Abacus, with the deepening of awareness, many regions and countries as a special education and educating people, as a means to improve the quality of citizens entering kindergarten and primary school classroom. That being the case, how to grasp the laws of teaching and children's learning abacus abacus own psychological characteristics, in order to better improve teaching effectiveness, reduce teaching blindness, randomness, it became a very worthy of study, now this combined with my many years of teaching experience, understanding from talking points on effective teaching strategies. 

A grasp of the feasibility of the target 

General requirements for teachers teaching goal is to complete the task of teaching when raised, is teaching activities to achieve the expected results. On its own, it has the inherent requirements of the dominant teaching practice, and plays a dominant role in the process of teaching and guidance, but also teachers fundamental basis of classroom teaching. 

Abacus classroom setting goals, it is necessary to consider the overall requirements of teaching content, but also the actual situation of learning objects, to fully understand and accurately grasp the psychological dynamics and cognitive level of the child, in particular, should focus on the future in favor of children development and established. 

It can be said, abacus is an established curriculum goals, but the specific goal of teaching is generated. That so-called generative established goals to the dynamic changes in the actual process of teaching, teachers and students in the process of teaching and learning activities in the mutual exchange gradually formed, and with the progress of the classroom and continue to be adjusted. It is correct or not depends on whether the teaching practice, there is no maximum mobilization depends children to explore their own interests and enthusiasm. 

Here is a fragment selected from a teacher teaching large classes for children, "15-8 =?" When, from the analysis may allow us to get some inspiration. 

Review: 15-9 = 17-9 = 25-9 = 26-9 =, and then show: 15-8 =? 

Teacher: Do you count? Please think of a way you can dial wave on the abacus, also can do the math on paper. If two people at the same table are considered good, you can tell each other how they are counted. 

Young :( thinking algorithm, at the same table AC) 

Teacher: Who knows 15-8 is equal to how many? (A child: 15-8 = 7) 15-8 = 7 then you talk about how the count? 

Young: 15 minus 8 bits minus five minus eight is not enough, look up the number two 8 plus ten retreat from a position on the two, was 7. 

Teacher: Well said bad? (Child: good) everyone a round of applause (infant applause). You have other algorithm? 

(Infant wordless repartee) ...... 

After school I had exchanges with the classroom teacher, learned of his thoughts: First, want a variety of algorithms, such as the well 10-8 = 2,2 + 5 = 7; 8-5 = 3,10-3 = 7 and so on. Second is to make the children feel the superiority of the abacus method in the process of exchange in a variety of algorithms. 

In fact, this is a very subjective teacher's personal wishes. First, from the level of knowledge of view, there is a school of this algorithm first, second graders will not be able to successfully answer out, not to mention the four-year-old child, which is obviously too improve the objectives and requirements, from a child's cognitive psychological and knowledge levels. In addition, the abacus beads code with operating results were semi-abstract and semi-specific characteristics, which in itself is the greatest advantage abacus, help children to understand and accept, without having to complicate the problem, with other algorithms to aid in understanding the merits of Abacus . 

Second, the importance of school with abacus 

Operating abacus as learning tools, not only has the general physical learning tools, and intuitive, there is a half-specific semi-abstract and other unique. 

Abacus beads to show the number of bits used bins, rational and intuitive, the concept of "Shuoxingjiege" modern mathematics education ideas, establish a quantitative relationship between the number of stages of primary school-one correspondence with the beads. After positioning on the abacus, by dialing wave, think about it, from the "in-kind (concrete) - Pearl code (preliminary abstract) - Digital (abstract)" to complete the process of understanding numbers. For example, "3", for young children is a meaningless abstract symbols. However, when using the abacus teaching, in guiding the child to physical, graphics operations, on the basis of count by counting beads represent a specific kind, on the beam, such as a lower bead represents an apple, a pencil, a lamb and other such individual objects, and then guide the children on the abacus as dial "1" on the dial "1" on the dial "1" to practice, then the beads on the abacus code can be used to represent three apples or three pencils, or three lamb and so on. Pearl dial operation to achieve the kind where symbolic integration and operations, helping children complete the preliminary abstract of the kind. In this case, the results of beads with a digital dial "3" in the form of written down, "3" this abstract numbers and specific form of organic combination, not only for the children understand the "3" of the specific significance, but penetrate the three by three a l composition and "l + l + 1 = 3" adder thought. 

Large numbers, more than the median knowledge is a major difficulty for young children, but with the knowledge digit combination dial abacus beads multi-speed train and gear division, to help children perceive, know more than the median, is a convenient pieces, simple things. 

Abacus calculation magic is achieved by operating the counting beads, reflecting the combination of beads yard operations and calculations, while also reflecting the significance operations. Such as: Two beads codes together (toward the beam), indicating that the two addends merger, reflecting the essence of the addition; dial beads from beam to cut, reflecting the significance of subtraction; this profound demonstration of unity from the inverse relationship between addition and subtraction. These are not the biggest advantage of an abacus with other forms of learning. 

