First, the wisdom of effectively creating situations-"near? Real? Live broadcast "
In actual teaching, many teachers only create "flashy" but similar situations. These situations not only can't stimulate students' interest in learning, but also hinder the "germinal" of effective teaching. In order to fully mobilize students' enthusiasm for learning mathematics and make mathematics teaching activities pragmatic and efficient, the created mathematics teaching situation should embody closeness, reality and vividness.
1? Effective teaching situation pursues a word "near". One is to be close to the real life of children. Teachers should start from children's life experience and psychological characteristics, use children's eyes to find realistic, interesting and challenging materials closely related to children's life background, and create learning situations that children are willing to accept. The second is to accept the starting point of students' learning. Effective mathematics teaching activities must be based on students' real learning starting point. If the teaching situation is out of touch with the learning starting point, it will be difficult to achieve the expected results. The third is to approach the theme of mathematics learning. Situational creation should be closely related to mathematical knowledge and skills, without which it is not a math class. Teachers should deal with the relationship between "width" and "orientation" when creating problem situations, so that students can enter the subject of mathematics as soon as possible and start mathematical thinking.
2? Effective teaching situation pays attention to one word "reality". First, the content should be true. Teaching situation should be true and possible in practical application and social life, not artificially fabricated for the situation. Second, the form should be simple. The real teaching situation is not for viewing, not for deliberately creating anything, and not for adding anything extra. Don't artificially complicate simple things in pursuit of superficial stimulation and some form. Third, the application should be pragmatic. The situation created should serve the teaching objectives. If a situation can't effectively promote the achievement of teaching objectives, it is worthless, just pursuing the superficial "sensational effect", just the decoration or decoration of the classroom.
3? Effective teaching situation highlights the word "live". The first is to activate thinking. Valuable teaching situations should include some thinking mathematical problems in vivid situations, which can make students "touch the scene and think". The second is to lure the atmosphere. On the premise of ensuring that thinking can be activated and operation is simple, the created situation should fully mobilize students' emotions, stimulate their interest in learning and induce them to actively participate in learning. The third is to use the life situation. Instead of creating too many situations in a math class, we should make full use of a central situation and skillfully run through many teaching links, so that the setting of situations can play a guiding role in the students' learning process from beginning to end.
[Case] A teacher created such a situation when he was teaching "Application Problems with Problems": "Classmates, Xiaohong's exercise book was accidentally put into her schoolbag after school and brought home. What can Xiaohong do if she wants to do her homework? " The students immediately talked about it. Some people think that Xiaohong went to Xiao Ming's house to get it, while others think that Xiao Ming should send his exercise book to Xiao Hong's house on the grounds that Xiao Ming took it by mistake and he was a boy. The teacher asked: Is there a better way? The students are thinking again. First, they think they will meet somewhere. Later, they found it might be a waste of time, because the first party had to wait for the other party. So the discussion continued, and finally it was agreed that it was most reasonable for two people to start at the same time and meet halfway. Then, the teacher told everyone the speed of Xiaohong and Xiaoming and the distance between them, and asked the students to calculate the meeting time. This situation subtly implies the essential structure of "meeting problem" in a life event, creating a situation that is close to students' life (the events around them) and contains the connotation of mathematical thinking (the essential structure of meeting problem); Authentic and easy to operate; While solving this important event in life, students have a deep understanding of the connotation of "the application of problems encountered", which runs through the whole process of learning new knowledge.
Second, the wisdom of effective learning guidance-"Enlightenment? Release? Receive "
In the classroom of the new curriculum, there are two tendencies that deserve our consideration. One is teacher-centered, students dare not let go, students' active learning can not be effectively implemented, and it has become "wearing new shoes and taking the old road"; The other is that in order to highlight the students' dominant position, teachers blindly let students "learn by themselves", lacking effective inspiration and guidance, only "letting go" without "receiving", students' cognitive structure is fragmented, and the teaching effect is not ideal, which has become "wearing new shoes and taking the old road". In view of these phenomena, we put forward the "guiding learning" strategy of "opening-releasing-receiving".
1? Enlightenment is the premise. The first is to provide a "self-study outline" to inspire students to think independently. The first step of students' active learning is autonomous learning, but autonomous learning is not a simple "free learning", but an effective independent thinking process under the guidance of teachers. In order to make autonomous learning fruitful, teachers should provide a "self-study outline" based on problem thinking to guide students' learning ideas. The second is to provide a "cooperation guide" to inspire students to cooperate and explore. In order to make students' cooperative learning proceed in an orderly way, so that everyone has something to do, and everyone does everything in the cooperative group, and to avoid the phenomenon of "unity without reality" or "cooperation without action", teachers should provide students with a "cooperation guide" before carrying out cooperative inquiry on the premise of reasonable grouping of students, so that students can carry out cooperative inquiry in an orderly and efficient manner. The third is to put forward communication suggestions to inspire students' "mathematical expression". After students think independently, teachers should put forward concise communication suggestions before students communicate, so that students can have something to say. Guide them to carry out effective communication activities and express their learning results in mathematical language.
