Although some students can answer the algorithm of surface area when asking questions, it is actually a kind of rote learning. In fact, the graphic relationship involved in body knowledge is very abstract. Therefore, quite a few students often make mistakes when learning the knowledge of "circle", so it is naturally difficult to learn and master the surface area of "cylinder". That's because their cognitive level can't produce a firm perception of the quantitative relationship simply by means of the image relationship they see, and can't form the corresponding geometric intuition.
Learning does not mean understanding, and understanding does not mean understanding. Educator Whitehead said that the core problem of education is to make knowledge "live". How to help students, make knowledge full of vitality and realize effective construction?
Ma Yun said that knowledge can be taught and wisdom depends on enlightenment. Piaget, a cognitive scientist, pointed out that wisdom starts automatically. Children's cognitive law is "from intuitive action thinking to concrete image thinking, and finally to abstract logical thinking". It can be said that hands-on operation is the basis and starting point for children to understand objective things.
To this end, the homework of "making pillars" was arranged last night: measure the length and width with a rectangular piece of paper and record it. Then use this rectangular piece of paper to make a complete cylinder (including sides and two bottoms). The manufacturing process can be expressed in words or language by drawing or taking photos. In the manufacturing process, the area of materials used (that is, the surface area of cylinder) and the area of scraps can be calculated and expressed.
The original intention of homework design is to hope that children can construct the mathematical model of lateral area and surface area, develop the concept of space and form the ability of geometric intuition in the process of "doing mathematics".
If students want to make a cylinder, they need to find a rectangular piece of paper and measure its length and width. Then consider the composition and relationship of the cylinder: three faces, one side face and two bottom faces. The length of the rectangle after the side is unfolded is equal to the perimeter of the bottom circle. According to this quantitative relationship, it is necessary to determine the circumference of the bottom of the cylinder according to the length of the large rectangular paper, and then calculate the diameter and radius of the bottom circle in turn according to the circumference of the bottom circle.
Next, you need to operate according to the results of mathematical thinking. First, draw the edge of the cylinder on a big rectangular piece of paper, that is, a rectangle. When measuring, one side of this rectangle should be equal to the perimeter of the bottom, and the other side is the height. Then, according to the calculated base diameter length, two squares with side length equal to the diameter are drawn side by side on the remaining figures, and then two circles with the same radius as calculated are drawn in the squares.
Finally, cut two circles and rectangles (the sides of the cylinder) and splice them, and it is finished.
After the cylinder is completed, the surface area, that is, the material area, is calculated according to the recorded data, and the remaining area can be easily calculated.
The process of making a cylinder is to internalize and absorb knowledge in silence, and enrich students' cognition and experience in mathematical activities with the help of action thinking, image thinking and logical thinking, while the new mathematics curriculum is to accumulate experience in mathematical activities dominated by operation and practical activities.
Judging from the homework submitted by students, some children's homework is remarkable, gratifying and perfect.
Originally, I wanted to show a video of the production process of children taking selfies, but without this function, I could only send a few pictures. )
Laozi once said that the world is difficult and easy, and the world affairs are detailed. I hope to teach more effectively from every detail, make students learn more interesting, better guide children to construct knowledge and make learning really happen.
I hope every child can take every homework seriously and add luster to his growth!
Off-topic: I began to study how people learn these days. This is a study science monograph that integrates brain science, cognitive psychology, pedagogy and developmental psychology. I hope it can inspire and better help children to progress and grow!