Design of the Guiding Scheme of "Solving Problems in Proportion"
First, be clear about your goals (read silently and remember the main points)
1 Understand the generation and structural characteristics of the positive-negative ratio problem.
2 can accurately judge the proportional relationship between the two related quantities involved in the problem, clarify the relationship, and solve the problem according to the relationship with the idea of positive and negative proportion.
3. Understand the mathematical ideas such as "correspondence" and "invariance" in autonomous learning and apply them flexibly in solving problems.
Second, knowledge memory.
1 Judge the proportional relationship between the following two quantities (write the relationship and judge).
A The total number of pages is fixed, and so are the number of pages and books in each book.
B The average number of trees planted per person is fixed, and the number of trees planted is fixed.
Distance and time from a to b.
Fill in the form according to the relationship between x and y in the form and think about how you worked it out. (table omitted. )
A, guide die design instructions
1 Clear objectives: Let students clear their learning objectives and exploration direction at the beginning of new teaching, and promote students to actively explore around the objectives in all subsequent links. Because the learning goal is often the embodiment of the main knowledge and requirements of a class, long-term persistence in revealing the goal can cultivate students' generalization ability. This requires teachers to study teaching materials and curriculum standards carefully and set learning objectives accurately, which can neither improve the requirements nor lower the level. The expression of each goal should be clear, concise and measurable, guide students to read silently and remember the main points.
2 knowledge memory. The acquisition of any new knowledge is the result of absorbing and adapting to the original knowledge. Therefore, designing the knowledge recall link from the old to the new is the starting point of students' learning, and the accuracy of the starting point positioning directly affects the efficiency of students' learning. "Solving problems in proportion" is the application of the concepts of positive proportion and inverse proportion in practical problem situations, and it is the key to correctly judge the proportional relationship between two related quantities in practical problems. For this reason, three questions are designed in the knowledge recall part, and students are required to write a relational expression before judging. This writing and judgment is to prepare for the equation.
3 self-study thinking. The purpose of "learning according to plan" is to let students learn to learn independently, that is, what students can learn will never be replaced by teachers. Therefore, we should try our best to guide students to think and explore independently. A lot of prescribed knowledge in mathematics is suitable for accepting meaningful learning. Teachers can save their breath by letting students learn by themselves through effective study plans. Put "solving problems in proportion" into the system of equation solutions, so that students can compare, understand and communicate their relationships carefully. For this reason, three tables (four meanings) are designed: (1) diversified fill-in-the-blank infiltration algorithm is adopted to cultivate students' thinking ability of seeking differences. (2) Deepen the understanding of the method of judging the proportional relationship between two related quantities. (3) Communicate the internal relations between different solutions, so that students can realize that grasping the proportional relationship between two quantities can make the thinking of solving problems flexible and diverse. (4) Permeability function and corresponding ideas. From a realistic point of view, make students understand the corresponding relationship between x and y and prepare for the equation; In the long run, do some infiltration for the learning function of middle school. Let students read (three tables), think and fill in the blanks, and learn how to solve problems and write formats. Through the study and thinking of three tables, let students understand the internal relations and differences between using proportional solution and using equation solution.
4 Answer independently. Take the examples in the textbook as "test questions" and let the students answer them themselves. The purpose of designing this link is to strengthen self-study ideas, consolidate self-study achievements, conduct basic training, internalize in practice, and provide a platform for communication with peers. Through this part of learning, teachers can collect information about students' self-study and communication, promote classroom generation, give targeted guidance to students with learning difficulties and help them achieve their goals.
5 summarize and reflect. On the basis of self-study communication and understanding of various knowledge points, guide students to reflect and summarize in time, understand the internal relationship between knowledge, establish mathematical models, recall the modeling process and summarize learning methods. For example, guide students to review and reflect: how did you think about solving problems in proportion through the study just now? On this basis, students are prompted to compare the four key words of "judgment, search, answer and test" in the study plan, so that students with learning difficulties can be inspired.
6 self-test. One of the characteristics of "learning according to plan" mode is to save classroom teaching time, improve teaching efficiency, and make it possible for students to finish their homework or conduct self-test in class. To fully reflect this feature, how to choose exercises has become a key link in the design of learning plans. Because the exercise is done in class, its purpose is to test the students' academic performance in this class. Therefore, the difficulty of practice should not be too great, and it should be based on the degree that most students can master. However, in practice, we find that many students have digested the content of classroom learning in advance because of the use of learning plans, and the basic exercises have lost their challenges. How to deal with their relationship? We adopted a hierarchical approach. In practice (or self-study), it is divided into basic questions, improvement questions and challenge questions to meet the learning needs of students at different levels, so that the "foundation" is guaranteed and excellent students are improved. Students gained a successful experience by testing their learning situation on the spot, which enhanced their self-confidence in learning mathematics well.
