Mathematical situation is the environment for engaging in mathematical activities and the soil for generating mathematical problems. In classroom teaching, classroom questioning is an effective means and a classroom organization form widely adopted by all teachers. Setting clever mathematical situations and classroom questions can fully arouse students' learning enthusiasm, let students actively participate in the interactive process of teaching and learning, and let students become the main body of the classroom, thus achieving a double harvest of knowledge and ability in this process. However, in teaching, many teachers' preset situations and problems are superficial, which can not be linked and promoted step by step, and can not reveal the process of knowledge generation, which hinders the "dialogue" and interaction between teachers and students. In this case, not only can students not be guided to participate actively, but even their enthusiasm for learning will be dampened. The author believes that only by skillfully setting situations and problems can the effectiveness of mathematics classroom teaching be improved.

First, cleverly set the situation to make math class more effective

1. Use games skillfully to create situations.

If mathematics teaching is really student-centered, it should be guided by stimulating students' interest in mathematics, making mathematics learning a lively, proactive and personalized process. Psychologists believe that interest is a person's conscious tendency to explore knowledge and know things. Only when students are interested in learning can they show initiative, enthusiasm and creativity. In mathematics classroom teaching, teachers' plain and direct explanations generally do not arouse students' interest in learning. If teachers can create interesting and exploratory problem situations according to the teaching content and students' intellectual development level, they can often arouse students' curiosity, attention and thirst for knowledge, cultivate students' strong interest in learning, so as to let students learn actively in a relaxed and happy teaching situation and cultivate students' emotional attitude and values. For example, to find the approximate solution of the equation by dichotomy, I created the following situation: "Today we are going to play a guessing game. The price tag of this ruler in my hand is an integer of 5 ~ 15 yuan. You can guess its exact price. I'll give you a hint. Your answer is' on the high side',' on the low side' or' correct'. Who can answer this pen accurately and quickly?

Use interesting games in life to create problem situations, stimulate students' interest in learning, and enable students to actively learn in a relaxed and happy teaching situation, and develop their emotional attitude and general ability.

2. Create a situation with allusions

Teaching activity is not a simple process of "giving-absorbing". In classroom teaching, teachers should be the promoters of students' learning activities, rather than the imparting of knowledge, which requires teachers to create appropriate problem situations, build a platform for students to develop cooperative consciousness and ability, let students learn new knowledge in "cooperation" and actively construct knowledge in "inquiry", thus cultivating students' thinking ability and cooperative inquiry ability. Through the problem situation, let students feel that cooperation is a learning need, and inquiry learning is an effective way to acquire new knowledge, and gradually cultivate students' awareness of cooperation and inquiry. For example, in the first N-sum teaching of Geometric Series, I designed such a situation: After Tang Priest and his disciples went to the West to learn Buddhist scriptures, Pig Bajie returned to Gaolaozhuang to develop aquaculture, and gradually developed from a migrant worker to a large-scale boss. However, after communicating with several fellow villagers online, he found that their assets were all over 100 million yuan, so he wanted to expand the scale of livestock farms and set up a Gaolaozhuang Group integrating breeding and processing. Because of lack of funds, he thought. Pig Bajie: "Can you help me ..." Wukong: "No problem! I invest 1 10,000 yuan every day for one month (30 days), but there is one condition: I will return 1 yuan on the first day, 2 yuan on the second day, 4 yuan on the third day, and 8 yuan on the fourth day ... The amount returned on the second day is twice that of the same day, and after 30 days, I will not owe each other. " Pig Bajie thought, "On the first day, 1 ten thousand yuan voted for 0 yuan, on the second day, 1 ten thousand yuan voted for 2 yuan, and on the third day, 1 ten thousand yuan voted for 4 yuan ...! (thinking: Is there such a good thing? Is this monkey playing me again? ) In order to rapidly expand the livestock farm, Pig Bajie signed a contract with the Monkey King. Is Pig Bajie fooled by monkeys? " This case uses allusions to ask questions, which arouses students' curiosity, drives students to think positively and produces the desire to explore. Students are very interested and soon enter the state of active learning.

3. Contact life and set the situation

Mathematics is the science of thinking. In students' thinking activities, finding and solving problems are two important aspects. Therefore, it is of great significance to cultivate students' problem consciousness for cultivating students' thinking ability and innovative mathematics talents. Creating problem situations is to expose students to the atmosphere of problem research, and to let students actively discover, ask, analyze and solve problems, thus cultivating students' problem awareness.

