For example, in the teaching of Translation and Rotation, the author first created a playground situation to bring students into different projects, so that students can look at pictures while doing actions. Imagine what people who play this project will do. Seeing the ferris wheel, merry-go-round, and other projects, the students couldn't help but start their hands. When they saw the spring bed, rocket launch and other projects, the students made exaggerated gestures of moving up and down. After all the projects are presented, the author will finalize these projects, let students face these projects, recall the gestures just now, and try to classify these projects according to the different movement patterns in different projects. Students naturally divide these movements into two types: rotation and movement. On the basis of this understanding, the author asks students to name these two different motion patterns themselves, and find out which motion forms of objects in life are consistent with these motion patterns, so that students can go deep into life and find many examples. In this case study, the author did not define what kind of movement is called translation and what kind of movement is called rotation, but gave students a familiar life situation, let them observe with their eyes, imitate with their gestures and think with their brains, let them abstract out two different ways of movement, and then let students enter a broader life world to enrich their existing knowledge, so that their understanding of these two forms of movement will be clear enough. Another teaching example is "angle understanding". Because the angles that students know in life are three-dimensional and diverse, and the angles in mathematical concepts are relatively standardized, the author tries to let students abstract "mathematical angles" themselves in teaching. In practical teaching, the author introduces this situation: the mouths of two hippos are wider than the others. Can you be a fair referee? In the situation, the author please demonstrate how the mouths of two hippos are open with two hands, and let the students find that judging the size of hippos' mouths depends on the degree of opening their hands. If we draw the hippopotamus's mouth open, we can only use two lines with one end connected. Of course, we can also make a "corner" with the activity stick in the school box. In this process, students' first understanding of the diagonal line is established, and they also perceive that the size of the judgment angle is the degree to which two straight lines open.
After that, the author guides students to observe the angle and know the names of each part of the angle, and the concept of "mathematical angle" in students' minds is initially established. Obviously, this angle is different from some angles in life, such as the angle of animals. When students reach a certain level of learning, the author will take this angle out for students to compare, and students will establish that the angle in life is an object, and the mathematical angle reflects the openness of both sides. In this kind of learning, students' understanding of diagonal has gone through three processes, from the appearance of hippopotamus's mouth opening to hand simulation and then to drawing the key factors that determine the degree of hippopotamus's mouth opening. After three processes, students' understanding has moved from life to mathematics, forming a clear understanding.
In both cases, the construction of mathematical concepts is divorced from life experience. The difference is that in the first case, learning is more about the mathematicization of life experience, while in the second case, life experience is "taking its essence and discarding its dross". In practical teaching, students should gradually mathematize their life experience according to their own understanding and establish rigorous and accurate mathematical concepts. This kind of study will benefit students a lot. A lot of mathematical knowledge is interrelated. In mathematics learning, we can't isolate knowledge, but put new problems in the environment that students are familiar with, mobilize students' existing knowledge and experience, and find a breakthrough to acquire new knowledge, so that students will get twice the result with half the effort and be more handy. At the same time, students can find the similarities and differences between old and new knowledge in the process of exploration and comparison, and distinguish them by grasping their essential characteristics, which plays a vital role in deepening students' understanding.
For example, in the teaching of "Percent Understanding", because students have come into contact with a large number of percentages in their lives and have encountered percentages in previous mathematics learning, the author directly asks students to tell the meaning of percentages they found in actual teaching. Several students came forward to introduce the percentage they found: the label of clothes says "cotton: 40%", and students can easily apply the meaning of score to explain that the percentage of cotton in clothes accounts for 40% of all 100 materials; "30% of the students in the class can swim", and the students quickly said, "Among the students in the class 100, 30 can swim". After they habitually applied the meaning of fraction to try to explain the meaning of percentage, the author put forward higher requirements: "Can we know at a glance what the percentage you bring means in another form?" After independent thinking and group communication, the students showed their own understanding: some used line charts to express simple percentages; It is suggested that a square of 100 can be used to represent the percentage. The author affirmed their practice and supplemented the method of expressing percentage by circle, which made students' perception of percentage rise from language level to intuitive image.
After that, the author asked the students to compare the connection and difference between percentage and score, and the students found various things. Some students said: the meaning of percentage and fraction is the same, which means that the unit "1" is divided into several parts on average. The difference is that the percentage stipulates that the score divided into the unit "1" can only be 100, but the ordinary score is not necessarily. Some students said that percentage is actually a special grade. Other students realized that the biggest difference between the two is that the score can not only represent the relationship between two quantities, but also represent a specific quantity, while the percentage can only represent the relationship between them, not a specific quantity. The author thinks that the reason why students have such a profound understanding is because the past mathematical experience can not be ignored. Based on the understanding of the meaning of fractions, students not only understand the meaning of percentages, but also fully realize their connections and differences, which lays a solid foundation for their profound understanding.