(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 like 39? . 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 3111=13 (person)
(3) Similar to (2), but they see that there are four 9s.
9 9 9 9 3=39 (block)
↓↓↓↓↓
3 31=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)
↓ ↓↓↓
10111=13 (person)
(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 been engaged in primary school mathematics teaching research, and has conducted many investigations and experiments on primary school mathematics teaching reform before and after the Cultural Revolution. He 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 kind of explanation is targeted and based on students' initial understanding of what they have learned. When students have learned or partially learned the problem-solving methods in some way, they can highlight the key points.