The Outline of Curriculum Reform of Basic Education points out: Change the current situation of overemphasizing learning, rote memorization and mechanical training in curriculum implementation, advocate students' active participation, willingness to explore and diligence in practice, and cultivate students' ability to collect and process information. The curriculum standard clearly points out: "Students are the masters of learning." Suhomlinski, an educator in the former Soviet Union, once said: "In the depths of people's hearts, there is always an inherent need to regard themselves as discoverers, researchers and explorers, which is particularly important in the spiritual world of primary school students." Those students who have been bound by teachers, textbooks and classroom circles for a long time are afraid to cross the line. Today, we need to change the way of learning, and inquiry is the way of autonomous learning. Therefore, we should attach importance to the learning strategy of independent inquiry, so that they can become discoverers, researchers and explorers, thus releasing their repressed personalities. Mathematical problem-solving teaching can give full play to the initiative of students' independent inquiry learning.
First, guide discovery and perception, and pay attention to the trial of independent inquiry.
Discovery is the beginning of exploration. Because curiosity is a psychological feature of children, it can often urge students to make further in-depth and meticulous observation, thinking and exploration, thus asking exploratory questions. Allowing students to ask questions and explore independently is not only a matter of methods, but also a matter of educational ideas, teaching quality and students' ideas. If we can create a positive, relaxed and harmonious classroom teaching atmosphere and let students become the subject of "questioning" and "information source", then the enthusiasm and initiative of students will be greatly stimulated. Because students always ask questions on the premise of their own positive thinking. Because of this, we say that teachers don't "give" students 10 questions, but let students discover and "generate" a problem by themselves.
In the problem-solving teaching of two-step calculation, I skillfully changed the examples and greatly stimulated the students' desire to explore.
Teacher: Do you want to play a guessing game?
Health: Yes!
Teacher: I have three boxes of different colors (red, white and black boxes respectively), and each box contains some coins. Now, I ask you to guess how many coins are in the red box.
Health: (various guesses)
Teacher: No one guessed right. Can you guess how many coins are in the red box at once before you get the relevant information?
Health: No.
Teacher: Then I'll give you a message: there are 15 coins in the black box. With this information, can you accurately guess the number of coins in the red box? Why?
Health: No, the number of coins in the red box has nothing to do with the black box.
Teacher: I'll give you another message: there are 10 coins in the white box. Now, can you guess the number of coins in the red box? Why?
Health: Still no good. Because the numbers in the red box have nothing to do with the numbers in the white box.
Teacher: Knowing these two pieces of information, what other information do you want to know to guess the number of coins in the red box? Share your thoughts with the group members.
Students can guess the number of coins in the red box if they know another piece of information that can relate the red box to the numbers in the white box and the black box. For example, how many coins are there in the red box than in the black (white) box? The number of coins in the red box is many times that in the black (white) box; The number of coins in the red box is more (less) than the total number of black boxes and white boxes; How many times the number of coins in the red box is the total number of black boxes and white boxes, and so on. At this time, we can find that some students only need one-step calculation, while others need two-step calculation. Let the students talk about why two-step calculation is needed. In the process of putting forward and comparing problems, students not only strengthen the structure of two-step problem solving, but also have a preliminary position on the choice of quantitative relationship in problem solving teaching. The teacher finally showed the relevant information, and the students finally guessed the number of coins in the red box.
Only when students take the initiative to ask questions can they really play the main role and reflect independent inquiry and discovery. Therefore, teachers should always pay attention to the hidden "discovery" factors in textbooks, create situations that enable students to actively discover problems and ask questions, inspire students to discover problems and explore knowledge themselves, and make the teaching process revolve around the problems generated by students in learning. Teachers must actively create problem situations, guide students to ask questions closely related to the learning process, and make the questions to the point, so as to promote independent cooperation and inquiry and achieve the purpose of learning to learn.
Second, encourage participation in cooperation and pursue the interactivity of independent inquiry.
1. Create scenarios to stimulate interest and provide space for active exploration.
Don't tie students to textbooks in teaching, let them recite what they think is boring. Teachers should try their best to choose valuable mathematics content that students are willing to accept according to the psychological law of mathematics learning. If you find the prototype of mathematics in your life, let students experience that "learning mathematics" is not "remembering mathematics, memorizing mathematics, practicing mathematics and testing mathematics", but using mathematics.
