First, the principle of creating problem situations.
The creation of mathematical problem situations must be scientific and moderate. Teachers must comprehensively consider students' physical and mental characteristics, knowledge level, teaching content and teaching objectives, compare available situations and choose situations with better educational functions.
1 the principle of pertinence should put an end to the situation design that emphasizes form over substance. The purpose of situation design is to make students better master the mathematical knowledge they have learned, so the situation should reflect the essence of mathematics, which is intended to arouse students' thinking, rather than creating a situation that is divorced from students' reality or mathematical essence.
The principle of reality, the problem comes from life, production practice and students' existing mathematical experience as far as possible, which makes students feel approachable and attractive.
3 the principle of openness, the problem has a certain openness, there are many different results, or there are many possible solutions, which is very beneficial to the development of students' thinking and creativity.
According to the developmental principle, when a satisfactory answer is found, the question is not over, and the found answer may imply that all parts of the original question can be changed. And lead the answer to the question to the general, so as to get more things, which also indicates that some new rhyming questions can be brought out.
5 The generative principle, the teacher creates a problem situation, in which the implicit mathematical problems are best put forward by the students themselves, and at least some students can put forward them in the situation created by the teacher.
The principle of simplicity, the expression of questions should be concise and not vague, so as not to let students blindly cope and confuse their thinking. If a situation design is far-fetched or even cumbersome, it will not only fail to achieve the teaching purpose, but will give students more pressure.
Second, the method of creating problem situations
There are many ways to create problem situations. According to my own teaching practice, the author summarizes the following three methods.
1 Create problem situations by using practical problems that students are familiar with in their lives.
For example, when merging similar items in teaching, I designed the following two questions.
Question 1 Can two quantities in each of the following formulas be combined? If they can be combined, find out the result; Can't merge, explain the reasons, and say what conclusions can be drawn from it.
①3 pencils +2 pencils;
② 3kg apple +2kg apple;
③3 pencils +2kg apples.
Students complete the above questions independently and communicate the results with their peers. Finally, the teachers and students concluded:
(1) can be combined, and the result is 5 pencils;
② It can be merged, and the result is 5 kilograms of apples;
(3) can't be combined, because they are not the same kind.
This makes students understand that similar quantities can be combined. If the quantities are different, they cannot be merged.
Question 2: each exercise book is x yuan. Xiao Qiang bought five books and Xiaohua bought two. Represented by algebra: two people spent _ _ _ _ _ yuan.
Answer: 5x+2x.
Then ask: Are 5x and 2x the same quantity here? Can we merge? What is the result of the merger? By analyzing problems, students can deepen their understanding of the same quantity and the combination of the same quantity. Then, you can guide students to compare and transfer their perceptual knowledge, and ask further questions: Which of the following monomials do you think are the same?
5a2b，4xy2，-2ab2，2ba2，-6x2y，3，-3xy2，-8 .
Students discuss in groups, send representatives to write the results on the blackboard, and the teacher and students revise them together. After induction, the teacher asked further questions: On what basis do students classify them? Is 5a2b the same as 2ba2, 4xy2 and -6x2y? Why?
Students' thinking is active at this time. Interested in exploring new knowledge, on this basis. Then the teacher takes the opportunity to guide students to explore the concept of similar items and the rules of merging similar items. In the whole process, students have experienced a process from concrete things they are familiar with to abstract things, and their interest and enthusiasm in learning have been stimulated. Students think seriously, discuss actively and speak enthusiastically. The classroom atmosphere is very active, and they have a deep understanding of the concept of similar items and the rules for merging similar items.
2 Design a math experiment for students to do and create a problem situation.
For example, in the teaching that the sum of any two sides of a triangle is greater than the third side, I designed the following problem situations.
Before class, each student prepares four sticks with different lengths to meet the following requirements:
(1) the sum of the two shorter lengths is less than the length of the third;
⑦ The sum of the two shorter lengths is equal to the length of the third;
③ The sum of the lengths of the shorter two articles is greater than the length of the third article.
Practice in groups: According to the above conditions, try to spell a triangle with four sticks prepared before class. What will happen?
It is easy for students to draw the following conclusions: ①, ② Neither situation can be spelled into a triangle, and only the third situation can be spelled into a triangle.
Through practice. Students have a perceptual knowledge that when the sum of the lengths of two shorter sticks is less than or equal to the length of the third stick, a triangle cannot be formed. Only when the sum of the lengths of two shorter sticks is greater than the length of the third stick can a triangle be formed. Then, the teacher continued to ask: Is the sum of the lengths of any two sides in the triangle formed greater than the length of the third side? Ask the students to continue to practice in groups and discuss the results. It is not difficult for students to get the perceptual knowledge that the sum of any two sides of a triangle is greater than the third side. The whole teaching process follows the cognitive law from special to general, and students operate by themselves. Greatly improved the interest in learning and awareness of participation, improved the practical ability and innovation ability, and had a clear understanding of the trilateral relationship of the triangle.
3. Use the conflict between old and new knowledge to create problem situations.
For example, in the teaching of trigonometric functions. I designed the following two questions:
① In the right-angled triangle ABC, the hypotenuse AB and the right-angled side AC are known. How to find the other right-angled side BC?
② In the right triangle ABC, given the angle A and the hypotenuse AB, how to find the opposite side BC of the angle A?
Question 1: Students naturally think of using Pythagorean Theorem, but question 2: It can't be solved by Pythagorean Theorem, resulting in the conflict between old and new knowledge-how to solve such problems? Students' desire to explore new knowledge will spontaneously arise. Under the correct guidance of teachers, the teaching task of this course is not difficult to complete.
In a word, creating problem situations is an important part of a class. Teachers should exert their subjective initiative in teaching, carefully and skillfully create various rhyming problem situations, stimulate students' interest in learning, arouse students' exploration and thinking, and cultivate students into useful materials with rich knowledge, flexible thinking and innovative spirit.
(Editor Zhao)