For example, in the teaching of mean inequality, I created such a situation: a shopping mall conducted a price reduction activity before the festival and planned to reduce the price twice. There are three schemes a, the first discount sale; Plan C is to sell it twice (A+B)/ 20% discount. Second discount sales; Scheme B is the first discount sale and the second discount sale. Which scheme reduces the price more? The problem situation in this case is close to life, which creates a process of observation, association, abstraction, generalization and mathematics for students. In such a practical problem situation, students will definitely want to learn, enjoy learning and take the initiative to learn.

4. Create a situation with the realistic value of mathematical knowledge.

Mathematics has a wide range of applications. If we can properly reveal the practical value of mathematics in mathematics teaching, we can stimulate students' interest in learning to a certain extent, which is beneficial to students' learning. For example, in the "stratified sampling" class of senior one, I set the following mathematical situation: "In order to investigate the average height of students in my class (46 students in this class, 28 boys, and 0/8 girls/kloc), we take a sample with a capacity of 5 and use the average height of the sample to estimate the average height of students in this class. Can a representative sample be obtained through simple random sampling or systematic sampling? " I asked the monitor to get 4 males and 1 female by simple random sampling, and then I got 3 females and 1 male by systematic sampling. Students find that these two methods can't solve problems, resulting in cognitive conflicts, which greatly stimulate students' interest in learning new knowledge. This course adopts the methods of inquiry and cooperative learning, and has achieved good teaching results.

Second, skillfully set questions to make math class more efficient

1, avoid "full house full of colorful questions" when writing questions.

After the implementation of quality education, teachers have accepted many new educational ideas, changed the previous "cramming" teaching methods, strengthened interaction with students, and attached importance to students' subjectivity in the classroom. Teachers take the number of questions in class as the standard to measure whether students really participate in teaching in a class. But some teachers use "full-time questioning" instead of "full-time irrigation". Because there are too many problems in the class, the students are too busy to cope. The interaction between teachers and students seems to be in full swing. In fact, because the questions are not clear and prominent, students have not left any impression on these questions. Students don't have their own process of digestion and absorption, and the final result is that students can't acquire complete knowledge, let alone understand the whole process of knowledge production in class. In the long run, students will lose their patience in learning in the face of classroom teaching, and will not become the main body of the classroom, thus forming a vicious circle. Therefore, questions in class should be clever, focusing on quality rather than quantity.

2. Set questions and let the students "jump, that's enough."

According to psychology, people's cognitive level can be divided into three levels: known area, newly developed area and unknown area. People's knowledge level hovers back and forth between these three levels, constantly transforming and spiraling up. Asking questions in class can't stay in the "known area" and "unknown area", that is, it can't be too easy or too difficult. If the question is too simple, it will not arouse students' interest and waste limited classroom time; If it is too difficult, students will lose confidence and will not be able to maintain their persistent exploration psychology. Otherwise, the problem will lose its value. An experienced teacher's questioning can "affect the whole body". Appropriate questioning will moderately inspire students' mathematical thinking, and will certainly inspire students to actively explore new knowledge, so that old and new knowledge will interact and produce an organic knowledge structure. For example, when explaining function images, first help students recall some basic function images in junior high school. Before explaining how to draw the image of the function y=|x-2|+ 1, help students review the function y=x first, and then draw the image of y=|x| with the help of the teacher. In this way, most students can draw the image of function y=|x-2|+ 1, but it may be difficult for students to draw the image of function y=|+x-2|+ 1 directly.

3. Set questions skillfully and return to the situation

When designing a class, many teachers set the situation at the beginning of the class. At the end of the class, they just design some exercises related to the knowledge of this class and ignore the situation at the beginning. If students are directly allowed to imagine out of thin air, they will find it difficult. For example, when I explained the concept of set, before giving the nature of set, I put forward the question "Please pick out the tall people in the class". Only then did I know that the students were at a loss. Then I asked, "Please stand up if the class height exceeds 175cm". At this time, students will definitely find the answer in the teacher's two questions. In such a suitable problem situation, students will quickly enter their own roles and successfully complete the teaching tasks.

Suhomlinski said: "There is a deep-rooted need in people's hearts to feel that they are a discoverer, researcher and explorer." How to make students become discoverers, researchers and explorers of learning requires teachers to skillfully set up situations and questions in classroom teaching, stimulate students' vitality of development and innovation, and give students a chance to feel the joy of success.