1. Based on students' knowledge. According to the theory of educational psychology, whether students can obtain new information has a great relationship with the existing knowledge and experience in the cognitive structure. Mathematical knowledge is systematic and logical, and most new knowledge is based on previous knowledge. Therefore, fully understanding students' original knowledge base is an important condition for teachers to create effective problem situations in teaching, mobilize students' active and lasting learning enthusiasm, help students realize knowledge transfer, and finally obtain good learning results. Whenever students come into contact with new knowledge in the process of learning, the existing knowledge, experience and thinking methods are not used for a while, and there is a psychological state of being eager to explore the crux of the problem and unable to start. For example, when learning fractional subtraction with different denominators, first review the rule of fractional subtraction with the same denominator-numerator subtraction, and then let students try out 1 \ 3- 1 \ 4. Students can't calculate the subtraction of different denominator scores according to the existing calculation experience, so they create a problem situation, which makes students hit a wall and leads to intense students.
2. According to the psychological characteristics of students. The results of psychological research show that children like to study in relaxed and happy situations, and the better their emotional state, the better their learning effect. Students' psychological factors directly affect the improvement of learning effect. If teachers don't understand students' psychological characteristics and create problem situations according to these characteristics, they can't make students enter the psychological state of high emotions, and they can't stimulate students' interest in learning and improve teaching effect. Because mathematics teaching is not only a process of imparting knowledge, but also a process of psychological activities of teachers and students; It is not only a process of students' cognition, but also a process of emotional communication between teachers and students, temper of will and formation of personality psychology.
3. According to the age characteristics of students. The content and form of problem situations should change according to the different age stages of students. For junior children, colors, sounds and animations are very attractive. Teachers can use stories, games, simulated performances and intuitive demonstrations to create vivid and interesting problem situations. For senior students, we should focus on creating a situation of students' autonomous learning and cooperative communication, attract students with the charm of mathematics itself, and try our best to make them feel satisfied because of their inner successful experience, thus becoming the driving force for the next step of learning.
In an open math class in the sixth grade, a teacher gave a topic "the circumference of a circle". With the bright pictures and sweet music of multimedia courseware, the teaching teacher created such a situation for the students: Students, have you heard the story of "the race between the tortoise and the hare"? The animal kingdom will hold another tortoise and rabbit race, but this time they run around a round pond. The teacher is telling a story endlessly, but some students are muttering, "It's the animal kingdom again ..." "We have heard this story dozens of times and treat us as children." After a class, the students are sleepy, and their participation is not high. The effect can be imagined. This makes people wonder: Isn't a child the most willing to find his fantasy in fairy tales? Teachers create vivid and interesting fairy tale situations for students. Why can't they move students' hearts and arouse their interest? In fact, students complain that "teachers treat us as children" tells a truth-primary school students at different stages and different psychological stages have different interests in the situation. Junior students are particularly interested in beautiful and vivid fairy tales, lively and interesting games and intuitive simulation performances, and are keen to play their roles. This is in line with the naive and imaginative nature and psychological state of children in this period. Middle and senior students are more willing to accept the situation of independent cooperation and communication. For those animations that are too "fancy", I feel very "naive". Therefore, for middle and advanced students, teachers should try their best to attract students with the charm of mathematics itself, make them feel interesting and challenging, stimulate their curiosity and competitiveness, and let them have the enthusiasm for further study.
After class, we all reflect that primary school students really need lively and interesting situations because of their cognitive and psychological age. But "lively and interesting" is not the standard of effective situation. The key is whether these situations can effectively promote students' "happy and effective" learning. In the process of establishing the concept of circle circumference, multimedia courseware can also be independent. We might as well design this way: show the real circle and circle it with a red ribbon, so that the red "circumferential boundary" can be separated from the background to help students perceive it successfully for the first time and form a bright appearance. Then let the students have a look and touch to deepen their understanding. Later, the red ribbon can be pulled down from the circumference, so that students can intuitively understand that a circle is a line segment after being straightened, and can find its length and infiltrate the idea of turning it into a straight line. When discussing the relationship between circumference and diameter, we can use the straightened red ribbon to measure the diameter, which proves that the circumference is indeed more than three times the diameter.
The above points show that only by designing problem situations according to students' basic knowledge, psychological characteristics and age characteristics can students understand mathematics knowledge, and such situations are effective problem situations.
