Zhejiang University Liu Li

　　Abstract:Abacus and abacus calculation are the treasure of Chinese culture;the instruction mode of the abacus mental arithmetic is based on the integration of the three arithmetic methods,and is also the crucial outcome of modern basic educational creation.This article argued the necessity of the instruction experiment,the property of the calculation,the credibility of the outcome of the potential ability exploration experiment of children,the necessity of putting the abacus mental arithmetic into the mathematic reformation and the feasibility of it,which will be benefit the reformation of the new mathematic curriculum.

　　Keywords:Abacus mental arithmetic;instruction experiment;study

　　Abacus is the treasure of Chinese culture;the calculation capacity is the basic and core component of individual mathematical abilities,whereas the “abacus mental arithmetic” is a unique calculation skill.The instruction mode of the abacus mental arithmetic is based on the integration of the three arithmetic methods,and is also the crucial outcome of modern basic educational creation.“Abacus mental arithmetic” depends on internal “metal abacus” and quickly and efficiently carries out the complicated number calculation in the mind.From the 1980s,a number of schools led by Minghe Primary School in Zixi City of Zhejiang Province actively carried out the “abacus mental arithmetic” instruction experiment to explore in practice and made remarkable achievements,which was called “uniqueness in China”.Since then,heated academic discussions on this experiment have been developed and put forward different opinions on the problems in experiment.In this paper,we choose the representative ideas among them,put forward the facts and theories of this experiment,and analyze the criticism with down-to-earth spirit for discussion and reference.

　　Chapter One:Whether the starting point of promoting the national culture to explore the mechanism of “abacus mental arithmetic” will be approved?

　　Some experts have put forward the questions:Do the mathematical thought-way and basic mechanism containing in “abacus mental arithmetic” still have advantages? Under such training mode,will the children have great pressure? Will the “child prodigy” who comes out top,gets unique skill and excels in abacus and mental arithmetic become the robot? The benefit of “abacus mental arithmetic” is not enough,will this teaching reform be approved? This paper explains that a large number of examples show that the query and criticism on superiority mechanism of “abacus mental arithmetic”teaching lacks adequate scientific basis.

　　In order to systematically summarize and scientifically demonstrate experimental teaching and effectiveness of “abacus mental arithmetic” in Minghe Primary School,publicize successful experience of Minghe Primary School,popularize the teaching method of abacus mental arithmetic,and even for rural education reform,we accepted commission from leadership team of the National Education and Science Planning,which was led by the author to form a special group.Since the second half year of 1990,the long and in-depth studies and researches were carried in Minghe Primary School,the “abacus mental arithmetic” interest groups and experimental class teaching activities were mainly investigated.The investigation methods were:individual visits,lectures,demonstration activities,questionnaires,symposium,collection for experiment materials,education implementation and psychological measurement (such as standardized tests and intelligence tests) and so on.Moreover,the backbone of Minghe Primary School in experiment and special grand teacher Wang Weida and three “child prodigies” were invited to university and carried out a short-term collaborative research.In the sufficient investigation and research course,the subject group gradually developed a following basic view.The “abacus mental arithmetic” teaching experiment led by Minghe Primary School materializes the national,scientific,and general direction of the new culture in society,it assimilates excellent Chinese culture and the reform results of “ three arithmetic methods ” integration,carries forward the national culture to lay a solid foundation for China's compulsory education,improves the reform of the national quality,serves for economic construction and rural development,and carries out the educational policy.The fact proves that this reform experiment is a success.It is not only provided with scientific theories,new reform ideas,unique teaching methods,but also has the striking teaching effectiveness.

