On the cultivation of children's mathematical thinking 1 1. The content of the activity comes from children's life.
For a long time, children's mathematics has been confined to a specific teaching environment because of its rigorous structure and strong logic. Indeed, according to its subject characteristics, children's mathematics must be carried out in an orderly manner, but only by combining this order with children's life scenes can its educational value be more widely reflected. When mathematics returns to children's life scenes, it can stimulate children's greater interest and desire in learning and give them opportunities to practice and apply mathematical thinking. The goal of the new syllabus in the field of mathematics is to "feel the quantitative relationship of things from life and games and realize the importance and interest of mathematics". It can be seen that the value orientation of mathematics education in the new curriculum no longer pays too much attention to the transmission of static knowledge, but pays attention to feeling and experiencing the practical significance of mathematics from life, and tries to find and answer vivid practical problems by using mathematical viewpoints and methods.
In this teaching activity, we aim to make children feel the rules in life, so as to be interested in regular activities. Therefore, we have chosen many contents close to children's lives as the teaching materials for this class, such as children's clothes, children's familiar kindergarten environment, mother's necklace and so on. We introduce the observation of children's clothing, so that children can enter the teacher's preset link in a relaxed and natural atmosphere. In this link, children can not only initially perceive the meaning of laws, but also stimulate their interest in discovering more laws of things. With this preparation, children will naturally look for rules in these things when the teacher presents courseware made by kindergarten scenes that children are familiar with. In this link, teachers guide children to further perceive and understand the concept of law, and review and consolidate several laws to pave the way for the next link.
The courseware ends with a mother's regular necklace, which aims to play a transitional role in the later link-"making a necklace". Necklace comes from life, and because of its unique aesthetic feeling, it is very concerned by children, but it is also a familiar and attractive life activity for children. These elements are based on life and make the whole educational activities closer to children.
Second, the operating materials are based on children's lives.
Homework materials are the material premise and necessary condition for children to learn mathematics knowledge. Whether the materials provided by teachers are appropriate or not is directly related to children's interest in operation, the effect of exploring operation and the realization of educational goals. The more operating materials, the better; The newer the better. The operating materials we provide in this activity are all from children's daily necessities and toys, such as ropes, wooden beads, snowflakes, straws and so on. It not only avoids the distraction of new materials to children, but also increases children's interest in operation from another level, making them feel novel. So these things can also escape from the necklace.
Thirdly, the activity method pays attention to children's experience and learning characteristics.
"Outline" clearly states: "Provide rich operational materials to provide conditions for every child to explore in various senses and ways". Psychological research also shows that children's mathematics learning activities must take concrete operation activities as the carrier. This is determined by the specific image thinking of preschool children. We hope that children can recognize mathematical knowledge and construct mathematical thinking in the process of concrete hands-on operation, so that children can gradually construct, integrate and correct their own mathematical concepts and skills through interaction with the physical world, teaching AIDS, peers and teachers.
In the process of jumping the necklace, we let the children jump with a rule. This design can not only understand the existing development level of each child, but also lead to the key content of this lesson, that is, learning in the form of AABC and other sorting. In the process of displaying and classifying children's necklaces, every child has a process of upgrading at the original level through the exchange of information between peers and the combing of teachers' appropriate knowledge. In the process of discussing the rules of companion necklaces, children not only confirmed the correctness of their own sorting methods, but also learned more sorting methods. In this way, in the process of interaction with materials and peers, children gradually establish their own new knowledge and understanding of the mathematical concept of law.
Fourth, the activity process pays attention to the transmission of children's experience.
Dewey once said: "Education should be life itself, not preparation for life." Kindergarten mathematics education is not for pure education, but the noumenon of children's life, which is characterized by children's life, which requires us to base ourselves on reality and closely link with children's life to carry out education. In order to make children more aware that the knowledge of regular sorting can be widely used in our daily life, the last link is designed to let children take themselves as objects to embody the rules. The child's first thought may be to line up according to the interval between boys and girls, which is completely derived from the child's daily life experience. In this process, it may not have played a role in consolidating the previous knowledge, because it is the order of the two elements, but it has played a very good role in linking children's knowledge with practical application. In the next link, we guide children to express rules by moving movements, because in the process of learning rhythm and dance steps, we adults will help us remember by looking for rules, while children are weak in this respect. We hope to help them establish a certain thinking connection through this link. Children can use their hands, feet and head; The combination of patting, stepping and shaking shows the law, which has both experience and challenges for them, and their knowledge and experience have been well transferred.
