Mathematics Curriculum Standard for Compulsory Education (20 1 1 Edition) points out in the curriculum goal of "problem solving": initially learn to find and ask questions from the perspective of mathematics, comprehensively use mathematical knowledge to solve simple practical problems, enhance application consciousness and improve practical ability. It can be seen that "asking questions" and "solving problems" are both important parts of mathematical activities. Ask more questions and learn more; Ask deeply and learn deeply; There are no more questions, most of my thinking has stopped, and most of my study has stopped. In today's class, we can only see students raise their hands to answer questions, but we rarely hear students ask questions that they don't understand. In a primary school mathematics teaching video quality class evaluation, only two classes in 120 have links for students to ask questions, which is really too low. Even if teachers set aside time for students to ask questions and wait for a long time, the result is mostly silence or loudly "no problem". Most teachers are also willing to push the boat with the tide. Why do students have doubts? Why don't students ask questions?
First, the reasons for students' lack of ability to ask questions
One of the reasons: being poisoned by exam-oriented education. Nowadays, teachers know that students should be allowed to explore independently in the classroom, but under the pressure of exam-oriented education, they still have to hurry up, ask more questions and explain more, as if they had grasped every minute of the classroom and felt at ease. As for students' questioning ability, under the current examination system, it is still very difficult for us to test. Therefore, the teacher did not pay enough attention to the importance of asking questions, and naturally gave up training. Instead, it focuses on letting students solve the ready-made problems provided by teachers.
The second reason: I am worried that I can't control the classroom. The level of students' questioning is bound to be uneven, and the problems involved are bound to be extensive. Faced with this unpredictable and complicated situation, teachers' teaching will inevitably not proceed smoothly according to the established plan. In order to avoid trouble and embarrassment, it is only a formality to arrange a small amount of time for students to ask questions. Students are also observant and tacitly aware, and gradually, we get used to and recognize the classroom without students asking questions.
The third reason: the limitation of objective conditions. In the classroom, the limited teaching situation resources are almost equipped with related questions, and teachers and textbooks arrange almost all the questions in the classroom. As for students, just raise your hand and answer ready-made questions. Students are deprived of the right to ask questions and cut off the "source of thought" from the upstream, so students naturally cannot ask valuable questions.
Feelings: The loss of students' interest and ability to ask questions will inevitably lead to the lack of learning initiative, which is a terrible phenomenon in learning. The questions raised by students may be simple, but they are the crystallization of students' knowledge internalization. Research shows that students are far more interested in asking questions than answering them. By asking questions, students can inspire each other and form a pluralistic and open question system. Teachers can ask questions about things that are not involved in students' questions. Therefore, we might as well let students use their brains to ask questions after presenting the study materials, and the effect is self-evident!
Second, students' ability to ask questions training methods
The factors that constitute students' questioning ability at least include: the ability to observe and explain situations, the ability to know and understand the structure of mathematical problems, and the ability to reinterpret known problems. Therefore, teachers can design the following training to cultivate students' questioning ability.
1. Reasonable expansion ―― Asking questions in the created mathematical situation
Mathematical situation is a situation that contains relevant mathematical knowledge and mathematical thinking methods, and it is also the background of mathematical knowledge. It can not only stimulate the raising of mathematical problems, but also provide corresponding information and basis for the raising and solving of mathematical problems. Let students form their own mathematical understanding and corresponding mathematical structure through self-observation and explanation of situations in mathematical situations, then mathematical problems will naturally form in their minds.
For example, in the general review of plane graphics, in order to cultivate students' comprehensive ability to extract knowledge, the teacher showed the following information combined with pictures and texts:
The picture on the right is a plan of a business district.
Ask the students two easy and difficult questions according to this situation.
In addition to the obvious difficulty of some students' questions, students' questions mainly include the following types.
Class A: Unexpanded problems. For example, "How many kilometers is Xinhua Bookstore south of the central square?" Such questions do not extend to a given situation in any way.
Class b: the problem of expansion. For example, "the post and telecommunications building is located 3 kilometers east of the central square, please use"? " The location of the post and telecommunications building is shown in the figure. "This kind of problem is a good question to extend the situation reasonably through imagination.
Class C: The question raised is "unclear or unclear". For example, "the pedestrian street is 3 kilometers east. Please draw this street. " "Where is the Cultural Palace in the west?" Wait a minute.
D: The question is completely taken out of context. Such as: "How to calculate the triangle area?" "How to draw a vertical line?" Questions like this.
Unfortunately, without the teacher's prompt, students can't ask life questions outside the picture, such as "How much does it cost to take a taxi from Xinhua Bookstore-Central Square-somewhere (marked on the picture)?" "Xiao Ming 1 minute walk 100 meters. How long does it take Xiaoming to walk from Xinhua Bookstore-Central Square? " And so on, this kind of problem is a combination problem that is separated from mechanical imitation and reasonably recreated within a certain range. This is an important way to create new problems.