Page 45 of Book 9 of Nine-year Compulsory Education and Six-year System published by People's Education Press, with application examples 1 as follows:
A clothing factory planned to make 660 sets of clothes, which took five days, with an average of 75 sets per day. The rest will take three days to finish. How many sets do you have to make every day on average?
This type of problem solving is very boring, far away from students, and students are definitely not interested. Without interest, there can be no interest in inquiry. I made the following amendments to this question:
(1) Courseware shows the situation or organizes students to have a dialogue.
Guest: Hello, Director Zhou! What about the production of the 660 sets of clothes we ordered?
Director: It has been done for five days, with an average of 75 sets per day.
Customer: We are waiting for the goods. Can you finish them in three days?
Director: Yes.
(2) Teacher: Students! According to the information provided by the factory director and customers, what math problems did you think of?
According to the students' answers, the teacher sorted out the above example 1.
(3) Teacher: Can you answer? If not, we can discuss it in groups.
Health: ellipsis
This way better embodies the two aspects of "life mathematics problems" and "autonomous learning, exploration and innovation", puts learning activities into social life problems, and skillfully turns the problems to be solved into students' dialogues. Let students take the initiative to acquire knowledge and combine perceptual practical activities with students' inner feelings and experiences. Students not only learn this kind of mathematics well, but also lay a good foundation for becoming successful people in all walks of life in the future.
2. Give students the right to choose freely and provide space for active exploration.
Every student has his own unique inner world, spiritual world and inner feelings, and has different ways of observing, thinking and solving problems from others. Modern education pays more and more attention to the development of each student's potential and personality. Because students' cognitive level and habits are different, they often come up with different calculation methods, which is the embodiment of students' different uniqueness. Therefore, in the teaching process, teachers should encourage students to use knowledge flexibly and try various algorithms.
No matter which method students use to solve this problem, they should be affirmed. Students should not be forced to solve the same problem in a unified way. On the basis of students' independent thinking and solving this problem, conduct group communication. Every student will express his opinions and listen to his peers' solutions, so that every student can feel the flexibility and diversity of the solutions. This kind of teaching is conducive to cultivating students' independent thinking ability and to students' learning and communication. Let every student have the pleasure of success, and let different people learn different mathematics, and different people get different development in mathematics.
3. Establish cooperation teams and provide active partners.
Set up a cooperative group before class, and divide students with different learning abilities, learning attitudes, learning interests, gender and personality into the same group to form a group of four or six people, and then give the members of the group a special identity and a special responsibility. For example, "moderator" (responsible for the overall discussion of the group, allocating speaking opportunities, coordinating the procedures of group learning, and observing the performance of students' cooperative skills in the group, such as voice control during discussion and politeness when asking and answering questions). Finally, each group is required to design a group name and logo, so as to promote the cooperative learning group to form an atmosphere of "mutual assistance and cooperation within the group and winning the bid among the groups".
Solving problems is abstract, and sometimes students can't understand the meaning of the questions well, which causes obstacles to solving problems. In this case, teachers should attach importance to the problem-solving process, so that students can understand the meaning of the problem, so as to easily master the problem-solving methods.
4. Choose special topics, cooperate with each other, and strengthen the ability of active inquiry.
In the limited classroom time, we can closely follow the teaching materials, choose key points, difficulties and doubts as special topics, and use research-based learning and division of labor to improve students' initiative, research and discovery ability. In order to reduce the gradient of students' research and inquiry learning, it is essential to carry out special research in class by using the characteristics of teaching materials, but in extracurricular inquiry learning, more problems are how to collect and process information and how to cooperate with others. To this end, we should guide students to take the initiative to seek help when encountering difficulties and enthusiastically help others solve problems. If you have materials urgently needed by others, you can complete others' plans and learn to be a man while learning and exploring.
Third, activate the thinking of seeking differences and cultivate the originality of independent inquiry.
Solving problems in different ways, angles and ways not only enlivens students' thinking and broadens their thinking, but also promotes students to develop the habit of being good at seeking differences, which plays a decisive role in cultivating students' innovative ability. In teachers' teaching, through the change of expression, understanding angle, thinking method and problem design, we can provide various forms of knowledge information, create diversified thinking environment and connect multi-directional problem-solving ideas, thus promoting the deepening of content and understanding and improving the flexibility and broadness of students' thinking. People are used to using a certain way of thinking in the process of understanding knowledge, which will produce a set psychology. Teachers should seize the opportunity in teaching, create thinking situations and do everything possible to provide innovative materials and space for students. Only by using the innovative fire of "teaching" to ignite the innovative fire of "learning" can we effectively cultivate the originality of students' independent inquiry.
