Mathematics Teaching Papers for Preschool Education (1)
In the past, the traditional teaching mode was often used to teach children mathematics, that is, the teaching method of teachers talking and children learning. Although it also emphasizes intuitive images, children lack the initiative to learn. Therefore, I organically combine the teaching of knowledge with the cultivation of intelligence and skills, so that children can acquire mathematical knowledge, experience and skills in the process of their own attempts.
First, provide materials and create an environment for children to try.
The process of trying is a process in which children use their brains to do things, and encourage them to find out for themselves. Therefore, I have prepared rich materials for children to try: reviewing the composition of exercises, addition and subtraction, various graphics, countdown painting, comparing the thickness and width of objects in the activity area, and fully letting children find the operation. This is only the material basis for trying teaching, and it is also the basis for creating a good teaching environment, so that children can interact in materials and environment.
Second, stimulate interest and encourage children to try boldly.
Inspired by the teacher, children are often curious about a certain problem. At this time, they have the desire to have a try. At the same time, the child's attempt itself also mobilized the child's emotions, stimulated the child's enthusiasm for thinking and interest in learning, made it in a positive state, and produced a desire to learn and a feeling of loving learning. For example, in the study of "bisection", I asked my children to divide a snack into two parts to remind them that they should get the same share. They became interested in activities, dared to try and explore actively, and the flexibility and agility of thinking also developed imperceptibly.
Third, mistakes are allowed in the attempt.
For young children, the process of trying is more important than the conclusion of trying. Children's understanding of things is formed by their own perceptions and activities. Hands-on attempts provide children with methods and opportunities to learn, find answers and solve problems. Because children's development is different, their abilities are strong and weak. In the process of trying, we allow children to make mistakes, treat their own mistakes correctly, and mobilize all factors to promote their success in trying. For example, in the activity of learning dichotomy, children divide a snack into two parts with different sizes. At this time, I will guide them in time: "Brother Rabbit and Brother Rabbit want to give each other the big one, so that no one will eat it." What should we do? " Many children came up with the idea of dividing a snack into equal parts, which not only achieved the teaching purpose, but also gave children moral edification.
Children learn mathematics by their own experience, not the experience of teachers. We should not only make use of the special function of mathematics activities to promote children's thinking development, but also try to tap the general function of mathematics in promoting children's all-round development, so that mathematics education can really serve the whole education.
Mathematics Teaching Papers for Preschool Education (Part Two)
Mathematics is a science with strong potential aesthetic feeling, as the British philosopher and mathematician Russell said: "Mathematics, if viewed correctly, not only has truth, but also has supreme beauty." Mathematics teachers often consciously cultivate students' aesthetic consciousness in teaching, so that students can experience beauty from mathematics learning, especially its ideological beauty, which will be more attractive than literature and art. For example, we use discovery teaching to let students learn to discover knowledge by themselves, and guide induction to let students learn to extend and broaden their associations. When infinitely wonderful conclusions or ingenious solutions come from students' own discoveries, the feeling of enjoyment will follow. Therefore, it is really beneficial to give full play to the charm of mathematical beauty and inspire students to understand it and have it. As long as we pay attention to the induction of inspiring beauty in the derivation and extension of every property and formula, in the exploration of the solution of every exercise, and in the induction and arrangement of every knowledge system, mathematics learning will become a pleasant thing over time. Let's talk about aesthetic education in mathematics teaching from three aspects.
First, feel the beauty of simplicity.
Mathematical phenomena, like other natural phenomena, are complex and confusing in the eyes of naive children. However, when we guide students to induce, reason, compare and generalize, find a simple and clear law through thinking, or express it clearly with a concept, law and formula, students will immediately have a simple and neat aesthetic interest.
Second, experience the beauty of harmony.
Bida Dollas, a famous mathematician in ancient Greece, pointed out: "Beauty is a harmony composed of a certain number of relationships." Mathematics shows the harmonious beauty of the unity of content and form, and students are trained to create harmonious beauty through mathematics.
