Primary school students are at the most active age, so six years of primary school is the basic stage to lay a good foundation for students' innovative thinking. Therefore, mathematics teachers should make full use of various effective teaching means and methods in the teaching process to cultivate the creative thinking ability of primary school students. Based on years of teaching practice, I have some superficial ideas on how to cultivate the innovative thinking ability of primary school students:
First, setting doubts to stimulate interest and broaden the time and space of thinking
The ancients had the admonition that "thinking is useless and doing is dangerous" and the teaching that "learning without thinking is useless and thinking without learning is dangerous". Without necessary deliberation, it will not promote the instantaneous leap of thinking from quantitative change to qualitative change, and generate will spark innovation. There is no doubt that the key to all science is a question mark, and the wisdom of life probably lies in asking why everything happens.
In teaching practice, teachers should create sufficient time and space for students to think. They should not only relax, but also follow the periodic ups and downs of primary school students' physiology and psychology. They should also "pay attention to looking around and consciously or unconsciously connect other activities or things they come into contact with with their own thinking problems." In this way, when you meet the right stimulus, it will trigger inspiration. "Therefore, teachers should flexibly arrange the suspense of questions, strive to create problem situations, and stimulate students to think positively. In particular, we should be down-to-earth, make full use of the space and time of classroom teaching, grasp the content characteristics of textbooks, and explore ways to cultivate innovative thinking.
Take the teaching of "10" as an example. I prepared a box in advance, which contains 10 pencils. As soon as the class started, I asked a student to touch the pencils on the stage, and then the teacher guessed how many pencils were left in the box according to the number of pencils touched by the students. After several guesses, the students are all curious. Then the teacher struck the iron while it was hot and said, "Because the teacher knows there are 65,438+00 pencils in the box, and then he can guess by dividing it by 65,438+00. Do you want to learn this skill? " The magical power of mathematical knowledge arouses students' strong interest in knowledge, which makes them participate in learning with interest and think positively.
Another example: At the beginning of the teaching of the third volume of primary school mathematics, Possibility, I asked a boy representative and a girl representative to touch the ball on the stage. The rule of the game is to touch the ball blindfolded five times, and the person who touches the red ball more times wins. As a result, the girl representative is always a red ball. At this time, the boys were angry, blamed and resisted, saying that the teacher had a "conspiracy". The creation of this situation stimulates students' interest, creates suspense among knowledge, and guides students to try to change the fixed and traditional way of thinking and broaden the thinking time and space of mathematical thinking.
Second, make bold guesses and cultivate the heart of seeking differences.
The heart is an intuition and a very flexible and complicated psychological activity phenomenon. On the basis of original knowledge, it can judge the essence of things by leaps and bounds through psychological activities such as memory, imagination and guess, and is the soul of creative thinking. Newton thought that "there would be no great discovery without bold speculation." In cultivating students' intuitive thinking, we should encourage students to guess boldly, dare to innovate, break through the mindset, get rid of the shackles of convention, and allow students to have whimsy, even whimsy. Don't be too strict and comprehensive in answering students' questions, let them say what they have found and how much they want to say, and say what they understand or guess, not necessarily why; Teachers should guide students' unique opinions or strange ideas according to the situation, lead them to the track of thinking and let them come up with some doorways.
For example, when teaching "Numbers divisible by 3", I ask students to guess first: What are the characteristics of "Numbers divisible by 3"? Some students may be influenced by the feature that numbers can be divisible by 2 and 5, and they are all guessing that the feature is "numbers with three digits: 3, 6 and 9". The teacher conveniently showed a group of numbers 3, 6, 9, such as 13, 16, 19, 23, 26, 29 ... As a result, the students found that these numbers could not be divisible by 3, and their thinking was in a state of confusion because of the failure of guessing, which triggered their psychological tendency to puzzle. The teacher took the opportunity to list another set of numbers, such as 12, 15, 18, 2 1, 24, 27 ... The students found that these numbers were divisible by 3. In this way, through a series of conjectures and puzzles, students' cognitive imbalance is caused, and students' desire to continue to explore is stimulated: why can the latter group of numbers be divisible by 3? Curious about this question, the students guessed and explored, and finally found that the original number divisible by 3 is characterized by: the sum of the numbers of each digit of a number can be divisible by 3, and this number can be divisible by 3.
The basic procedures of this exploration method are: asking questions, students guessing, exploring laws and verifying conclusions. It is to let students dare to guess boldly about mathematical problems first, and then find the law through exploration. The knowledge obtained in this way is effective for students, not only a kind of knowledge, but also the training of mathematical thinking ability.
