Classification thought is a basic mathematical thought. It is a process of orderly division and organization of things according to certain standards.
Regarding the specific function of classification thought, Qiang and Yang Lei believe that when knowledge accumulates to a certain extent, it is necessary to use the idea of classification and induction to help students build their own knowledge network, enhance the rigor of thinking and improve their ability to solve problems. Zheng Yuxin thinks that classification can provide the necessary foundation for the corresponding abstraction, and points out the possible ways for how to understand it step by step.
As for how to infiltrate the classification idea, Jin Woo and Yang Lei strongly believe that to infiltrate the mathematical classification idea in teaching, we should tap the opportunities provided by textbooks and grasp the opportunity to infiltrate the classification idea; By mastering reasonable classification methods, clarify mathematical knowledge; Guide students to have classified discussions and solve complex problems. Gu believes that students' life experience should be tapped and the classified experience in students' life should be transferred to mathematics. Only through continuous thinking and application can the classification idea be internalized into students' own things and form mathematical methods; In teaching, we should flexibly use the classification thought, pay attention to cultivating the order and generality of students' thinking, and promote the formation of classification thinking methods. Wu Zhenjin believes that it is important for students to learn how to choose different classification standards, so as to cultivate the openness and flexibility of students' thinking. Professor Zheng Yuxin believes that students should be guided to classify according to the quantitative characteristics of mathematics.
Second, the significance of primary school mathematics classification thought
The development of classification ability reflects the development of students' thinking, especially the development level of generalization ability. It is not only an important aspect of the development of students' logical thinking ability, but also plays an important role in promoting the development of students' logical thinking ability
1. provides the necessary foundation for mathematical abstraction.
Classification needs to analyze and compare objective things, and abstract the general characteristics and essential attributes of things. Specifically, children should first specifically judge the similarities and differences of objects, treat some objects as the same kind or treat some things as the same kind (classification), that is, they mainly focus on one (some) characteristics of objects and think that they are the * * * nature of these things, while temporarily ignoring other attributes. In other words, an important role of classification thought is to provide the necessary foundation for the corresponding mathematical abstraction.
2. Point out the possible ways of further understanding.
If classification is mainly to highlight the similarity of things, then the function of classification of different categories is to point out possible ways for how to understand step by step. From this point of view, we can re-understand the significance of triangle classification, that is, why triangles are divided into right triangles and non-right triangles (acute and obtuse triangles), isosceles triangles and non-isosceles triangles. Because it provides a possible way for us to study triangles from special to general.
3. Lay the foundation for reaching advanced thinking.
The hierarchical relationship between Gagne's learning process and the conditions of intellectual skills is: discrimination → (with discrimination as the condition) specific concepts → (with specific concepts as the condition) concepts → (with defined concepts as the condition) rules → (with rules as the condition) advanced rules. Because classification activities often involve discrimination, learning can often start with classification, then abstract it into concrete concepts and defined concepts, and finally lay the thinking foundation for forming rules and advanced rules.
4. Form a perfect and reasonable knowledge structure.
Classification is often to establish a certain order, so knowledge is accumulated to a certain extent, and the application of classification ideas can help students to summarize and sort out knowledge in an orderly way, without repetition or omission, thus forming a perfect and reasonable knowledge network diagram. The study of learning psychology shows that a good knowledge structure is very important for extracting knowledge and solving problems.
5. Develop children's organizational strategies.
Organizational strategy is to classify, arrange and summarize the learning materials systematically and orderly according to the internal relationship between knowledge and experience, so as to rationalize their structure. The application of organizational strategy can deeply process the learning materials, and then promote the understanding and memory of the learned content. It can be seen that learning to classify is an important prerequisite for formulating organizational strategies. The research shows that children in the lower grades of primary and secondary schools can learn to use organizational strategies after a period of strategy training, although they can't spontaneously generate and use organizational strategies. Through the infiltration of classification ideas in mathematics learning, children's organizational strategies can be developed and transferred to other disciplines.