We all know that the use of science to guide children with "small round" learning 4 + 2 =? , Is to put four "O", and then put two "O", to count a total of six "O"; either side while carrying a finger aside from 4 to 5, 6 to number 2, so as to arrive 4 + 2 = 6. The abacus is credited to four, "under 8" directly obtained, that the results of six. Beads moving digital display, intuitive and efficient, and five liters decade, digital size, how much limited. System features abacus can even integer, decimal and operational methods, and operator management, law and other scientifically demonstrated. 

From these sense, abacus math as a learning tool for children with other forms of learning with unparalleled advantages. Minister of Education, Dr. �����ȱ��� American University of South California once said: "abacus beads by one operator and orderly arrangement of stalls stood composition, conceptual understanding count the number of foster size and number, it compared to the past in any way, have made very different results. Therefore, to lay the foundation of elementary mathematics education, it is contributing. "

Interesting three, highlighting activities 

Children (especially young children) fun, active, curious, inquisitive, interested in things easy to focus attention, but time is short instability; understand things in a specific image thinking dominant feature of memory with a visual image; imagine mainly of recycled imagination, creating imagination is at the development, the theme is easy to imagine the change, and often exaggerated. These psychological characteristics of children will determine our teaching process to select a reasonable teaching strategies to take advantage of the psychological characteristics of children, effectively mobilize their enthusiasm for learning. For young children, telling stories, playing games, singing songs, fairy tales, as well as singing and dancing, are the common way of teaching hands-on, group work, etc., the key is how to use, used properly can greatly enhance the teaching and learning activities fun, improve classroom teaching. The following comparative analysis of two sets of teaching cases, it may make us realize from that truth. 

The first group [Case], "Chu said on 5" understanding 

Case one: 

Review the abacus on Bobo 1,2,3,4, the show five flowers, five fish and so on. 

Teacher: kids, you have to count, they are how much? 

Young :( count back) has five flowers, five fish ...... 

Teacher: You're smart, have a few right. So, five on the abacus how dialed it? 

After the division :( children discuss) You see, under the bead enough 5, we will use a beads to represent, that is, the beads represent a 5. 

...... 

Case two: 

Teacher: kids, one on the abacus how said it? 2 it? 3 it? 4 it? 

Teacher: awesome you are dialing the right. (Produce five flowers, five small wafer ......) we count, they were much? 

Young: There are five flowers, five small discs ....... 

Teacher: Yes, you have a few very well! So, five on the abacus and how said it? They talk about the same table. 

Teacher: You will do? Does not matter, let's look at the first operation with learning tools, will you be seen as a pencil horizontally abacus beam on the table, there are four vertical position below the crossbar, ask you to put them out of five small discs came in under four positions on the beam. Four (children operating) position put five small enough wafer row it? 

Young: enough. 

Teacher: a few more, (young: more than one) that teaches you a good way to please you put five small discs overlap, put them on as a bead onto the beam, which is an upper bead how many said it? 

Young: an upper bead represents 5. 

...... 

Compare: 

A lower bead represents 1, so easy to accept a one to one relationship between the child, with a bead on said five such "a corresponding 5" relationship a bit confused child. Case one by one on the bead represents 5 is the teacher's "subjective will," is imposed on, there is no children's participation and experience, when children may be reluctant to accept, but to learn to use the back of the upper and lower bead represents 6,7 , there will be difficulties when 8,9. The case of two arrangements interesting operation, which not only effectively stimulate children's interest in learning, but also allow them to intuitively understand the bead represents a specific meaning on 5 and experienced process. This is for children 5 and a correct understanding of the bead represents five, or even in the future "full five plus" of learning have a role can not be underestimated. 

The second group [Case] "broken five minus" of Abacus (6-2 for example) 

Case one: 

(Leads to questions 6-2 = after) 

Teacher: Dial 6, minus 2, the next bead only one, minus minus two is not enough, how do? Bobo you look at the abacus. 

Young :( try dialing 6-2) 

Teacher: will dial it? Not reverse it does not matter, look at the teacher teach you the following dial. Under the bead is not enough, we cut from the beads 5 to go two, dial to 5, more than a few allocated to it? (David: 3) so we credited the next bead in three, how many have? (David: get 4) 6-2 equal to a few? (Young: equal to 4) according to the teacher and then dial your way on their own calculations dial wave. ...... 

Case two: 

Create situations, leads to questions 6-2 = after, in the form of the story of the classic is tinted dial, guide children to learn abacus 6-2: 

Dial 6, where 6 represents six apples, Xiao Ming thirsty, want down by two apple beads sister thirst, but only under an apple beads sister borrow enough, then the beads on the abacus big brother said: "I've got five, you all take it. "(allocated to the beads 5) is pleased to thank Xiao Ming Chu brother, holding five apples to eat two, left a few? ("Left three") So he put the remaining three into the next bead sister (dial 3), then the next bead sister a total of a few? ("There are four ') right, so 6--2 equal to the number? ("Equals 4") 

Here let us recall dial bead process, minus two, is not enough to spend the next pearl beads, 5 can be divided into two and three, dial 3 dial to 5, namely: 8. 

