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How to design effective problems in mathematics classroom teaching
In mathematics classroom teaching, we can seek practical methods around the theme of problems, effectively carry out teaching activities, guide students to combine learning and life practice, initially learn to ask questions from the perspective of mathematics, flexibly understand problems, creatively solve problems and rationally apply problems. Classroom questioning is a comprehensive teaching art of asking questions, stimulating interest and inspiring thinking. It is one of the ways to realize teaching feedback, and it is the basic control means for teachers to open students' thinking, promote students' thinking and enhance students' awareness of active participation. It is not only widely used in teaching and advocated by ancient and modern teachers, but also has a long history as teaching itself. Improve students' mathematical quality, innovative consciousness and practical ability from the process of asking and solving problems. In primary school mathematics teaching, teachers should not only ask questions, but also pay attention to cultivating students' questioning ability, which has a positive effect on developing students' intelligence and thinking, changing passive learning into active inquiry and truly improving students' comprehensive quality.

First of all, first of all, reflect on the status quo of classroom questioning:

1, only ask 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 controlled by the teacher.

Sometimes, unconsciously, even if students are given the opportunity to answer questions, we will still interrupt the students' answers with trepidation, or hastily add personal comments, which will affect the expression of students' personal ideas and make them unable to express their ideas wholeheartedly.

The waiting time is too short.

Students need time to brew and think when answering questions. Teachers stop in a very short time, students' thinking can't enter the real thinking state, and teachers don't give students enough time and space. Classroom questioning is the mobilization of intellectual and non-intellectual factors, which can guide students' thinking, stimulate their interest in learning and stimulate their desire to actively participate in mathematics learning activities. Mr. Smir once said: We advocate big questions (with a certain space) from the perspective of developing students' thinking, and we should be good at designing appropriate question spaces (with a certain direction) from the perspective of primary school students' cognitive level, characteristics of mathematics subjects and the 40-minute limit of classroom teaching. Therefore, teaching should leave enough space for students' activities, imagination and communication, and teachers' questions should be enlightening and challenging, so that students can actively think and explore.

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

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, how to effectively ask questions in classroom teaching strategies

Effective questioning is relatively inefficient and ineffective. Effective questioning means that teachers' questions can arouse students' responses or answers, which can make students participate in learning more actively, thus achieving concrete progress and development.

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

1, prepare the textbook for understanding, infiltration and transformation.

This is known to most teachers, but whether it can really go deep is something that every teacher needs to reflect on. It is mentioned in the New Curriculum Standard that the learning of textbooks should achieve the purpose of understanding, infiltration and transformation.

Understanding is understanding textbooks. Only by understanding the textbook can we distinguish which questions are basic, what to use and how to ask questions. Which questions are expansionary, we can ask them with your ideas; Which questions are inquiry questions, it is necessary for students to discuss and explore.

To be thorough, it is necessary to master the systematicness, key points and difficulties of the teaching materials and achieve mastery through a comprehensive study. It means to experience and feel students' learning not only from the teacher's point of view, but also from the student's point of view. Only by doing this can teachers skillfully ask questions, guide students to think and improve teaching quality to a greater extent.

2. Let students prepare for reality.

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. I want to add some life examples to the classroom teaching to guess this knowledge point, which can subtly reflect the possibility of guessing. Many students have never heard of an example that they think is very simple for the first time, let alone something related to mathematics. After class, I reflect on myself in time, find some classmates and chat with them to understand their knowledge and understanding of real life. Finally, I adjusted the content of the question according to the students' situation. In the last class, the students explained the content smoothly, and it 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. Students should be highlighted in the process of questioning.

In actual teaching, we often naturally ask students: Are there any questions? Students often cooperate with the answer: no problem. If there is always no problem, then this phenomenon is extremely abnormal, and I am afraid there is really a problem. 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 a problem.

