First, perceptual experience-the cornerstone of abstract generalization
Perception is feeling and perception, which is the primary stage of human cognitive activities and the cornerstone of abstract generalization. Adequate perception can help students obtain a large number of perceptual materials and create conditions for students to abstract effectively.
1? Enrich perceptual materials. The process of abstract generalization is actually a process of introducing "three" and opposing "one" The richer, more comprehensive and more typical the perceptual materials are, the more conducive it is for students to accurately abstract and summarize.
Strategy 1: put the concept in the background where it comes into being. Our understanding of logarithm and shape is not isolated. If we put the cognitive object in its background, or communicate with similar concepts and compare with relative concepts, it will be easier to get a clear, accurate and comprehensive understanding.
For example, teaching "mutual understanding" can display the following set of formulas:
Ask students to calculate the results of these formulas first, and students can easily find that their numbers are all 1. Then ask the students to classify these formulas with the number 1. Students can divide according to the number of numbers involved in the calculation or according to the operation symbols. The first method can divide the above formula into two categories: the first category is the one in which three numbers participate in the calculation; Other formulas belong to the second category. The second division divides the second formula in the first division into four categories: multiplication: ×3, ×, 2×, ×; Addition:+; Subtraction: 3? 5-2? Thulium 5; Division: 3÷3. On the basis of two classifications, the teacher pointed out that the product is 1 and the two numbers are reciprocal. Ask the students to extract the formula whose product is 1 from various formulas whose number is 1. In this way, the concept of reciprocal is put in its background, so that students can understand the two connotations of the concept of reciprocal more thoroughly: "product is 1" and "two numbers".
Strategy 2: Strengthen perception by comparing relative (or adjacent) concepts. Our understanding of a concept is not necessarily based on the concept itself. When it is difficult to deeply understand the concept because it is limited to the scope of the concept itself, we might as well understand the concept by comparing adjacent or relative concepts.
For example, in the teaching of "expressing the possibility with scores", the textbook first presents the following situation diagram:
In teaching, students all think that the method of guessing left and right is fair, but the reasons given are not sufficient-table tennis may be in the left hand or the right hand, and there are only two possibilities, so it is fair. Students only see "there are only two possibilities" and don't feel that "the two possibilities are equal". How to strengthen students' second feeling? I took another way to decide the right to serve: throw a steak on it, serve with the chassis on the ground and serve with the feather on the ground. Is this method fair? The students said it was unfair because it was almost impossible for a chicken feather to land. With such an opposite situation, students have a comprehensive perception of the possibility of an event: they should not only pay attention to several possibilities, but also pay attention to whether these possibilities are equal. However, it is difficult for students to get in-depth feelings simply by relying on the situation provided by textbooks.
2? Strengthen the perceptual experience. Limited by age, pupils' cognition of things often has the following characteristics: (1) average. Lack of detailed analysis and carelessness. (2) Unconscious. Strong perception of strong information factors, easy to ignore background information, and the perception process is mostly chaotic and lacks sequence. (3) passive. They can't consciously perceive from the need of solving problems, and are often disturbed by things that arouse and stimulate their interest. It can be seen that teachers do not necessarily rely on the arrangement of teaching materials when presenting perceptual materials. They can flexibly change the presentation of learning materials according to children's perceptual characteristics, so that students can pay more attention to the key elements of learning materials and consciously, orderly and emphatically perceive them, thus strengthening the perceptual experience.
Strategy 3: Focus on strengthening the stimulus. What students need to see and hear clearly must be stimulated to a certain intensity. In general, we can emphasize the key content with the help of clear and organized blackboard writing and cadence tone, so that students can concentrate on the essential elements of concepts, thus helping students to abstract effectively.
For example, there is such an exercise in the teaching of "Preliminary Understanding of Fractions":
After the students correctly expressed the colored parts in each picture with scores, I said, "Students look at these pictures and their corresponding scores carefully and understand the meaning of each number while reading. Think again, what are the similarities and significance of these scores. " Due to the intense stimulation of writing, reading and reading just now, it is easy for students to say, "They all divide a graph into several parts on average, indicating that one part can be represented by a score." Without the strong stimulation of reading, it is impossible for students to have a deep understanding if they write down their scores and rush to summarize them abstractly.
Strategy 4: Dynamic handling of teaching process. Influenced by various factors, teaching materials can't fully show the whole process of knowledge formation, and often only statically arouse students' thinking about understanding and learning. Static things are generally dull, so it is difficult to attract students' attention, and it is not conducive to focusing students' attention on the essential attributes of research concepts. Therefore, teachers should make static materials and monotonous learning process dynamic and help students get a profound experience.
