The first lesson I listened to was "The Circle of Motion" by Mr. Liu. He started by chatting with the students: classmates, did you miss me? At first, the students were reserved and didn't talk. Teacher Liu is not in a hurry. She keeps smiling and asking the same question. Did you miss me? The students began to respond, to be honest: I didn't expect it! Why? The student said: We don't know you! The teacher continued, but I miss you. You know what I'm thinking? I think how many people are there in our class? Do the students in our class like learning math? You know, you really didn't want to come to class on Saturday morning? The child began to say, think, think about what knowledge will be learned in this class, and so on.
Teacher Liu said that this idea is different from the original idea of "thinking about me". This is an imaginary idea. At the same time, write "imagination" on the blackboard. In this lesson, we learn to imagine. From a mathematical point of view, after this lesson, let's see who has a new understanding of imagination.
Firstly, the trajectory of the center of a circle moving along a straight line is studied. Children can answer that the trajectory is a straight line because the radius is the same, that is, the distance from the center of the circle to the straight line is the same.
The second problem is to study the trajectory of a small circle when it moves around a big circle. Children can also answer that the trajectory is a big circle according to the condition that the radius is constant.
The third problem is to study the trajectory of the center of a small circle when it moves around a square. Children, including me, according to past experience, the first reaction is a square. Teacher Liu neither denied nor affirmed, but asked the children to take out the homework paper prepared before and explore independently. Then show the students' works. The center of the circle is a square. Teacher Liu looked at the children and gently reminded: imagine in your mind and let the circle move. Imagine moving the circle. Under the guidance of Teacher Liu, the children began to imagine that some children had an epiphany. Teacher Liu continued to prompt: calm down and think about it. Any questions? What should we do?
Practice makes true knowledge, let's move! But when you move, move with thinking. At the same time, ppt presentation requirements: 1. See what to do? 2. Do it and draw the track. 3. Think about it, why is the trajectory like this?
Work in groups and study the trajectory with learning tools. The display trajectory is really not square. Teacher Liu throws a question: Why not a square? What knowledge did you use? Students answer that the radius of a circle is the same. Teacher Liu concluded: It seems that imagination also needs the support of knowledge.
Then observe and study this trajectory. What shape is this? Four rectangles and four right-angle sectors. Can you give this trajectory a name? A square without corners? Real name is rounded rectangle. Have you ever seen a rounded rectangle in your life? Corner of the table, etc. Jobs is a big fan of rounded rectangles! Rounded corners make people feel safe.
The fourth question is: show a picture directly (draw a circle around the triangle). Do you know what to do? Please tell us clearly when drawing: where did it start to become an arc? Let the children finish the research by themselves. When there are different answers, let the children state the reasons. This is really like what Wu Zhengxian's teacher said, "It's right to say what you said is wrong".
Fifth question: Now close your eyes and imagine the trajectory of the circle along the regular pentagon, regular hexagon and regular heptagon. What did you find? Students have been able to sum up that with the increase of the number of sides, the trajectory is more and more like a circle.
Finally, this interesting math class ends with Descartes' heart-shaped curve. This wonderful heart-shaped curve, perhaps like a seed, is planted in a child's heart and will take root and sprout one day.
In this class, Mr. Liu strengthened the understanding of the essential characteristics of the circle and developed the students' concept of space by observing, guessing and operating the trajectory of the center of the circle. In the process of thinking collision, cultivate students' experimental consciousness and problem-solving ability. From beginning to end, Mr. Liu did not deny the students' answers, but only guided the students to find the mistakes they had recognized before and correct them in the discussion and debate, so as to obtain correct cognition. Believe in children, give them enough time and space, and children will bloom differently!