The structure and relationship of numbers show a kind of harmony, for example, 75008 is pronounced as 75008 instead of 75008, which is evidence of seeking the beauty of music; The equation of 100-25= 17+□ and the conversion formula of 1 minute =60 seconds give people a sense of symmetry and balance. 1 km = 1000 m and so on, and x? Y=K (certain) is proportional, completely proportional and harmonious; C = 2 лгл = л d, which shows the relationship between them in a unified way and has the beauty of unity and harmony; Various symbol tables, graphic lines and geometric shapes not only show the beauty of the image, but also show the internal balance and symmetry; Rules, postscript and rules have an abstract aesthetic feeling, which gives people a correct, standardized and concise aesthetic feeling except for meticulous expression and indissoluble addition and subtraction. For these, teachers are well aware that striving for perfection and elegance in teaching form is of great benefit to inducing students to develop in the direction of loving beauty.
Mathematics teaching allows students to experience the inner beauty of harmony, mainly the beauty of rigorous logical structure. Teachers' questions and explanations should be accurate and clear, demonstrations and diagrams should be intuitive and clear, and the deduction process should follow the students' thinking process and be orderly and clear, so that mathematics learning is almost an artistic appreciation and wonderful.
Third, appreciate the strange beauty.
Successful mathematics teaching always makes students marvel at the novelty of mastering scientific laws, and always feels a pleasure of exploring mysteries. For example, when teaching the commutative law of addition, the teacher wrote two addition formulas: 60+70= 130, 70+60= 130. Why are their results equal? Let students be surprised and eager to explore new knowledge. For example, when teaching the concept of "mutual opposition", the teacher designed it? ( )=5? ( )= ? () = 1 for students to fill in the blanks. When the students feel difficult, the teacher takes the initiative to fill in the blanks quickly and adds, "Who can write several such questions?"? You can finish them at any time and I can finish them at any time. Who can try? " As soon as the voice fell, the students began to ask questions with great interest, and the result was just as the teacher said. Why is this? Students feel strange, so that students will rise to explore mysteries and learn new knowledge in the process of longing? The concept of "equivalence". With the growth of grade, positive mathematics knowledge and skills, and the effective inspiration of teachers, students will find the magical internal connection of mathematics knowledge, and the strange beauty of mathematics can be seen everywhere.
In a word, mathematics teaching cultivates students' feelings of beauty, so that students can enjoy beauty, imagination and success. As long as teachers integrate knowledge teaching with ability training, and intellectual education teaching with incisive moral education training, students will be able to develop in a balanced way in morality, intelligence, physique, aesthetics and labor, and become all-round talents.
On Mathematics Teaching Papers in Early Childhood Education (3)
Childhood is the best period of wisdom development in one's life. The knowledge of different subjects plays an important role in promoting the development of children's wisdom. The inherent logic and abstraction of mathematics are of special value to the development of children's mathematical logic wisdom. Mathematics education in kindergarten is to use this special value of number to promote the development of children's logical thinking, and at the same time cultivate children's interest in mathematics learning, so as to make psychological preparations for future primary school mathematics education.
First, mathematics and interest in learning mathematics.
Mathematics is characterized by high abstraction and strict logic. As far as these two characteristics are concerned, mathematics is a subject that is not suitable for children's cognitive characteristics and thinking development level. If kindergarten mathematics education is regarded as simply teaching children some superficial mathematics knowledge, and children are only satisfied with remembering some numbers and words that can express a certain concept in the teaching process, then children will lose interest in learning mathematics and teachers will lose interest in teaching mathematics.
Children's interest in learning mathematics is an important non-intellectual factor that affects children's learning mathematics well, and also affects children's learning attitude and confidence. Early childhood is an important period to cultivate interest, attitude and confidence in learning. Studies have shown that adults' dislike of mathematics and failure in learning are often caused by some unique reasons in infancy.
