the basic nature of proportion?
② Guide self-study and summarize the rules.
Guide the students to observe the two proportions and say the meaning of the proportions.
Guide students to discuss collectively: the conditions of composition proportion.
Ask students to convert the proportion into a fraction.
Guide students to practice and think about the difference between ratio and proportion.
Let the students know the names of the parts of the proportion.
Guide students to explore the basic nature of proportion by using different methods of addition, subtraction, multiplication and division.
(3) Questioning and giving careful guidance.
According to students' questions and on the basis of dispelling doubts, teachers point out the basic nature of proportion: in proportion, the product of two external terms is equal to the product of two internal terms, which is called the basic nature of proportion.
(4) Classroom exercises
(D) "inquiry-discussion" method
The "inquiry-discussion" method was put forward by Professor Lambenda, an American pedagogic expert. Have a certain influence in the United States. Introduced to China in the early 1980s. It is widely used in science teaching and mathematics teaching.
1, the basic content of "inquiry-discussion" method
The basic idea of "inquiry-discussion" method is to divide teaching into two major links, namely "inquiry" and "discussion".
The first link "inquiry" is that students explore by themselves under the guidance of teachers. Teachers provide students with certain problem scenarios and necessary operating materials, so that students can study the relationship between various factors or quantities in the problem through operation and fiddling. Teachers should give appropriate guidance in the process of teaching activities.
In the process of inquiry, it is an important factor to provide structured materials for students. Teachers should choose enough materials for students to study and study according to the teaching content. Such as colored wooden strips, geometric puzzles, etc.
The second link "discussion" is to give students an opportunity to fully express their opinions. In the previous stage, students have a certain understanding of the research problems. At this stage, teachers organize students to express their opinions on what they see and think, and make full use of language communication to make students know more information. And in the process of discussion, we can inspire each other and have a more comprehensive and profound understanding of the problems studied. Finally, teachers and students work together to find out the rules or conclusions of learning problems.
In the specific teaching process, it can be flexibly organized and used without the restrictions of these two links.
2. The main characteristics of "inquiry-discussion" method
The "inquiry-discussion" method has the following main characteristics.
First of all, it can give full play to students' initiative and creativity.
Second, the leading role of teachers is to choose suitable materials and design problem situations that are conducive to students' exploration.
The third is to form a classroom teaching atmosphere of multi-directional communication.
3. Application example of "inquiry-discussion" method (solving the average problem)
First, divide the class into several groups with four people in each group.
Measure the height of each student and cut a piece of paper according to the measured height. The teacher asked, "How do you know how tall four people are together?" "How tall are four people on average?"
Then the teacher explains what the average is. And put forward "how to find the average height of the class?" "How do you express this average height?" The students said that you can add up the height of the class and divide it by the total number of students. Then the students put a note indicating everyone's height on a piece of paper nailed to the wall and draw a line on the average place. Found some offline, some online. Represented by "-"and "+"respectively. Students cut off the high part just to make up the low part. The students are very excited.
Next, some students put forward a simple method to calculate the average. Find out the height of the shortest classmate. Add up the values above this number in the class, divide by the total number of students in the class, and add the height of the shortest student, which is the average height of the class.
Some students put forward a simple method, randomly find a standard line and compare it with this standard line to calculate the average height.
Second, the characteristics of the reform of primary school mathematics teaching methods
In the past, most people thought that students' mathematical knowledge in class mainly refers to mathematical facts (such as concepts, formulas, rules, arithmetic, etc. ), but with the development of subjective education theory, the deepening of mathematical education research and people's in-depth reflection on the essence of school mathematics education, mathematical theories and practitioners gradually realize that sample mathematics is mainly "active and operable" mathematics, not formal mathematics. "Students should experience mathematization, not mathematization; Abstract, not abstract; Step by step, not in one step; Formalization, not form; Arithmetic, not algorithm; Language expression, not language. " So the understanding of mathematics in class includes not only mathematical facts, but also the experience of mathematical activities. The new teaching mode should no longer be a one-way teaching mode for teachers to systematically teach textbook content, but a process of interactive development between teachers and students. Mathematics teaching should be closely linked with students' real life. Starting from students' life experience and existing knowledge, we should create vivid and interesting situations to guide students to carry out activities such as observation, calculation, guessing, reasoning and communication, so that students can master basic mathematical knowledge and skills through mathematical activities, learn to observe things and think about problems initially, and stimulate students' interest in mathematics and their desire to learn mathematics well. Teachers are the organizers, guides and collaborators of students' mathematical activities; According to the specific situation of students, the teaching materials are reprocessed and the teaching process is creatively designed; It is necessary to correctly understand the individual differences of students, teach students in accordance with their aptitude, and let each student develop on the original basis; Let students get a successful experience and establish self-confidence in learning mathematics well. "With the new concept of mathematics curriculum reform and the development of philosophy, politics, science and technology, culture, etc. The development of modern teaching methods presents new characteristics.
