First, create a thinking situation.
Teachers' teaching language plays a guiding, regulating and dominating role in children's perception, thinking and emotional activities. Beautiful teaching language can reproduce the situation expressed in the textbook, stimulate students' interest in learning and activate their thinking ability. In classroom teaching, we should also organically create thinking situations through various means to guide and help students think. Introducing multimedia into mathematics teaching is an important way to create teaching situation. Vivid pictures and vivid audio-visual effects present relevant situations expressed in textbooks to students, which can effectively enrich appearances and activate thinking and emotional activities. Using visual teaching AIDS and providing operating conditions is a necessary means to cultivate students' thinking ability and help them rise from perceptual knowledge to rational knowledge. For example, when teaching the practical problem of finding one number more (less) than the other, let students prepare various graphs such as disks and triangles (each person should prepare at least two graphs), use two different graphs to represent the two actual quantities in the problem respectively, and put them on the table with their hands, so that we can visually see who is more and who is less, and the gap between the two quantities is clear at a glance. And will use "() is greater than () () or () is less than () to express the same meaning, to promote thinking, to lead thinking, and finally sum up" how to find one number more (less) than the other "to understand the quantitative relationship between the two, so that students can experience the formation process of knowledge. This vivid and intuitive method has played a very good role in the sublimation of students' sensibility to rationality.
Second, teach students to think in mathematical language.
Language is a tool of thinking, and thinking is expressed through language. People always use language to think. The development of primary school students' thinking is almost synchronous with their external language, so the training of students' language should run through the training of their thinking ability. The thinking of junior students is in the stage of thinking with sound, and their own voices are often accompanied in their thinking activities. For example, when doing a problem, you should recite it in your mouth and say it while doing it. This is the characteristic of lower grade thinking. If you don't talk, your thinking will not be smooth. If we absolutely demand silence in the classroom, or even forbid students to talk to themselves, students will often be afraid to think. The effective way to attach importance to language training is to encourage students to speak boldly and improve their oral expression ability. Teachers teach by talking, and teachers and students can talk directly to guide students to answer every question. In this way, students not only gain new knowledge, consolidate old knowledge, but also cultivate their language expression ability. For those students who don't like to talk, or dare not speak, we should encourage them to speak enthusiastically. For example, when teaching 14-9, we didn't rush to tell the students the calculation method, but respected the students' existing experience, left them with the opportunity to perform and let them become the masters of learning. I'll throw out a sentence first: "Who can tell the teacher how to calculate 14-9?" "The students have raised their hands to express their views. The students' methods are summarized as follows: 1. Because 9+5= 14, 14-9=5. 2. (Decimal method) If 4 minus 9 is not enough, you need a decimal number to help. Borrow from the tenth 1 is 10, 10-9= 1, 1+4=5. 3. (Continuous subtraction) Minus 9 can be divided into 4 and 5, 14-4= 10, 10-5=5. It is not enough to subtract 9 from 4 in the unit of minuend. Borrow 5,4+5 from the tenth company = 9,9-9 = 0, and then borrow 5, so 10 has 5 left, and the final result is equal to 5. 5. Take 14 as 19, the total is 5 more than the original, and finally subtract 5. 19-9= 10-5 = 5. 6. By counting, according to the chart, cross out 9 from 14, leaving 5. 7. Take the subtraction 9 as 10, 14- 10=4, and 1 is missing, so add 1, 4+ 1=5. 8. Use sequential method. 10, 1 1, 12, 13, 14。 Add 5 to get 14. 9. Divide 14 into 9 and 5, 9-9=0, 0+5=5 and so on. In the process of speaking, fully embodying students' individual thinking is conducive to developing students' potential and cultivating their innovative ability. Sometimes the way students speak will be unexpected, so we should give full play to the advantages of students as a whole. Only when the methods are diversified can students have a choice and choose the method that suits them. At the same time, teachers should optimize methods among many methods and cultivate students' awareness of optimization. Therefore, letting go in mathematics teaching is a good teaching method, which is conducive to cultivating students' self-study ability, and more importantly, training students' oral expression ability. In addition, reasoning in the process of understanding promotes the formation of students' thinking ability.
Third, leave enough time for students to think.
In classroom questioning, children with high intelligence can raise their hands to answer quickly, while other students, especially those with backward intelligence development, may need some time. In order to prevent most children from becoming accompanying students, it is more important to let them participate in thinking activities. In teaching, we should be more patient and willing to leave enough time for students to think. Don't let the teacher's thinking lead the students, and don't let a few students with strong thinking ability "help". As a teacher, we should understand and respect students' individual differences in time, establish a harmonious teacher-student relationship of equality, trust, understanding and mutual respect, and create a democratic classroom teaching environment. For students with difficulties, teachers should give timely care and help, encourage them to take the initiative to participate in mathematics activities, and try to solve problems and express their views in their own way. Teachers should affirm their little progress in time, patiently guide them to analyze the causes of mistakes and encourage them to correct themselves, thus enhancing their interest and confidence in learning mathematics. For example, after teaching "Understanding RMB", I designed a thinking training class for this part. In class, first show "80 cents for a mechanical pencil, how should I pay?" In view of this problem, I put forward three different requirements: ① I will correctly say at least one way to pay 80 cents. (2) Will correctly say at least three ways to pay 80 cents. (3) Be able to use the sequential thinking method to list all possible payment methods and find out the simplest payment method you think. These three different requirements give children more space to express and develop their individuality; One layer is more challenging than the other, which can stimulate students' curiosity and interest, especially the third layer, which contains the ideas listed in mathematics and lays the foundation for elite education in the future. The idea is as follows:
5 jiao
2 jiao
1angle
1
1
1
1
three
four
three
2
2
four
1
six
eight
For another example, when students learn simple application problems of one-step addition and subtraction, they are asked to do the problem on page 76 1 1 in volume 2 of the first volume of grade one. The black cat catches 15 fish, the brown cat catches 20 fish, and the flower cat catches 8 fish. Ask math questions according to the conditions. Different requirements are put forward for students at different levels. For students with quick thinking, they are required to put forward different questions in turn according to certain thinking (using the method of two combination), write them out in turn and answer them correctly. Students at different levels can give full play to their potential and improve and develop on the original basis. The idea is as follows:
How many did the black cat and the brown cat catch? 15+20=35 (article)
2. How many did the black cat and the flower cat catch? 15+8=23 (article)
3. How many did the brown cat and the flower cat catch? 20+8=28 (bar)
4. How many black cats, brown cats and flower cats have you caught? 15+20+8=43 (pieces)
5. How many fewer black cats did you catch than brown cats? 20- 15=5 (pieces)
6. How many brown cats did you catch than black cats? 20- 15=5 (pieces)
7. How many more black cats did you catch than flower cats? 15-8=7 (article)
8. How many fewer flowers do cats catch than black cats? 15-8=7 (article)
9. How many brown cats did you catch than flower cats? 20-8 = 12 (article)
10. How many did the flower cat catch less than the brown cat? 20-8 = 12 (article)
This teaching method takes care of every student in the class and makes every student develop to varying degrees on the original basis.