Therefore, when learning mathematics, teachers should encourage every student to have a little sense of daring to guess and do more "guessing" activities. Conjecture is not bound by ready-made facts, it contains valuable elements of bold imagination and speculation. Teachers should dare to expose students' thinking process and guide students to think along reasonable problem-solving ideas through the creation of problem scenarios such as "trying" and "guessing".
Of course, in guessing, students should be reminded to observe carefully, analyze the known, find the law, and so on; Or remind students to use the results, guess and summarize. In a word, guessing exercises students' ability to discover laws and solve problems by using them, which can make students' active thinking stimulate the spark of innovation in the process of generation and collision.
Third, develop ideas and induce divergent thinking.
Professor Xu Lizhi once pointed out: Creativity = knowledge × divergent thinking ability. Divergence of thinking is manifested in the process of thinking, that is, thinking is not bound by a certain problem-solving model, and exploring * * * from the personality of the problem is an uncertain thinking form, seeking variation, speculation, extension and exploration from multiple angles and levels. Divergent thinking is changeable and open, which is the core of creative thinking. In teaching, we can use various exercises to train:
Fill in the blanks with different answers.
Teachers should be good at changing the limitation of teaching materials and teaching plans, adapting the unique fill-in-the-blank form into the form of empty filling, and cultivating students' divergent thinking. For example, after teaching carry addition in 20 minutes, in order to let students calculate carry addition more skillfully, arrange a group of blanks and let them fill in the blanks as much as possible, so that the equation is established: 8+5 = □ +□, □+3 = 6 +□, □ +□ = 6+5, 9 +□ = □+7.
(B) Multi-directional answer questions
It is the key to multi-directional thinking to make a multi-angle and all-round investigation of known conditions. As long as students are good at guiding them to connect the knowledge and methods they have learned in the past or from life, accurately dig deep into the known conditions in the problem, and make efforts to explore, then students will be unique in finding and solving problems.
For example, when I was teaching Statistics, the fourth volume of primary school mathematics, I arranged for students to do some exercises: first, I showed some cups, and the teacher asked, "What do you want to classify and count according to?"
Student 1: Some cups have handles, while others have no handles.
Teacher: Yes, it can be divided into cups with handles and cups without handles.
Student 2: Some cups are 2 yuan, some cups are 3 yuan and some cups are 4 yuan.
Teacher: Yes, statistics can be classified by price.
Student 3: Some cups are colored, others are not.
Yes, it can be divided into colored cups and colorless cups.
Student 4: Some cups are high, others are low.
Teacher: Yes, it can also be classified according to height. ……
We can see that because each student's observation and thinking about things have their own personality characteristics, if they are limited to their own personal thinking, they can only realize the extremely limited statistical standards of things. However, under the teacher's intentional guidance, the students answered one after another, so that different sparks of wisdom flashed in the classroom, and each student was enjoying the crystallization of collective wisdom, which opened the door to thinking.
(C) the problem design autonomy
This way means that the exercises only give known conditions, and what to solve and how to solve them need to be set by the students themselves. The purpose of training is to let students design problems in various directions and solve them in corresponding ways. For example, "9 yellow flowers and 3 red flowers are known", and the teacher asks "What questions can I ask?" Students put forward many questions about the relationship between sum, difference and multiple. This kind of training can give every student a chance to discover his own mathematical wisdom and stimulate the initiative of innovative thinking.
(D) Different ideas to solve the problem
In mathematics teaching, cultivating students' innovative thinking ability is the most practical and effective method, and it is also a good way to cultivate students' divergent thinking. Teachers should pay attention to guiding students to explore and develop its "potential value" after solving a problem. They are not satisfied with the conclusion, do not stick to the routine, and are not bound by a fixed model. Instead, they should find the best solution through targeted, mathematics-based positive thinking, bold imagination and reasonable analysis, and exercise students' agile problem-solving ability. Specifically, we can achieve the effect of drawing inferences from others and achieving mastery through vertical and horizontal divergence, knowledge series and comprehensive exchange.
1. Cultivate divergent thinking in solving application problems.
Diversification of methods to solve practical problems is mainly conducive to cultivating students' profundity of thinking. For specific problems, students may find different methods, think and analyze from another angle, and may have unexpected gains.