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

The basic state of effective teaching is dialogue and interaction. In this kind of dialogue and interactive teaching, teachers can teach, but not always with one voice. Whether teaching appears and maintains a certain state of dialogue and interaction depends on whether teachers can ask questions effectively. After repeatedly advocating dialogue teaching and interactive teaching in the education field, it seems that no more teachers still maintain the teaching habit of focusing on full-time irrigation. However, after teachers got out of the teaching habit of centralized full-time irrigation, they unexpectedly encountered the embarrassment of full-time questioning.

Third, how to solve these problems in the classroom?

1, change ideas and establish problem consciousness.

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. When introducing new lessons and asking questions, we should find the connection point of knowledge. Mathematics knowledge is closely related. Every new knowledge is based on old knowledge, and new knowledge is the extension and development of old knowledge. Their internal factors build a bridge for students to master new knowledge. Therefore, in teaching, we should make full use of the connection point of old and new knowledge to promote the students' transformation from unknown to known. For example, in the second class of "Preliminary Understanding of the Corner", I adjusted the cognitive structure of the textbook according to the children's cognitive structure. First, know the right angle. Q: Make it yourself and then fold it in half. What is the angle? Which angle on the triangle is a right angle? Then the right angle is displayed on the projector. Then, fold the angle less than the right angle and draw an angle less than the right angle. Students can fold angles smaller than right angles and naturally fold or draw angles larger than right angles. The advantage of doing this is to follow the cognitive structure of students, from easy to difficult, easy for students to accept, and easy to form clear concepts from various angles. Therefore, teachers can grasp the connection point between old and new knowledge, ask questions, and let the teaching of new knowledge come naturally.

2. The key to effective questioning is to accurately grasp the opportunity in class.

Asking questions in time actually plays a role in mobilizing students' emotions, activating classroom atmosphere, ensuring the quality of thinking and improving teaching effect. Generally speaking, the opportunity to ask questions in class comes from subordinates:

(1) is the time when students get to know, feel and want to communicate;

(2) When students are suspicious, confused and want to ask questions;

(3) It is the time when students' learning emotions need to be stimulated and mobilized;

(4) It's time to promote students' self-evaluation. Teachers should grasp the opportunity of asking questions and give students some time to think, form answers and react after asking questions, so that the effectiveness of asking questions will be obviously improved.

3. 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.

4. 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. 4. Ask questions carefully in class.

Teachers' higher language literacy is an important condition for rational use of time, which largely determines the efficiency of students' mental work in class. This sets a high standard for teachers: classroom questioning should be not only scientific, but also artistic. Then strengthening questioning means that teachers pay attention to the combination of scientific and artistic questions, carefully design and refine some inspiring, emotional, flexible, challenging and valuable questions, guide students to think, expand their thinking scope and improve their thinking level.

(1) requires a small number of questions, but it is accurate.

This requires teachers to grasp the key points (key points, difficulties) and essence of mathematical knowledge according to the characteristics of teaching content, use inductive and comprehensive methods, design large-capacity questions as much as possible, avoid problems being too cumbersome and straightforward, improve the density and effectiveness of students' thinking, and achieve the purpose of promoting deep thinking with accurate questions.

(2) The difficulty control of questioning should be moderate and reasonable.

Difficulty refers to the depth and breadth of the problem, while moderate difficulty refers to the fact that the problem should be in line with the students' reality, and attention should be paid to the adaptation of the problem to the students' intelligence and knowledge level.

6. Ask questions comprehensively in class.

Classroom questioning is an important means for teachers to understand students' learning situation and stimulate students' desire to explore new knowledge. Therefore, classroom questioning should be oriented to all students and become an information exchange between all students and teachers, and should not be the patent of a few top students. In actual teaching, if only the top students are allowed to make an appointment and the students with learning difficulties are excluded, the students with learning difficulties will be distracted, in the classroom and outside the window. In classroom teaching, teachers should pay attention to students with learning difficulties and give priority to asking them.

First of all, we should pay attention to the level of questioning, so that students with learning difficulties can follow the teacher to ask questions and think positively.