First, the basic feature is to fully mobilize students' learning initiative, give full play to teachers' leading role, and strive for the best combination of teaching and learning. The traditional "three centers" represented by J.F.Herbert emphasized the absolute authority and strict discipline of teachers and regarded students as containers of knowledge. The "new three centers" represented by J. Dewey compares students to the sun, regards teachers as planets, absolutes the possibility of children's autonomous learning and denies the leading role of teachers. Our teaching method avoids these two extremes, organically combines the main role of students with the leading role of teachers, and regards the main contradiction of this teaching as the unity of opposites with dynamics, transformation, development and hierarchy. In the teaching process, teachers can guide students to think independently and communicate cooperatively. Teachers and students have different cognitive preparations for situational problems, and their ideas will be different. The communication between students and between teachers and students can promote each other. Therefore, teachers can effectively combine the whole class with group cooperative learning, encourage students to put forward and elaborate their own ideas in groups, and learn to communicate and learn mathematics through group communication or class communication, thus developing students' mathematical thinking ability, language expression ability and sense of responsibility for their own learning.
Second, through vivid and interesting learning situations, stimulate students' learning motivation, inspire students to think, speak and do things, and guide students to explore and discover. Teachers make full use of students' life experience and knowledge background to design vivid learning situations that students are interested in, so that students can gradually understand the process of the generation, formation and development of mathematical knowledge through observation, operation, speculation, exchange and reflection, feel the power and beauty of mathematics, and master the necessary basic knowledge and skills. That is, learning mathematics in the process of "doing mathematics".
Third, pay attention to the individual differences of students and encourage the diversification of learning methods and problem-solving strategies. Encouraging the diversification of problem-solving strategies is an effective way to teach students in accordance with their aptitude. For example, in calculation teaching, students can be encouraged to explore the calculation results by using the existing knowledge background, instead of being demonstrated by teachers first, explaining written calculation rules and reasoning, and limiting students' thinking. The teacher first shows the problem situation with certain practical significance, so that students can estimate it first and then calculate it independently? On this basis, communicate in groups and feel the diversity and flexibility of problem-solving strategies.
Fourth, pay attention to the study of students, especially the research and guidance of learning methods, so that students can gradually learn in the process of learning. Learning method is the basic activity mode and thinking method adopted by students in the process of acquiring knowledge and forming ability. The research and guidance of learning methods is a necessary link to ensure the implementation of modern teaching methods and the key to improve teaching quality.
Fifth, in addition to enabling students to acquire important mathematical knowledge, basic mathematical thinking methods and necessary application skills necessary to adapt to future social life and further development, we should pay more attention to cultivating students' attitudes, emotions and values. Attitude, emotion and values, as internal driving forces of learning, play an important role in learning. Modern primary school mathematics teaching methods fully consider this point, pay attention to the cultivation of students' interest in learning, stimulate students' learning motivation, emphasize emotional communication between teachers and students, make full use of the role of emotion, and open the door to students' cognitive structure.
Sixth, emphasize the cross-use and mutual cooperation of various teaching methods. Attach importance to the application of modern teaching methods. Traditional teaching methods often adopt fixed teaching methods and form a set of models. With the development of modern teaching theory, the increase of teaching methods and the in-depth study of the nature of teaching methods, educators gradually realize that there are various teaching methods and there is no one omnipotent teaching method. Teaching methods vary according to math subjects, styles of children and teachers. Teaching methods are not single, and there can be different combinations. In addition, attaching importance to the use of modern teaching methods, combining form, sound and light, and combining vivid pictures to explain vivid, vivid and abstract mathematical concepts and principles can better attract students' attention and improve their interest in learning. Deepen the understanding and memory of teaching materials. CAI and microteaching in China. It is the direct product of the application of modern technical means and the development of modern teaching methods. The role and position of modern educational technology must be considered. Considering the impact and change of the introduction of modern technology and equipment on traditional teaching methods, the combination point and development direction of serving teaching methods are found.
These are the new features of modern teaching methods. But looking at all kinds of primary school teaching methods. There are still some problems: some teaching methods are not worthy of the name, subjective and arbitrary, and not scientific enough; The connotation and extension of some teaching methods are unclear; Some teaching methods tend to solidify and model a certain teaching method; Some teaching methods lack teaching theoretical basis; Wait a minute. These problems need to be solved well. Otherwise, it will not only hinder the improvement of teaching quality, but also hinder the in-depth development of teaching methods research.