Mathematics learning is essentially a process of thinking. All thinking begins with the problem. Students' "questions" need to be artificially set, especially in the learning stage of new knowledge. By setting questions, teachers can make students face thinking difficulties, stimulate students' thirst for knowledge and stimulate their thinking. Therefore, the essence of classroom teaching is to ask questions. Compared with other subjects, questioning is more important in mathematics teaching. Whether the question is correct or not directly affects the realization of high efficiency in mathematics classroom teaching. In the new curriculum reform which takes students as the main body and cultivates creative thinking, how to effectively optimize classroom questioning is more important and prominent. This paper makes some discussions on this.
(A) the main problems existing in the current junior high school mathematics classroom questioning.
According to the survey results of "Research on the Effectiveness of Questioning in Junior Middle School Mathematics Classroom", the present situation of questioning in classroom teaching is not optimistic, and there are mainly the following problems:
1, the number of questions is too dense and there are too many repetitions.
The results of questionnaire survey show that most classroom questioning times account for 30% to 50% of classroom time, and the overall questioning frequency tends to be reasonable. However, there are also problems such as too many local questions and too many repetitions. In a paper, the author saw that in an open class, the teacher asked 56 questions in a 45-minute class, and in the five minutes of the "peak period" of a question, he asked 12 questions, with an average of 2.4 questions per minute; Around a certain teaching content, the teacher raised eight questions at once. Some of these questions are repetitive and have no thinking value, which leads to repeated teaching steps. It is not conducive to students' thinking exercise. If students are led by some trivial and meaningless questions, they will lose themselves and their own direction, which will affect the learning effect.
2. The direction of the question is not clear, which makes it difficult for students to answer.
A question must be accurate, specific and clear. Some teachers' questions are so vague that students cannot answer them. For example, when explaining rational number multiplication, after the students work out the result of "(-3)× 7", the teacher asks "What will be determined after the symbol is determined?" Students answer "results". "What else is there in the result besides symbols?" The students don't know how to answer. Another example is teaching "three-dimensional graphics in life". At the beginning of the class, the teacher showed boxes of various items and asked, "Can you classify these items?" Because the direction of the question is not clear, the students don't know where to answer it. The wording of such questions is not clear, which is not attractive to students, and it is difficult for students to understand and think, and it is also difficult to express.
3. The waiting time is short, and students don't have enough time to think.
It can be seen from the questionnaire survey that about 45% of the students think that the response time given by the teacher is "a little short". It takes time for students to answer questions, and the teacher stops in a short time, so the students' thinking can't enter the real thinking state. It often leads to starting without sending.
4. Questioning lacks respect for students and ignores the generation of the classroom. .
Although some teachers give students the opportunity to answer questions, they still interrupt students' answers with trepidation, or when students can't answer their own preset questions, they throw students' answers aside and add personal comments hastily, which affects the expression of students' personal thoughts. The following is a teaching clip of a young teacher teaching "One-Yuan Linear Equation":
How to solve the equation 3x-3 =-6 (x- 1)?
[Student] Teacher, I read it before I started to calculate, x = 1!
[t] you can't just look at it, you should work it out as required.
[Health] Divide both sides by 3 at the same time, and then … (interrupted by the teacher)
Your idea is right, but you should pay attention in the future. When learning new knowledge, remember to understand it according to the format and requirements of the textbook and lay a good foundation.
The teacher interrupted the students' novel answers when asking questions, only satisfied a single standard answer, and blindly emphasized the general steps and "general methods" of mechanically applying questions. It stifles students' innovative thinking, and in the long run, it will definitely dampen students' enthusiasm for learning. In fact, even if students' answers are wrong, teachers should listen patiently and give encouraging comments, which can not only help students correct their misconceptions, but also encourage them to think positively. Teachers should not only ask questions, but also listen to students' answers, so as to capture the available generating resources, otherwise the questions will lose their proper meaning.
(2) Countermeasures to improve the effectiveness of classroom questioning.
According to the investigation and analysis of junior high school mathematics classroom questioning, it can be seen that teachers' design of questioning content, attitude towards questioning objects and classroom questioning situations all affect the actual effect of mathematics classroom questioning. Therefore, we should start from these three aspects, improve the teaching process and improve the efficiency of classroom questioning.
1, optimize the content of the question.
(1) The problem design should be purposeful and targeted.
Pre-designed questions should have clear goals: either lead to new lessons, or link up before and after teaching, or break through difficult teaching points, or cause students to argue, or summarize. For example, when explaining "the nature of triangle edges", you can set the question "If you give three lines at will, can they form a triangle?" Through this question, students can be organized to discuss and operate, which is helpful for students to understand the essence of triangles, broaden their thinking and cultivate their ability of analysis and summary.
(2) The problem design should pay attention to hierarchy.
