Mathematics originates from life and is applied to life. Teachers' clever setting of realistic problem situations can help us solve the difficulties in teaching. The concepts of "area" and "volume" often confuse students, especially the understanding of "volume" is vague. We can help students to establish the concept of "volume" in this way: first, take two identical glasses, fill them with the same amount of water and ask the students, "What do you see?" Then, put a stone in one of the cups and ask, "What do you see? What else did you find? " The students found that the height of the cup had risen. The teacher asked, "Does this mean that the water in this cup has increased?" The students immediately denied it. "Why is that?" The students rushed to answer: "teacher, what you put takes up space, and the water is crowded up." Students have entered the state of establishing the conceptual model of "volume". The teacher took out another stone and put it in another cup, and asked, "What did you and I find this time?" The students found that the water level of the first cup exceeded that of the first cup. The teacher asked again, "Do you know why?" The student replied positively, "The second stone is bigger than the first one, so it takes up more space." On this basis, the teacher put forward that "the size of the space occupied by an object is called the volume of the object." Naturally, the spring breeze turned into rain and it came naturally.
In addition, familiar problem situations are more conducive to students to consolidate and apply what they have learned. For example, in teaching estimation, students can estimate the number of pulse beats per minute, the number of words read, the number of skipping ropes, the number of walking steps, and so on. You can also design such a problem: the school organizes a group of excellent three-good students to go for a spring outing, 62 of them need to take a bus. There are two kinds of cars to choose from. Cart limit 10 person, each time 108 yuan. The car is limited to four people at a time and 52 yuan at a time. Encourage students to be organizers of this activity, design a ride plan and predict which plan will cost the least. Problem situations are closely related to students' lives. In the process of students' tireless problem solving, they not only consolidated new knowledge, but also felt the application value of mathematics.
Creating realistic problem situations is to provide students with knowledge materials that come from their real life or come into contact with them, so that students can learn naturally, devote themselves to learning and study firmly, and let our mathematics show life scenes from time to time.
Second, interesting question situations can stimulate students' thirst for knowledge, activate students' thinking and turn mathematics classroom into a paradise for learning.
Interest is the best teacher. Students have a strong interest in learning, which will be their greatest motivation to acquire knowledge and develop their abilities. Creating interesting question situations to make students interested in the learning content itself is the most practical and direct internal motivation to stimulate students' active learning.
For example, teaching "circular decimals". At the beginning of the class, let the students listen to a short humorous story with music: "Once upon a time, there was a mountain, a temple on the mountain, and there was an old monk in the temple. He told the young monk that there was a mountain and a temple on it. He said to the young monk, Once upon a time … "Listening to the students' involuntary laughter, the teacher smiled and asked," Who wants to continue? " As the students went on talking, someone pointed out, "This story will never be finished. Don't waste time. " "Why can't this story go on forever?" "Because this story always repeats these words." "Very well said. In the kingdom of mathematics, there is a decimal, and the decimal and the numbers in the decimal part will appear repeatedly like a few words in this story. Do the students want to know? " This kind of "prologue" can make students enter the best learning state at once, which not only stimulates students' interest, but also enables students to initially perceive the meanings of keywords in concepts such as infinity, continuity and repetition in a pleasant and harmonious atmosphere, laying the foundation for the formation of concepts.
Another example is to design such a problem situation when teaching "circumference": the teacher asks, "How do you measure the circumference?" "I measured the circumference of this circle by rolling." "If you want to measure a large circular pool, can you stand up and roll it?" "Is there any other way to measure the circumference of a circle?" "Wind the rope around the circle and measure the length of the rope, that is, the circumference of the circle." At this time, the teacher demonstrated: fix the other end of the ball on the blackboard, shake the ball hard, and let the students observe the circle formed by the trajectory of the ball when it shakes. Q: "Can you measure the circumference of this circle with a rope?" It is not difficult for students to realize that there are limitations in measuring circumference by rolling method and rope method. "Can you explore a rule for finding a circle? What determines the circumference of a circle? " Observation experiment: two balls shake at the same time to form two circles with different sizes. Students are delighted to find that the circumference of a circle is related to its radius and the circumference of a circle is related to its diameter. What is the relationship between the circumference and diameter of a circle? Students' exploration is no longer passive. Teachers' questions activate students' thinking, making students feel that learning mathematics is not boring, but interesting. Mathematics classroom has become a paradise for students to learn.
