The new curriculum standards are quite different from the traditional teaching requirements. Therefore, in teaching, teachers should beware of four disadvantages when setting questions: First, asking too many questions such as "yes", "right" and "do you understand", which seems to be a bilateral activity, but in fact there are not many effective participants, which is a formalistic interactive teaching. In the long run, students will form a bad habit of answering without thinking. Second, questions are inscrutable, divorced from students' life experience and cognitive rules, and students are confused about teachers' questions, which dampens students' enthusiasm and is not conducive to the cultivation of students' self-confidence. Third, when setting questions, students are not given proper time to think and discuss, and they are worried that they will not be able to answer, which is not conducive to the cultivation of students' thinking ability and innovation ability. Fourth, it is not conducive to the solution of problems and the cultivation of students' problem consciousness to only care about their own questions and not give students the right to ask questions. So, how to set questions in teaching? I think the following principles must be followed.
First, ask questions in the situation.
Mr. Cui Qi, winner of the Chinese Nobel Prize in Physics, said: "Like and curiosity are more important than anything else." The most important thing to ask questions is to stimulate students' interest and curiosity. Interest is the best teacher, and curiosity is an important source to induce students' strong thirst for knowledge. Putting forward novel and attractive questions to students can often stimulate students' sense of competition and interest in learning and arouse their enthusiasm for learning. Example (1) For example, when teaching "Judgment Theorem 2 of Triangle Congruence", I set a question at the beginning: Yesterday, I accidentally broke a triangular decorative glass into two pieces (as shown in the figure), and I wanted to go to the glass shop and cut another piece of glass with the same size. Can you do that? Take one, will you? If possible, which one do you think you should choose? Why? Students are very interested. Through spelling, drawing, cutting and other experiments, it is found that it is ok to take a second piece of paper. Then the teacher guides the students to observe what the cut triangle has in common with the second piece, so that the problem can be solved through the teacher's questions, students' experiments, guesses and verifications, and students can also experience the process of knowledge generation and explore ways to solve the problem.
Second, pay attention to students' personal knowledge and existing life experience when asking questions.
"New Curriculum Standard" points out that mathematics curriculum "should not only consider the characteristics of mathematics itself, but also follow students' psychological laws of learning mathematics, emphasizing that starting from students' cognitive development level and existing life experience ... mathematics teaching activities must be based on students' cognitive level and existing knowledge and experience". In other words, when setting questions, teachers should take students' personal knowledge, direct experience and the real world as the basis for setting questions. "Xue Ji" also has "a good questioner, such as tackling a problem, making it easy first, then saving it." In other words, the problem setting should follow the students' cognitive rules, from intuitive representation to concrete image, from image memory to abstract memory, from mechanical memory to understanding memory. If students are divorced from the actual problems above or below their cognitive level, it will either bring a heavy burden to students and dampen their enthusiasm, or make them feel tired of learning. Only by designing order questions scientifically can students achieve the purpose of asking questions and explore the ocean of knowledge.
For the difficulties in teaching, teachers should try their best to establish "steps" to help students "climb up the steps" and help students overcome their learning difficulties. Example (2) In the teaching of "polygon interior angle sum", the following series of questions can be designed to make ideological and methodological preparations for the proof of the theorem:
(1) We have learned the theorem of interior angles of triangles. What is the sum of the angles in a triangle?
② What is the sum of the inner angles of a rectangle? Guess what the sum of the internal angles of a quadrilateral is? Can you prove it with what you have learned?
After the tangent length theorem in case (3) is finished, you can set such a question: Xiaoming's pot cover is broken. In order to match a pot cover, it is necessary to measure the diameter of the pot. However, the only one of Xiao Ming is 500px long, which is not long at all. What should I do? Xiao Ming thought about it and took the following measures: first, put the pot flat on the wall, the edge of the pot just leans against two walls, measure the length of the horse with a ruler against the wall (as shown in the figure), and find out the diameter of the pot. Would you please explain why he did this? This kind of questioning embodies the idea that mathematics comes from life and serves life, and that everyone is learning valuable mathematics, which is useful and not difficult to learn, thus helping students build their self-confidence.