Interest is the motivation of learning, which can stimulate children's curiosity and learning motivation. Only when children are interested in something or an activity will they actively participate, actively explore and consciously learn. Interest is also the basis of forming attitude and confidence. If children are not interested in mathematics when they first come into contact with it, and their learning attitude is not positive, it is likely to affect their academic performance in learning mathematics in the future and lead to failure in mathematics learning.
There are three main factors that affect children's interest in mathematics: first, the learning content is not suitable for children to accept; Second, the teaching method is not suitable for children's cognitive characteristics; Third, the teacher's attitude towards children's academic performance.
The teaching content that can arouse children's interest in learning is the knowledge and skills of "let children jump and get it". In the activities of mathematics education, when children can skillfully divide a group of objects into several groups according to their attributes, the most interesting learning activity for children is to compare the number of objects between groups. Ask the children to find the most or least objects in these groups. In fact, this activity leads children's thinking about the external physical characteristics or quality of things to thinking about quantity, and makes them begin to step into the process of forming the concept of number, which is a leap in children's thinking.
After learning a skill or understanding a concept, children have a strong desire to practice the skill or understand the concept repeatedly. At this time, teachers provide children with a set of activities to satisfy their desires, which can stimulate children's interest in actively participating in activities. There is a four-and-a-half-year-old girl who is very interested in organizing group activities. The main reason is that she has mastered sorting skills and cannot understand the transfer relationship of objects in the sequence. After several failed attempts, she lost interest and confidence. At this time, the teacher specially gives individual counseling to help her understand the law of arrangement, guide her to compare two adjacent objects, gradually increase the comparison of a group of objects in a sequence, and gradually increase the comparison of a group of objects in a sequence to help her discharge a sequence, so that she can quickly understand the law of activities and understand the meaning of the sequence. After the teacher left, she repeated the order of 10 objects for six times, and actively participated in the sorting group in future math activities.
Therefore, the organization of teaching content should arouse children's interest. First of all, we should choose challenging knowledge or skills that adapt to children's abilities. Second, children who have just learned a certain skill or concept should be provided with sufficient opportunities to practice or apply it. This kind of practice or use opportunity should be of the same type.
Different situations of experience. For example, once children master the skills of classification, they can provide different physical materials, so that children can classify according to the shape, color and size of objects, and they can also classify according to the internal properties of objects, which is not only conducive to the formation of children's class concepts, but also can promote the development of class concepts, thus cultivating children's ability to summarize mathematical materials.
Different teaching methods also have an impact on children's learning. The teaching method that can arouse children's interest most is the teaching method suitable for children's cognitive characteristics. In children's mathematics education, teachers often only pay attention to the visual characteristics of children's thinking, while ignoring the intuitive and dynamic characteristics of children's thinking in the process of solving abstract problems. Therefore, in mathematics teaching, children are usually taught to explain and demonstrate, and children are rarely allowed to directly operate materials. This often makes children remember some mathematical languages or concepts without understanding them. In this way, languages and concepts that do not understand the connotation become boring memory symbols, which makes children lose interest in mathematics. Mathematics comes from the abstraction of the real world, and many of its concepts and attributes can be transformed into concrete things and become materials that children can operate. Children abstract conceptual attributes in the process of perceiving operational materials. The concept thus obtained is understandable, meaningful and interesting for young children. For example, a natural sequence within 10 can be perceived by placing a button with "1" as the arithmetic difference and increasing to 10.