Secondly, give priority to students with learning difficulties to respond or perform, so that the questions that students with learning difficulties can answer after thinking will never be made by top students, so that students with learning difficulties also have the opportunity to express themselves and feel the joy of success.

Thirdly, we should encourage students with learning difficulties to speak boldly, affirm them in time if they answer correctly, and don't blame them if they answer wrong, so as not to dampen their enthusiasm. Teachers should make use of the feedback information obtained by asking questions, grasp the teaching progress in time, take advantage of the situation and improve teaching in an all-round way. In addition, teachers should pay attention to the language of questioning in class. Psychology believes that rigorous language makes people credible, humorous language makes people happy, passionate language makes people excited and vivid language makes people clear. Therefore, when teachers ask questions in class, they should constantly hone their questioning language to be accurate, concise, vivid, friendly, touching and humorous. Use delicate language to turn boring into interesting, silent into sound, invisible into tangible, and create a democratic, relaxed and harmonious classroom environment, so that students can enjoy learning, learn well and learn well in a good learning atmosphere.

Fourth, teaching effective questioning is also an art.

Effective questioning means that teachers' questions can not only arouse students' responses or answers, but also enable students to participate more actively in the learning process. The validity of the problem lies not only in the choice of words, but also in the change of mood, stress, choice of words and the context of the problem. There are many ways to ask questions, and each way can determine whether students will understand them as questions and why.

Effective questioning is a very subtle teaching skill (whether it is technology or art). In fact, the real effective problem lies in listening. Once students take the initiative to learn, the teacher's responsibility changes from teaching and asking to listening. The key strategy is to make your students feel that the teacher is waiting and listening. Let all students participate in asking and answering questions.

1, let the students feel that the teacher is listening.

Teachers' feedback behavior will encourage or hinder students' participation to a great extent. In the face of students who have difficulty in answering questions, teachers should not interrupt students' answers, even if they are wrong. Sometimes, students begin to answer, but are interrupted in the middle, so they can only listen to the teacher's prompt for the answer; Or, if a student starts to make a mistake, he is immediately interrupted by the teacher, so that another student can answer or the teacher can say the correct answer for him. In this way, students will feel frustrated and unwilling to actively participate in classroom activities.

2. Teachers need to learn tolerance.

Teachers need to tolerate differences, give intellectual and emotional encouragement, at least not to ask questions as a means of punishment. When necessary, teachers need to ask questions, supplement and appreciate students' answers. This will make students feel that the teacher has been paying attention to the progress of answering questions. Effective listening will naturally turn students' responses into teaching resources. In this listening environment, students become important curriculum resources rather than simple recipients. Students' answers should be the starting point and ladder for teachers to further ask questions and guide. Really effective teaching always means that teachers are good at listening to students' voices, developing and changing students' views, and triggering more complicated answers. This will naturally stimulate students' active participation.

As we all know, there is no fixed pattern in a class, and classroom questioning is by no means the same. In the teaching practice of quality education, we can also choose and create other colorful classroom questions according to the teaching requirements and students' reality. The artistry of classroom questioning is reflected in teachers' infinite creation. It casts teachers' strategical and far-sighted wisdom and shines with the brilliance of teaching style. It is a window to show teachers' teaching art. Therefore, artistic classroom questioning is always colorful. No matter what form of classroom questioning is adopted, the best effect should be achieved in imparting knowledge, enlightening wisdom and cultivating sentiment. As long as it can stimulate students' interest in learning, strike a chord in students' thinking, let students devote themselves to learning in the best state in the teaching process, and lay the foundation for the whole classroom teaching, it is a successful classroom questioning.

In a word, it is very important for teachers to ask questions scientifically in class in order to improve the teaching quality in an all-round way, develop students' comprehensive quality, especially cultivate students' innovative quality. Only when teachers ask appropriate questions in class can students have a proactive thinking process and a high-quality classroom teaching effect. Therefore, proper classroom questioning is the key to improve the quality of classroom teaching. Today, when quality education is strongly advocated, teachers should pay more attention to the art of classroom questioning and really play an important role in primary school mathematics classroom teaching.