2? Sincerity is the key. First of all, students should let them operate what they can do. Piaget, a famous psychologist, said: "Children's thinking begins with action. If the connection between action and thinking is cut off, thinking will not develop. " Teachers should carefully analyze the characteristics of students' learning practice and what they have learned. Anyone who can learn by hand should be allowed to operate and start thinking with the help of operation. Second, students should let them explore the problems they can find. For those learning contents with exploratory value, teachers should provide students with time and space to explore and let them feel and understand the process of knowledge generation and development by themselves. Third, students should let go of what they can experience. Only by participating in various mathematical activities can students experience, do, experience and experience by themselves. Only in this way can mathematical knowledge, mathematical thinking method and mathematical ability be understood and developed in practical activities. Fourth, let students practice what they can learn. Practice is a bridge between mathematics, life and human society. Teachers should be the "designers" of this bridge, so that students can understand the things around them with mathematical viewpoints and methods and solve some simple practical problems in life.
3? Timely harvest is the guarantee. One is when the mind is stuck. When students' understanding of learning content deviates or their inquiry activities deviate from the direction in active learning, teachers should take back students' thinking in time and guide them to the correct thinking by inspiring, enlightening and even explaining. The second is to collect when refining and summarizing. After students' independent exploration and cooperative communication, teachers should guide or explain students' learning results according to the situation, sublimate students' scattered views into rational knowledge, make them systematic and orderly, reveal deeper connotations and improve students' cognitive structure. The third is to collect when reflecting and summarizing. While allowing students to acquire new knowledge or practice independently, teachers should also do a good job of "ending", that is, guide students to actively review and reflect on their own learning process and results, so as to improve students' self-evaluation ability in learning.
[Case] Learning "quotient invariance", taking "60÷20=3" as an example, this paper studies how to keep the quotient unchanged when the dividend 60 and divisor 20 change. Provide the following inquiry materials for students to explore:
①(60×2)÷(20×2)
②(60÷4)÷(20÷4)
③(60×2)÷(20×3)
④(60÷2)÷(20÷4)
⑤(60×3)÷(20×3)
⑥(60×5)÷(20÷5)
⑦(60×4)÷(20÷2)
⑧(60÷ 10)÷(20÷ 10)
In order to make the exploration fruitful, this paper provides enlightening and guiding exploration ideas: ① Which formulas are still equal to 3? Divide these formulas into two categories. ② Observe the dividend and divisor of these two formulas respectively. What are the changing rules? ③ Why have the quotients of other formulas changed? Through the analysis of the changing law, the quotient invariance is summarized.
When students use the invariance of quotient to explore the law of change and practice, they debate one of the judgment questions, 25÷5=(25÷3)÷(5÷3). Some people think that the quotient is unchanged, and some people think that both 25÷3 and 5÷3 have a remainder, and the final result should also have a remainder. When students are arguing endlessly, the teacher should close the net when it is time to close it, and make a suggestive summary: as long as we have the condition that the dividend and divisor are reduced by the same multiple at the same time, we must firmly believe that the quotient remains unchanged. As for the calculation methods of "25÷3" and "5÷3" and how to express the calculation results, wait until you learn the knowledge of fractions.
Third, the wisdom of effective use of resources-"smart? Wonderful? Good "
The teaching process is not a rigid process of implementing the teaching plan, but a "dynamic" process. In this process, there are both the realization of preset content and the generation of temporary resources. Some of these temporary "generated" resources are directly beneficial to teaching, some belong to irrelevant information, and some seem to be unable to be used directly, but after mining, processing and transformation, unexpected gains may be obtained. How to filter and integrate the captured information, make full and reasonable use of it, and serve the dynamic promotion of teaching objectives? We offer the strategy of "pushing the boat with the current".
1? Use students' "answers" skillfully-improvise and push the camera. In class, some "small episodes" often occur, such as students' answers being different from teachers' presuppositions and so on. These are the "original resources" produced in the classroom. If teachers can master these "answers" in time, skillfully use them and adopt targeted promotion programs according to the situation, some unforgettable highlights will appear in the classroom. The characteristic of this teaching strategy is that by capturing the meaningful "next crop" in students' answers, teachers can break through the design of the scheme and produce a new teaching idea of "strike while the iron is hot", which is the embodiment of the concept that "teachers should use teaching materials instead of teaching them" put forward in the new curriculum.