For example, for fifth-grade students, after learning the application problem of three-step calculation, I designed an open question close to students' lives, so that students can think flexibly:
The school organizes teachers and students to watch movies. There are 950 students and 27 teachers. The theater ticket office said:
Today's screening
The universe and human beings
Adult Tickets: 8 yuan per ticket.
Student Tickets: Each 4 yuan.
Group tickets: each 6 yuan.
(Group tickets can be purchased for more than 30 people)
Please design a ticket purchase plan that you think is the most economical and work out how much it costs to buy a ticket.
As soon as the topic was put forward, the students were full of interest and actively used their brains to find the best solution.
The following are different ways for students to solve problems:
Methods 1: 827+4950 = 40 16 (yuan)
Method 2: (27+950) 6 = 5862 (yuan)
Method 3: Take out three students and form a group with the teacher.
306+9474=3968 (yuan)
……
In view of this problem, students of different levels have different solutions, and each student has been fully exerted in such a problem situation. Through practice, cultivate students' ability to actively apply mathematical knowledge.
Fourth, design open homework and strengthen the practicality of independent inquiry.
Mathematics teaching is an open system. Mathematics is everywhere in life, and it is also used everywhere. Piaget believes that "education can't be successful if children don't have their own real activities." How to design open-ended homework so that students can gain something from the practice of independent inquiry? First of all, we should respect students' job-hunting requirements, and secondly, we should open the form and content of homework.
1, migrate the sample solution.
If you teach the problem of planting trees, you can suggest that students take a walk on the pedestrian street, count the number of trash cans on the pedestrian street, visually measure the distance between every two trash cans, and then calculate the total length from the initial trash can to the last trash can.
2, combined with hot spots in life.
During the National Day, New Year's Day and other festivals, many stores offer discount promotions. Under the guidance of parents, you can go shopping in the store to see what the original price of the goods is, what the discount is, and how much it is cheaper than the original price. Record your findings. After returning to school, you can organize a discussion: stores use discounts to promote goods. Do you earn more or less? Will you lose money? Let students really feel that mathematics is around us.
3. Strengthen special practice.
After learning the calculation of rectangle and square area, you can design some decoration schemes for your home with your parents. For example, measure the length and width of the room and calculate the area of the room. If you buy a floor, according to the family's economic strength, go to the market to understand the price of the floor, choose the right price, and buy it, how much will it cost?
Such open homework content is not only linked to the content of teaching materials, but also combined with students' life and social activities. Students have the space of self-study and free exploration, and only in practice can they be full of vitality, growth and creative life.
Problem-solving teaching is rich in connotation, and how to make students like it is the problem we are facing at present. But I firmly believe that as long as teachers adopt certain strategies to create a relaxed atmosphere for students and make students feel that the problems to be solved are not far away from themselves, problem solving is valuable. Only in this way can students enjoy the pleasure of solving problems. So as to truly master the solution. To reach this level is successful and excellent teaching.
First, the current background.
Second, analyze the outstanding changes of "problem solving" teaching under the new curriculum.
Third, collect and sort out the problems and puzzles of "problem solving" teaching under the new curriculum.
Fourthly, it puts forward practical suggestions on "problem solving" teaching under the background of new curriculum.
Fifth, construct the "problem solving" teaching mode of primary school mathematics.
Sixth, the place to pay attention to when solving problems.
Seven, problems and thinking.
Aristotle defined mathematics as "quantitative science", which lasted until18th century. /kloc-since the 0/9th century, mathematical research has become more and more rigorous, and it has begun to involve abstract topics such as group theory and projection geometry that have no clear relationship with quantity and measurement. Mathematicians and philosophers have begun to put forward various new definitions. Some of these definitions emphasize the deductive nature of a lot of mathematics, some emphasize its abstraction, and some emphasize some themes in mathematics. Today, even among professionals, the definition of mathematics has not been reached. Whether mathematics is an art or a science has not even been decided. Many professional mathematicians are not interested in the definition of mathematics or think it is undefined. Some just say, "Mathematics is done by mathematicians".