Third, the teaching strategy of primary school mathematics classification thought
The classification idea runs through the whole primary school mathematics stage. Teachers should dig out the classification idea hidden in textbooks and infiltrate it into students. For example, in the first grade, textbooks usually arrange to classify things in life, and the results obtained according to different standards are different; When understanding objects, classify cuboids, cubes, cylinders and spheres ... Teachers can adopt the following strategies in teaching:
1. Introduce new knowledge through classification activities.
From the perspective of learning psychology, in the lower grades, students often set up specific classification activities to let students form concepts and reach the stage of not strictly defining specific concepts. For example, when you know triangles and quadrilaterals, you can show a dot diagram, which can be divided into closed graphs and non-closed graphs according to whether the graphs are closed or not. In a closed figure, there are several line segments around the figure, which are divided into three categories: triangle, quadrilateral and pentagon.
In junior and senior high school, a well-defined concept can be gradually formed through concept assimilation according to students' thinking ability in time, thus promoting the development level of students' abstract thinking. For example, when introducing the concept of parallel lines, many of them are introduced through concrete examples in daily life, and then the concept of "parallel lines" is formed through abstract generalization. Therefore, students can classify the relationship between two line segments in the same plane and get two situations of intersection and non-intersection, so as to understand the two positional relationships of intersection and non-intersection of two lines in the same plane and lay a good foundation for defining parallel lines through conceptual assimilation.
In addition, when introducing concepts, teachers should guide students to think about why they should be classified like this and how to classify them more reasonably. For example, the teaching of "triangle classification" should focus on "why this classification is needed" and "how to classify it reasonably", and should not spend too much time and energy on practical activities such as "angle measurement". Teachers can review the classification of diagonal angles first, especially remind right angles to be special in various angles, and then guide students to think about how to classify triangles and analyze the rationality of this classification method in detail. In particular, first, is there any overlap, that is, is a triangle both a right triangle and an acute triangle? Second, is there any omission in the classification, that is, is it possible to have such a triangle, which is neither right nor acute?
2. Summarize and organize knowledge with classified ideas.
When knowledge is accumulated to a certain extent, it is often necessary to classify and summarize the knowledge learned, especially in middle and high grades. Therefore, students need to master reasonable classification methods to conform to the principles of mutual exclusion, no omission and simplicity, thus forming a sound and reasonable knowledge network.
In the primary school stage, students need to master the content, according to the mathematical classification methods often have the following:
(1) is classified according to quantitative characteristics and quantitative relations. For example, the classification of integers, decimals and fractions, the classification of algorithms and so on.
(2) According to the characteristics of graphics or the relationship between them. For example, triangles are classified by angle, including acute triangle, right triangle and obtuse triangle.
(3) According to the exploration direction of solving problems. For example, the problem of straight-line travel and the problem of circular travel, we can see that they have similarities in solving problems.
In order to make students form a good knowledge structure, it is often necessary to highlight the differences and connections between different knowledge by means of comparison, comparison and examples, so as to fill in the gaps and eliminate the wrong impression of knowledge. In order to be more intuitive, tables and charts are often used, such as "Wayne diagram" is a good tool.
In addition, teachers should guide students to build their own knowledge network when sorting out and summarizing knowledge with the idea of classification.
3. Solve the problem with the idea of classification.
Solving problems with classification is an important and effective method in primary school mathematics. The key lies in correct classification, no repetition or omission, which can effectively correct students' disorder or even blind patchwork and cultivate students' careful thinking.
For example, with the number plate of 1, 2, 3, you can arrange several three digits. Let the students do it and form a row. Some students leave the hospital quickly, while others leave the hospital incompletely. At this time, the teacher should guide the students to discuss in groups. 1. When the number in the hundreds is 1, which three digits are there? (123, 132), when the number in the hundreds is 2, how many three digits are there? (213,231), when the hundredth digit is 3, how many three digits are there? (3 12、32 1)。
4. Classify according to the quantitative characteristics of mathematics.
Professor Zheng Yuxin believes that due to the particularity of mathematical abstraction, we only pay attention to the quantitative characteristics of objects, that is, quantitative relations and spatial forms, without considering their qualitative contents at all. For example, in the teaching of classification, teachers often come up with some modules prepared in advance, which not only present various shapes, such as triangles, quadrangles, circles and so on. But also painted with various colors, such as red, yellow, green and so on. They are made of different materials, including wood, cardboard, plastic and so on. Teachers ask students to classify these modules. Under normal circumstances, students often give different classification methods, and teachers often generally affirm this, and even actively encourage students to put forward new and more classification methods. In mathematical abstraction, we pay attention to the quantitative characteristics of objects (including quantitative relations and spatial forms), and completely abandon the "non-mathematical components" (qualitative content). Therefore, only if all triangular modules are classified into one category and all quadrilateral modules are classified into another category, can it be regarded as directly related to mathematics, while other classification methods, such as color and material classification, are not the main concern of mathematics. Therefore, we should not equally affirm all possible classification methods, but should "optimize" the methods given by students.