Third, ask questions to make mathematical thinking methods stand out in the process of solving problems.
This is an important measure to guide learning methods and develop and improve students' ability in classroom teaching. Generally speaking, combined with the function of each teaching link and the specific teaching content, questions are asked about mathematical thinking methods, the characteristics of subject structure, the process of knowledge understanding and the general methods of learning mathematics. Example (4) To sum up the lesson of "Sum of Interior Angles of Polygons", you can ask questions like this:
① What mathematical ideas and methods are used in the process of theorem proving? ("analogy" and "transformation")
② What are the characteristics of this mathematical thinking method? ("Turning the Unknown into the Known")
③ What is the guiding role of mastering this method in solving mathematical problems?
What inspiration did you get from solving this problem?
Through these problems, students have mastered not only knowledge, but also scientific methods to acquire knowledge, enhanced their ability to analyze and solve problems, further improved their skill structure and improved their learning ability.
Fourth, setting questions should be conducive to guiding students to actively participate in the exploration of mathematical problems.
"New Curriculum Standard" points out that "effective mathematics learning activities can't just rely on imitation and memory, and hands-on practice, independent exploration and cooperation are the main ways for students to learn mathematics". Therefore, the problem setting in teaching should be conducive to guiding students to actively participate in the exploration of mathematical problems, constructing mathematical knowledge, mastering mathematical methods and forming mathematical thoughts, so as to cultivate students' innovative spirit and practical ability and enhance their self-confidence and willpower to overcome difficulties. Example (5) When talking about "triangle drawing", the teacher can set a question like this: An engineer must draw a picture before building a building. So how are the drawings drawn? Today, let's start with the simplest, and learn how to draw a triangle (give the drawn triangle to the students). Then, we need to know a few effective information before we can draw a triangle that coincides with what has been handed down from generation to generation (guess). Please try to draw on paper (do it yourself and explore). In the process of exploration, students will find that there are many painting methods, and at the same time, they will experience the fun of exploring different solutions from local angles and different angles (such as corners).
Fifth, set appropriate divergent questions to cultivate students' divergent thinking and innovative ability.
Guildford once used "divergent treatment" as an index to measure creativity. Innovation requires divergence and fluency of thinking, breaking the mindset and thinking from multiple angles. Professor ╳ also pointed out: "The creativity of any scientist can be estimated by the following formula: creativity = knowledge. From this, we can see the importance of cultivating students' divergent thinking ability. In order to cultivate students' divergent thinking ability and seek the opposite sex, for the same problem, teachers can use the increase and change of conditions and the extension of conclusions and the exchange of conditions and conclusions to design multiple solutions to one question and get many new questions, thus broadening students' horizons and improving students' thinking ability, exploration ability and innovation ability. Example (6) When proving the theorem in the teaching of "the sum of internal angles of polygons", the following questions can be set for students to think about:
1. In the book, a quadrilateral is divided into two triangles to prove it. Can it be divided into three triangles and four triangles and proved?
2. Just now, we proved that the sum of the internal angles of the quadrilateral is 360 degrees by division and transformation. What is the sum of the internal angles of a Pentagon? What is the sum of the inner angles of n sides? Say what you think about solving the problem.
A small change in this topic can turn into many different topics. In this way, students' thinking is led to the broad world. Students are innovative, quick and excellent in solving problems, which cultivates the breadth and depth of students' thinking. Of course, these solutions and changes may be the results of previous studies, but we believe that this should also be regarded as an innovation for beginners.
Sixth, create problem situations and cultivate students' problem consciousness.