The three main mathematical definitions are called logicians, intuitionists and formalists, each of which reflects a different school of philosophical thought. Everyone has serious problems, no one generally accepts it, and no reconciliation seems feasible.
The early definition of mathematical logic is Benjamin Peirce's Science of Drawing Inevitable Conclusions (1870). In Principles of Mathematics, Bertrand Russell and alfred north whitehead put forward a philosophical program called logicism, trying to prove that all mathematical concepts, statements and principles can be defined and proved by symbolic logic. The logical definition of mathematics is Russell's "All mathematics is symbolic logic".
The definition of intuitionism comes from mathematician L.E.J. Brouwer, who equates mathematics with some psychological phenomena. An example of the definition of intuitionism is that "mathematics is a psychological activity constructed one after another". Intuitionism is characterized by rejecting some mathematical ideas that are considered effective according to other definitions. In particular, although other mathematical philosophies allow objects that can be proved to exist, even if they cannot be constructed, intuitionism only allows mathematical objects that can actually be constructed.
Formalism defines mathematics through mathematical symbols and operational rules. Haskell Curry simply defined mathematics as "formal system science". A formal system is a set of symbols, or marks, and there are some rules that tell how the marks are combined into formulas. In the formal system, the word axiom has a special meaning, which is different from the ordinary meaning of "self-evident truth" in the formal system. Axiom is a combination of symbols contained in a given formal system, and it is derived without using the rules of the system.
How to teach ppt courseware for solving math problems in primary schools? Baidu's "Li Tao Tianxia Courseware" contains many courseware, lesson plans and other resources. If you don't have it, you can leave a message in Shi Ming University, and the website administrator will help you find it through other channels. I hope it helps you. ...
How to teach, how to do well and how to teach "problem solving" in primary school mathematics has become a problem worth discussing. With the development of information society, the application of mathematics is deepening and expanding. We should pay more attention to learning mathematics and solving problems in real situations. The teaching strategies to solve the problems are designed as follows:
1. Create a situation and collect information.
When teachers start classes, they can create vivid and interesting teaching situations with the help of theme maps or teaching courseware, and connect abstract mathematics knowledge with real life. The information in the theme map or teaching courseware provides clues for students' thinking in a certain sense. After the students report, the teacher instructs the students to sort out the collected information and find out the problems that need to be solved. Observation and report can also provide a cognitive basis for solving problems, stimulate students' desire for knowledge, glow students' subjective consciousness, and create an atmosphere for students to explore and solve problems independently.
2, group cooperation, explore the problem
When students are clear about the problems to be solved, they should leave enough space and time for students, so that each student can use the existing knowledge and experience to independently find ways, methods and strategies to solve the problems, or they can discuss and communicate with each other in groups to form a preliminary plan. In this process, teachers should participate in the group to obtain information in time, and conduct appropriate guidance and norms.
3. Exchange evaluation and solve problems.
Communication evaluation is a key link in the organic combination of teacher-led and student-centered. The main duty of teachers is to organize students to communicate effectively in mathematics, activate students' thinking and broaden their thinking. After thinking clearly, let the students choose their own algorithm. When students have their own ideas, let them further summarize and sort out the algorithm through group communication. Finally, through collective communication, the algorithm is clear.
4. Consolidate methods and expand thinking.
Students have mastered the method, but also continue to practice and deepen their understanding in application. In this link, arrange some basic questions for students to answer with the knowledge they have mastered, so as to consolidate the application. Some expanding exercises are also arranged to enable students to use their existing knowledge flexibly and solve problems from different angles, thus expanding their thinking and cultivating their application consciousness.
How to teach the math problem-solving course in primary schools well; Analysis of the current background; Outstanding changes in problem-solving teaching under the new curriculum.
Collect and sort out the problems and puzzles of "problem solving" teaching under the new curriculum.
Put forward practical suggestions on "problem solving" teaching under the background of new curriculum.
Constructing "Problem-solving" Teaching Mode in Primary Mathematics
What should we pay attention to when solving problems?
Problems and thinking
How to learn how to solve problems well in primary school mathematics, teach children abstract thinking and turn words into situations. Then do more questions and read more questions, and copy the questions that you don't understand repeatedly. The process of copying is the process of examining questions, which is an important habit of beginners.