And how to find solutions to new problems? Knowledge can solve problems, and solving problems requires knowledge. However, knowledge and problems are often unwilling to "tie the knot" easily. There is a distance between them, or a veil. And strategy is a necessary bridge between knowledge and problems. It is particularly important to use knowledge to embody the power of mathematics around the world and explore strategies to solve problems. Strategy is an action guide to solve problems, which is instructive and flexible. The application of one-person strategy directly affects the process of solving problems. Let's discuss how to solve this problem effectively.
First, ask questions.
Thinking begins with problems, and only when there are problems can you think. Cultivating students' problem consciousness is the first step to implement problem-solving strategies. To cultivate students' awareness of questions, we should make asking questions become students' own needs. In teaching, I purposefully and consciously create problem situations, set obstacles and establish doubts, so that students feel that they have problems to think about and contradictions to solve. To cultivate students' problem consciousness, we should not only have a good education and teaching environment, but also pay special attention to guidance, from scratch, from less to more, and provide scientific methods for cultivating students' problem consciousness. Therefore, we should not impose "problems" on students, but cultivate students' awareness of problems through inspiration and induction. Excavate interesting things in life and some materials that meet students' tastes, such as small animals that students are interested in, watching movies, doing good deeds, performing programs and so on. With the help of multimedia and vivid performances, students' interest is extremely high, which makes them realize that the problems are actually some small things in life that we encounter every day.
For example, when teaching application problems of addition and subtraction, I started with students' life and made a beautiful courseware to show students some problems related to them in life that need to be solved. For example, "The shop bought five pencils in the morning and sold seven pencils in the afternoon. How many pencils does it sell a day? " The students' enthusiasm was aroused at once, and it was well solved. They solved the problem through their own efforts. Finally, I let them ask their own questions. Of course, it is also the following question. "Can you ask some questions about buying pencils in the shop?" Many students asked, "How many more pencils do you sell in the afternoon than in the morning?" Some children also asked, "There were originally 20 pencils in the shop, five in the morning and seven in the afternoon. How many are left? " This is a spark of thought that has been completely generated. Next, many students raised many other life problems and solved them. It can be seen that students understand the importance of mathematics to life. I don't have to waste my breath at all.
Second, explore the problem
With a problem, there is a goal to explore. To solve the problem smoothly, we must first analyze the problem. Traditional problem-solving emphasizes the analysis of the relationship between structure and quantity, and constantly makes students repeatedly analyze the same example in a fixed mode, which is mechanical and inflexible, easy to increase students' learning pressure, makes students feel bored, and is not conducive to the cultivation of students' inquiry ability. There is a saying in mathematics: "Thinking thoroughly about a problem means that the problem is half solved." "Curriculum Standard" points out: "Problem solving should proceed from the original knowledge and experience, and be explored from multiple angles, levels and aspects, so as to achieve active exploration, active communication and active application, and diversify the" strategies "for problem solving. The strategies to solve the problem include guessing strategy, drawing strategy, trial strategy, operation strategy, simplification strategy and so on. For example, "It takes three seconds to climb stairs, and how many seconds does it take to climb six floors? "For the students in the second grade of primary school, if they just think in their heads, I'm afraid it will be difficult to get the answer for a while, but if you draw a picture, it will greatly reduce the difficulty of solving problems. Due to the limitation of children's age, the calculation of pure symbols is often difficult. Using auxiliary strategies and drawing on paper can help them expand their thinking and find the key to solving problems. For another example, using operational strategy is also a strategy to concretize the problem situation. Through children's own exploratory hands-on operation, students' perceptual knowledge can be increased, vivid images can be formed in their minds, and it is also conducive to cultivating students' creative thinking quality.
Third, infiltrate the thinking method and pay attention to the teaching of open questions.
The infiltration of mathematical thinking method is the necessary way for students to solve practical problems smoothly. Problem-solving strategy is to take problem-solving methods as explicit behavior, and gradually enrich and deepen with the accumulation of students' problem-solving experience. Therefore, students' understanding and mastery of practical problem-solving strategies can't just stay on the surface of experience. In teaching, teachers should fully activate students' existing knowledge and life experience, consciously guide students to compare and analyze various methods derived from empirical cognition, and construct certain mathematical models, so as to successfully solve various specific practical problems.
