Source: China Teachers' Newspaper Author: Li Hanhuaqiu Added: 2008-12-1710: 34: 00.

First, reflection on the status quo of classroom questioning

Questioning in primary school mathematics classroom is an important part of classroom teaching and one of the most commonly used teaching methods. Teachers' well-designed and appropriate classroom questions can effectively stimulate students' curiosity and imagination, ignite students' enthusiasm for exploring knowledge, and thus greatly improve the quality of classroom teaching. However, in daily teaching, there are still some problems in teachers' classroom questioning.

1. Ask "only quantity, not quality". Too many questions and answers in the classroom often make students lack the space and time to think. On the surface, they are busy, but in fact, students are at a low level of cognition and thinking.

The answer is completely in the hands of the teacher. Sometimes, unconsciously, even if we give students a chance to answer questions, we will still interrupt students' answers with trepidation, or add personal comments hastily, which will affect the expression of students' personal thoughts.

The waiting time is too 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.

4. Do not pay attention to the use of resources generated in the classroom. 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.

The existence of the above problems seriously restricts the effectiveness of classroom questioning, making it inefficient or even ineffective.

Second, effective questioning teaching strategies

Effective questioning is relative to "inefficient questioning" and "ineffective questioning". The so-called "effectiveness" is explained by modern Chinese dictionaries as follows: "It can achieve the expected purpose; Effective. " "Effective questioning" means that teachers' questions can arouse students' responses or answers, which can make students participate in learning more actively, so as to obtain concrete progress and development.

Effective questioning contains two meanings: one is effective questioning; The second is an effective questioning strategy. In order to realize the "optimization of teaching process" and fully reflect the scientificity and effectiveness of classroom questioning, we should pay attention to the following points in practice.

1. Writing textbooks should be "easy to understand, thorough and comprehensive"

This is known to most teachers, but whether it can really be "in-depth" is something that every teacher needs to reflect on. The author believes that the learning of teaching materials should achieve the purpose of "understanding, infiltration and transformation".

"Understanding" means understanding textbooks. Only by understanding the textbook can we distinguish which questions are basic and ask questions with "what" and "how". We can use "what do you think" to ask which questions are expansionary; Which questions are inquiry questions, it is necessary for students to discuss and explore.

"Penetration" means mastering the systematicness, key points and difficulties of teaching materials, so as to achieve mastery and mastery.

"Culture" means that we can experience and feel students' learning not only from the perspective of teachers, but also from the perspective of students. Only by doing this can teachers skillfully ask questions, guide students to think and improve teaching quality to a greater extent.

2. Let students do "real" preparation.

We often say, "when preparing lessons, our teachers should not only prepare textbooks and teaching methods, but also prepare students and learn methods."

The so-called "reality" means that teachers must go deep into reality and understand students' basic knowledge, acceptance, thinking habits, difficulties and problems in learning. Only by truly understanding students can we ask questions with a clear aim, properly grasp the difficulty of the questions and make the questions more effective.

For example, the author wants to add some idioms commonly used in life to the teaching of the fifth book of junior high school mathematics, which can skillfully reflect the possibility. Many students have never heard of idioms that are considered simple for the first time, let alone related to mathematics. After class, I reflected on myself in time, found some classmates and chatted with them to find out their understanding and mastery of idioms. Finally, I adjusted the content of idioms to be asked according to the students' situation. In the last class, the students explained the content of idioms smoothly, which was closely related to what they learned in class. After class, many students were impressed by this link and wanted to talk about it after the teacher finished.

3. The questioning process should highlight the students' main body.

Thinking comes from doubt. The average teacher only sees that letting students solve problems is a kind of training for students. Actually, the response is still passive. It is a more demanding training for students to ask questions and explore problems by themselves. Teachers should try to make students doubt again on the basis of doubt, and then encourage and guide them to question and resolve doubts. So as to improve students' ability to find, analyze and solve problems.