Five, the educational goal should pay attention to children's lifelong development.
In children's mathematics teaching, we should not only pay attention to the rigor of mathematics, but also pay attention to the internal logic of mathematics, so that children can form mathematical thinking mode in the process of thinking, reasoning, explanation and adjustment. We believe that in children's mathematical activities, the process of solving problems is as important as their answers. In the process of letting children acquire knowledge, adults should pay attention to inspiring children's thinking potential, that is, giving children a potential for mathematics learning, giving them a key to open the door of mathematics knowledge, and laying a foundation for children to acquire new mathematics knowledge and solve new mathematics problems faster and better in their later studies.
In this activity, because the children in the big class have rich sorting knowledge and experience, it is easier for them to understand and master many sorting methods, so we have positioned the starting point for children to learn new rules through their own exploration and discovery. During the whole activity, the teacher did not explicitly give the children any learning mode, but kept asking questions to the children during the game, operation, discussion and communication, such as: What are the rules in these scenes? What is the law? Please think about the rules of wearing a necklace yourself. How can we design regular movements? In the process of comprehensively and creatively using their existing sorting knowledge and methods to solve these problems that are not simple exercises, children gradually form a mathematical way of thinking. In this process, children do not passively accept a mathematical conclusion or result and remember a ranking model, but build their own understanding of the law through active exploration and active learning.
In a word, we should walk into children's life, choose mathematics activities that children are really interested in according to their actual situation and age characteristics, and at the same time pay attention to expanding children's experience and vision, as well as cultivating children's practical application ability. This kind of mathematics education is really beneficial to children's lifelong development.
On the Cultivation of Children's Mathematical Thinking 2 Abstract;
Mathematics is a creative and applied subject. This paper discusses how to cultivate children's creative thinking ability in children's mathematics activities from the aspects of renewing mathematics teaching concept, cultivating learning interest, cultivating the ability to find problems, cultivating the quality of creative thinking and optimizing teaching process.
Key words:
Mathematics teaching; Creative thinking; cultivate
16 years old, the French mathematician Vincent Lafarge took part in the 3 1 International Mathematical Olympiad for Children and won the gold medal in Beijing. Five people from our national team also won the gold medal. 10 years later, Vincent Lafarge became a world-renowned mathematician, and how many China children who won the gold medal with him at that time became internationally renowned mathematicians? This is an embarrassing question, but it should arouse our educators' reflection.
2 1 century needs pioneering and creative talents, and an important aspect of the cultivation of creative talents is the cultivation of children's creative thinking. Creative thinking is the core of creativity and the basis for people to complete creative activities. As we all know, education can promote the development of children's creativity, and mathematics is a subject with strong creativity and application. Mathematics education can not only develop children's logical thinking, but also cultivate their creative thinking. In recent years, I have carried out various creative activities in the field of mathematics in large classes, trying to develop the flexibility, flexibility and uniqueness of children's thinking, cultivate their enthusiasm for exploration and discovery, and thus develop their creative potential.
To this end, I have infiltrated the spirit and practice of creative education into various existing mathematics education methods, and explored teaching methods to promote the development of creativity in practice.
One. Teachers must renew their concepts of mathematics teaching.
Children's mathematical activities are actually a kind of preparatory learning, which is a gradual process in which children initially establish the concept of numbers and form logical thinking. Experiments show that in early childhood, especially at the age of 4. 5 "Six years old is a critical period for children's cognitive development. It is during this period that children established and formed the concept of number, and they sprouted their interest and enthusiasm in solving problems. At this time, their mathematical thinking is extremely active. We should correctly grasp this critical period and provide mathematics education suitable for its learning characteristics.