　　Further analysis indicates that from the mathematical way of thinking and the basic mechanism,the advantages of teaching mechanism of “abacus mental arithmetic” are unimpeachable.The Academician Wu Wenjun pointed out in the prelude of “Chinese Mathematics history”:The ancient Chinese tradition of mathematics led by “The Nine Chapters on the Mathematical Art” and Western mathematics led by Euclid's “Elements” present two different system,and their ways of thinking show their own characteristics.The former one focuses on the application and calculation,whereas the results are often expressed by the form of algorithms.The latter focuses on concepts and ratiocination,whereas the results are generally displayed by the theorem.The former thinking way is structure and mechanization,while the latter lays particular stress on non-structural and pure logic thinking.As the mechanical way of thinking and concrete results of algorithms form,the former is fit for times' requirements from the ideology and methods.To carry forward the mechanical mathematical thinking can promote the development of artificial intelligence and human capacity.The researches on mathematical mechanical theorem proving presented by Mr.Wu Wenjun belong to the former;whereas “abacus mental arithmetic” is applied to mathematics education research,so it belongs to the latter.However,the studies on these two aspects all could benefit for future generations.

　　As to the worry for great pressure on children's mind,it is also totally unnecessary.The author made a forceful response in the research report “Theory on Teaching Experiment Effect of ‘Abacus Mental Arithmetic’” published in the third publication of “Educational Research”,1993.Because these students who are called “child prodigies” both have better physical and mental development and good marks for each subject in the classes.They are interested in learning and self-confident and they have strong will and perseverance,mental health,and different characters.The so-called the criticism for non-high efficiency is also unfounded.Some people say that the abacus mental arithmetic achieving a certain level needs a lot of time and energy but only get a skill.If we spend same amount of time and energy,we could also master other skills,such as concept of mental arithmetic and even we could reach a higher level.It seems full of reason,but is not the case.If learning “abacus mental arithmetic” is just for mastering a skill,it also may say so,now it has confirmed through investigation that “abacus mental arithmetic” teaching not only makes student obtain a skill,but also improves students' intellectual development and people's quality,and comprehensively promotes the quality of education.For such teaching method which is conducive to students' development,why not we spend more time? Moreover,we need not over-burden.It only requires training the teachers and increasing appropriate extra-curricular practice for students.If the same amount of time is spent in the concept of mental arithmetic,it is almost impossible to achieve such results.The concept of mental arithmetic needs heavy memory,it is also very difficult to increase one digit in a multi-digit calculation,while it has high rate to make error.However,compared with it,the abacus mental arithmetic is provided with fewer burdens of memory and errors.

　　Chapter Two:Whether the algorithm of “abacus mental arithmetic” has any scientific basis?

　　Some Experts also questioned:is there any scientific basis for the acquisition of the effectiveness from the “abacus mental arithmetic”? Which factors decide the master of algorithm and acquisition of skills? These questions have not been fully explained theoretically.However,we believe that,in recent years,the related research results have provided scientific basis for abacus mental arithmetic.Especially,the psychology and neuroscience research results have provided more solid scientific basis for abacus mental arithmetic.

　　The biggest difference of “abacus mental arithmetic” from other mental arithmetic is the existence of “abacus” in “abacus mental arithmetic”.Psychology and cognitive neuroscience studies have shown that a variety of sensory channels make for the memory and maintenance of learning results.“Abacus mental arithmetic” ties to human vision,hearing,feeling and other sensory organs and transfers the abstract numbers into a visual image of abacus,so in people's mind,people could calculate according to the formed abacus.It is different from general mental arithmetic;the calculation processes of the latter are mainly the digital concept (mainly Arabic numerals),which are formed in the brain.Its basis is written calculation;we can see it is a lack of visual images to support the processing of symbols,and some of them need to be accompanied with some form of skeletal muscle movement as a “strong point” to complete the calculation in the mind,so its “internalization” process is incomplete,which will affect the speed and accuracy of calculation.“Abacus mental arithmetic” makes full use of abstract symbols and concrete picture,carries out a certain amount of practice by procedural language,so as to exert the synergy of human brain and gradually move away from physical operations (calculate on an abacus) and skeletal muscle movements of external constraints,to achieve a high degree of “internalization”,finally,it forms new special operation whose arithmetic processing is different from general mental arithmetic,that is,it fully internalizes abacus metal arithmetic,in other words,it internalizes the intelligence operation of “mental arithmetic”.