Einstein said, "It is often more important to ask a question than to solve it". In teaching, students should be encouraged to dare to question, be good at asking questions and dare to challenge authority. Innovation often begins with problems, and only by asking valuable questions can further innovation be possible. For example, Einstein asked questions and answered them from the contradiction between Newtonian mechanics and Maxwell's electromagnetic theory, which led to the birth of special relativity. Our students are often good at learning and imitating, but not good at asking questions. In our teaching, students are often taught how to answer questions, and a class often ends with students having no questions. Students are rarely taught how to ask questions, how to find and ask valuable questions. Therefore, our students are often superstitious about books, authority, insensitivity to problems, and lack scientific skepticism and spirit.
Practice has proved that if you don't ask questions, you won't be good at thinking, you won't critically observe the world, and you won't have creative behavior. Therefore, in mathematics teaching, in order to develop students' personality and cultivate their innovative ability, we must pay attention to guiding students to find and ask questions, allowing students to make mistakes and correct them within a certain range. Teachers should learn to correctly analyze and treat students' "tales of mystery and abnormal behaviors" to support their innovative behaviors. So I often ask students in class: "Who can find the problem?" "Who can put forward different opinions" can stimulate students' interest, cultivate students' problem consciousness and make students realize the importance of problem consciousness.
At the same time, to create a good "questioning" atmosphere, teachers should encourage students to make bold guesses, make bold doubts and ask their own questions. Every activity allows them to find their own way, show themselves, appreciate themselves, and make them complacent in the process of self-innovation. Even if they make mistakes, they should be allowed to complete the whole process, affirm their motivation and purpose of innovation, and then give appropriate evaluation to the questions raised by students. Example (7) After-class tutoring, there is a question: There is a river by the roadside, and there is a TV tower AB on the other side, with a height of 30m. Only protractor and tape measure are used as measuring tools. Can you find the distance between the TV tower and the road? The teacher drew a good picture on the blackboard and got the answer through guiding analysis. But as soon as the teacher's voice fell, suddenly a student shouted, "Don't ask for it!" " "This is from the mouth of naughty and active students. Experienced teachers will not use the tone of blame to discipline, but take each student's ideas seriously with sincere heart, analyze and guide them, and kindly say, "How do you ask? "Please say it!" Encouraging students to express their opinions eliminates students' fear of being criticized, and they can freely explain that they can use a tape measure. One can take one end at the roadside and the other end, swim across the river and climb to the top of the tower. People standing on the roadside move their positions, straighten the tape measure, and use a protractor to measure that the angle formed by the tape measure and the roadside is a right angle, so that the distance can be obtained. After listening to the students' answers, I said, "It's very kind of you to have this idea. This is also a way, but will it be difficult to actually try?" Is the measurement result the same as our calculation result? "Such a sentence not only warms students' hearts, satisfies their psychology, but also regulates the classroom atmosphere. Finally, the teacher pointed out that the method of field measurement is hard and inaccurate, and using textbook knowledge can solve problems conveniently and accurately. Field measurement begins with direct thinking, and the way for teachers to analyze and solve problems is "reverse thinking". From direct thinking to reverse thinking is an innovative process. This not only solved the problem, but also cultivated students' innovative thinking and achieved good teaching results. For students who are not good at asking questions, once they ask questions, they should first praise their courage and then help them analyze; For students who are curious but always can't grasp the main points, help them find out the reasons for not grasping the main points, guide them patiently, and don't criticize, dig or hurt their self-esteem; Students who ask good questions should be encouraged to explore further and innovate boldly.
In short, the setting of classroom questioning is a teaching art, which requires us to carefully design, repeatedly compare, select and refine the best questioning methods according to the requirements of teaching objectives on the basis of in-depth study of teaching materials and understanding of students' reality, so as to give full play to the main role of teachers as organizers, guides, collaborators and students in mathematics learning, create a positive classroom psychological atmosphere, optimize classroom structure and improve teaching efficiency.