Children's mathematics learning ability is manifested in their enthusiasm and enthusiasm for mathematics learning, creativity in mathematics activities, mathematical thinking ability and problem-solving ability, the core of which is creativity in mathematics activities. Maybe some people will say that mathematics needs to be created. Three plus two equals five. Can you create anything else? Yes, this result is equal to 5, but 3 plus 2 equals 5. Problem situations provide conditions for children's creative activities. Faced with different problem scenarios, children should not only recall and mobilize the original knowledge and experience, but also analyze, judge and compare the current specific situation, and flexibly use different ways of thinking and operation. Children's creativity and enthusiasm in mathematics learning are gradually improved in the process of solving various problems. Therefore, we should change the traditional mathematics education: pay more attention to logical thinking ability, calculation, creation and application, and cultivate people's ideas and tendencies. In mathematics teaching activities, it is established that the learning of basic knowledge will not be lost or weakened; Children should not only understand the basic knowledge, but also learn the concept of problem-solving ability and attach importance to the creative cultivation in mathematics teaching activities. Only in this way can we effectively cultivate children's problem-solving ability and innovative ability, continuously improve the teaching quality, and make efforts to cultivate more innovative talents in mathematics instead of mathematics craftsmen in China.
Second, children's interest in mathematics is the key to cultivating creative thinking ability.
Wu Shen, an educator, said: "Compulsory learning without the slightest interest will stifle children's desire to seek truth." Interest is an important driving force for learning, and interest is also an important driving force for creative thinking ability.
First of all, teachers should ask questions properly in mathematics teaching, so that children can feel that they can pick peaches in one jump. The difficulty of the question should be moderate, which can stimulate children's cognitive contradictions, cause cognitive conflicts and arouse strong interest and curiosity. When children are interested, they will think positively, ask new questions and solve them consciously, thus cultivating the ability of innovative thinking.
Secondly, children in early childhood can be said to be curious and good at smelling and exploring. They are full of energy, full of energy, and tirelessly explore the world around them. They want to know everything, and their problems are endless. Children are born with the instinct of investigation and exploration, and exploration is the instinctive impulse of children. Curiosity, thirst for knowledge and spirit of exploration are the innate characteristics of children. However, if they fail repeatedly in the process of learning mathematics activities, they will lose confidence in learning. It is necessary for teachers to create suitable opportunities in the teaching process, so that children can feel the joy of success, thus cultivating children's creative thinking ability. Organize some activities that are conducive to cultivating creative thinking, such as geometric design competitions, logical reasoning story speeches, life math games, etc. Let them fully display themselves in activities, find the combination of life and mathematics, experience the opportunities and happiness brought by mathematics to children, and thus cultivate their creative thinking ability.
In addition, make full use of the beauty of graphics in mathematics, try to link beautiful graphics in real life to classroom teaching, and then apply graphics to artistic creation and living space design, which will produce the sound of * * *, make them have the desire to create the beauty of graphics, and drive them to think positively and be brave in creation, thus improving their creative thinking ability.
Third, cultivate children's ability to find problems.
Creative thinking begins with finding problems. Creative thinking itself is a process of discovering problems, clarifying problems, putting forward hypotheses and verifying hypotheses. Finding and asking questions is the premise of solving problems, as Einstein said: "Asking a question is often more important than solving a problem, because solving a problem may be just a mathematical or experimental skill, and asking new questions and new possibilities to look at old problems from a new perspective requires creative imagination and marks the real progress of science." For children, the process of exploration is far more important than getting results quickly, because the process of children solving problems and understanding the relationship between numbers in their own way is an important means to promote the development of children's creative thinking ability in mathematics, and it is also the performance of children's thinking ability, creativity and playfulness.
It is children's nature to cultivate their ability to find problems, encourage them to dare to question, and be good at questioning curiosity. With the growth of age and knowledge, curiosity will gradually become indifferent. The indifference of curiosity is an important reason for the dilution of the problem. Einstein criticized the compulsory perfusion teaching method when he recalled his childhood. No matter how good the food is, it will spoil your appetite and stomach one day. The spark of pure curiosity will gradually die out. "The reason why we should fully carry forward democracy in teaching, create a relaxed and harmonious environment for children, care for and stimulate children's curiosity, and encourage children to dare to question and be good at asking questions, thus enhancing children's problem awareness.