The objects that teachers face are not static, and the level of students is different for the same teaching content. Teachers are required to design different grading questions according to the actual level of students. For students with learning difficulties, try to let them answer some basic or simple questions in class. Encourage them to actively express their views. For students with good academic performance and strong ability, arrange appropriate answers to difficult and in-depth questions. When designing a problem, we should pay attention to its hierarchy. For example, there is a problem in the teaching of the application problem of quadratic equation in one variable: make a rectangular kite frame ABCD with a piece of wood with a length of 10 meter, and point a piece of wood parallel to the rectangular length AB in the middle, so that the kite will not be deformed. When the width AD is long, the rectangular area is 4 square meters. In teaching, the teacher didn't tell the whole story, but broke it down into several questions: ① How many ways are there to make a rectangular kite frame with a piece of wood 10 meter long? (2) What are the similarities and differences among these methods? ③ When is the area the largest? (4) In order to keep the kite from deforming, set a board parallel to the rectangular length AB in the middle, and let the width AD=x, and what is AB equal to? ⑤ When x is equal to what, the kite frame is square? ⑥ When the width AD is long, the kite frame area is 4 square meters? ⑦ Can the kite stand reach 5 square meters? This design not only reduces the difficulty, but also gives students at different levels the opportunity to answer, and also enables students to sort out what they have learned, learn to analyze problems and see the essence of the problems clearly.
(3) The questions should focus on "internalization, understanding and extension".
Teachers' questioning should play a role in developing students' thinking ability. We should design enlightening questions according to the teaching emphasis. Doubt promotes thinking, and thinking promotes learning. While implementing the basic knowledge, we should pay attention to deeper understanding and extension, and put forward some creative questions appropriately to expand students' thinking space. For example, when teaching "the sum of interior angles of polygons", teachers can design the following questions: ① What is the sum of interior angles of triangles? ② If two triangles can be combined into a quadrilateral, can you find the sum of the internal angles of this quadrilateral? (3) Can the sum of the internal angles of all quadrilaterals be "transformed" into the internal angles of two triangles? How to "transform"? (4) Can the sum of the internal angles of the N-polygon also be used in the above method? Have a try. ⑤ Do you have any other methods? Through the guidance of these questions, students can better grasp the key to proof and find solutions. This step by step is conducive to students' thinking, and at the same time, it further clarifies the mathematical thinking method of "returning", which lays the foundation for further learning mathematics.
For another example, when using the function image to find the approximate solution of a quadratic equation, all students turn the equation into x2-x-3 = 0, draw the image of function y = x2-x-3, and observe its intersection with the X axis to get the solution of the equation. In response to this phenomenon, we can ask: "Is it troublesome to draw an image like this?" "Can it be regarded as the abscissa of the intersection of two function images: y= x2 and y= x+3?" "How many ways do you think?" Through the setting of questions, students are guided to seek solutions to problems from multiple angles and ways, broaden their thinking and cultivate their divergence and flexibility. After solving this problem, we can further ask, "How many solutions are there to the equation x =x2 +3?" In this way, the above ideas and methods to solve problems have been sublimated, thus further cultivating students' exploration ability.
(4) Pay attention to the generation and changes in the classroom when answering questions.
Teaching is a complex activity, and the development of teaching activities sometimes coincides with the pre-class presupposition, but more often it is different from the presupposition. As a teacher, we should be good at catching the bright spots or wrong information of students' thinking and guiding students' learning. In class, the author once met a teacher who wrote two topics for two students to perform on the blackboard while teaching "Solving Binary Linear Equation". After a few minutes, most students finished the exercise accurately. At this time, a classmate raised his hand and said, "Teacher, I found a rule: when the coefficient of the X term, the coefficient of the Y term and the constant term are continuous integers, the solutions of the equations formed by these two binary linear equations are X = 1 and Y =-2." The content of this lesson is only to solve binary linear equations, and does not involve the law of solutions. After listening to this question, the teacher looked surprised, and should not have considered this question when preparing lessons. But the teacher didn't change the subject in a hurry, but fully seized the opportunity to ask, "Do you think this rule is right?" "Would you please try to write more and work it out?" The student immediately wrote an equation satisfying such conditions to test the laws discovered by the student, and the results were all correct. Teachers should use the situation to guide "how to verify this law?" Students use algebraic expressions to express binary linear equations satisfying the above conditions, and get general expressions, the solutions of which are x= 1 and y=-2. The teacher's questions are undoubtedly witty, and through the interaction between teachers and students, students' innovative thinking is cultivated.
2. Respect the questioner.
Taking teaching as the leading factor and learning as the main body is the basic principle of modern teaching. The subject of learning is students, and teachers should take students as the center and respect students in questioning, so as to mobilize students' initiative and enthusiasm in learning and give full play to the effectiveness of classroom questioning. In the concrete implementation, we should do the following:
(1) Give students enough time to think.
