First, to create mathematical problem situations, teachers should pay attention to students' real life, grasp the interests of most students, set clever questions and ignite passion.
Students' lives are rich and colorful. In order to attract students, we must dig out mathematical factors from things they are interested in, arouse students' suspense, arouse students' thinking, and make them enter new knowledge learning conveniently.
When I was teaching the seventh grade mathematics (Beijing Normal University Edition) "Understanding Triangle", I caught the idolization of middle school students and designed a problem situation in view of the fact that most middle school students like basketball star Yao Ming very much. I gave a photo of Yao Ming by multimedia projection and a small file of Yao Ming by words: height 226cm, weight 125kg, arm span 22 1cm, leg length 14 1cm. Ask a question: Some people say that Yao Ming has a big step, and he can walk more than 3 meters in one step. Can you believe it? Tell me your reasons.
As soon as the question was raised, it immediately attracted students. At this point, the teacher guides the students to say that after knowing the triangle, you can definitely use the relevant knowledge of the triangle to explain the reason. With an impulse, students can't wait to learn to understand triangles, which not only solves the problem about Yao Ming, but more importantly, the knowledge difficulty that three lines meet certain conditions to form triangles is broken through by students in excitement.
Second, to create mathematical problem situations, teachers should grasp students' existing mathematical knowledge or experience, sum up the essence and bring forth the new.
The purpose of creating mathematical problem situations is to let students actively construct knowledge and learn new knowledge. Therefore, the problem situations created by teachers must conform to students' cognitive level and knowledge experience, and aim at students' recent development fields. Because the problem situation is only the opening "prelude" of this class, it is not the theme and climax of this class, so it can't be complicated. To cut to the chase, pave the way and lead to the theme.
Case teaching seventh grade mathematics (Beijing Normal University Edition) "Multiplication with the same base", I designed such a problem situation:
Calculation: (1)102×102 (2)102×103.
After the students worked out the results, the teacher wondered: How many times can you guess about102×102 =104? Which form is the correct result of the two questions? Through thinking, discussion and communication, students have two conjectures:102×102 =102+2; 102× 102= 102×2。 But students denied the latter by observing102×103 =105. This design is based on students' mastery of power and familiarity with multiplication knowledge. Through clever doubts and reasonable guidance, students have cognitive conflicts in normal thinking, form a preliminary perceptual knowledge of power multiplication with the same base, and enter the recent development zone, paving the way for students to learn the following questions in textbooks independently:
Calculation: (1)105×108; (2) 10m× 10n； (3)2m×2n； (4) () m× () n (both m and n are positive integers), and summarize the law of power with the same base.
Third, to create a mathematical problem situation, teachers should understand students' existing life experience and cognitive level, grasp the connection between old and new knowledge, and expand the new with the old.
Cognitive theory tells us that students' perceptual knowledge of things in life is the basis for their understanding of things to rise to rational knowledge. In order for students to learn and construct knowledge effectively, it is necessary to know the students' preparation. When creating problem situations, math teachers must make clear the starting point of new knowledge that students want to learn in this class, prepare for students' learning, and start with the relevant practical experience and experience in students' life.
Case When teaching seventh grade mathematics (Beijing Normal University Edition) "How Numbers Are Not Enough", the textbook leads to negative numbers from the question of knowledge contest score. Considering the reality of rural seventh-grade students, I designed such a problem situation:
Question 1: Xiaodong bought a notebook with 4 yuan money. If each notebook is 1 yuan, how much money does he have left when he buys three, four or five notebooks? Express it with an expression.
Question 2: The Meteorological Observatory predicts that the temperature will drop by 4-6℃ tomorrow. If the temperature is 5℃ at some time tomorrow, what will be the temperature at some time when the temperature drops by 4℃, 5℃ and 6℃ respectively? Express it with an expression.
For the above two problems, students have life experience and understanding, and negative numbers can be used to represent the operation results that are not reduced enough, that is, formulas 4-5=- 1 and 5-6=- 1, that is, the temperature is 1 yuan, and the temperature is reduced to-1℃. The teacher told the students that in China, Through these two problems, which are closely related to students' life experiences and experiences, the difficulty of introducing negative numbers has been successfully solved, and the foundation has been laid for students to further study negative numbers in textbooks.
In mathematics classroom teaching, in order to create a good teaching situation, mathematics teachers should not only grasp the above three aspects, but also make good use of the situation provided by textbooks, at the same time, they should catch students' new ideas and discoveries in time, make full use of network resources, communicate with people frequently and learn with an open mind. Mathematical problem situation is the beginning of a math class, and everything is difficult at the beginning, but the creation of every good problem situation is the best reward for the difficulty. It is necessary to advance despite difficulties, so that students can learn mathematics with great interest, enjoy happiness and be full of endless fun.