In the process of finding problems, there is no doubt that there is no problem at all. The creativity of thinking is mainly manifested in seeing differences in similarities, seeing strangeness in differences and seeing strangeness in mediocrity, and being able to see problems from places that are difficult for ordinary people to perceive. If finding problems is the beginning of solving problems, then doubt is the starting point of finding problems. Therefore, to cultivate children's creative thinking ability, we must actively encourage children to dare to question and cultivate their ability to find and ask questions.
Fourthly, cultivate the quality of children's creative thinking.
Every child has different ways to solve problems. Whether these methods are effective or not, they embody the way of children's intellectual activities. However, in the teaching process, many teachers only ask children to remember and absorb knowledge according to the guidance of teachers and books, so from primary school to middle school, children's learning depends almost entirely on teachers. Children have neither the pressure of creative thinking nor the corresponding training. Therefore, we should cultivate the quality of children's creative thinking. First of all, we must cultivate the quality of children's independent thinking. To cultivate children's independent thinking quality, we should strengthen their psychological consciousness in three aspects in the teaching process: (1) being bold and reasonable in doubt; (2) increase the pressure-resistant psychology of not blindly following the majority; (3) Cultivate their psychology of constantly denying themselves. Secondly, we should cultivate the quality of children's divergent thinking. Cultivating children's divergent thinking quality is to cultivate children's thinking speed, so that they can express more concepts and list more ways to solve problems in a short time; Flexibly consider the quality of the problem from different angles; The spirit of boldly breaking through convention and daring to innovate. That is, we should gradually cultivate children's fluency, flexibility and novelty. In addition, we should pay attention to the cultivation of children's imagination. Creative thinking generally uses existing knowledge and experience to produce things that didn't exist before through conscious imagination, so imagination is the starting point and necessary process of creative psychology. In fact, cultivating children's imagination is an important link to improve their creative psychological quality. As the philosopher Kant said, "Imagination is a powerful creative force, which can create the second nature from the materials provided by the actual nature." Therefore, the cultivation of imagination should include the following two aspects: (1) maintaining and developing curiosity; (2) Broaden knowledge.
Fifth, attach importance to children's mathematics learning in daily life and cultivate children's mathematical creative thinking ability.
"Outline" points out: "Science education should be closely linked with children's real life". In the teaching process, we reproduce the life situation in a simulated way, and integrate mathematics knowledge into it, so that children can learn mathematics in the imaginary life situation and feel more relaxed, natural and real. Mathematics comes from life, and numbers, shapes and quantities are everywhere. Mathematics in life is vivid, concrete and close to children, which is very suitable for children's learning characteristics. Therefore, the main source for children to learn mathematics is in life. In the "countdown to learning order" activity in the middle class, we let the children feel the changing law of stairs from low to high and from high to low through the operation of "taking stairs"; Through the plot of "a little mouse goes up the stairs in the rice", let the children move their mouths during operation and play, so that the number of hands and mouths is consistent with the countdown; Through the association of "traffic lights" and "countdown" in life, we can intuitively perceive and discover the sequence law of countdown and countdown. Another example is the theme activity of "Beautiful Autumn". We design the plot of "going to the park by bus" with "autumn tour" as the main line, guide children to learn to look at the "road map", compare the length of line segments and the number of overlapping results, and find out the most suitable route recently. Because the activity content comes from life, the activity plot is rich and interesting, which arouses children's great interest in participating in the activity and satisfies children's desire for self-exploration. Children perceive and discover various quantities and spatial forms of the world around them in a large number of life activities. This experience accumulation process is of great benefit to children's understanding of various simple quantitative relations and spatial forms. On the basis of a lot of activity experience, children think and improve the simple laws of things and phenomena in order to develop their thinking level.
Sixth, through the optimization of teaching process, create favorable conditions for stimulating children's positive thinking.