The significance and teaching strategy of mathematics classification in primary schools Chapter 2 "Triangle classification" is a teaching activity after the fourth grade students have a preliminary understanding of triangles. I think classification is a mathematical idea, and it is a process of orderly dividing and combining things according to certain standards. The classification of triangles lies in giving students a mathematical model, which lays a knowledge foundation for students to better apply triangles in the future and further understand and study triangles. In order to effectively integrate and implement the three-dimensional goals in the classroom, I designed it like this:
(A), create a situation to stimulate interest in the introduction
At the beginning of the class, I first created a mathematical situation for students to classify the students in the class according to certain standards, such as: classifying boys and girls according to gender; According to the group ... according to age ... the purpose is to make students pave the way for triangle classification from multiple angles, create a happy emotional state for students, and make students naturally enter the best learning state.
(B), to explore cooperation and exchanges
The teaching of a class focuses on guiding students to operate, classifying triangles cut by students themselves and exploring classification methods. In the process of exploring triangle classification, I first change the way of presenting knowledge, so that students can operate, observe, reason, verify and summarize with questions. Guide students to explore independently, cooperate and communicate, and find problems in communication. Students begin to operate and divide the triangle into angles: three angles are acute angles, one angle is right angle and the other angle is obtuse angle, and then guide the students to name them respectively. Let me summarize it in the form of a collection. Then ask the question: how to divide it? The students proposed dividing by edges. By measuring the side length, students divide triangles into three categories: isosceles triangles, equilateral triangles and equilateral triangles. Teachers and students know isosceles triangle and equilateral triangle together. After teaching, some conceptual problems have been completed, which makes students have a further understanding of concepts. In the process of consolidating the knowledge learned, students not only cultivate their practical ability, but also pay attention to the cultivation of their thinking ability, so that students can comprehensively use the knowledge and skills they have learned to solve problems and cultivate their application consciousness, practical ability and innovative spirit. The classification of triangles is a process that allows students to create and experience the fun of learning mathematics with their heart, and allows students to operate, think positively, communicate with classmates and show themselves under the guidance of teachers.
(3) Consolidate knowledge and improve ability
I designed a step-by-step consolidation review question, so that students can always consolidate their knowledge and expand their thinking in a pleasant learning atmosphere, so that the three-dimensional goals of knowledge and skills, processes and methods, emotional attitudes and values complement each other and blend into one, thus achieving the integration of the three-dimensional goals.
The Significance and Teaching Strategies of Primary School Mathematics Classification Thought Part III I. teaching material analysis and Students' Understanding
1, teaching material analysis
As for the "angle", students have had initial contact in Grade Two, but most of them are intuitive descriptions. Now, on the basis of the second grade, they properly abstract the characteristics of graphics and systematically learn the concept, measurement, classification and drawing of angles. The classification of angles is based on students' preliminary understanding of angles and their ability to measure angles with protractors. According to the degrees of angles, they can distinguish right angles, right angles, acute angles, obtuse angles and rounded corners.
2. Student analysis
Students will come into contact with many angles of different sizes in daily life, but there is little knowledge about the classification of commonly used angles in life, which is more abstract. Although the abstract thinking of grade four students has developed to some extent, they still focus on concrete thinking in images, and their ability of analysis, synthesis, induction and generalization is weak, which needs further training.
Second, teaching experience
Mathematics comes from life. Our daily life is a big classroom for learning mathematics and a vast world for exploring problems. The ultimate goal of mathematics learning is to apply what we have learned to life practice. Therefore, I set out from the reality of life, let students capture their own life materials, and then set out from their life experience and existing knowledge background, so that they can get the pleasure of actively exploring mathematics.
1, introduced by knowledge transfer, reflects that mathematics comes from life.
