How to help students build a mathematical model of "application problems"?

First, the problem scenario-to help students build an intuitive action model when they encounter problems.

The teaching link of "creating realistic situations, finding problems and asking questions" in the lesson example has mainly gone through three steps: animation demonstration of school situations-performing simulation of school situations-adding information to situations. From the situation of school animation demonstration, with the help of the animation situation of "Wang Ming and Li Hua walk to school", Mr. Liu let students perceive the movement of two objects for the first time, and with the help of students' observation and description of the movement process of two objects, thus cultivating students' observation ability, imagination ability and language expression ability, and preparing for mathematical modeling. Teachers and students simulate the movement process of "two students go to school" four times on the spot, and guide students to understand the connotation of "two places start at the same time, move in opposite directions and finally meet". In the performance again and again, teaching is closer to students' real life, attracting students to actively participate in inquiry learning activities. The classroom demonstration is concrete and can break through the difficulties, and an intuitive action model is established. Students are very interested in this link and can actively participate.

Second, a variety of problem-solving strategies-to help students initially form a mathematical model of the problems they encounter.

Teacher Liu's class is very practical, which allows students to make full use of methods and strategies such as simulation and experiment, calculation and drawing, abstraction and listing, classification and comparison, synthesis and analysis to solve problems, and further stimulates students' interest in learning. The teacher mainly introduced the method of "drawing line segments", so that the mathematical model of the problem can be initially constructed after the teacher and students draw step by step and the middle school students explain.

Third, a variety of autonomous learning methods-to help students build mathematical models of problems.

In the classroom, teachers use seven learning methods, such as independent thinking, simulated performance, independent information sorting, hands-on operation, group cooperation, communication and reporting, and independent problem solving. In seven different forms of autonomous learning, teachers and students simulate performances, so that students can experience and understand keywords such as "two places, simultaneous, relative and meeting", and the problem of meeting is intuitively established in students' minds.

Through careful construction, teachers make full use of students' existing experience and boldly give students enough time and space, so that students can fully mobilize their existing mathematics learning experience and sort out information. The process of sorting out information is the process of analyzing the quantitative relationship, which is the key to solve the problem. In the activity, let students organize information independently, and turn abstract and difficult text information into easy-to-understand pictures and charts, so as to help students clarify the quantitative relationship between information intuitively and vividly, clarify the thinking of solving problems, guide students to observe, compare, analyze, synthesize and abstract the process of solving problems, guide students to extract the structural knowledge behind the encounter model, and describe this mathematical structure with formal mathematical symbols-"speed and x time ="

However, there are two points in Mr. Liu's teaching that are worth discussing. Please ask experts and tutors to criticize and correct the improper points. First, the time left for students to sort out information is too short. In the link of "using existing experience and sorting out information independently", Teacher Liu completed "The information on this topic is more complicated. In order to make the topic concise and clear, please sort out the known information and questions in the topic in your favorite way now. Start! " From then on, I feel that the time left for students is about 1 minute. Some students just picked up their pens and haven't started sorting yet. The teacher asked the students to communicate in groups. "There are several different methods in your group, …" I think it can give students more opportunities to think and the teaching effect may be better. The second is to pay attention to poor students. It is inevitable that there will be poor students in every class, and it is common for poor students to make mistakes in class. In the basic exercise, students calculate "How many kilometers is the total length of Jinan-Qingdao Expressway?" In the future, when correcting collectively, Mr. Liu only asked the students who did the right thing to raise their hands, and ignored the students who did the wrong thing, leaving them no time to correct their mistakes. If the teacher does this for a long time, students who often make mistakes will feel forgotten by the teacher in class. Let the students who made mistakes talk about their ideas and practices. In fact, it is also a reminder to other students. This mistake may be a beautiful mistake!

After more than 20 days of long-distance training, I feel that there are too many things to learn. In teaching, I need to change the existing teaching concept, change the existing teaching ideas, optimize my teaching methods and strive to improve the efficiency of classroom teaching. ...

I need to study, study, study again, work hard, work hard and work hard again. Seize the opportunity of "face-to-face communication with experts and zero-distance dialogue with famous teachers" in this distance training, and improve yourself through continuous learning, mutual communication, in-depth exploration and gradual reflection.