All the conditions, environment, means and management in the process of mathematics teaching are directly related to the cultivation and development of children's creative thinking ability. Therefore, our whole teaching process should conform to the law of children's thinking, improve the situation and be enlightening, so that children's thinking is in a positive state. To optimize the teaching process, we should start from the following aspects:
(A) improve mathematics teaching methods
Teaching method is an important factor to achieve teaching objectives, implement talent training mode and improve the quality of education and teaching. Traditional education methods obviously cannot cultivate children's innovative thinking and ability. Only through advanced teaching methods such as discovery, heuristic and discussion can children's initiative and consciousness be mobilized. Stimulate children's imagination and thinking ability, and guide children to explore problems bravely and boldly by means of inspiration, guidance and active participation. To cultivate children's courage and ability to discover, analyze and solve problems, we should proceed from the reality of kindergartens, choose one or several optimal teaching methods in mathematics teaching according to different contents, different teaching objectives and children's personality differences, and use them comprehensively and flexibly. For example, when teaching children to measure or compare the above three, measure the height of a bottle and a cup with a pen. From the fact that the cup is shorter than the pen and the bottle is higher than the pen, we can know that the bottle is higher than the cup, and so on, giving children time and space to think for themselves and cultivating their creative thinking ability. While carrying forward our excellent traditional culture, we should absorb and learn from the advantages of foreign teaching methods and learn from each other's strengths.
(B) to create a good learning environment for mathematics
Provide a happy, harmonious, free and relaxed learning environment for children through practical operation and experience. For example, in the activity of teaching "juice bar", a juice shop was set up in the math corner before class. The shop is filled with several empty fruit juice bottles, boiled water and honey or orange juice, 10 paper cups of the same size, colored pens and so on. The teacher is the owner of the juice shop. Choose another corner of the classroom to arrange juice, and let the children take turns to be bosses and guests. In this way, children learn the capacity relationship between bottles and cups in a pleasant and relaxed environment, let children share the fun of opening juice bars with everyone in the process of learning, and concretize the abstract concepts of mathematical knowledge, which will have a multiplier effect.
(c) Providing variability in handling materials
Homework materials play a particularly important role in children's learning mathematics. This is because the development of children's movements affects and determines the development of thinking. The more diverse the movements, the richer the content of thinking. Therefore, I provide them with changeable operating materials and encourage children to explore in the operation. For example, in the calculation area, many geometric figures with different colors, sizes, shapes and thicknesses are placed. Teachers consciously inspire children to pose various regular geometric figures. Some are arranged according to the law of size, some according to the law of color, some according to the law of quantity, and some according to the order of graphics. Through such activities, children's thinking is more active, agile and creative.
(4) Guide children to discover themselves in exploration.
"Discovery" is closely related to creation. The characteristic of this teaching method is to let learners "explore" and "discover" problems and solve them by themselves. Its root lies in forming creative attitude and cultivating creative ability. This is because the process of exploration is to give full play to the initiative of learners, so in the creative activities of children's mathematics, I actively create an exploration environment for children, provide opportunities for discovery, and urge children to learn through discovery in exploration.
For example, "learn to measure with natural objects." In the past, the teaching method was to let children imitate all the practices with the same measuring tool, but I prepared many beverage bottles with different thicknesses for children in group activities and put the same amount of water in them. In activities, children have no strong purpose, no fixed behavior patterns, no norms and habits, and a large thinking space. They can express their creativity truly, freely and without modification. Some children blindly tell the results only by visual inspection; Some children find two identical bottles, pour two bottles of water into them, measure them and find that there are as many as others; Some children just find a bottle that is completely close to one of them and pour out the water in the other bottle to see if their liquid levels are the same. During the exploration, children found that we can't just look at which bottle has more water, nor can we just look at which bottle's water thickness. We should put water in two identical bottles and compare their quantities.
Doing so can not only let children learn to measure, but also cultivate their independent thinking ability, which is permeated with the concept of conservation. At the same time, in this creative process, it not only satisfies children's curiosity, but also allows children to get a pleasant experience in the process of self-discovery.
Practice has proved that it is feasible to carry out creative activities in the field of mathematics, which is not only beneficial for children to master mathematical concepts, but also conducive to the development of children's creative thinking and the cultivation of children's creative personality. At the same time, as the German psychologist gottfried Heinert pointed out, "If creativity is the goal of education, then the prerequisite for achieving this goal is creative teachers". Because teachers are executors and practitioners of implementing educational goals, only by making themselves creative and constantly having new ideas, new pursuits and new explorations in education can children's creative potential be fully tapped and their creativity be cultivated.