The most direct expression of this "obedience" is to realize the docking with children's experience. A poet said: All experiences are flashing arches, reflecting the unexplored dust of the world. As long as I get closer to it step by step, the edge there will disappear. Classroom is a dialogue between life and life, and it is the docking of experience and experience. "Knowing decimals" is the teaching content of mathematics in the third grade of primary school. When many versions of textbooks are arranged to learn decimal knowledge for the first time, the generation of decimal and the relationship between a decimal and a fraction of a tenth (decimal) are the focus of the first lesson. The figure on the right shows the arrangement of the content in a textbook by taking the conversion between the length unit "decimeter" and "meter" as an example and the conversion between the price unit "yuan" and "angle" as a reinforcement. This arrangement fully embodies the connection between the old and new knowledge, that is, when students know the score initially, they already know that "5 decimeter" is "5/10m", "4 decimeter" is "4/10m" and "2 jiao" is "2/ 10 yuan". It can be said that it goes straight to the theme "the correlation between decimals and decimals". However, according to students' existing life experience, their contact and feelings about "decimals indicating length" are far less profound than "decimals indicating price". We have investigated 1200 third-grade students in county primary schools, township central primary schools, small villages and remote primary schools, and found that 60% of the students know that "0.4 yuan" is a decimal, and 75% of the students know that "0.4 yuan is a four-corner school". Therefore, from the students' life experience, it is more appropriate to take "the conversion between prices" as the example material and "the conversion between lengths" as the exercise material. If we think deeply, we can also find that the conclusion that "5/ 10 meter can also be written as 0.5 meter" directly shows the correlation between scores and decimals, so teachers have no choice but to "tell" students directly by way of explanation. On the contrary, if we start with the price in decimal form (such as 0.4 yuan), we can guide students to make use of their existing life experience of "0.4 yuan" to further explore the relationship between "0.4 yuan" and "1 yuan", and intuitively express the meaning of decimals in the exploration activities of painting and painting, so as to better understand the internal relationship between decimals and fractions. Mathematics itself comes from life and is higher than life. Learning decimals in connection with decimal phenomena in life is not only to "put students on familiar mathematics", but also to realize a leap from life to mathematics.
Because of the connection with real life and children's experience, students' understanding of decimals can be accomplished through "slow motion". As a concept teaching, the whole class grasped the relationship between knowledge (decimal and decimal, decimal and integer decimal, etc.). ), but did not stop at the teacher's direct explanation and "telling", but let students fully explore the process and establish an "intuitive model" of decimals (rectangular division and coloring) with the image support of intuitive charts. This "intuitive model" not only bridges the gap between decimals and fractions, but also has a powerful function of "derivation", and also provides a basic "model" for learning two decimal places, three decimal places and abstractly summarizing the meaning of decimals. Teaching needs "slow motion", especially the initial understanding and formation stage of concepts, methods and principles. Students need to gain experience and experience in activities and make new discoveries through continuous exploration and understanding. Because the experience of students' mathematics learning can not be separated from his inquiry process, the more thorough the inquiry is, the more full of twists and turns, the stronger the feeling and the deeper the understanding.
Through the "slow motion" of this lesson, we can also capture such an important cognitive principle-"The more abstract, the more vivid". In the initial understanding of decimals, "decimals on the number axis" is often a difficult point in teaching because of its high degree of "mathematicization" and abstraction. This lesson begins with the specific "1 meter scale" to understand "zero point", and then extends "1 meter scale" to "2 meter scale" to understand "one point". After the "ruler" is gradually changed into "axis" by using the animation effect, students can understand the number axis. Mr Xu Lizhi said: "Mathematical intuition is both the starting point and the destination of abstract thinking. Through abstract thinking, we can gain insight into the essence of mathematical objects and generalize them, thus forming a higher level of intuition, which can lead to a higher level of creative thinking activities. " [2] It can be seen that nourishing abstraction with images and cultivating thinking with intuition are important "magic weapons" to help students clearly master mathematical knowledge. In fact, the survey shows that most mathematicians think with the help of intuitive images. The famous Soviet mathematician Colmo Golov once pointed out: "Whenever possible, mathematicians always try their best to visualize the problems they are studying with geometry." [3] Generally speaking, the thinking of primary school students is mainly in images. When learning abstract mathematics content, it is often necessary to concretize the content and present the learned content in an image way. The more abstract mathematical knowledge is taught, the more image support is needed. Of course, this does not mean removing the essential characteristics of mathematics. One of the important reasons why math class becomes math class is that math class should embody the essence of mathematics. How to make students understand and master what they have learned in an easy-to-understand way without affecting the essence of mathematics is a great challenge to primary school mathematics teachers and mathematics classroom teaching.
There is a proverb: as long as the direction is right, no matter how far the goal is, it can always be achieved. Mr. Cheng Shangrong mentioned in the article "Children's Position: Education Begins Here" that "education is for children, and education is carried out and implemented by children. The position of education should be that of children. Children's position clearly reveals the fundamental significance of education and directly reaches the main purpose of education "[4]. Children are free men and explorers in the original sense. To establish a true children's standpoint, we should follow the psychological law of children's mathematics learning, and experience the process of abstracting practical problems into mathematical models, explaining and applying them, so that students can get comprehensive development while gaining mathematical understanding. It is undoubtedly a blessing to understand that the teaching of decimals can be regarded as an exercise of children's concept of position to a certain extent.
References:
Wang Yanling. Children-oriented: the transformation of curriculum development in China ―― An interview with Professor Zhong Qiquan [J]. Basic education curriculum, 20 10 (1-2).
[2] Xu Lizhi. The role of intuition and association in learning and studying mathematics ―― On the methods of learning and studying mathematics [M]. Dalian: Dalian University of Technology Press, 1989.59.
[3] Quoted from Zheng Yuxin. Mathematical thinking and elementary mathematics [M]. Nanjing: Jiangsu Education Press, 2008.85.
[4] Cheng Shangrong. Children's standpoint: Education begins here [J]. People Education, 2007 (23).
(Xu Weibing, Hai 'an Experimental Primary School, 226600)
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