The key to this kind of training is the reasonable setting of problem situations, which can choose some problems in real life, the original problems in mathematics and some problems in the history of mathematics. In teaching, teachers should be good at creating mathematical situations that form problems and make them adapt to students' existing mathematical cognitive structure. Only in this way, students can put forward more meaningful mathematical problems by digging mathematical relations in mathematical situations, so that their ability to ask and solve mathematical problems can be further developed.
2. Comparative association-questions in the process of self-study
The process of students learning textbooks by themselves is also a process of absorbing, understanding and generating problems. The more thoroughly students understand what they have learned, the more profound their questions will be. Students at different levels will have such and such problems in the process of self-study. What teachers need to do is to give guidance in the direction, strategy and expression of questions, so that students can gradually master the methods and improve their ability to find and ask questions.
For example, in the class "Scale" taught by myself, students raised many questions, which can be roughly divided into the following categories: Class A, practical questions. For example, what is a scale? How to find the proportion of a picture? Class B is a question raised by induction and comparison. For example, what should I pay attention to when calculating the distance on the map or the actual distance? Why is the first part of the scale usually written as 1? Is the scale a ruler? Class C is a new question raised by association, variation and divergent thinking. What's the use of scale? Are there any other scales? The presentation of different levels of questions reflects students' different cognitive levels and problem-solving strategies, and also provides a basis for how to cultivate different students' questioning ability. Of course, this does not mean that teachers should respond positively only to "better questions", but also to general questions and handle them properly. In the process of asking questions, students usually combine existing knowledge or ask questions around the contents of books. In addition, teachers should guide students to ask questions in real life. Practice has proved that raising mathematical questions related to real life can effectively stimulate students' interest in asking questions and enhance their self-confidence in asking questions.
3. Questioning-asking questions in reflection.
Reflection is an essential link in solving problems. It can effectively improve students' problem-solving ability. In the reflection and introspection after learning, it is helpful to promote students' understanding of the whole problem, to help students change their position and to help students better understand knowledge.
For example, after teaching the calculation of surface area and volume of a cylinder, most students are easily confused about the calculation method of surface area and volume. A teacher in our school asked students to reflect on the learning process and ask questions to help them understand the different calculation methods of surface area and volume. After waiting for the question, a naughty boy said, "Please design an experiment to prove that it is wrong to calculate the volume with the bottom circumference × height, ok?" After students define their tasks, they discuss and put forward their ideas in groups, and then collect materials for confirmatory experiments. Wonderful questions lead to wonderful demonstrations. When students report and communicate in groups, they give full play to their own advantages and adopt various methods. Method 1: Fill a cylindrical can with water, pour it into a measuring cup to measure the volume of water, and then measure the circumference and height of the bottom of the cylindrical can to find their products. At this time, comparing the calculated results with the measured volume of the dose cup, we can find that the results are inconsistent. Method 2: Two rectangular cardboard with the same size are respectively enclosed into a cylinder and a cuboid (with the width of the rectangle as the height), so that the circumference and height of the enclosed body bottom are equal. We put them flat on the board and fill them with sand (don't press them). By weighing, the students found that the volumes of sand contained in two objects are not equal, so it can be inferred from the opposite side that the circumference × height of the bottom surface does not accurately reflect the volume of the container. Method 3: Use a small cube to form a cuboid with the same perimeter and height at the bottom but different shapes. Calculate the unit of volume contained in the box. Judging from the volume of a cuboid, it cannot be calculated by the bottom circumference × height. Similarly, the volume of a cylinder can't be calculated by the bottom circumference × height ... Students reflect on the reasons and ask questions, and find that "the bottom circumference doesn't represent how many unit volumes can be put on the bottom." Questioning after reflection not only activates the "nourishment" of students' knowledge, enhances students' ability to use knowledge flexibly, but also enables students to learn and develop more actively. This kind of questioning effectively expands and innovates the general questioning, and the level of questioning is quite high. Of course, you don't need to ask all questions, but you need to seek differences, doubts and changes in order to ask creative questions.
Asking questions is a remarkable feature of mathematical activities; Asking questions is also a means to improve students' ability to solve problems; Questioning is also a window to promote students' understanding of mathematics; Asking questions can improve students' attitude towards mathematics. Innovation begins with asking questions. "Creativity in mathematics is manifested in the ability to ask a large number of different questions to a certain extent". The core of more concerned "research learning" is also the raising of students' questions, and "dialogue teaching" also emphasizes teaching through mutual questioning and equal dialogue between teachers and students. Generally speaking, putting forward mathematical problems is an important topic in front of every mathematics educator in the new period, which deserves our in-depth study!