[Source: Qixia Education Home_School News]
In November 2022, the mathematics teaching and research activities of Jinling Primary School (Xianlin Lake Campus) arrived as scheduled. Teacher Wu Han led the students from Class 6 (10) to study "Problem Solving Strategies - Hypothesis".
[Think carefully before class]
Assumption is one of the common strategies for solving practical problems. It is of great significance for students to analyze the quantitative relationship of actual problems, accumulate experience in solving problems, understand some basic mathematical ideas and methods, and improve their ability to analyze and solve problems. The focus of this lesson is to understand the quantitative relationship of related practical problems and to initially learn to use hypothetical strategies to solve some practical problems containing two unknowns. At the same time, it is hoped that through the teaching of this class, students can initially learn to put forward reasonable assumptions based on the conditions and problems of actual problems, achieve the goal of turning difficulties into easy things, initially form a strategic awareness of solving problems, and improve their ability to analyze and solve problems.
This lesson takes problems as the main line and takes "problem solving" as the cornerstone. In the introduction part of the class, from intuitive balance diagrams, to sensory numbers combined with , and then to abstract reasoning and calculation, it awakens students' existing life experience in their minds, laying a good foundation for the following exploration process. Then, through the raising of problems, students can conduct sufficient independent learning and exploration around the problem before class. In class, students can share their preview results through group cooperation and solve confusions in independent learning. Then, through in-class display and communication, students can fully interact with students. Students can master knowledge in the process of solving problems, form independent learning ability, and cultivate students' ability to learn to discover problems, raise and solve problems, and effectively improve students' mathematical literacy.
[Classic Record]
1. Contact experience and introduce strategies
Experience is the basis for learning to occur. The learning process is a process of using existing knowledge and experience to construct new knowledge. Although this is the first time that students have formally learned to use hypothetical strategies to solve problems, they have had similar experiences and contacts in their lives, but they have not yet established a complete mathematical model. At the beginning of the classroom, Teacher Wu started from a simple "balance" situation, which not only helped students review the simple quantitative relationship, but also activated students' original knowledge reserves to understand the quantitative relationship of related practical problems. He initially learned to use hypothetical strategies to solve some practical problems containing two unknowns, laying the foundation for the next learning.
2. Explore the problem and understand the strategy
Then give an example question. Teacher Wu asked students to express the "the capacity of a small cup is a big cup" in different ways, so that students can fully understand the relationship between two unknown quantities. Then let the students explore and communicate by themselves through the activity requirements. Through group discussions and cooperative communication, students are encouraged to exchange and question their research results, so that students can further understand the process of using strategies to solve problems and enhance their strategic awareness of solving problems.
Next is the whole class exchange. In this session, Teacher Wu focused on letting students explain their own problem-solving ideas, and helped students intuitively feel the process and reasons of "replace two unknown quantities with one unknown quantity". And by displaying, communicating and comparing different problem-solving ideas that appear among students, feeling the connections and differences between different strategies, further deepening students' understanding and experience of relevant strategies. Help students understand the thinking process of using hypothetical strategies to solve problems, understand the diversity of strategies, and thus improve their mathematical literacy.
Finally, through thinking and discussion: "Why do we have to assume?" "What is the basis for hypothesis" further feels the role of hypothesis strategies in solving problems.
3. Deepen the problem and experience strategy
In terms of practice consolidation, Teacher Wu set up four different levels of exercises. First, by changing the quantitative relationship of the example questions: the capacity of the small cup is a large cup, let students feel through different assumptions. Although they are all assumptions, it will be a little more troublesome to calculate the assumptions. So when there are many methods, we have to consider how to assume it to make it easier to solve the problem.
Then go back to the balance and ask "If you buy 1 pineapple, 1 pear and 1 peach weigh 1,000 grams in total, how much does one pineapple weigh?" "If you buy 4 notebooks 36 yuan more than 2 exercise books, how much does one notebook and 1 exercise book cost each?" Let the students understand that although there are three quantities involved here, you can also assume that 1 quantity based on their multiple relationship. By comparing the above two questions, students can distinguish between feelings and differences.
" equal amount substitution " is the core idea of the hypothesis strategy, and the assumption is implemented based on the relationship between two unknown quantities. Finally, the difficulty is upgraded, leaving behind a thought question, hoping that students can transform flexibly.
[After class dispute]
After class, the teachers discussed the afternoon teaching and research class. The teachers believe that Teacher Wu used the problem of equal quantity substitution familiar to students in the introduction part, guided students to describe the quantitative relationship between the two quantities, laying the foundation for learning the new lessons later. In the new teaching section, the teacher guides students to think actively and open up their thinking through various assumptions and can explain their thinking process clearly. Not all children have the opportunity to explain their ideas in class, so they can give students time to discuss and let students explain their ideas to each other, which can give students more opportunities to speak.
Water is unpretentious, and it ripples with each other; stones are without fire, and it radiates with each other. Every mathematics school-based teaching and research will make friends full of rewards. I believe that under the guidance of the new curriculum standards, the mathematics teacher will continue to explore and move forward!
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