For example, the fourth volume of primary school mathematics has such an application question: "35 people get on a bus, 9 people get off, 12 people get on." How many people are there in the car now? " Most students have the formula: 35-9+ 12=38 (person), which is undoubtedly correct. However, I was not satisfied and continued to ask, "Do you have any different ideas?" At this moment, a child raised his little hand: "I made this: 12-9=3 (person), 35+3=38 (person)." Many children were dumbfounded and said, "Isn't it?" . In addition, several children made different voices: "Yes". I asked the child to explain the reason, and he said, "12-9=3 (people) calculated that there were more people coming up than going down, and the number of people coming up plus the original number is now." What a refined answer!
The above two methods have their own characteristics and are full of fun. I seem to see students' thinking galloping freely in the field of mathematics.
2. Cultivate divergent thinking in solving computational problems.
In mathematics problem-solving learning, students' main task is not to solve problems, but to learn to solve them. Therefore, the focus of teachers' teaching and students' learning is not "solving", but "learning to solve". Therefore, teachers should try their best to let students do math problem-solving activities independently without providing ready-made conclusions, which requires us to preset not only the process and methods of solving problems, but also the process and methods of teaching, advocate the multi-directional interaction between students and groups, and let students exchange information about solving problems constantly. In this process, teachers and students share the experience and knowledge of solving problems with each other, and exchange the feelings and experiences of solving problems, which really provides the possibility for promoting the thinking innovation of solving problems. This concept should be carried out even in the problem-solving training of calculation problems.
For example, the pen-based addition in the fourth volume of primary school mathematics is based on the study of oral addition. I gave an example (352+234=? Then let the students try to practice by themselves, and then patrol. Unexpectedly, after thinking, exploring and communicating, the solutions provided by the students will be so colorful, so I quickly let them perform on stage.
This third method surprised me, especially when students have such an unexpected sense of numbers. This also proves that the practice of various problem-solving methods in calculation is also very beneficial to induce students' creative thinking and divergent thinking.
Fourth, use analogy to train flexible thinking.
Analogy is a way of thinking that another thing may have certain attributes according to the same or different attributes between two objects or things. Finding problems and exploring ways to solve them is a common mathematical way of thinking and the essence of creative thinking. Using analogical thinking can help students deepen their understanding of basic knowledge, draw inferences from others, learn from others and discover new mathematical knowledge; It can cultivate students' divergent thinking, creative thinking and rational reasoning ability, that is, when encountering new problems, they associate with familiar old knowledge from the appearance of formal structure, deepen their perceptual knowledge to their internal relations, compare the old with the new, compare new knowledge and discover new theories.
For example, there is a topic in the sixth grade: "A and B are 240 kilometers apart. It takes 4 hours for the express train to go from place A to place B, and 6 hours for the local train to go from place B to place A. Both trains leave from two places at the same time, in opposite directions. How many hours did you meet? " The teacher asked the students to answer and say what they thought.
Born in 1: 240 ÷ (240 ÷ 4+240 ÷ 6), first find the speed sum of A and B, and the distance divided by speed equals time.
At this time, the teacher asked, "Is there any other solution?" A student who usually doesn't like to talk raised his hand. He said, "I think the distance between the two places can be expressed as1÷ (1÷ 4+1÷ 6)".
Obviously, this classmate uses the analogy thinking mode. In the process of solving problems, he started from the problems to be solved and was inspired by "the characteristics of questions". He thinks that he has done a similar problem, that is, an engineering problem, and uses this similar problem as an intermediary to think of some problem-solving methods and skills, and then analyzes and uses the familiar solution to think about the problem to be solved. This spark of creative thinking can infect every student in the class.
5. Practice is the training ground for creative thinking.
(1) Make full use of games to stimulate innovative thinking in practice.
Dr. Yang Zhenning once made such a comparison. The academic performance of China students is much better than that of American students who study together. However, ten years later, the scientific research results are much less than others. Why? In fact, it lies in American students' active thinking, strong hands-on ability and strong innovation ability. In view of the lack of participatory activities in primary school students' daily study, the new textbook has designed a large number of games and competitions with thinking value for students (such as password, guessing, frog crossing the river, etc.). ) I attach great importance to these forms of topics, and always give students more free time in class, so that students can carry out more creative activities, so that every student can actively participate in the classroom, use their brains and broaden their thinking.