After a teacher asks a question, he usually pauses for a certain time, allowing students to think before answering. Some teachers let students answer questions as soon as they ask them. Students have no time to think and can't answer questions well. How long is the appropriate pause? It depends on the difficulty of the problem, the students' knowledge preparation and the agility of thinking in the formed students' ability structure. Under normal circumstances, the pause time can be shorter for relatively simple paving and transition questions, or to examine students' proficiency and reaction speed to a certain problem; For more critical questions or questions raised to consolidate review, the pause time can be slightly longer; After asking more important questions, let the students think for a long time before they answer. After the students answer the questions, sometimes the teacher can wait for a while, let the students' answers spin in everyone's mind, and then specify the students to supplement and evaluate, or turn to new questions. Studies have shown that the waiting time is at least 3 to 5 seconds. Three to five seconds can produce satisfactory results. Classroom practice shows that when teachers use waiting skills, students' answers will change greatly: 1, and students will make longer answers. 2. More students will answer questions voluntarily. 3. Students' answers are analytical and creative. The phenomenon that students can't answer is reduced. 6. Students' sense of accomplishment in classroom teaching is obviously enhanced.
(2) Pay attention to the integrity of the problem.
Asking questions in class should attract the attention of the whole class, rather than just asking top students for the sake of smooth teaching. The whole class should actively participate in thinking activities. Generally speaking, the teacher asks questions first, makes the class think, and then assigns a student to answer. Important questions can be answered by more students, and after answering, other students can discuss and supplement them. Doing so can make every student think seriously and be prepared to answer questions. Especially for some students with poor foundation, it helps to improve their enthusiasm for speaking.
(3) Ask and comment.
Timely comment after asking questions plays an important role in students' enthusiasm for thinking and learning. When commenting, we should follow the principle of "praise first". We should affirm students' independent thinking and original answers in time and encourage everyone to follow suit; If the answer is different from the teacher's expected answer, be sure if it is reasonable; If you want to verify the basis of students' answers, it can be used as a different understanding. Please think after class. Teachers should pay attention to discovering students' bright spots, let students experience the joy of success and stimulate their enthusiasm for learning. Ask or supplement questions in time according to the classroom situation. "Is this idea feasible? Why? -Is there any other way to solve the problem? -Can you understand XX's thinking? -What do you think? Can you describe your point of view? -Can you explain it again and make the meaning more clear and concise? " Through a series of questions and supplementary questions, students are given practical thinking, so that they can clearly understand the answers in different situations, which not only cultivates their independent thinking ability, but also cultivates their questioning ability.
3. Create a harmonious questioning atmosphere.
(1) Create the situation presented by the problem.
The problem situation refers to the teachers' purposeful and conscious creation of various situations to urge students to ask questions and explore solutions. The biggest advantage of creating problem situations is to make it easier for students to break through difficulties. The purpose of creating problem situations is to stimulate students' interest in learning, improve students' desire to explore problems, promote students' thinking and help teachers develop teaching content. The survey shows that the psychological characteristics of adolescent students affect the external performance of students in answering questions in class. Sometimes just because the students who answer questions are nervous, it affects the efficiency of classroom questioning, which requires teachers to find ways to create a good atmosphere conducive to questioning. For example, when talking about the "golden section", first ask: "Why don't the announcer or soloist stand in the center or corner of Taichung on the stage? In art and photography, why don't painters and photographers put the subject image in the middle? Why do adult ladies like to wear high heels? " Constantly asking questions, arousing students' curiosity, connecting abstract mathematics knowledge with life background, and making boring mathematics content interesting. So as to stimulate students' learning motivation and encourage students to participate in classroom activities.
(2) Reasonable application of nonverbal behavior. .
Nonverbal behaviors include expressions, eyes and body movements. The greatest advantage of applying nonverbal behavior to teachers' questions lies in the integration of teachers' questions and students' thinking answers. A good question can activate students' thinking sparks, and nonverbal behavior is the catalyst to activate the thinking sparks. In classroom teaching, many minor problems can be supplemented by nonverbal behaviors. For example, in the process of students' answers, teachers express their expectations with eyes and smiles, and nod their heads from time to time. When the students finish answering, the teacher will clap his hands before commenting (sometimes, if the teacher is next to the students, he can clap his shoulders to show his approval). How much encouragement this classmate will receive in his future study! Maybe he will love mathematics from now on and like this teacher's math class. American psychologist Albert? Merabin's experiment shows that the total effect of information = 7% words +38% tones +55% facial expressions and movements. It can be seen that nonverbal behavior plays a very important role in information expression.
Creating a good questioning atmosphere is not to bring students into the circle predetermined by the teacher and get a predetermined unified answer, nor is it just the teacher's sincere treatment and encouragement to students, but to push students to the main position of learning, encourage students to question and ask questions boldly, and encourage students to be innovative and different. Let students fully express their opinions in class. The most important thing is to guide students to ask. On the one hand, in teaching, students are encouraged to find problems, go deep into them and explore their essence. On the other hand, in the face of students' complicated problems, teachers should learn to listen, keep interest and patience. Take students' problems seriously and guide them to find solutions.
A good teacher must be good at asking questions, and classroom questioning means "there is no fixed way to ask questions." In the final analysis, to improve the effectiveness of classroom questioning, it is necessary to take students as the center, create problem situations that can effectively carry out classroom teaching, present targeted questions in an appropriate way, and finally achieve the purpose of improving the effectiveness of classroom teaching. In order to achieve this goal, we need further exploration and practice.