...... 

Compare: 

A clear case of a dial beads principles and methods 6-2, basically also allows children to learn. But Case II classic is tinted in story form to side dial and guide children living in specific examples from experience and experience to truly understand why go five minus two plus three, and learned the abacus method from minus 2 8 , so that the image reflects the abacus processes and principles to facilitate children's thinking and accepted. While greatly enhancing the fun, to effectively mobilize the enthusiasm of the children's learning. 

Scientific four, losing methods 

Since abacus as a discipline for teaching, of course, will shoulder the responsibility of a child's future development, which determine our teaching activities can not blindly pursue formal bustling, while ignoring the knowledge, skills, training, especially to impart knowledge scientific accuracy and teaching methods. Teaching introduction to links with the lives of children, to focus on problem solving mathematical thinking, mathematical methods and rules of penetration, from an early age they use mathematics to solve real life problems of consciousness and thinking and ability. 

Such as teaching, "1 to 4 of breaking five minus", the idea of such a teacher teaching: 

Teacher: Little Rabbit children basic skills that we learned so well, as we encourage everyone brought a big cake. However, the little rabbit said, the children only continue to do the calculation of each question on the cake to eat cake, we have confidence? 

Teachers open the first layer of cake, revealing a card 5-1 =? (Explain abacus 5-1 after) 

Open the second layer of cake, revealing a card 5-2 =? (Using the same method to explain the 5-2 abacus, followed by similar events in the process of teaching entirely a 5-3 = 5-4 =.) 

Such mechanical repetition of the teaching process, not only tedious, affect a child's enthusiasm, but not conducive to training to master the ability of children to learn and explore methods, and even restricted the children play creative thinking. If you dial in clarifying 5-1 bead method based on the use of tactics to try teaching or migration guide children through group work, independent study to explore a few questions later, it is worth learning approach. 

Another example: Some teachers in teaching "4 of understanding" of this design: 

Teacher (to produce four birdies in the picture): children, you count, which is a few birds? 

After the young :( number) has four birdies. 

Teacher: Yes, this four birdies can use the number "4" to represent. Below please follow the teacher to write about four, raised his right hand, with the index finger ....... 

For example, with a 4 on the number "4" to indicate that this is certainly not conducive to the child correctly understand the meaning of the expression of four, is not in line with the basic idea of mathematical methods, can not be good to help children to be done by a specific kind of abstract figures excessive, even young children will have a "four birdies can be represented by four, four apples and how should we say then?" questions. If you make the following improvements would compare science. 

Produced four birdies guide children to count, and then produce multiple sets of four physical four apples, four-pointed star, four pencils, etc., so that children count respectively, on this basis, then give "like Thus some four four items, we can use the number "4" to represent. "so to summarize it without loss of generality, help children to recognize and understand abstract numbers really 4. 

Five, focusing on mental arithmetic permeability 

Teaching abacus, abacus is a means, considered the heart of the purpose, so the abacus mental arithmetic over to one of the key issues of our concern. Abacus Mental Arithmetic over when to how excessive the abacus industry has a different understanding and views, but I believe that the heart be recognized bead yards from the beginning with the development of Abacus capacity gradually increased, in this sense, but also is to focus on mental arithmetic training permeability. 

Permeability of mental arithmetic training is conducive to do step by step, making identification beads when teaching reading, you can have the formation of beads like brain training, such as learning to count 1, 2, when ...... let children in real dialed basis beads were wanted on dial code, ......, with the corresponding figure for children to control bead yards; learning "direct plus lapse", it may be appropriate to guide children subtraction mental arithmetic, but the content should be slightly behind, such as learning Fourth, plus five straight straight abacus, mental arithmetic can be three pen training, for example: 3 + 5-7 =? Can guide children to want to dial: get results 1; during the three-digit basis with the abacus can guide children's double-digit mental arithmetic. Let gradually improve mental arithmetic with the abacus while to develop, so that children abacus mental arithmetic skills formation formula unknowingly. 

Learning abacus mental arithmetic training while reasonable penetration is also conducive abacus, mental arithmetic and promote each other, but also conducive to the classroom combined static and dynamic, changing monotonous, boring training methods, so that movement with, in various forms, interspersed with a variety of exercises, children hands, brain, eyes, ears combine to fully mobilize the various organs of the child's perception and learning initiative. 

Abacus classroom teaching is a complex and systematic activity patterns, and teaching practices can only reflect the individual or group to this understanding, but not teaching law itself, but the same can not be the ultimate truth. The paper spoke of "five" of the practice, but abacus classroom teaching himself by thinking after some reflection and analysis of the work of many years of teaching abacus some teachers on instructional design, and obtained some superficial view, inevitably there are omissions and not reasonable, it nevertheless seeks to initiate exchanges, hope colleagues in the joint efforts to make more and better teaching abacus teaching law itself tends to promote better working abacus development of.