? First of all, the audience of this math class is fourth-grade students, and the content of teacher Zhang's teaching is the content of grade five, six or even seven-the problem of meeting. Teacher Zhang's preparation before the formal class is also very interesting (and important). By asking students to give each other and answer brain teasers, tell students that this class should break the traditional way of thinking and go to Teacher Zhang's class with divergent thinking. This method not only stimulates students' interest in learning, but also encourages students to use their brains actively and express their ideas bravely. Later, in the process of learning, Mr. Zhang simply wrote a sentence on the blackboard, "Party A and Party B started from two places at the same time and went in opposite directions." It is natural for fourth-grade students to question this sentence. Teacher Zhang asked the students to guess boldly and got three answers, one face to face, two in the same direction and three back to back. After questioning, it is natural to check. Here, some students mentioned the use of Xinhua dictionary. Teacher Zhang suggested that dictionaries are not exclusive to Chinese classes, but can also be used in math classes, even English-Chinese dictionaries (Teacher Zhang mentioned why after the lecture). After Baidu search, I got an accurate explanation of the term encounter before I could move in another direction. So I asked two students to demonstrate.
? At this point, teacher Zhang throws a question, what is the positional relationship between the two students when they face each other? It also throws out the most important research point of this class-encounter problem. After teacher Zhang made a demonstration diagram for the students, let the students begin to draw the possible positional relationship between A and B, and then collect the sketches drawn by the students and show them on the blackboard in a planned way according to the students' answers. According to the students' drawings, they are divided into four categories, which are named no meetings, meetings and too many meetings (in the subsequent discussion, this category is carefully divided into meetings that Otawa does not cross the border). Children's thinking is really divergent. Ashamed to say, I didn't expect to go out of line when I met too many people. My mind was fixed and sweaty ... Teacher Zhang also used letters to express the distance in equations to guide students to find A and B in different situations.
As can be seen from the above picture, Mr. Zhang's knowledge capacity in this class is quite large. I feel that it also involves junior high school physics knowledge, which spans a lot and is very challenging. However, Mr. Zhang finished the course easily. As Mr. Zhang himself said in the lecture, this class doesn't have a number and too many problems, but it keeps students involved and enjoys it. In fact, at this time, I still don't understand what panoramic mathematics education is, and I don't quite understand the design concept and significance of this demonstration class. Don't worry, the second paragraph of the lecture made me feel enlightened. )
? The second paragraph is quite wonderful (unfortunately, because of time, Teacher Zhang only talked about four items of panoramic mathematics education). First of all, Teacher Zhang explained what Panoramic Mathematics Education (PPME) is (including the source of the design idea of this name). Panoramic mathematics education is to let students know mathematics without dead ends, and then know the world.
? This part is really wonderful. Teacher Zhang talked about four points about panoramic mathematics education and a lot of classes. I'll just briefly talk about the lessons that impressed Mr. Zhang the most. It is these lessons that make my view on panoramic mathematics education change from confusion to curiosity, and I want to try (a little bit overreached _).
1. Rich teaching materials (supplement and improve the teaching materials)?
Lesson 65438 +0: quadrilateral in grade three. Just after teaching this unit this semester, Mr. Zhang gave an error-prone example, as shown in the figure.
Indeed, in daily class, most students think that this is not a quadrilateral without thinking, and the reasons given are particularly simple. There is no such kind of picture in the textbook. Teacher Zhang pointed out in particular that the quadrangles appearing in the textbooks of primary school people's education edition are all convex quadrangles, so to some extent, they give children a fixed thinking. Later, Mr. Zhang pointed out that quadrangles include plane quadrangles and space quadrangles, and plane quadrangles include concave quadrangles and convex quadrangles, thus supplementing and perfecting the knowledge of quadrangles and enriching the teaching materials. That's all about quadrangles, that is, the "panoramic mathematics education" was realized.
? Lesson 2: Needless to say about symmetry, students, in fact, most of our teachers' understanding of symmetry only stays in the central symmetry, so it is wrong to think that the three sectors of the fan are asymmetrical. Teacher Zhang asked the students to search for symmetry knowledge before class, and found that symmetry means that every part of an object appears according to the same law, including rotational symmetry, compound symmetry and radiation symmetry. Rotational symmetry includes well-known central symmetry, namely 180 symmetry and 120 symmetry (fan blades belong to this category). All the knowledge about symmetry is presented here, um, panoramic mathematics education (my Chinese is not very good, but I can't understand it) (...).
