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A New Breakthrough in the History of Mathematical Operations
Time: 2020-4-23 10:26:00 Access: 985

A new breakthrough in the history of mathematical operations

On the abacus mental arithmetic teaching method

Chen Gaomu

[Abstract] Abacus is one of the excellent traditional cultures of the Chinese nation. It is the duty and responsibility of every Chinese child to inherit the abacus culture! Since the 40 years of reform and opening up, based on the inheritance and promotion of the abacus culture, teachers have continuously practiced, explored, and researched, formed a consensus, and concluded the "Abacus Mental Arithmetic Teaching Method", which has improved the accuracy and speed of calculation and become the history of mathematical operations. New breakthrough. It not only conforms to the principles of pedagogy and psychology, but also plays a positive role in developing children's intelligence.

[Keywords] Abacus and Mental Abacus Innovation Breakthrough Migration Internalization]


General Secretary Xi Jinping pointed out: If you do not forget history, you can open up the future, you can be good at inheritance, you can be good at innovation. Excellent traditional culture is the foundation of the inheritance and development of a country and a nation. If you lose it, you will cut off the spiritual lifeline. We must be good at promoting excellence. The traditional culture and the development of real culture are organically united, closely integrated, and developed in succession and inherited in development. 

As we all know, abacus is one of the excellent traditional cultures of the Chinese nation, and it is listed in the intangible cultural heritage of China and the world. It is protected by law. It is our common responsibility and responsibility to inherit and promote, innovate and develop the abacus culture.

Since 1980, a small number of schools in China have explored a way to improve the degree and reduce the burden in deepening the mathematics teaching reform in primary schools. They have continuously explored and innovated in abacus teaching and conducted abacus teaching experiments, which have achieved remarkable results. With continuous promotion and expansion of experiments, thousands of schools conducted relatively extensive and in-depth research and formed a consensus.

The teaching of abacus and mental arithmetic can use special textbooks or general primary school mathematics textbooks, which can be appropriately handled according to their teaching characteristics.

1. Introducing abacus from the first grade, combining beading for bead training, combining bead for literacy training, and calculating for bead exercise training. In the above-mentioned training, the bead statue is gradually strengthened, and through the actual dialing > empty dialing >watching dialing >wanting to dial, the bead statue internal training is formed, that is, the material abacus is converted into a mental abacus. The requirements are consistent with the current mathematics curriculum standards, and can also be adapted to local conditions. Starting from the actual situation, it is slightly higher than the curriculum standards.

2. In the process of forming abacus and mental calculation, adhere to the basis of real dialing, empty dialing is the key, watching dialing is a transition, wanting to dial as the goal, and finally realize the movement of abacus and beads on the mental abacus in the brain according to the rules or rules Count out and get the results accurately, and complete the calculation quickly and efficiently.

3. In the case of direct addition or subtraction, the calculation rules of "adding to the outer bead are enough to add the direct addition" and "decreasing to see the inner bead are enough to reduce the direct reduction"; Form the calculation rule of "not enough to add beads, add five minus", "to add enough beads to reduce, plus five minus"; when the carry is added or decremented, the formation of "the file is full ten, minus make up one", The calculation rule of "This file is not enough to be reduced, one is added". The addition and subtraction from within 10 and within 20 are gradually extended to enable students 'cognitive structure to have assimilation and adaptation when learning addition and subtraction within 100, 10,000, and even multiple digits, and to enhance students' ability to learn by analogy and bypass.

4. In the multiplication and division teaching, multiplication can use "big nine nine" or "small nine nine", combined with mantra teaching to carry out full-scale training, double-level training, third-level training, multi-level training, multiplying one number by two or three Numbers are multiplied for proper penetration, while mantra reduction training is performed to make necessary penetrations for the corresponding division. The abacus division method adopts the quotient division, so that it is basically consistent with the pen calculation in terms of arithmetic and algorithm. Multiplying and multiplying multi-digit numbers into unit product recursive superposition or recursive subtraction, simplifying the calculation sequence and complicated process.

5. Addition and subtraction are taught at the same time, and multiplication and division are taught at the same time. Appropriately increase the practice density, speed up the mental calculation speed, intersperse the abacus and pen calculations appropriately, form skilled calculation skills and improve teaching efficiency.


Simply put, the abacus is to plan in your head. Due to the progress of a person's abacus, the abacus can be internalized, that is, the number becomes an abacus and comes to the brain for calculation. A good abacus user can use the "psychological abacus" (bead statue) to perform complex numerical calculations without actual abacus, and can quickly get the correct answer.