Fourth, encourage students to ask their own questions.
Einstein said, "It is often more important to ask a question than to solve it." Tao Xingzhi also said: "The invention is thousands, and the question is at a starting point." Mathematics is generated and developed by problems, and the generation and solution of problems cannot be separated from doubts. Without doubt, there is no exploration, no thinking and no innovation. Starting from the lower grades, it is necessary to cultivate students' good habit of asking questions if they don't understand. Teachers should enthusiastically encourage students to ask questions and praise students who don't understand. Only by thinking repeatedly can students find and ask questions. For example, in the teaching of "seeking the practical problem that a number is more (less) than a number", some students think that the word "more" appears in the topic and should be added. In this regard, students should be allowed to express their opinions, and at the same time, students should be required to make clear who is more and who is less on the basis of careful reading of the topic, and to make clear whether they want more or less, so as to compare the similarities and differences with the previous topics that want more, so as to eliminate them. For another example, when students are doing "Exercise 10" on page 100 of Volume II of Grade One, they ask such a question: Teacher, the little girl in the picture says, "My family lives on the left side of her house." The little girl lives on the () floor. Who should be judged? Although "left-right relativity" is not taken as the content of the exam, we should tell the students about this kind of problem in the book. But it can't be overemphasized. Just let students know under what circumstances to consider the relativity of left and right. If the teacher pays special attention to this problem, it is easy for students to make mistakes in simply judging the left and right questions. Therefore, how to grasp the relativity of left and right should be illustrated vividly through some examples. Considering that the relativity of "left and right" is difficult to understand, the textbook only helps students distinguish it through some activities and games (such as shaking hands and listening to irony). ), and there is no practice to judge the left and right relativity without operation. In teaching, appropriate activities should also be organized according to the age characteristics of first-year students. For example, when two students face each other, the teacher gives a password: clap one's left (right) shoulder, clap the opposite classmate's left (right) shoulder ... Students press the password to let them feel the relativity of left and right in the activity. In teaching, students should be inspired to draw, remember and say things they don't understand at any time, so that they want to ask, dare to ask, like to ask and know how to ask, and gradually cultivate students' study habits of careful examination, independent inquiry, positive thinking and active learning.
Fifth, help students develop good thinking habits.
In classroom teaching, students should be taught to listen, see, think and remember, so that their eyes, ears, mouth, hands and brain can be used together to achieve the best learning effect. Keep your eyes on the teacher in class, follow the teacher's thinking, think positively about the question, and bravely raise your hand to answer the question. Students' thinking should follow the teacher's thinking to reach the realm of understanding, and students can understand every word and every action of the teacher. When learning to think, students must think in an orderly and well-founded way, and extend and develop what they have said, which will have the effect of drawing inferences from others. For example, in the teaching of "Circular Arrangement Law" in the second volume of Grade Two, students can understand the periodicity of circular arrangement law in the dynamic picture through the vivid demonstration of multimedia courseware. The arrangement law of lines 5, 6, 7 and 8 is exactly the same as that of lines 1, 2, 3 and 4. The teacher then asked, "If we continue to queue up, how should we queue up?" Courseware transforms static thinking into dynamic demonstration through students' thinking, and the whole graph is unfolded up and down, left and right, which reflects the arrangement law of four lines in a cycle. In the exercise, three fruits appear as a group, and then students are asked to tell how each group is arranged according to the characteristics of circular arrangement. Students understand the three-fruit rule in the process of applying the law to do problems, that is, there are three groups in a cycle and three groups appear repeatedly in a cycle. After class, a classmate asked me: teacher, is it a group of five numbers, that is, five elements and five elements appear in a cycle? A group of 9 graphics, that is, 9 rows and 9 columns appear cyclically? Inspired by these students, other students also realized the connotation of knowledge. Finally, it is concluded that when several figures appear as a group, several lines will appear, that is, several lines are a cycle. Only through meditation can students sort out the context of knowledge, truly master knowledge and internalize their own understanding. Only in this way can classroom teaching be effective and students' thinking ability can be really cultivated, and students' sustainable development should be considered in the classroom.
If you learn a little mathematics, you can only manage it for a while, and if you learn the way of thinking, you can manage it for a lifetime. Scientific thinking is the golden key for students to explore and acquire new knowledge, analyze and solve new problems. Every teacher, especially a math teacher, should help students master thinking methods, improve their thinking ability, form good thinking habits and let students master this golden key.