[Case] Teaching "Reading and Writing Grading", after the students read books and taught themselves, the teacher asked them to talk about how to write a grade and gave the reasons for doing so. A student replied, write the fractional line first, and then write it from bottom to top. When explaining the reason, he even said such a sentence: "Without a mother, there would be no son." There was a burst of laughter at once and the teacher encouraged him to continue. He said: "The denominator is the average number of copies, and the numerator is the number of copies taken. Only the average number of copies can be taken first, so the average number of copies is called denominator first, and the number of copies taken out is called numerator. Isn't it like having a mother before having a son? " The words sound just fell and applause rang out in the classroom. From here to there, the teacher immediately thought of the authenticity of the score, so he struck the iron while it was hot, broke the class boundary of the textbook, advanced the authenticity of the score in the next class, and continued to guide the students: "Is there a son in the world who is bigger than or equal to his mother?" Thus, it is vividly concluded that the score of a son who is younger than his mother is a true score, and the score of a son who is older than or equal to his mother is a false score. This flexible way of dealing with textbooks makes students impressed, even unforgettable for life, and the effect is much better than the blunt way of cooling down and starting a new stove.
2? Make good use of students' "mistakes"-make mistakes and make good use of them. It is normal for students to have some wrong ideas in the process of thinking because of their limited knowledge level. If teachers can start from these original "error resources", turn mistakes into mistakes, find the "growth elements" of teaching promotion, and draw correct ideas and logical conclusions according to the situation, they will receive unexpected results. The characteristic of this teaching strategy is to make use of students' mistakes, fully expose the process of mistakes, analyze the causes of mistakes, and thus generate the discrimination point of right and wrong knowledge. It is the embodiment of the teaching concept that "students' mistakes are also a valuable teaching resource".
[Case] Learn "area calculation of parallelogram". The computer displays a rectangle. Students review the method of calculating the area of rectangle by themselves: length× width (a×b). Then the computer draws this rectangle into a parallelogram. Students guess how to calculate the area of this parallelogram. Due to the influence of negative transfer, many students mistakenly think it is "a×b" when they think independently. At this time, the teacher will make mistakes and make the best use of the situation: if it is "a×b", then the areas of rectangle and parallelogram should be equal. Then use computer animation to move the parallelogram into a rectangular diagram, and guide students to compare whether the two figures are the same size and which is larger. After careful observation and comparison, the students found that the areas of the two figures are not the same, and the shaded part is the part where the rectangular area is larger than the parallelogram area, thus understanding that "a×b" is not the parallelogram area. The teacher further guided: how to calculate the area of parallelogram? Through intuition, most students can say that the small right triangle outside the rectangle is translated into it, and the parallelogram is transformed into a rectangle to deduce its area formula, and finally the correct conclusion of "base × height" is drawn.
3? Make good use of students' "questions" ―― Grasp doubts and deepen understanding. The new curriculum advocates interactive communication and questioning, the purpose of which is to know what "original resources" students have in their minds and what problems can become "growth elements" of new teaching problems, and extend them with students' questions, so as to promote teaching through step-by-step thinking and deepen students' understanding. This strategy fully embodies the teaching idea that "the core of the art of learning guidance lies in deepening students' thinking and deepening students' thinking" put forward by an education expert.
[Case] Teaching "the application problem of average value", the example is: "Two coal mining groups go to mine coal. The first group 10, with an average of 6 tons per person, and the second group 10, with an average of 8 tons per person. How many tons are mined by each of these two groups? " Through autonomous learning, students have successfully found a solution: (6×10+8×10) ÷ (10+10) = 7 (tons). At this time, a student asked: Can we use "(6+8)÷2" to calculate? Isn't it easier this way? The teacher seized this opportunity to guide everyone to discuss "can" and "why" in time. Then change "there are 10 people in the second group" to "there are 9 people in the second group" and ask the students if they can answer in the second way. Through discussion, and with the help of the line diagram, students found that if the revised topic is still done according to the second method, then the tonnage of the first group 1 person is not equal to the tonnage of the second group, so this method can not correctly find out how many tons each person in the two groups mined. Therefore, it can be understood that only when the number of copies of two related quantities is the same can the average of two be added and divided by 2, and then it is extended that when the number of copies of three related quantities is the same, the average of three can be added and divided by 3 ... Through this step-by-step reflection, students will not abuse the second method and have a deeper understanding of the meaning of "total amount ÷ total number of copies = average".
The above only introduces the breakthrough wisdom of three "bottlenecks" in the implementation of the current new curriculum. The teaching of new mathematics curriculum is a systematic project, involving many factors. We need to constantly explore in practice, and strive to find effective ways to improve teachers' educational wisdom, and through tempering and accumulation, we can independently control the new curriculum as a smart classroom.
Author unit
Zhejiang province Wuyi county education bureau teaching and research section
Editor in Charge: Cao Wen