? This training focuses on two fields: "number operation" and "graphics and geometry". Very wonderful, very shocking! However, we often feel that the lessons of famous teachers can only be observed from a distance, and it is difficult to imitate them, so it is difficult to flexibly apply them to our own classrooms. Therefore, in this study, I focus on the value behind a good teacher's class, that is, what we have learned from a good class. Among them, three "shots" touched me the most.
First, multiplication-"division and combination", early infiltration.
? In primary school mathematics textbooks, integer multiplication is divided into four stages: table multiplication, two or three digits multiplied by one digit, two digits multiplied by two digits, three digits multiplied by two digits, and then there are five major algorithms to learn. Among them, the multiplication and division method involves two levels of operation, and its model is more complicated and its application is more flexible, which has become a difficult point in teaching and learning. At the training site, Professor Wu Zhengxian, a special famous teacher, and Professor Liang Yan, an experimental school in Guangming District, gave me a new idea on the teaching of multiplication table and distribution method, that is, to infiltrate the idea of division and combination as soon as possible.
? In the teaching of multiplication formula, students have the ability to transfer, and they are used to deriving new formulas from the relationship between adjacent formulas. For example, they forgot six or seven (? ), children will add 1 seven on the basis of five sevens with the help of "five seven thirty-five". However, if we always borrow only adjacent formulas, students will not think deeply enough. In the lesson of multiplication formula of six, teacher Liang Yan designed a "schematic diagram" to make students realize that six sevens can be divided into two sevens and four sevens. If "274" and "4728" are added together, you can get "6742". This link gave me a great touch-the original "multiplication and division method" came to the second grade children! It is in this process of "division and combination" that the essential understanding of the meaning of multiplication is deepened and the law of multiplication distribution is infiltrated.
? In the study of "Multiplying two numbers by two numbers", Wu Zhengxian designed a bitmap of 12× 14 to help students understand arithmetic and refine the algorithm in the process of circling. There is such a fragment:
Teacher: (pointing to the vertical form of 14× 12) We are obviously calculating 14× 12. Let's multiply it. Why did you add it at the end?
Health: Because we took 12 apart.
Health: Yes. We split 12 14 into 10 14 and two 14, and finally we will add them up to make 12 14.
Teacher: Then look at your conceptual drawing. What does this circle mean?
Health: two copies 14.
Teacher: What about this circle?
Health: 10 14.
Teacher: What are we going to do?
Health: Draw a big circle and add it up.
? In the usual teaching, we usually only draw two small circles on the ideological map, but never consider adding the last "big circle", which is equivalent to "only dividing and not dividing". In the operation teaching of multiplication, the idea of "dividing and combining" runs through. Although we haven't moved out the name "multiplication table" at this time, we should infiltrate this idea as soon as possible so that students can understand and construct the model.
Second, the division operation-"minutes" as the core, subdividing units.
? I still remember when I first joined the company, a student asked me, "Why is vertical multiplication from the unit and vertical division from the high position?" Yes, why? In Professor Wu Zhengxian's fractional division class, I seem to have found the reason why division must start counting from high places.
? Teacher Wu said, "It costs 97 yuan for four people to eat a meal, AA. How much does everyone have to pay? " The briefing is simple and direct. Faced with the answer "97 ÷ 4 = 24 (yuan) ... 1 (yuan)", many children fell into thinking: AA system, how to divide this 1 yuan? This connects the children's experience from "division with remainder" to the "fractional division" to be learned today-constantly dividing the remainder. The remaining 1 yuan is evenly distributed to four people, and each person is not enough 1 yuan, so the unit "yuan" should be subdivided into "10 angle". 10 ÷ 4 = 2 (angle) ... 2 (angle), and the remaining two angles are not enough for everyone to score 1 angle, so the unit of "angle" needs to be subdivided again. Later, Mr. Wu removed the model of "Jiao Yuanfen" and led the children to explore the arithmetic and algorithm of "97÷4" again from the perspective of decimal meaning, bit value and counting unit. 1 divided by 4, it is subdivided into 10 0. 1 and 0. 1.
? I believe that although Mr. Wu didn't reveal the essence of fractional division, the decimal point is a "fixed needle", and we should continue it whenever it is not enough. The students' feelings are very profound.
Third, review lessons-reject "cold meals" and introduce new ones.
? "It is difficult to have a review class" is the unanimous sigh of many math teachers. In review teaching, teachers often sort out and explain what they have learned, and then fall into the strange circle of "doing problems, doing problems, talking about problems, and doing problems again". In the last training, Mr. Liu, a primary school mathematics researcher at Beijing Academy of Educational Sciences, taught the review class of the sixth grade geometric volume, which successfully linked the shapes of cuboids, cubes, cylinders and cones that students learned with the common cylinders and cones in life, opened up the connotation of geometric volume and the meaning behind the calculation formula, and also made the students feel what it means to "review the past and learn something new"-not only to sort out the knowledge they learned, but also to let the students feel the calculation.
? In this training, Jin Cai, a primary school teacher attached to the First Normal University, once again confirmed the importance of "bringing forth the old and bringing forth the new" in a fifth-grade "decimal multiplication review class". Teacher Jin Cai designed a familiar grid diagram (10× 10). Let the students determine the unit length of each grid, draw a picture and calculate the area of six small squares, and connect integer multiplication with decimal multiplication. There are also six small squares, which can represent 20×30, 2×3, 0.2×0.3 ... What changes is the counting unit, and what remains unchanged is the number of counting units, so that students can understand why decimal multiplication should be calculated by integer multiplication first, and then several decimals should be counted at the end of the product. The former is the number of statistical counting units, and the latter is the determination of counting units.
? In this way, there is not only the consolidation and combing of knowledge, but also the overall connection between old and new knowledge, so that students can have a "new" harvest on the basis of combing and make the cognitive structure have growth vitality. Similarly, the review course design of fractional multiplication is also coming to the fore.
? The five-day course provides many good experiences worth learning. Teacher Zhang, a primary school mathematics researcher in Shunyi District, Beijing, mentioned that in class, we often ask students "What do you think" and rarely ask "How did you come up with it", but the latter is more important. Similarly, when observing a good class, teachers should not only look at what others think, but also think deeply about what others think. I think these teachers can design teaching in this way, which is inseparable from their in-depth research and thinking on the nature of knowledge. Therefore, we should start from the daily dribs and drabs, consciously learn the essence of a certain kind of knowledge, and grasp the knowledge structure as a whole, so as to have a thoughtful lesson.
(Shenzhen Guangming New District Aihua Primary School? Lai Wenqi)