Second, non-traditional mathematical content.
Teacher Zhang and his team boldly innovated and introduced non-Euclidean geometry in primary schools, such as topology in grade one, fractal in grade two, Riemann in grade three and Roche in grade four ... (It's embarrassing, all the mathematics knowledge learned in college has been returned to the teacher, and I still have to pick it up! )
? Teacher Zhang, Senior Two, spoke very carefully about fractals, and I also increased my knowledge. Through fractal, students can learn to transfer their thinking. In the lecture, Mr. Zhang also mentioned a very important idea in mathematics-modeling. No matter what mode it is, it will solve many problems. ...
? In fact, for the second part, it is not true that we failed the exam, but teacher Zhang said that we would take the exam without taking the paper. The purpose of studying mathematics is not to get into the exam, but to learn about the world, understand the world and break the mechanical score brain by studying mathematics.
Lesson 3: Teacher Zhang gave a wonderful lesson to the students he taught. The initial understanding of the score is only my knowledge of the teaching grade this semester, so the feeling will be deeper. This lesson breaks the traditional teaching method in textbooks, previews first, and then starts with the explanation of phenolphthalein tablets in life. Paper is used instead of pills. By dividing paper, students can grasp the key point-average score, and then guide students to say the meaning of numerator denominator, then divide cookies, feel the score by eating cookies, and then ask students to answer how many points the boys drank orange juice to solve the addition and subtraction of the same score. In a series of practical operations, students actively grasp the understanding, comparison and addition and subtraction of scores. This process is quite smooth, students participate in it and discover and feel for themselves. This advantage is thorough understanding, full of fun and making children fall in love with mathematics. Although this class was relayed by teacher Zhang, I still felt the charm of that class at that time, which made me dumbfounded. So this unit can be designed like this.
? Lesson 4: lateral area, a cylinder, was in Grade 6 three years before I worked, so this lesson was particularly impressive. The unit of cylindrical cone is a big difficulty for students, and it is more abstract. Every year, when I meet this unit, I have to spend a lot of time studying, but it has little effect. Teacher Zhang gave him a demonstration in this class. For example, lateral area, a cylinder, will tell students that the area rolled over by the roller is a lateral area of a cylinder, but Mr. Zhang will really let his students roll sand on the playground and then go back to the classroom to do the math themselves. I think the double blessing of theory and practice will make children understand more thoroughly. Even when studying the volume of irregular objects, Mr. Zhang will donate his shoes to the children to learn. This spirit of inquiry is worth learning.
? The third is the reconstruction of learning reality.
? Lesson 5: Proportional distribution of sixth grade. To tell the truth, when I was talking about this lesson, I used textbook examples in a rigid and dogmatic way. Teacher Zhang suggested who would care about things that have nothing to do with him, and grasped the idea that only his own things are what students care most about, so as to contact and understand the distribution through chorus. Even after this lesson, some students will still think that this lesson is the secret of learning strings. Teacher Zhang really said that learning just hides learning and really makes education interesting ~ (to be honest, I envy these students for taking such interesting and meaningful math classes ~)
? The fourth is the restoration of history and culture.
? In fact, mathematical culture is a hot topic recently. Teacher Zhang gave a simple example. In fact, the addition practice in grade one also implies a function. What is a function? To tell the truth, I really didn't know before listening to teacher Zhang's detailed introduction today. A function contains only one variable, called number for short. In ancient times, it contained a circular letter, so it was called a function. The concept of function was first put forward by Li in Qing Dynasty (1895)-any formula containing heaven is a function of heaven. The ancients were really powerful, and it is particularly important to cultivate the mathematical culture of contemporary primary school students, not only to learn knowledge, but also to understand where knowledge came from. In this area, the teacher also gave an example. Why are the length units of millimeters and centimeters expressed in millimeters and centimeters? Why can't millimeters be called centimeters, and centimeters can be called millimeters? These can be found in Xinhua dictionary and English-Chinese dictionary ~
? I hope the remaining six aspects can have a chance to make up for it. This seminar really gained a lot and opened a new door to mathematics education. It takes a while to digest. There is no end to learning. It turns out that I still have so many knowledge loopholes. Fortunately, it's not too late for me to realize this, so I must work hard! We must constantly absorb "nutrients" so as not to be eliminated by the times!
At this moment, I seem to have tasted a glass of wine, dizzy, hot, full of excitement and emotion ~
Dare to go out and discover the new continent!