7 feedback correction. This link is divided into the following steps. (1) Show the correct answers for students to compare and find the mistakes. (2) Students are free to correct and express their opinions. (3) Guide the discussion, tell the reason of the mistake and the truth of correction. (4) Guide induction, rise to rational understanding and guide application. The principle of this link is: let students solve whatever they can independently correct and solve; Find out the problems that need teacher's guidance and teaching and mark them. The teacher asked the students to express their opinions and make targeted guidance and correction. This link is not only to make up for the differences, but also to cultivate outstanding students, improve students at different levels and promote the development of students' innovative thinking.
Second, the strategy summary of learning guidance mode
1 Learning guidance opportunities-combination of in-class and out-of-class. It is a good study habit for students to study in advance after class. We combine the experiment of "Learning Plan Guidance" to carry out targeted training. Therefore, the "study plan" designed by us can be distributed not only in class, but also before class, so that students can study in advance according to the guidance of the study plan, and teachers can guide them in class according to the students' study in advance to achieve a higher level of guidance.
2 learning guidance atmosphere-dynamic and static combination. According to students' psychological characteristics and cognitive level, the guidance of primary school students' learning plan should create appropriate situations and create a good classroom atmosphere, so as to organically combine static learning plan guidance with dynamic teacher-student interaction, stimulate students' learning enthusiasm and break the boring state of the classroom. For example, in Solving Problems in Proportion, after reading and thinking, I asked such a question: "What ideas were used to solve the first and second questions, and why?" The third question is what the idea of proportion can't answer? " Organize the students to exchange and compare, and then ask the students to guess what math problem the teacher will ask next. By guessing and editing, students' interest in learning is stimulated, and the classroom is dynamic and orderly, with both calm and deep-seated thinking activities and lively emotional experiences.
3. Learning guidance mode-the combination of self-study and thinking. In the process of autonomous learning according to cases, it not only provides students with ideas, but also leaves room for thinking, so that students can think and write while learning, which makes the learning activities have certain acceptability, understanding and creativity, and enables students to develop a good attitude of being open-minded and innovative. For example, when guiding students to read problem-solving ideas, I provide suggestive answers to the problem-solving structure, leaving a certain space for students to fill in while thinking; In the self-answering feedback exchange, I asked students to interpret the answers put forward by their classmates and let them think about what methods they have learned for ideas and equations. Teachers guide students to explore independently through guiding questions, which not only deepens students' understanding of what they have learned, but also improves students' self-learning ability.
4 guiding strategy-combining positive examples with counterexamples. Although students' knowledge level and life experience are different, they can learn correct answers by themselves on the basis of group communication. At this time, collect some typical mistakes and correct answers, and let students compare and analyze them in depth, and the effect will be very different. Students will try their best to explain the causes of mistakes and solutions to problems, and will also remind their peers of problems that should be paid attention to. They will all become "little teachers" with high learning enthusiasm. Therefore, we should pay attention to the organic combination of positive cases and negative cases in the communication and display after the guidance of the study plan, so that they can complement each other.
The extension of guiding learning-combining guiding thinking with guiding doubt. Cultivating students' problem consciousness is a highlight of learning plan guidance. After each learning session, students should be guided to reflect on what problems they still have, what problems they need to solve and what methods they need to learn. For example, some students asked when to solve the problem with the direct proportion method and when to solve the problem with the inverse proportion method; Is it necessary to list the proportional formula when solving in proportion? It has also been suggested that in the past, simple arithmetic methods could be used to solve problems, so why use complex proportional solutions? Thinking and solving these problems will deepen students' understanding of proportional problem solving. Therefore, the "guidance" of learning plan guidance should not only "guide learning" and learn knowledge, but also "guide thinking", think of methods and even "guide doubts", thus deepening learning activities and raising awareness.
"Learning plan guidance" always takes learning as the center, students learn independently with the help of learning plans, and everyone participates in the activities of doing mathematics. In order to make students' study more solid, the design of study plan should take care of differences, pay attention to innovation and hierarchical design, let students at different levels participate in learning and acquire knowledge on their own basis, and overcome the disadvantages of "not having enough to eat" or "not having enough to eat".
Author unit
xiamen foreign languages primary school
Editor: Li Ruilong.
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