Second, the characteristics of effective problem situations
1. Fun. With a strong interest in learning, students will naturally have a sense of participation, and they will be able to smoothly enter the state of autonomous learning and active exploration. Therefore, the problem situations created by teachers should be interesting, which will help to stimulate students' enthusiasm for exploring problems and urge students to devote themselves to learning activities. For example, when teaching "circumference", the multimedia courseware can be displayed at the beginning: a little monkey rides a car with rectangular, square, triangular, oval and round wheels on the road one after another, and only a car with round wheels can run smoothly. Along the way, the little monkey jumped up and down funny, and the students were full of interest. With the question "why should the wheel be designed as a circle", they are eager to learn new knowledge. Then in the process of establishing the concept of circumference, it is completely independent of multimedia courseware. We might as well design this way: show the real circle and circle it with a red ribbon, so that the red "circumferential boundary" can be separated from the background to help students perceive it successfully for the first time and form a bright appearance. Then let the students have a look and touch to deepen their understanding. Later, the red ribbon can be pulled down from the circumference, so that students can intuitively understand that a circle is a line segment after being straightened, and can find its length and infiltrate the idea of turning it into a straight line. When discussing the relationship between circumference and diameter, we can use the straightened red ribbon to measure the diameter, which proves that the circumference is indeed more than three times the diameter.
2. enlightening. Doubt in learning is the performance of active learning. The purpose of creating inspiring question situations is to promote the transfer of students' mathematical thoughts and thinking. For example, before teaching the concept of volume, you can tell students the story of "crow drinking water" and guide students to think: crow couldn't drink water originally, so why did it drink water later? What is the relationship between the stones put in and the rising water level? What does this phenomenon mean? Through experiment, observation and discussion, let students understand and firmly grasp the concept of volume. In teaching, it is the "golden key" for students to break through difficulties by creating problem situations from the connection point between old and new knowledge and the law of knowledge itself.
Step 3 think. The core of creating problem situations is to activate students' thinking and guide students' creative thinking, which requires teachers to design problems with thinking. For example, when teaching "area unit", after students know the unit of "square centimeter", they can use the square of "1 square centimeter" to measure the size of math textbook surface, classroom desktop and blackboard surface. Students will find that the measurement standard is too small, the measurement times are too many, the measurement results are inaccurate, and so on, resulting in the contradiction between old and new knowledge, and then use the existing knowledge and experience to explore and "create" a new area unit "square decimeter". I believe that with the increase of the measured object area, students will "derive" a "square meter" in their minds. The creation of this effective problem situation has changed the traditional "spoon-feeding" teaching method, guided students to think actively and explore boldly, and enabled students to understand the truth, master the methods and comprehend the thoughts in the process of active learning.
4. challenging. Pupils are not only interested in "fun", but also interested in "useful" and "challenging" mathematics. Therefore, we should also attach importance to students' mathematical thinking in creating situations, give students the opportunity to experience "doing mathematics" as much as possible, and let them express themselves and develop themselves in open and exploratory questions, so as to feel that mathematics learning is a very important activity and initially form "I can and should learn mathematical thinking". For example, in the second-grade mathematics Division with Remainder, teachers can use multimedia to show the situation map: 45 numbered colored balls are arranged in the order of red, yellow and blue.
Teacher: Students, there are many colorful balls on the screen, and each ball has a number. The teacher doesn't look at the screen, just tell me the number of the ball, and I can tell its color right away. Do you believe it? Who will test the teacher? (Students ask questions and the teacher answers)
Teacher: Why can the teacher guess the color of the colored ball quickly? Want to know the mystery here? You must have such skills after learning today's knowledge. Introducing the situational question of guessing the color of colored balls in the new class can stimulate students' curiosity and thirst for knowledge, skillfully take care of the teaching content of this class, and be relaxed and natural, and go straight to the point. The problems left by the situation can make students actively explore knowledge and seek mysteries.
5. Reality. The problem situations created in mathematics teaching should conform to students' real life, and introduce "life around us" into the classroom, and then introduce "mathematics knowledge" into "life around us". Its purpose is to make students realize the connection between mathematics and real life, let students unconsciously understand the true meaning of mathematics, learn to observe and analyze the real society with mathematical thinking mode, and solve problems in life, so as to realize the value and strength of mathematics.