At the beginning of the class, I asked the students to recall the concept of angle and how to measure it, which paved the way for the study of new knowledge in this class. Then I showed the common clock face in life, and asked the students to measure the degree formed by the hour hand and the minute hand on the clock face with a protractor. After measuring the degree, I asked, can you classify the angles according to the size of these angles? Students have questions, and then I said: after learning this lesson, everyone can classify diagonally. In this way, it is logical to introduce new lessons with knowledge from life, which shows that knowledge comes from life.
2. Let students experience the formation process of knowledge through hands-on operation.
For right angles, students have been deeply impressed in the second grade, so when learning right angles, I directly ask students to fold right angles with rectangular paper, and then measure the degree of right angles with a protractor, so that students can know how many degrees the right angles are more accurately. When learning acute angle and obtuse angle, I always let students feel whether it is greater than right angle or less than right angle with movable angle. For the learning of straight corners and rounded corners, students also feel their shapes by rotating their hands with the active angle, and measure the degrees with a protractor. In this way, students fully feel the formation process of various angles in the process of hands-on operation, and are deeply impressed by the range and accuracy of values.
3. Give students rich learning resources and enough learning space.
(1) provides students with rich learning resources: rectangles, activity corners, etc. Using the intuitive characteristics of learning tools, organize students to fold and flip, and experience the formation of various angles in intuitive operation. Provide students with visual courseware, so that students can see at a glance.
(2) Promote the development and deepening of inquiry activities. Let students experience the process of exploring new knowledge through practical operation, observation, thinking and induction, and experience the joy of successful exploration, and under the appropriate guidance of teachers, lead the exploration process deeper.
Third, insufficient analysis.
1, the textbook mining is not deep enough.
When teaching the knowledge of Boxer Rebellion and Rounded Corner, I simply let the students feel the shapes of Boxer Rebellion and Rounded Corner by rotating the movable angle, and deduce their degrees, instead of further asking the students to draw a picture to talk about them, so as to deepen their understanding of these two corners. After class, I think my understanding of the textbook is still not deep enough, and I only pay attention to the surface.
2. The key knowledge is not thorough.
In the process of listening to lectures and practicing after class, I found that students have only a little knowledge of various angles and degrees, but they have not fully mastered them. So I reflect that I didn't put the key points in place when teaching new knowledge, which led to students not really knowing why and why.
3. There is no good breakthrough in the difficulties.
The difficulty of this lesson is to make students understand the difference between straight lines and flat angles, and the difference between rounded corners and rays. Perhaps it is because the teaching design simply considers the differences according to their own characteristics, without further considering the students' ability to accept and understand, so some students make mistakes in the later exercises.
The order of teaching procedure is reversed.
After teaching boxers, students should be directly guided to explore the relationship between boxers and right angles. But after teaching fillet, I only led students to explore the relationship between right angle and square angle and fillet, and the teaching procedure was reversed.
5. The teaching language is not refined enough
The teaching language is not rigorous, such as the accurate expression of concepts such as Boxer Rebellion and Rounded Corner.
6. The evaluation method is too monotonous
The evaluation of students is not enough, and students' learning enthusiasm can not be well mobilized.
7. The classroom atmosphere is not active enough
The classroom atmosphere is rather dull, and students' enthusiasm for learning and answering questions is not high, which may be related to the design of teaching and the encouragement of teachers.
Fourth, the direction of efforts.
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2. Strengthen the tempering of teaching language and use teaching evaluation language timely and reasonably. Through teaching, I deeply realized my own shortcomings in this respect. Therefore, I decided to keep exploring and learning in my usual teaching, be strict with myself, strive to make students learn what they should learn with refined language in class, and skillfully use evaluation to make students learn easily and happily.
3. Carefully design teaching. Teaching design is related to the success or failure of the whole class. Therefore, when I design teaching, I must consider it comprehensively, combining the age characteristics of students, combining students' cognitive ability and so on. Design a reasonable teaching process, highlight key points and reflect students' dominant position.
4. Make proper use of students' evaluation, learn to use your quick wits in teaching, and reasonably handle the resources generated by teaching. Teaching tact can't be practiced overnight, it needs to be accumulated over time, and it needs to be constantly summarized and studied, and it needs to be constantly learned. Although it takes a lot of time and energy to practice this ability, I will try my best to keep working hard.