In the textbooks of the new curriculum standard, most of the lower grades present problems in the form of pictures, tables and dialogues. This arrangement not only makes students' mathematics learning more vivid, but also makes the presentation of problems closer to the original state of real life. However, the known conditions needed to solve practical problems are not clearly told to students. Therefore, students need to go through a process of collecting information before analyzing and solving problems. In teaching, I first guide students to observe pictures and tables carefully and say "What mathematical information do you know", so that students can express known conditions and problems to be solved in an orderly way. In this way, through the interpretation of information, we are ready to analyze the quantitative relationship and explore ways to solve problems. Secondly, painting is also a specific strategy, which conforms to the thinking characteristics of primary school students. For example, a question like this: Are there 10 children waiting in line to do exercises, five left and five right? For such a problem, we can draw a physical diagram to help us understand and solve the problem.
When solving practical problems, we can also use various strategies such as trying, looking for laws and thinking in the opposite direction. In teaching, we should consciously help students sum up the strategies and methods to solve problems, so that each student can master the effective strategies to analyze problems and improve their ability to solve problems.
In short, in the face of various practical problems, teachers must adopt effective strategies, actively lead students to enrich their life accumulation, strengthen their experience, actively try to use the knowledge and methods they have learned to seek solutions to problems from the perspective of mathematics, and experience the whole process of solving problems and gain experience; Facing new mathematical knowledge, we can actively seek its practical background, explore its application value, and strive to improve students' ability to solve practical problems reasonably and flexibly by using mathematical knowledge, principles, ideas and methods.
The new curriculum standard takes solving problems as an important goal. The famous mathematician Paulia said that solving a problem is to find a solution when there is no ready-made solution, that is, to find a way out from difficulties, that is, to find a way around obstacles and reach an answer that can solve the problem. An important goal of the new curriculum standard is to cultivate students' innovative spirit and practical ability to solve problems. Students can not only learn knowledge, but more importantly, they can use what they have learned to analyze and predict specific problems in an orderly manner in complex situations. They are no longer fixed questions, but flexible and challenging, and can think creatively, explore and solve them. It enables primary school students to use the original knowledge, skills and methods to migrate to the curriculum situation to solve new problems. There are also practical problems extracted from real life, which are solved, assumed and reasoned through mathematical models.
And how to find solutions to new problems? Knowledge can solve problems, and solving problems requires knowledge. However, knowledge and problems are often unwilling to "tie the knot" easily. There is a distance between them, or a veil. And strategy is a necessary bridge between knowledge and problems. It is particularly important to use knowledge to embody the power of mathematics around the world and explore strategies to solve problems. Strategy is an action guide to solve problems, which is instructive and flexible. The application of one-person strategy directly affects the process of solving problems. Let's discuss how to solve this problem effectively.
First, ask questions.
Thinking begins with problems, and only when there are problems can you think. Cultivating students' problem consciousness is the first step to implement problem-solving strategies. To cultivate students' awareness of questions, we should make asking questions become students' own needs. In teaching, I purposefully and consciously create problem situations, set obstacles and establish doubts, so that students feel that they have problems to think about and contradictions to solve. To cultivate students' problem consciousness, we should not only have a good education and teaching environment, but also pay special attention to guidance, from scratch, from less to more, and provide scientific methods for cultivating students' problem consciousness. Therefore, we should not impose "problems" on students, but cultivate students' awareness of problems through inspiration and induction. Excavate interesting things in life and some materials that meet students' tastes, such as small animals that students are interested in, watching movies, doing good deeds, performing programs and so on. With the help of multimedia and vivid performances, students' interest is extremely high, which makes them realize that the problems are actually some small things in life that we encounter every day.