For example, the practical course of carry addition is taught. The main purpose of this course is to make students master the oral calculation of carry addition within 20. So I used three games throughout the class. The first is the individual competition. The design of this game is mainly to cultivate the agility of students' thinking. Then there is the team competition. In groups of four, use three numbers to form four formulas. Compare which group thinks the most formulas. This kind of game not only makes students have a deep understanding of the relationship between the whole and the part, but also cultivates students' thinking integrity and sense of cooperation and competition. Finally, the game of "eating fish" set off the whole classroom atmosphere, and the students were eager to try and their learning mood was high. The game is like this: everyone has a fish, and each fish has a problem. As long as you can read out the question, you can have the fish. Students should not only speak their own problems correctly, but also judge other students' problems, which greatly improves the intensity of practice. The game is played in the form of "driving a train", which improves the timeliness of practice. Although students are not allowed to write in this practice class, its practice intensity and efficiency are obvious, and students' thinking is extremely active in the practice class.
In this way, colorful and creative activities and exercises can not only achieve unexpected results, but also make every student experience the happiness brought by learning.
(B) capture the material of life, innovative thinking in practice.
Any knowledge comes from life and is formed in practice, which guides practice and promotes the development of science and technology. Learning to master it, if divorced from practice, will become passive water. Fuller said: "Theory is a treasure house, and practice is its golden key." We should try our best to guide students, through reading, practice, observation, experiment, discussion and other forms, so that students can use their brains to practice, acquire knowledge, master skills and understand the essence of theory with personal participation. Organize students to discuss with each other, give full play to the advantages of students' individual differences in thinking, make their mutual thinking "add fuel to the fire", and form a multi-dimensional and three-dimensional thinking information network. Teachers can guide them at any time to make their thinking jump.
For example, the first-grade children have just been exposed to subtraction, and the school has just organized an autumn outing. On the way to visit, I deliberately asked, "Wang Shen, how many oranges did you bring?" "Five." "How many did you eat?" "Two." "How many are left?" "Three." "Can I use an expression?" "5-2=3", other children also scrambled to shout.
On the way home, I asked my child, "Did you have a good time today?"
Health: "Happy."
Teacher: "What event are you playing?"
Health: "archery, balloon shooting, picnics, mountain climbing ..."
Teacher: "Did you find any math problems during your autumn outing today?"
Think about it.
Health 1: "My uncle gave me five arrows, and I shot them one by one, and then I shot them all."
Teacher: "Can you express it with an expression?"
Health1:"5-5 = 0."
Teacher: "Great."
Health 2: "Mom gave me money from 4 yuan, and I used up 2 yuan, leaving 2 yuan, 4-2=2."
Health 3: "I brought two loaves of bread, and I ate both. 2-2=0".
Health 4: "There are 10 balloons on the wall. I broke one balloon, and there are 9 left. 10- 1=9".
……
In this problem-solving situation, students are more willing to exchange and express their ideas, because they have been trained and consolidated in mathematics knowledge from their lives. Generation shows the spark of students' thinking, and innovative thinking is improved in practice.
For another example, when I was teaching the course of knowing Jiao Yuan powder, I created a simulated scene of buying and selling goods in a store in the classroom, and then extended it to family life, and arranged a special homework for students to go to the market to buy food or go shopping in a shopping mall with their mothers on Sunday, and try to help their mothers pay and settle accounts. After returning to school, they exchanged information about shopping, payment and settlement with each other and talked about what they knew. Summarize the students' communication.
For example, a classmate said his shopping experience: "I spent one yuan to buy two pencils and an eraser, 20 points for pencils, 4 points for * * *, and 50 points for erasers, and got back a dime."
It is difficult to achieve this effect only by explaining and practicing in class, and students are distracted in their personal practice.
Steve, an American educator, once said: "The art of teaching lies not in the ability to impart, but in inspiring, awakening and encouraging." Therefore, the essence of teaching is to stimulate students' self-conscious interest in learning and let them participate in learning personally. Only by participating in practice, experiencing life more, accumulating the first experience of life, and storing the perceptual materials of intuitive thinking can we sublimate into rational knowledge of abstract thinking, produce extensive thinking associations, and then conduct induction, analogy, guess, discover new things and construct new theories.
In short, although mathematics has strict logic, it is only for the deduction and demonstration of the theoretical form. The study and mastery of theory, the formation of problem-solving ideas or the application of mathematical knowledge, especially the development and perfection of mathematical knowledge, and the invention and construction of new theories are inseparable from flexible and free creative thinking, which promotes human progress and creates human civilization, and is a great wealth for human development and progress. Every educator must attach importance to the cultivation of students' innovative thinking ability, and provide students with the maximum open and selective space for thinking, exploration and innovation, so as to guide students to find problems, carry out creative learning and cultivate innovative thinking, and lay the foundation for becoming talents needed to adapt to the development of science and technology in 2 1 century.