In actual teaching, we often naturally ask students, "Are there any questions?" Students often answer with cooperation: "No problem." If it is always "no problem", then this phenomenon is extremely abnormal, and I am afraid it is really "problematic". The understanding of any math problem can never be kept at the same level, and there must be high and low levels and difficult points. In other words, there should be "problems".

The problem of "no problem" embodies a teacher's educational philosophy. It seems that only a smooth class is a good class. This kind of "smoothness" in class will only cultivate people who are angry with books, which is not conducive to the development of students' creative thinking; This "smoothness" in the classroom will also make students lack a spirit, a spirit of seeking truth from facts and being brave in asking questions.

So, how to solve this problem?

(1) Change ideas and establish a sense of "problems". Teachers should clearly realize that the most important point in mathematics training is problem consciousness. Therefore, it is one of the responsibilities of mathematics teachers to cultivate students' habit and ability to dare to ask questions, and it is also one of the standards to evaluate the quality of mathematics teaching.

(2) Create opportunities for students to think, think and ask questions. Teachers should not only create opportunities to ask questions in each class, but also let students really use their brains to think about problems and ask valuable questions or questions they don't understand. Really use this time instead of going through the motions. In order to let students ask questions, teachers can consciously carry out some training, and they can stand in the position of students and demonstrate questions as students. For example, the second-grade textbook has learned "the understanding of angles", and students already know what an angle is and the names of its parts. "The size of an angle has nothing to do with the length of its sides." "Are there any questions?" The student answered "no problem". Is there really no problem? "Then let me ask a question." I asked a question: "Why is the size of the angle irrelevant to the length of the side?" After discussion, we understand that the edge of an angle is a ray, and the ray has no length, so the size of the angle has nothing to do with the length of the edge. The size of the angle depends on the opening degree of both sides. The teacher demonstrated asking questions from the students' point of view. Over time, students have the consciousness of asking questions. While guiding students to ask questions, it also cultivates students' ability to think and solve problems actively.

(3) Be kind to students' questions and answers. No matter what kind of questions students ask, no matter whether their questions are valuable or not, as long as they are students' real thoughts, teachers should first fully affirm their children's courage to ask questions, and then take effective measures to solve the problems themselves or ask other students to answer them. For innovative questions or original opinions, we should praise him not only for daring to ask questions, but also for being good at asking questions and praising the value of asking questions, so as to guide everyone to learn how to think deeply about problems. Only in this way can students feel greater gains from asking questions, feel safe about asking questions, love asking questions more and more, and ask questions more and more. For students' answers, we should be careful to use habitual evaluations such as "very good", "very good" and "no, no". This evaluation puts too much emphasis on right and wrong. Over time, students' attention will focus on what the teacher wants. We can use a more neutral, acceptable or exploratory assessment as appropriate. For example, "Oh, that's a reasonable idea. Any other ideas? " "That's a good idea. What else can we add? " "Good idea, but how do we know ..." Encourage students to meet their needs and continue their studies.

In short, in practice, teachers should optimize the content of questions, grasp the opportunity of questions, pay attention to questioning skills and constantly improve their questioning ability. At the same time, it is also necessary to cultivate students' ability to ask and find problems, and really improve the quality of classroom teaching.

(The author is from Beijing Normal University Experimental Primary School and People's Education Publishing House)