For example, how long does it take to teach? The textbook presents:
Teaching step by step according to the content presented in the textbook, students' understanding of "around 7 o'clock" is mechanical and static, which is not conducive to students' active construction of cognitive structure. So, I created such a problem situation: Xiaoming and Xiaogang agreed to go to the library to read at 9 am. Then the multimedia shows a clock face of dynamic demonstration: the pointer has been moving, and Xiao Gang arrived at 9 o'clock. I asked the students, "Is Xiao Gang late?" The student said, "No." I then asked, "How did you see it?" The student said: "The hour hand is close to 9 o'clock, and the minute hand is close to 12, which means that it is not 9 o'clock yet." When the students understood that "it's not 9 o'clock yet", the pointer continued to walk. Just after 9 o'clock, I asked the students, "Is Xiao Gang late?" The student said, "I'm late." I then asked, "How did you tell?" The student said, "The hour hand just passed 9, and the minute hand just passed 12, which means just after 9 o'clock." On this basis, I revealed: "It's not 9 o'clock now, just after 9 o'clock, and these two times are very close to 9 o'clock, which can be said to be around 9 o'clock." With the help of dynamic display situation, students' understanding of "around 9 o'clock" becomes vivid and accurate.
Second, clever guidance-the magic weapon of abstract generalization
Pupils are in the transitional stage from thinking in images to thinking in abstractions. Abstract generalization is a leap in their cognitive ability, and it is also a difficult point in the learning process. With rich perceptual knowledge, it is possible for students to make effective abstract generalization. For students, the common confusion is: there are ideas in the brain, ideas in the heart and words in the mouth, but it is difficult to express them comprehensively, clearly and accurately. At this stage, teachers need to adopt some relevant strategies to help students make effective abstract generalization.
Strategy 1: Use blackboard writing skillfully to give thinking a support point. The process of students exploring new knowledge is like finding the way to their destination in a strange city. They are more concerned about their current position. With the deepening of exploration, students only have strong feelings about the current experience, but may gradually dilute the initial perceptual experience. The teacher's blackboard writing is very important for students to accurately grasp the whole inquiry process after inquiry. Writing on the blackboard is like a "landmark building" in the process of "finding the way", which can help us recall the whole inquiry process clearly and gain an abstract understanding.
For example, teaching "problem solving strategy-replacement". Example 1 Yes: Xiaoming pours 720 ml of juice into 6 small cups and 1 large cup, which is just full. The capacity of a small cup is a large cup. What are the capacities of the small cup and the large cup? Through thinking, drawing, talking and other activities, students independently explore two ways to replace large cups with small ones (1), calculate the capacity of small cups with 720÷(6+3)=80 (ml), and then calculate the capacity of large cups with 80×3=240 (ml). (2) Use a large cup instead of a small cup, calculate the capacity of the large cup with 720÷( 1+2)=240 (ml), and then calculate the capacity of the small cup with 240÷3=80 (ml). When the students reported, I wrote down two ideas on the blackboard:
With the help of the blackboard writing above, students can easily understand the idea of substitution method, and use the multiple relationship of two cups to abstract two cups with different specifications into one specification. Although the replacement method is different, the total amount after replacement remains unchanged.
Strategy 2: Introduce letters to make the expression focused. Primary school students' reflective ability and language expression ability are not mature enough, so it is difficult to express their thoughts and ideas clearly and accurately in language. Letters are abstractions of logarithms. Using letters to represent numbers can give students a key point of expression.
For example, in the teaching of "the change of surface area", there is such a link:
Students can easily fill in the data in the form through hands-on operation, observation and communication and full understanding. However, when asked about "what patterns are found on the table", many students think that jiaozi is cooked in a teapot ―― you can't pour it out. How do students express themselves accurately? I wrote the letter A after the ellipsis on the blackboard and asked, "If it is a cube, can I fill in the following form?" After the students have written 6a and 2×(a- 1), let them talk about the law of discovery. Students can easily say, "A cube and a * * * have 6a faces. When combined into a cuboid, there are (a- 1) knots, and each knot has two faces, so a * * *. With the help of letters, students can express themselves more clearly and form an abstract and general understanding of the changing law of surface area.
Strategy 3: Set up exercises skillfully to make abstract generalizations come naturally. When there are specific problems and data, students will rely on them. Omitting the data in specific questions one by one can encourage students to abstract effectively.
For example, teaching the meaning of fractions requires too many abstract concepts, such as "unit" 1', "average score", "several copies" and "1 or several copies", so it is difficult for students to make a clear, accurate and complete abstract summary. How to make students realize abstract generalization on the basis of full perception? I designed an exercise like this:
Say the meaning of each score below.
First, it is easy for students to say, "Divide the unit 1 into three parts, indicating that these two parts are used to express." In the second fraction, the denominator was omitted. On the basis of thinking, students naturally say, "Divide the unit' 1' into several parts, and express such1parts with". The third fraction omits the numerator, so students have the experience of representing the second fraction, and can easily sum up that "the unit' 1' is divided into seven parts on average, indicating that such1part or several parts are used". The last fraction omits the numerator and denominator, so the students naturally sum up the complete concept of the fraction: "Divide the unit' 1' into several parts on average, indicating such1part or several parts, and use the fraction to express it".
To guide students to abstract effectively, we should not only pay attention to whether students have gained sufficient perceptual experience, but also adopt some clever strategies to help students overcome obstacles in the process of abstract generalization, so as to gradually improve their abstract generalization ability.
Author unit
Jiangsu province Tongshan county sanbao experimental primary school
Editor in Charge: Cao Wen
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