For the teaching of applied problems, we are all familiar with its structure, types, ideas and solving methods. Since the new curriculum reform, "application problem" has been changed to "problem solving", and "application problem" is no longer a single unit, and problem solving runs through four learning fields. So what's the difference between applying problems and solving them? I quote a passage from Wu Zhengxian to share with you. 1. Pay attention to the teaching process: more emphasis on getting answers as soon as possible in application problems; And solving problems is to emphasize a process, that is, to seek ways and means to solve problems. It is more important to pay attention to the process of solving problems and seek methods and strategies to solve problems than to draw conclusions themselves. 2. Not just attached to a knowledge point: application problems are often combined with a specific knowledge point. For example, today's addition is an addition application problem, and tomorrow's multiplication is a multiplication application problem, and application problems are often attached to a certain knowledge point. The problem-solving emphasizes a specific real situation, and more importantly, the process of comprehensive problem-solving For example, after today's lecture on addition, the scene of solving problems may not be limited to addition or subtraction, but to mobilize students' existing knowledge to solve problems. Not just attached to a knowledge point. 3. Specific analysis of specific problems: application problems are classified in application problems teaching, and one kind of problems is focused on thinking, emphasizing speed and skills; Problem-solving emphasizes the concrete analysis of specific problems, in other words, how to use the learned knowledge to solve problems in new situations, making them more challenging, and one problem may follow. Students face different specific situations and different problems. Students should analyze specific problems. It is more challenging and innovative to find a solution to this problem. 4. Openness and diversity of problems: solving problems emphasizes universality, that is, finding and refining problems from life, from children's existing experience and from the current process of scientific and technological development and social development. The openness and diversity of the problem itself is also a very important feature. This is Mr. Wu's interpretation of the difference between application problems and problem solving. After understanding their differences, aiming at the problems existing in problem-solving teaching at present, we have formulated a small topic: how to cultivate students' ability to analyze and solve problems in mathematics classroom.
Second, the current "problem-solving" teaching problems:
1. As a teacher, how to teach the content of problem solving? Influenced by the old textbook "Application Problem", there are doubts about how to deal with "problem solving". Now the form of solving problems is different, not only limited to text narrative questions; No longer pay attention to problem education, no longer analyze according to the structure of application problems, and the conditions and problems are open. As a teacher, it is difficult to grasp how to guide children and how to teach this part of knowledge.
2. As students, there are problems in reading the meaning of questions and capturing useful information: the presentation of questions is mostly illustrated. In this way, students can't effectively extract picture information and accurately convert it into text information, and some children will miss picture information. At the same time, this is also a problem that teachers encounter in teaching.
3. There is no clear analysis for students in the textbook. What is the first step and the second step? There is a phenomenon that students can write but not speak. How to deal with it?
Three. Understanding of this content:
The presentation of solving problems in the new curriculum provides more thinking space for children and teachers! Now the problem-solving is not just the teaching of calculation skills, but more practical, more challenging and closer to real life. It doesn't simply stay in the process of "what do you think, first calculate what, then calculate what", but it will encounter various problems in the process of solving problems. For example, how to collect information, how to organize information, how to process information, how to analyze information and so on. These are all obstacles that teachers and students can't get through. However, while crossing this hurdle, students' problem-solving has been improved and exercised in all aspects. In addition, teachers have more room in the process of solving problems. As long as the teacher pays a little attention, he will find that many problems can be studied in depth For example, there is a question about buying tickets in the first volume of Grade Three. After solving the problem, I asked my classmates: when is it cheaper to buy group tickets, when do you need to buy your own tickets, and why? In this way, the problem-solving mode of this kind of topic has been memorized in children's minds, and what is more worth cherishing is that students have really accumulated life experience in class. The above is my simple understanding of solving problems.