On "Problem Solving" in Primary School Mathematics Classroom Teaching

A preliminary study on "problem solving" in primary school mathematics classroom teaching Abstract: In mathematics classroom teaching, around the theme of "mathematical problems", we should seek practical problem solving strategies, effectively carry out teaching activities, and guide students to ask questions from the perspective of mathematics, flexibly understand problems, creatively solve problems and rationally apply problems. Improve students' mathematical quality, innovative consciousness and practical ability from the process of problem solving and application. Key words: primary school mathematics problem-solving text: The specific objectives of the curriculum in "Mathematics Curriculum Standard" (experimental draft) for full-time compulsory education clearly point out that students should "initially learn to ask questions and understand problems from the perspective of mathematics, and be able to comprehensively apply the knowledge and skills they have learned to solve problems and develop their sense of application." "Form basic problem-solving strategies, experience the diversity of problem-solving strategies, and develop practical ability and innovative spirit." Based on this basic requirement, in mathematics classroom teaching, we can seek practical methods around the theme of "problem", effectively carry out teaching activities, guide students to put forward problems from the perspective of mathematics, understand problems flexibly, solve problems creatively and apply them reasonably. Improve students' mathematical quality, innovative consciousness and practical ability from the process of asking and solving problems. Based on the above understanding, we have made a preliminary exploration in mathematics classroom teaching and gained some superficial understanding. First, guide students to ask questions from the perspective of mathematics. Einstein believed that "raising a question is often more important than solving a problem, because solving a problem is only a mathematical or experimental skill, and raising new questions and new possibilities, looking at old problems from a new perspective, requires creative imagination and marks the real progress of science." In primary school mathematics teaching, cultivating students' questioning ability plays a positive role in developing students' intelligence, developing students' thinking, changing passive learning into active inquiry and really improving students' comprehensive quality. So, how can we make students ask questions from the perspective of mathematics? 1. Create question situations to stimulate students to ask questions. Life contains a lot of mathematical knowledge, and mathematical problems often arise in specific life situations. Teachers should grasp the hot spots and focus of students' thinking activities, provide students with rich and colorful background materials according to their cognitive "zone of proximal development", start with things and events that students are familiar with, and create interesting and challenging problem situations through vivid reproduction, guessing, storytelling, games and competitions, so that students can generate problems independently and stimulate their desire to explore. For example, when teaching "multiplication application problem", the teacher created such a problem situation: on Sunday, your mother asked you to buy two boxes of milk. Then what questions will come to your mind? According to their own life experience, the students spoke one after another: how much is each box of milk, at least how much should I bring? ; It can also be a bottle of milk. How much is it? How many bottles of milk are there in each box? How much should I bring at least? In this way, the students raised many pertinent and valuable questions. The teacher asked in time, "How are you going to solve the above problems?" Through discussion, we can get two methods: look at the price description; Ask the salesman. At this time, two situations can be presented: ① Through investigation, we know that each box of milk is 48 yuan, and we buy two boxes. (2) According to the survey, there are 24 bottles of milk per bottle, and 2 yuan buys 2 boxes per bottle. And asked: "according to the above two pieces of information, what math problem can you solve?" The student immediately put forward: according to the survey, how much does it cost to buy two boxes of milk? ; According to the survey (2), how many bottles of milk did a * * * buy, how much did it cost to buy one box and how much did it cost to buy two boxes? Waiting for math problems. Then the teacher organizes students to solve the above problems through independent thinking and cooperative communication? ..... In this way, teachers provide students with a broad thinking space by creating familiar shopping situations in their lives, so that they can think independently, comprehensively and from multiple angles. 