For example, when teaching application problems of addition and subtraction, I started with students' life and made a beautiful courseware to show students some problems related to them in life that need to be solved. For example, "The shop bought five pencils in the morning and sold seven pencils in the afternoon. How many pencils does it sell a day? " The students' enthusiasm was aroused at once, and it was well solved. They solved the problem through their own efforts. Finally, I let them ask their own questions. Of course, it is also the following question. "Can you ask some questions about buying pencils in the shop?" Many students asked, "How many more pencils do you sell in the afternoon than in the morning?" Some children also asked, "There were originally 20 pencils in the shop, five in the morning and seven in the afternoon. How many are left? " This is a spark of thought that has been completely generated. Next, many students raised many other life problems and solved them. It can be seen that students understand the importance of mathematics to life. I don't have to waste my breath at all.
Second, explore the problem
With a problem, there is a goal to explore. To solve the problem smoothly, we must first analyze the problem. Traditional problem-solving emphasizes the analysis of the relationship between structure and quantity, and constantly makes students repeatedly analyze the same example in a fixed mode, which is mechanical and inflexible, easy to increase students' learning pressure, makes students feel bored, and is not conducive to the cultivation of students' inquiry ability. There is a saying in mathematics: "Thinking thoroughly about a problem means that the problem is half solved." "Curriculum Standard" points out: "Problem solving should proceed from the original knowledge and experience, and be explored from multiple angles, levels and aspects, so as to achieve active exploration, active communication and active application, and diversify the" strategies "for problem solving. The strategies to solve the problem include guessing strategy, drawing strategy, trial strategy, operation strategy, simplification strategy and so on. For example, "it takes three seconds to climb stairs, and how many seconds does it take to climb six floors?" "For the students in the second grade of primary school, if they just think in their heads, I'm afraid it will be difficult to get the answer for a while, but if you draw a picture, it will greatly reduce the difficulty of solving problems. Due to the limitation of children's age, the calculation of pure symbols is often difficult. Using auxiliary strategies and drawing on paper can help them expand their thinking and find the key to solving problems. For another example, using operational strategy is also a strategy to concretize the problem situation. Through children's own exploratory hands-on operation, students' perceptual knowledge can be increased, vivid images can be formed in their minds, and it is also conducive to cultivating students' creative thinking quality.
Third, infiltrate the thinking method and pay attention to the teaching of open questions.
The infiltration of mathematical thinking method is the necessary way for students to solve practical problems smoothly. Problem-solving strategy is to take problem-solving methods as explicit behavior, and gradually enrich and deepen with the accumulation of students' problem-solving experience. Therefore, students' understanding and mastery of practical problem-solving strategies can't just stay on the surface of experience. In teaching, teachers should fully activate students' existing knowledge and life experience, consciously guide students to compare and analyze various methods derived from empirical cognition, and construct certain mathematical models, so as to successfully solve various specific practical problems.
In the textbooks of the new curriculum standard, most of the lower grades present problems in the form of pictures, tables and dialogues. This arrangement not only makes students' mathematics learning more vivid, but also makes the presentation of problems closer to the original state of real life. However, the known conditions needed to solve practical problems are not clearly told to students. Therefore, students need to go through a process of collecting information before analyzing and solving problems. In teaching, I first guide students to observe pictures and tables carefully and say "What mathematical information do you know", so that students can express known conditions and problems to be solved in an orderly way. In this way, through the interpretation of information, we are ready to analyze the quantitative relationship and explore ways to solve problems. Secondly, painting is also a specific strategy, which conforms to the thinking characteristics of primary school students. For example, a question like this: Are there 10 children waiting in line to do exercises, five left and five right? For such a problem, we can draw a physical diagram to help us understand and solve the problem.
When solving practical problems, we can also use various strategies such as trying, looking for laws and thinking in the opposite direction. In teaching, we should consciously help students sum up the strategies and methods to solve problems, so that each student can master the effective strategies to analyze problems and improve their ability to solve problems.
In short, in the face of various practical problems, teachers must adopt effective strategies, actively lead students to enrich their life accumulation, strengthen their experience, actively try to use the knowledge and methods they have learned to seek solutions to problems from the perspective of mathematics, and experience the whole process of solving problems and gain experience; Facing new mathematical knowledge, we can actively seek its practical background, explore its application value, and strive to improve students' ability to solve practical problems reasonably and flexibly by using mathematical knowledge, principles, ideas and methods.