Thirdly, exploring problem situations can meet students' knowledge needs, let students fully experience their sense of success as researchers, and turn mathematics classroom into a new knowledge development zone.
Students all want to be explorers, researchers and developers. The task of teachers is to create a problem situation with inquiry value for them, stimulate this desire for inquiry and knowledge, and guide them throughout the whole process of inquiry learning. For example, when teaching the law of whether fractions can be converted into finite decimals, students should first list their own fractions and convert them into finite decimals, and then lead to the question they want to explore: What kind of fractions can be converted into finite decimals? The teacher fully affirmed that the students asked a valuable question, and then asked the students to guess which part of the score was related to whether the score could be converted into a finite decimal. There are only two possibilities: related to numerator or denominator. Then, verify the conjecture. What method is used to prove that it is related to the numerator or denominator? After students' full discussion, guide students to adopt the method of "changing numerator" or "changing denominator", and draw a preliminary conclusion that "it has nothing to do with numerator but is related to denominator" on the basis of full examples. Then further discussion: What are the characteristics of the denominator of a fraction that can be converted into finite decimals? Let students go through the process of discussion, observation, analysis, comparison, judgment by examples and mutual verification. It is concluded that the denominator of fractions that can be converted into finite decimals does not contain prime factors other than 2 and 5, while the denominator of fractions that cannot be converted into finite decimals contains prime factors other than 2 and 5. When the students arrive at the elementary method, the teacher shows a score in the practice judgment stage, which arouses the students' doubts. According to the law obtained above, it cannot be converted into a finite decimal, but the calculation results prove that it can be converted into a finite decimal. What's going on here? Arouse students' cognitive conflicts and adjust the original cognitive structure. Push the exploration to a deeper level, and finally get a complete "law of whether a fraction can be reduced to a finite decimal". It is in this kind of inquiry experience that middle school students experience the pleasure and joy of being at the end of their tether and promising, their abilities are tempered and their wisdom is sublimated.
Fourthly, the open problem situation provides students with a broad thinking space, which encourages students to solve math problems independently and makes math classes unforgettable.
Creating open problem situations provides students with a lot of information to choose from, and students can choose different information according to their own understanding and hobbies, thus forming personalized problem-solving methods.
For example, when teaching "approximate number", we can create such an open situation: use a short story: "In math class, students are communicating and collecting the days of their lives. A classmate said,' The population of our country is 65.438+0.3 billion.' Xiao Ming immediately stood up and added,' Aunt Zhang upstairs in our house just gave birth to a little brother last night, so now the population of China should be 65.438+300 million 654.38+0.' "Arouse students' arguments, guide students to feel the inevitability of the existence of the divisor in the debate, and then trigger students to have rich associations and explore new knowledge with their own personalized understanding of the divisor.
Another example is the teaching of cognitive angle. When the class was over, the teacher took out a rectangular piece of paper and asked, "How many corners are left after this rectangle has been cut?" As soon as the problem comes out, students actively participate in knowledge exploration activities and come up with various solutions: some say there is one corner left, some say there are five corners left, some say there are four corners left, and some say there are three corners left ... This open question, which combines abstract mathematical problems with real life experience, fully mobilizes students' enthusiasm and initiative in learning, trains students' forecasting ability and mathematics application consciousness, and also cultivates students' exploration ability.
To sum up, well-created problem situations can attract students, stimulate students' desire for knowledge, ignite the sparks of students' wisdom, make them think positively, dare to explore, and actively participate in the exploration of boxing knowledge, so as to develop. That is to say, the mathematics classroom, which is moderately close to life, interesting, exploratory and open, will exude unique charm, firmly attract students, and bring fresh vitality to generate in an interesting atmosphere.