2. Develop democratic consciousness and cultivate students' ability to dare and be good at asking questions. It is a child's nature to be curious and ask more questions. Students' asking questions marks the germination of their thinking, and primary school students' asking mathematical questions directly reflects their thinking ability in mathematics in life. However, because primary school students have not mastered the methods and skills of asking questions, the classroom performance is "afraid of asking questions". If you want students to ask questions, you must cultivate their courage and courage to ask questions. Teachers should respect every student, give students emotional information of safety, trust and respect through their words, deeds and attitudes, stimulate students' emotional voices, and realize the learning behavior of asking questions independently. There was once such a class: a Chinese teacher was giving a lecture, and a student questioned "40 million" among "40 million compatriots". Many students laughed. The teacher didn't blame the student for his ignorance, but encouraged him. At the same time, on the basis of solving the concept that "40 million" is "400 million", the teacher conducted a study on "Why use 40 million instead of 400 million", which deepened students' understanding of the article. It not only achieves good teaching effect, but also enhances students' learning confidence and cultivates their determination to ask questions. It can be seen that only when students can think positively and express boldly can teachers know where students are "suspicious" and "confused". In order to effectively guide, guide and adjust the knowledge taught. On the other hand, if teachers treat students' heartfelt but whimsical questions as deviant and "deliberately disruptive" to suppress them, then, over time, students' enthusiasm and initiative in thinking and asking questions will be greatly reduced, or even stifled, and become a "container" for truly accepting knowledge. Therefore, cultivating democratic consciousness is the premise for students to dare to ask questions, and it is also the key to open the door of thinking. 3. Guide students to reflect actively and further grasp the pertinence of raising mathematical questions. Students' reflection in learning activities is a process in which students take their own learning activities as the object of thinking, examine and analyze their own behaviors, decisions and results, and it is a way to promote the ability development by improving the self-awareness level of participants. In the process of mathematics teaching, students are often guided to consciously reflect on the mathematical problems involved in this class, and gradually clarify which problems are valuable and which are irrelevant, so that future problems can be closer to what they have learned in mathematics, thus improving students' ability to ask mathematical questions. Second, guide students to solve problems flexibly and creatively. Guiding students to ask questions from the perspective of mathematics is only the beginning of teaching, and the core content of "solving problems" is to let students solve problems flexibly. At the same time, in the process of solving problems, the value of its activities lies not only in obtaining concrete conclusions, but also in letting students experience the original state of knowledge and different problem-solving strategies in the process of solving problems. Everyone should have their own understanding of the problem and form their own basic strategies to solve the problem on this basis. So it is possible to cultivate students' innovative spirit in the sense of encouraging individuality. How to enrich students' practical process of "solving problems", how to make every student give full play to the greatest potential of his thinking and how to make them feel the joy of the success of mental work has become an important topic in our mathematics classroom teaching. First of all, we should encourage students to explore independently and seek methods. In mathematics learning activities, students are the main body of learning. After students enter the role, teachers should set aside enough time for students to explore and communicate, seek solutions to problems and express their unique opinions and feelings. When a teacher called "two digits plus one digit (carry)", he changed the presentation mode of "explanation" (stick) in the textbook to "problem discovery", allowing students to explore independently. This teacher designed it like this: "Dad asked Mingming to calculate 18+7, and Mingming thought hard for a while and asked his classmates for help. Who has a clever way to help me? " A stone stirs up a thousand waves, and the students are in high spirits and think positively. At this moment, teachers organize students to discuss in time, give full play to the collective role and embody the spirit of unity and cooperation through group discussion and deskmate talk, so that every student has the opportunity to take the initiative to participate and strengthen multi-directional communication between students. Finally, the students came up with various methods: some took 18 as 20 (20+7-2); Some divide 18 into 13 and 5 (13+7+5); Some divide 7 into 2 and 5 (18+2+5); Having several fingers; There are vertical calculations, and so on. It is the embodiment of students' independent innovation to express their thinking process in language after their independent inquiry. Once the problem is solved through some efforts, students will have a tense and pleasant experience, a sense of accomplishment, pride and value. These psychological tendencies are the source of motivation to encourage students to explore further. Secondly, study groups can be established. Students' development is unbalanced. No matter which class students are, their intellectual development level, ability and understanding of life and mathematics problems are different. In the classroom, students have different solutions to some math problems that need to be solved. In order to enable students with different levels of development to solve problems, study groups can be established by group learning, students with high, medium and low learning levels can be reasonably matched, and a student with higher learning level can be recommended as the group leader, so that information contact and information feedback of students with different levels can be carried out in multiple levels and directions. In this way, team members cooperate and communicate on