Strategy 1: create an equal, relaxed and harmonious atmosphere, and let the energetic generation have a good "ecological environment"
[Case] I heard that a topic was the open class of Discovering Laws, and the teacher had such a question: L, 2, 4, (),
(), (), let the students add some numbers at the back to make these numbers look more regular. After a heated discussion, the students raised their hands. One student filled in the first answer: 7, 1 1, 16. The reason is that the difference between these two numbers increases in turn, increasing by 1, 2, 3, 4 and 5 respectively. The teacher smiled and nodded. Second, today's students thought of another filling method: 8, 16, 32 ... The reason is that the former number is repeatedly added to the latter number, and the teacher smiled with satisfaction. The teacher looked around the class and there seemed to be nothing wrong. Just as the bell rang, the teacher prepared a class summary. At this time, a little hand was timidly raised and secretly put down. I guess this is a student with low self-confidence and average grades. The teacher hesitated slightly: "Do you have any questions?" Student: "I want to fill in 1, 2, 4 ..." Suddenly, the whole class burst into laughter. The classmates buried their heads shyly. The teacher motioned for everyone to be quiet and said kindly, "Your idea is good. It's amazing! Give your reasons, will you? " The student held his head high and said, "I think repetition is also a law." How well you speak! Isn't simple repetition a rule? Probably inspired by this idea, students' enthusiasm rose again. "Teacher, I thought of another way to fill in, L, 2, 9, L, 2, 16 ... The reason is that the first two numbers are repeated, and the third number is filled with the square of 2 and the square of 3." , and the time has exceeded 3 minutes.
[Reflection] I applaud the teacher for creating such an atmosphere. Time has passed, and the students' ideas are too simple. The teacher can make a simple evaluation after class, but the teacher doesn't. Instead, he praised and encouraged the student to speak his mind, which triggered many associations among his classmates. This treatment is really great. Maybe the seeds of learning mathematics have been planted in the students' minds, and maybe he has become more confident since then ... As required, we won't discuss how many answers there are to this question. When a student's thinking deviates from the teacher's preset, the teacher should not be busy with his next step, but should first listen to the students' analysis and their ideas, because the students' thinking angle, thinking mode and thinking process are more important than the answer itself. This is the new concept advocated by the new curriculum: everyone learns valuable mathematics, and different people get different development in mathematics, and this different development must be based on sincere, equal and democratic dialogue between teachers and students. As participants, cooperators and promoters of mathematics activities, teachers should really respect students psychologically, listen to children's voices, let children open their hearts and let children speak with their own thoughts and feelings in a relaxed and positive psychological state. In this harmonious and equal "ecological environment", students will mobilize all their knowledge, experience, thinking and inspiration into classroom learning and boldly show their true inner experience. This kind of classroom is varied, beautiful and colorful, and teachers and students will get many unexpected surprises. Therefore, our teachers should change their ideas. Who should our class serve? Regardless of students' enthusiasm and efforts, should we serve the established teaching objectives or serve the students? Waiting for dialogue is obvious for students' smart experience and real feelings.
Strategy 2: Have a unique, smart and intelligent vision to make the generative teaching resources "shine"
[Case] When listening to a teacher's lecture on multiplication application, the teacher asked such a question: a room can accommodate up to 5 people, and a tour group has 6 rooms. How many people are there in this tour group? After thinking, the students listed this formula: 6×5=30 (person), and some students listed 5×6=30 (person). The teacher asked, "What do you think?" The student replied, "How many people does this tour group need?" ? How much are six fives? "The teacher asked the students to sit down satisfactorily. I never doubted the correctness of the answer. When the teacher was preparing the next question, a student raised his hand: "Teacher, is it possible that there are only 29 people in this tour group?" "How is that possible?" The teacher paused, and I quickly considered the possibility of the answer. The clever teacher kicked the ball to the students. "Can you tell me about your idea? ""actually, I didn't think much. I thought, why must the room be full? "The students' words made everyone suddenly enlightened." Then let's discuss it. According to the actual situation in our life, how many possibilities are there? "What a good teaching opportunity, the teacher seized it in time. A stone stirred up a thousand waves, and students' enthusiasm for learning came out, so the following wonderful scenes appeared:
Health 1: I think it may be 26 people, and the formula is 5×5+l=26 (people). The sixth room only holds 1 person. (A student interjects: It's too wasteful. We should pack a single room and make it cheaper. )
Health 2: There may be 27 people, and the formula is 5×5+2=27 (people). There are only two people in the sixth room.
Health 3: It may be 28 people, and the formula is 5×5+3=28 (people). There are three people in the sixth room.
