Is the pendulum spinning? -Reflections on Translation and Rotation Teaching
Basic information is the movement of the pendulum rotating? Several key words in translation and rotation teaching: pendulum, translation and rotation, circle. Abstract: Is the pendulum spinning? This problem has troubled many teachers and many students. This paper solves this abstract problem through careful teaching design. "Translation and Rotation" is the content of the second volume of mathematics in the third grade of primary school published by Jiangsu Education Publishing House. The content of this lesson is newly added to the textbook. It takes the common translation and rotation phenomena in students' daily life as the study and research object, and understands space and graphics from the perspective of movement change. Mathematically speaking, it is also a basic graphic transformation, which plays a great role in helping students to establish the concept of space and master the mathematical thinking method of transformation. When I got the new textbook to prepare lessons, I found a sentence on page 24 of the textbook: "The movement of the fan blade, propeller and pendulum is rotation." In my memory, the movement of the pendulum has nothing to do with rotation, but should be regarded as a swing. With this question, I asked many teachers and experts around me, and the people who were asked answered almost without thinking: "No, how can the movement of the pendulum be rotating?" It should belong to the swing. ""So, the swing of human arm should also be regarded as rotation? Physical education class should not say that his hands are swinging, but that his hands are rotating? "... but this experimental textbook concentrates the wisdom and experience of many course experts and special teachers! How could it be wrong? We must have been influenced by our previous life experience. Let's calm down and think about it! Yes, first, refresh the curriculum standard. The second section of Mathematics Curriculum Standard for Compulsory Education says: "Perceive translation, rotation and symmetry with examples. For example, the rotation of the steering wheel and faucet switch and the movement of the pendulum are all rotating phenomena of objects. " "Look up the dictionary how to explain the rotation? "Someone reminded me that I quickly checked the Modern Chinese Dictionary. The dictionary explains rotation as follows: "An object moves in a circle around a point or an axis, for example, the earth rotates around the earth's axis and also around the sun. "oh! It seems that the movement of the pendulum belongs to the local circular movement of the pendulum around a point and should also belong to the category of rotation. However, this concept is abstract and complicated for the third-grade students, among which the phenomenon of local rotation in rotation has not even turned the corner for our teachers, let alone students. How to turn abstract concepts into easy-to-understand life phenomena? What if the teacher didn't guide the students to understand what rotation is at first when teaching this course? What is translation? Ask the students to list the rotation and translation phenomena in their lives at once. It is easy for students to confuse rotation and phase shift. According to the traditional teaching mode, if the teacher tells the students these concepts in words, the students may master the corresponding exercises well, but they will not be applied in real life. We all know that mathematics comes from life. In fact, the phenomenon of translation and rotation is often seen in life, and every student has experienced it personally. I think the focus of the contradiction lies in the following issues: the movement mode of old-fashioned windows, the movement mode of opening and closing doors in classrooms, and the movement mode of pendulum, which is obviously rotation, but most students mistakenly think it is translation. Faced with this phenomenon, students will still be confused if they just blindly prompt, inform and repeatedly emphasize what kind of movement is rotation and what kind of movement is translation. So at the beginning of the class, I consciously guided the students to explore: "Is the pendulum moving in translation or rotation? "There is obvious controversy among the students. Faced with the students' confusion, the teacher did not answer, but took out a special teaching aid from his pocket: tied a white chalk head to one end of the rope, held the other end of the rope with one hand and shook it slowly and slightly. (refers to imitating the movement of a pendulum) Then, the shaking amplitude gradually increases, gradually forming a circular movement track on the blackboard (the teacher draws its movement track on the blackboard while shaking the chalk), and finally returns to the initial small-scale shaking. Ask the students to say, through the observation just now, do you think the pendulum is moving horizontally or rotating? Why? At this time, the students agreed that the pendulum should rotate, because it moves in a circle around a point, but it rotates a small part of it. Then, the teacher shows some pictures of the practice mode, so that students can judge whether it is translation or rotation. For example: the movement of old wooden windows, the movement of opening and closing doors in classrooms. Then, before class, I collected some life scenes around the students (amusement parks), such as tour buses, ferris wheels, windmills and so on. For students to judge, let students feel that mathematics is around us, and there is mathematics everywhere in life. Although translation and rotation can be seen everywhere in life, it is difficult for students to express their characteristics in language. So I use the accuracy of actions (gestures and physical demonstrations) to make up for the lack of language expression. When teaching translation and rotation, I ask students to show the movement mode of translation and rotation with gestures; When teaching objects to move vertically, I asked students to demonstrate the way the elevator moves up and down with their bodies. Let the students perceive the movement modes of translation and rotation in the demonstration of strokes. Finally, let the students list some phenomena of rotation and translation combined with their own lives. Because teachers make students observe with their eyes, operate with their hands and experience by themselves, and turn abstract concepts into phenomena that students can see and touch. So students can cite many facts about translation and rotation in life.