the mathematical problems to be solved, discuss the best strategies and methods to solve the problems, learn from each other's strong points, and achieve the goal of solving the problems satisfactorily. Improve the ability to understand and solve problems in regular cooperation and exchanges. Third, encourage students to practice and solve mathematical problems in operation exploration. Piaget thinks: "To know an object, we must move it by hand" and "All real knowledge should be acquired by students themselves, or re-invented by them, at least reconstructed by them, rather than passed on to them hastily." Therefore, teachers break through the limitations of textbooks, change their conclusions and encourage the discovery of new knowledge. Facts have proved that many questions raised by students can be obtained by students themselves through operational inquiry. For example, according to the student's question, "Are the areas of the top and bottom surfaces of the cylinder equal?" Teachers can guide students to operate their own cylinder model without telling them directly, and discuss "Is there any way to verify whether the two bottom surfaces of a cylinder are equal?" In this way, students actively discuss and explore through cutting, measuring, superposition and other methods, and come to the conclusion that "whether cutting and superposition completely overlap the upper and lower bottom surfaces"; "Measure whether the diameter, radius and circumference of the upper and lower bottom surfaces are equal"; "whether the symmetry axes of the upper and lower bottom surfaces are equal" and so on, and draw the conclusion that the areas of the upper and lower bottom surfaces of the cylinder are equal. Through this learning process, students can solve problems by themselves, use their brains, move their mouths and eyes, and let themselves know what it is and why. For example, when learning the content of "parallelogram", a teacher designed such a question: "Please draw a straight line on the parallelogram below to make the areas of the two parts equal." So the students devoted themselves to the learning activity of "How to Divide", discussing enthusiastically, trying boldly, operating independently and thinking positively ... So they found different ways to solve the problem. (as shown in the picture) ... It can be concluded that countless lines can be drawn. But the teacher didn't stop there, but continued to ask: Do these bisectors have any common features? Students' enthusiasm for inquiry is stimulated again. Through discussion, students understand that a parallelogram can be equally divided as long as a straight line passes through the center of the parallelogram, and it also breeds the knowledge that a parallelogram is a centrally symmetric figure. This approach organically combines students' acquisition of knowledge, expansion of ideas and cultivation of abilities. Third, guide students to apply knowledge reasonably and cultivate application consciousness. Students' application consciousness is mainly manifested in "recognizing that there is a lot of mathematical information in real life and that mathematics has a wide range of applications in the real world;" In the face of practical problems, we can actively try to use the knowledge and methods we have learned from the perspective of mathematics to find strategies to solve problems; Facing the new mathematical knowledge, we can actively look for its realistic background and explore its application value. "(Mathematics curriculum standard) Students should not only find out the problems raised in the classroom, master the ready-made mathematics knowledge and skills, but also know how to use the methods of solving problems in the classroom, consciously and consciously understand the surrounding things, understand and deal with related problems, so that the knowledge they have learned becomes closely related to life and society, and truly" comes from life and is applied to life ". In this regard, teachers should consciously be the guide of students' "using mathematics". For example, after learning "statistical knowledge, price and shopping calculation, length, area, volume, etc.", we should provide students with practical opportunities as much as possible and guide them to apply mathematics to their lives. We can ask students to measure the length and width of the classroom; Measure the length and width of blackboard, desk and book; Measure the length and width of home furniture and the height of mom and dad; Measure the weight of mom and dad; Calculate the price of goods purchased, such as shopping. In "using mathematics", experience the role of what you have learned, stimulate students' enthusiasm for learning, stimulate students' interest in solving problems, and let students taste the fun of applying what they have learned. Another example is that after learning the concepts of "interest rate and interest", a teacher creates a scene to guide students to communicate the relationship between mathematics and reality. He made up such a topic: "Today, my father kept this month's 1850 yuan's salary in the bank for three years, so how much can my father get back after three years?" This kind of problem is very close to life and can easily arouse students' interest. Through investigation, they understand the bank interest rate and apply the percentage knowledge they just learned. Through practical calculation, students not only consolidated their learning knowledge, but also learned financial knowledge, thus increasing their knowledge and cultivating their ability to apply mathematics in practice. Students' mathematical knowledge is constantly improved and developed harmoniously in the process of discovering, exploring, solving and applying problems.