1. It is a bilateral process between teachers and students to create problem situations and stimulate teaching interest in mathematics experiments, and mathematics teaching activities are no exception. Without the participation of students, the whole process will be difficult to flow smoothly. Some mathematical concepts can guide students to understand the formation of mathematical concepts from their own experiments, so that students can master mathematical concepts through hands-on operation, observation and discovery, exploration and reflection.
Case 1: the concept of ellipse
(1) Students do experiments to gain perceptual knowledge. Students are required to prepare a shoe box shell, two small thumbtacks and a thin thread one week before the lecture. ) Fix both ends of the thin line with thumbtacks first, then tie the thin line tightly with a pencil, so that the pen tip moves slowly on the paper, and the figure is drawn into an ellipse.
(2) Ask questions, think and discuss. Is it possible to draw an ellipse by fixing the thumbtack first and then tying the thin line? Just try it. What are the characteristics of the points on the ellipse? When the thin line is longer than the thumbtack, what is its trajectory? When the length of a thin line is equal to the thumbtack distance, what is its trajectory? When the length of a thin line is less than the thumbtack distance, what is its trajectory? Can you give the definition of ellipse? The atmosphere in the whole classroom was high, and students answered one after another.
(3) Reveal the essence and give the definition. After experiments and discussions, students can easily grasp the essence of the definition of ellipse, and it is not easy to make the mistake of ignoring that the fixed length in the definition of ellipse should be greater than the focal length.
Second, create situations and stimulate interest through interesting questions. Teachers should be good at using some interesting questions to create a harmonious and happy teaching atmosphere, which is another important link to guide students to learn new knowledge. If used well, it can greatly stimulate students' interest in learning and make them deeply understand the true meaning of learning new knowledge.
Case 2. Sum of the first n terms in geometric series
Teacher: Students, I am willing to give you 1 0,000 yuan every day for one month (calculated as 30 days), but within this month, you must give me a rebate, with 1 cent on the first day, 2 cents on the second day and 4 cents on the third day ... that is, the amount of rebate on the second day is twice that of the previous day. Do you want it? As soon as the question came out, it immediately aroused the students' great interest. Everyone talked about it, and some blindly answered "Yes!" Some students are silent because of the trap of "conditions", and some students are "accounting" and "income and expenditure". After a minute or two, a classmate suddenly raised his hand and answered: You have to work out the sum of 1+2+4+…+229, and then compare it with 1000×30× 100, and I can't work out 1+2+…+229. (Students burst into laughter) Teacher: This classmate is very clever! This is exactly the problem we have to solve in this course, that is, "the first N sums of geometric series" ... Through such an interesting problem situation, students not only have a strong interest, but also stimulate their desire to explore new knowledge, so that students have the internal motivation to "want me to learn" into "I want to learn". In fact, the students in this class showed high emotions and full mental state from beginning to end, and finally achieved the teaching goal well. I have to say that interest is the best teacher and the driving force for learning.
Third, the problems that should be paid attention to in creating the problem situation of mathematics concept teaching
1. Pay attention to the presentation of the problem situation. With a suitable problem situation, we should also pay attention to the presentation of the problem situation. The presentation of problem situations should be based on giving full play to students' subjectivity, attaching importance to the process of knowledge discovery and exploration, and attaching importance to students' emotional experience. Through the presentation of questions, students can fully explore their own thinking activities. Teachers should give students some time and space to think, don't tell students the answers in a hurry, give students the opportunity to find problems, and let students' thinking be fully exposed.
2. Pay attention to the principle of creating problem situations. Because mathematical concepts and laws are abstract, there are many ways to create situations, but they must be scientific and moderate. Specifically, there are the following principles:
(1) It must be difficult, but it must be in the "recent discovery area" of students, so that students can "jump and reach";
(2) Considering the cognitive level of most students, it should be designed for all students and not for a few people;
(3) Be concise, targeted, purposeful, concise and clear, and don't be vague, so that students can cope blindly and have confused thinking;
(4) Less but better, so that teachers ask less but better, and students ask deeper and deeper.