Teachers' attitude towards children's math scores is no less harmful than improper content and methods. Give an example to illustrate this problem. An old teacher recalled that she had studied mathematics when she was a child. Before entering primary school, she had learned four operations from her father and liked mathematics very much. When I entered school, I jumped to the third grade. Once the teacher asked the students to do division on the blackboard, and no one else wanted to go up, so she went up and worked it out with small division. But the teacher asked for a big question and denied his answer, saying, "What a fool, I don't even know the big division." This attitude of the teacher greatly damaged the old teacher's enthusiasm for mathematics in his childhood. From then on, he "bid farewell" to mathematics, and wanted to skip class as soon as he took math class. From this example, we can realize that no matter what the result of children's solving math problems is, teachers should not give a negative attitude, and encourage children to keep exploring until they get the correct answer. Protecting children's interest in mathematics activities and curiosity about mathematics in early childhood is more important than letting children get the correct answer. Research shows that children's attitude and interest in mathematics is very important before the age of eleven. For adults, saying "I don't like math" is usually formed at this age. If a person doesn't like something, he will avoid it and even be afraid of it. This is a psychological "block". It is very common for children to "block" mathematics, so in kindergarten mathematics education, teachers should pay attention to protecting children's positive and curious mentality as soon as they come into contact with mathematics, so as to prepare them psychologically for further mathematics education in the future.
Second, children can obtain mathematical knowledge and skills
A criterion for determining the content of children's mathematics education is that the structure of mathematics knowledge should adapt to the operational structure of children's intellectual development, and at the same time, it can guide and promote the development of children's logical thinking. Children's mathematics education can determine the following aspects:
(A) set and correspondence
Set and correspondence are two basic concepts in dangerous mathematics. They play a fundamental role in the formation of mathematical and logical concepts. One of their important features is that they can be operated and calculated in kind, which is just suitable for children's cognitive development level. The representation methods of sets include enumeration, description and graph, and graph can directly represent a set. This method is widely used in children's mathematics education.
One-to-one correspondence is a logical method for children to compare the number of two objects without counting. It is a necessary skill to form the concept of equality and is used to count activities. Therefore, children's mastery of one-to-one correspondence is the basic condition for the formation of their number concept.
(2) Numbers, technology and digital operation
Children's understanding of natural numbers and zeros within 10, understanding and writing of Arabic numerals, and mastering counting skills and addition and subtraction within 10 are the main contents of kindergarten mathematics education. These contents can help children develop logical thinking in the process of forming digital concepts.
(3) Quantity and measurement
Everything in the objective world has a certain amount, and children begin to deal with various measures very early in their daily life. Such as: the size of the object, the speed of walking, the distance of the object and so on. When children learn to compare various quantities, they can correctly understand the things around them and promote the development of thinking.
Let children learn to compare various quantities, which can help them establish the concept of order. For example, compare the lengths of a group of sticks and arrange them in order from short to long. Usually, comparing the quantity of things by sorting columns can also help children understand the relativity of quantity. Children usually learn to measure by measuring methods, instead of using general standard units of measurement, but using various natural objects as units of quantity to measure the length, weight and volume of objects. The significance of children's learning measurement lies in using the concept of number to experience the decomposition of the whole into parts, and the budget structure of parts is replaced by parts, thus establishing the concept of measurement unit system and preparing for daily learning measurement.
(d) space and geometry
Let children know some simple plane geometric figures and some simple three-dimensional geometric figures, which is helpful to cultivate children's concrete and preliminary spatial concept and spatial imagination ability. In order to achieve this goal, in addition to letting children know the names and characteristics of these graphics, the key point is to help children understand the relationship between various graphics.
All kinds of things in the objective world exist in a certain spatial form, and there are spatial relations between them, such as proximity, order, separation and encirclement. Understanding and mastering these spatial relationships is the basis of spatial intuitive thinking and learning geometry knowledge.
Children can understand the relationship between three-dimensional graphics and plane graphics at the same time. Help children think about the connections between things from the perspective of relationships. It is beneficial to the development of children's mathematical thinking.
As long as we adopt teaching methods that conform to children's cognitive development and stimulate children's interest in learning through various activities, we can make children understand and develop their thinking on the basis of understanding.
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