Fourth, specific practices:
1, focusing on cultivating students' ability to solve problems. With regard to problem solving, the teaching goal of the first phase of the Standard is: "Under the guidance of teachers, simple mathematical problems can be found and put forward from daily life. There are different solutions to the same problem. Experience in solving problems with peers. Initially learn to express the general process and results of solving problems. " In teaching, I make full use of the resources provided by textbooks. First of all, I use the lively contents of the school provided in the example as the material to show the calculation problems in the actual school sports meeting. There are many math problems in life. Choosing materials from school life will make students feel intimate and help them understand the basic meaning of mathematical problems. When teaching examples, I adopt the mode of "collecting data-asking questions-solving independently-group communication-class report-reflection-comparing similarities and differences", so that students can feel that the same problem can be solved in different ways because of different observation points. After getting the answer, I am not satisfied, but let students reflect on their own problem-solving process, so that they can sum up their own problem-solving strategies while experiencing it. We can start with the known information, first select two related information to ask questions, calculate the intermediate quantity, and then take the intermediate quantity as the known information and the rest information, and get the answer through operation. For example, according to "there are 10 people in each row and 8 rows in each square", students can calculate the median number of people in a square and then multiply it by 3 to get the answer. By selecting two related information, we can calculate an intermediate quantity, and then draw a conclusion with another information, which is also a faster and simpler method to solve this kind of problem. In addition, when I collect information, I pay attention to cultivating students' ability to collect and process information every time I ask a question. For example, students didn't find the information of three squares because they didn't observe deeply enough. After the students added, I asked the students to integrate the collected information and describe the information completely. For example, the third question contains too much information, which leads to the confusion of students' choice of information, that is to say, students have difficulties in the process of screening information. I will let the students give full play to the collective strength in class and exchange the information collected by screening. In this process, let students have the experience of communicating with their peers. Since doing so allows students to experience and gain, instead of staying at the superficial phenomenon of solving problems, that is, problem-solving skills, I think this is also the goal of changing application problems into "problem-solving" in the curriculum standard.
2. Reflect the diversification of problem-solving strategies. The textbook presents the problem-solving content and pays attention to the diversification of problem-solving strategies. So I encourage students to show different solutions to each problem, so that students can understand that there are different solutions to the same problem. For example, you can first calculate a square, or how many rows there are in three squares, or you can first look at how many people there are in a row horizontally ... You can do it while doing it ... (For example) In addition, some scenarios in the exercise contain a variety of problem-solving information, revealing that you can observe and choose information from different angles and adopt different methods to solve problems. For example, in the third question, students can solve the problem by counting the number of bottles on each floor or the number of bottles in each stack. They can also ... When doing this, students can calculate how many eggs are in a plate, how many rows there are, and even divide eight plates of eggs into several portions, which depends entirely on students' observation and thinking. These exercises enable students to find one or two ways to solve problems through their own analysis and thinking, and communicate with their classmates, so that students can develop their innovative consciousness in an atmosphere of continuous exploration and creation.
3. Let students actively explore ways to solve problems. Students can already solve the practical problem of simple two-step calculation by multiplication, division, addition and subtraction in the table when they are studying in grade two. The practical problems that need to be solved in the two-step calculation provided by our unit have expanded the scope of material selection and the scope of data provided. In teaching, I pay attention to mobilizing students' learning experience and life experience, and let students actively explore ways to solve problems with independent attempts and discussions. In the teaching process, students' knowledge and skills have a positive impact on solving new problems, which reflects students' autonomy in learning. For example, after showing the example, I didn't explain it too much, but let the students explore the solution independently. Through the communication between groups and classes, students can unify their thoughts and actions and achieve the unity of heart, hands and mouth.
4. Pay attention to let students talk about the thinking process.
In teaching, I ask my classmates to talk about their thoughts in the report, or talk about the thinking process with their deskmates and groups, so that they can speak out when they write.
These are some of my practices and ideas in this class. I still have a lot of puzzles about problem-solving teaching, please help me solve them.
1. Do you still use classification to solve problems as before? If you don't classify them, then nearly one-third of the students are still confused about solving problems. How to solve this?
2. Do you want to analyze the quantitative relationship for your child when solving the problem?
3. Pay attention to specific problems when solving problems, and the problems also appear in the form of pictures and texts. The lack of examples of knowledge in this subject leads to the confusion of students' main lines. For example, children have great difficulty in collecting information, even the most basic narrative problem. How to solve this problem?
4. In the process of solving problems, students can write formulas instead of thinking, and there is a phenomenon that they want to separate when they say it, so do you still need to let students write the subheadings mentioned above?
5. Are the two effective analytical methods, analytical method and comprehensive method, still told to students? It is suspected of leading students by the nose. If you don't speak, students' problem-solving ability will decline. How to deal with the contradiction between the two?
6. The new concept emphasizes the process, but does not describe the child's problem-solving process. From the formula alone, there is a certain deviation, and both parents and teachers feel that students' ability is declining. How to evaluate students' problem-solving ability?