Abacus and mental arithmetic teaching makes full use of the abacus, through the students skilled abacus operation, simulates the beading, and gradually makes them leave a clear and correct image of the abacus in the brain, forming the" improved abacus algorithm, skilled abacus skills, with the aid of simulated beading, adapt to mental arithmetic Requirement; Simulate abacus movements, conduct calculations in the brain; gradually get rid of the assistance and directly perform mental calculations "skills. The key to abacus mental calculation is how to turn "material abacus" into "psychological abacus". There are four steps in the teaching method, namely: bead calculation > idle calculation >watch calculation > want to dial calculation. (Simplified to real dial >empty dial > watch dial >want to dial), the number is from small to large, and the number of pens is from small to many. After continuous training, the calculation is automated.

In the above four steps, the actual dialing is the foundation, requiring students to play the actual abacus fast, and also to dial the beads correctly and clearly. Air dialing is the key (air dialing is simulated bead dialing, also known as imitation dialing or virtual dialing). It uses fingers to simulate bead dialing movements, which promotes clear "virtual bead image" and "bead image movement" of the brain, which is less than real dialing. A sense of touch is a higher level of skill than actual dialing. Seeing and dialing is a transition. It is calculated by looking at the abacus without dialing the beads. That is, looking at the abacus and thinking about the abacus, the brain gradually forms a "bead movement" to achieve the purpose of calculation. Wanting to dial is the goal. Train students to flash an abacus in their minds and perform bead calculation on this "psychological abacus" to achieve the purpose of abacus calculation. What should be emphasized here is the "air dial" training. According to the source of its incoming information, it can be divided into "listening to air dialing" (listening to other people's reports for air dialing) and "watching air dialing" (see numbers and calculation rules) There are two types of empty dialing; according to the size of the empty dialing action, it can be divided into "imitation dialing" (the movement range of the empty dialing action and the actual dialing action are the same) and micro dialing (the empty dialing action is slightly smaller than the actual dialing action, or even more Small) Two types; according to the distance of their empty dial fingers from the abacus, they can be divided into "near dial empty dial" (the finger is very close to the abacus when idling) and "far dial empty dial" (the finger is far away from the abacus when idling). Under normal circumstances, you should first train to listen to the number dialing, and then train to see the number dialing; first training imitation dialing is conducive to the formation of a clear bead, after the imitation dialing has a certain basis, then transition to micro dialing; training first Dial empty dial, then train far dial. Putting the abacus under the finger of the empty dial, students feel as if they are actually dialing the abacus, which is conducive to the clarity of the movement of the bead. Some students cannot form the bead in the brain. The main reason is that the near-dial dial training Too little. If students are able to skillfully dial and dial slightly, the abacus will come naturally.


Pedagogy and psychology related data show that children from 6 to 11 years old have the most abundant image thinking and strong imitation, and they are often most impressed by the action operation. The abacus teaching just fits the psychological characteristics of children.

At present, conceptual mental arithmetic training in mathematics is more difficult for students. According to the principles of psychology, the use of analogues as an intermediary or model in complex psychological activities can reduce the difficulty of activities and promote the effective conduct of psychological activities. In the entire mental activity of abacus mental arithmetic, the "abacus" is the intermediary for smooth calculation, which makes the difficult mental arithmetic reduce the difficulty and is mastered by the majority of students. Therefore, the key to abacus calculation is to use the level of intermediary, that is, the speed and efficiency of converting the abacus image stored in the mind from "static" to "dynamic".

From the perspective of migration, abacus mental arithmetic is a kind of learning psychological phenomenon that uses abacus to transfer abacus arithmetic and algorithms into mental arithmetic. You can always find traces of the abacus during the abacus calculation. So the mental preparation for abacus is to master abacus. In this way, students have a "abacus model" in mental arithmetic. Due to the formation of conditioned reflex and the improvement of proficiency, students from bead calculation to fake bead calculation, and then to non-bead calculation, the accuracy of calculation is increased and the speed is accelerated.

Abacus mental arithmetic is the highest stage of intellectual activity, and this intellectual activity is completely achieved through "internalization". At this time, the students' psychological activities have a new form of existence, mainly because compression and simplification do not require material means or external speech when computing, and the entire computing process is automated in the brain. The mental mechanism of abacus mental arithmetic is "internalization". It is precisely because of internalization that it brings high speed of calculation.


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