Health 4: It may be 29 people, and the formula is 5×5+4=29 (people). There are four people in the sixth room.
Health 5: I still have a different view. The title says: each room can accommodate up to 5 people. Is it possible that there are 4 people in each room, so it is 4×6=24 (people)?
Health 6: It is also possible that there are 3 people, 2 people or 1 person in each room, so this tour group may be 18 people, 12 people or 6 people.
Health 7: Then if we can't consider the whole situation, there will be many answers.
The ideas of students 5, 6 and 7 deviate from the meaning of the question. The teacher was moved by the high enthusiasm of the students and gave appropriate evaluation and guidance to the students' answers. I breathed a long sigh of relief, happy with the wonderful ideas of the students, and applauded the teacher for winning the prize in time.
[Reflection] When designing teaching, teachers usually try to exhaust all possibilities subjectively after careful consideration, but as Bloom said, people can't predict the full range of results produced by teaching. Faced with these real-time curriculum resources, teachers should seize the hand in time, develop and enlarge these effective teaching resources, and let them shine. On the one hand, they can go beyond the narrow textbook content, give teachers and students a broader thinking space, let teachers and students have more life experiences into classroom learning, and make classroom teaching more colorful; On the other hand, it can greatly stimulate students' enthusiasm to participate in the classroom, make "dead" knowledge come alive, make "quiet" classroom move, change simple "transmission" and "acceptance" into active "discovery" and "construction", and constantly generate teaching resources, teaching contents, teaching procedures and even new teaching objectives in the collision of living bodies. Of course, this requires teachers' teaching wit, teaching sensitivity and deeper teaching philosophy.
Strategy 3: Seize the opportunity of instruction, induction and guidance, and make the generated wrong resources "turn waste into treasure".
[Case] When teaching "8 plus several", a teacher first asked the students to observe the meaning of the picture and drew the formula 8+7=? . Then let the students swing with sticks and discuss how to calculate 8+7=? Students discuss through operation,
Knowing that "adding up to ten" is one of the most effective ways. Then let the students try to calculate 8+6=? (The following is a teaching clip)
Teacher: You know from the discussion that 8+6=? Really?
Health 1: I know 8+6= 14.
Health 2: No, 8+6= 15.
The students burst into laughter, and some pointed at him and said, What a fool! The second student blushes and deeply buries his head)
Teacher: (laughing at Sheng Er) Can you tell me what you think?
Health 2: (whispering shyly) Yesterday we calculated 9+8=? Didn't you say that 9 borrowed 8 1 to make up 10? And then calculate 8+6=? It was the same at that time. If 8 borrows from 6 1, and 6 becomes 5, isn't it equal to 15?
Teacher: You will get in touch with old knowledge and learn new content. It's amazing! (The second student raises his head slightly, and there is light in his eyes. At this time, the students are talking in succession. The teacher wrote the students' ideas on the blackboard and asked everyone to talk about the reasons for the mistakes. He seems to realize his mistake, too. After discussion, everyone found the correct answer. )
Teacher: What do you understand from the calculation just now?
Health 2: I know that 7+ must borrow 3 from another number to become 10, and to calculate 6+ must borrow 4 from another number to become 10. ...
The rapid migration of student 2: impress the whole class. )
[Reflection] Franklin has a famous saying: Garbage is a treasure misplaced. Under the new curriculum concept of all for the development of students, a situation, a problem, a message and a mistake in class are all valuable teaching resources. For these teaching resources, teachers must search quickly and classify them effectively. For effective generative resources, value guidance should be carried out in time, so that students can fully show their thinking process, reveal the "bright spots" in the resources, and activate "reasonable components" according to students' ideas. Teachers don't have to hide or cover up the wrong resources, but let students understand that "making mistakes" is not terrible or shameful, but a normal phenomenon. Teachers should design some links to expose the "blind spots" of students' knowledge, and let students "root out" mistakes through the collective activities of checking, thinking and correcting mistakes by teachers and students, so as to gain new enlightenment. Therefore, our teachers should firmly establish the consciousness of "wrong resources", have a cool head and be resourceful, and have a solid knowledge reserve. You should know that for teachers, "mistakes" are opportunities, challenges, and even a manifestation of their abilities.
Tao Xingzhi put it well: a good teacher does not teach, nor does he teach students, but teaches students to learn.
This is consistent with the "teachers leading students to knowledge" advocated by the new curriculum. In mathematics classroom teaching, curriculum resources from students and teachers are constantly generated. Teachers should cherish and make effective use of them, make the classroom lively and beautiful, and make the students taught comprehensive and individual.