　　In addition,some studies have shown that general mental arithmetic often requires the participation of language processing skills.In other words,when an individual obtains a certain degree of development in language ability,he can better complete the task of mental arithmetic.However,the abacus mental arithmetic has fewer requirements on language information processing;it seems to be more dependent on visual processing,visual-spatial processing and visual-motor processing.In other words,abacus mental arithmetic can promote the cross-modal plasticity of the brain.

　　At the same time,the memory task of “abacus mental arithmetic” also has its advantages.Cognitive psychology studies have shown that short-term memory capacity is 5-9 units.We have used a variety of forms (tests,interviews,symposiums,etc.) to make investigation on “abacus mental arithmetic” experts and found that the breadth of digital memory for “abacus mental arithmetic” experts has far exceeded the 7 +2 units.The foreign researches also have shown that “abacus mental arithmetic” experts can memory much longer numeric string than ordinary college students.We could think that “abacus mental arithmetic” experts memory the numbers by numeric “groups”.American scholar Stigler made an investigation on Chinese children and brought forward,“abacus mental arithmetic” experts could see a metal arithmetic like a real abacus.When “abacus mental arithmetic” experts solve the problems,they memory and manipulate the large amounts of data by the abacus in the mind (mental image of abacus).“Abacus mental arithmetic” is just the mental calculation depending on “abacus image”,that is,“to calculate on an abacus in the mind”.All kinds of evidence indicate that “abacus mental arithmetic” experts take “mental abacus” as imaginable strategy to help memory the numbers,whereas those who have no abacus experience could take this as the strategy.

　　On the basis of a comparative analysis between abacus mental arithmetic and written calculation,Shao Zongjie put forward that “abacus mental arithmetic” has the following four characteristics.

　　First of all,although they all belong to mental arithmetic,the memory task of written calculation is higher than abacus mental arithmetic,which is more obvious in the multi-digit calculation.For example,ten multi-digit numbers being added together,in the process of written calculation,the students need to bear the ten numbers in mind and calculate,which is a great number of memory;listening mental arithmetic is not so,in his mind (brain) only presents a “number” or a “abacus picture”,after listening to the number,he “move the abacus” to form another “abacus picture”.Therefore,his memory task is much more comfortable.Those who do not understand the reasons often feel that the memory task of abacus mental arithmetic is heavier than the written calculation;this fact is just the opposite.Secondly,why the abacus mental arithmetic has so alarming speed? When the one,who does the written calculation,just listens to ten numbers and starts to calculate,the one who does the listening mental arithmetic is ready to report the results,why does it happen? As in his mind,the “abacus picture” has already presented;when he listens,the number in his mind also changes,so when you complete the number report,he also “sees” the results.His strategy is to “move” a number when he listens to a number,the “abacus picture” in his mind also has been alternated.As soon as you finish the report,he also completes the count.However,the written calculation is difficult to achieve this,unless the digits are fewer.Thirdly,memory of abacus mental arithmetic is a piece of “abacus” picture,thus,the ability,developed from this,is highly conducive to the cultivation of creativity,which has great significance to the future development of children,especially in high-tech field.It also can be seen,the opinion that “abacus image” (constant movement,change,alternative abacus pictures in counter's mind) simply is regarded as “a kind of representation,a relatively low representation at cognitive stage” is open to deliberation.Fourthly,as to the written calculation,or daily mental arithmetic,the memory for people is a string of Arabic numerals,which are stored in the brain in linear form;the memory of abacus mental arithmetic for people is a “picture”,we know,two-dimensional picture carries more information than one-dimensional linear string of number.As the calculation strategy of abacus is the “stack and folding” of beads,so the abacus mental arithmetic is based on it,the strategy of abacus mental arithmetic is the change of “abacus picture”,the brain only needs to memory one “abacus picture” in an instant.In this way,the memory burden of the brain has been greatly reduced,while the information storage space has been greatly saved,in other words,it makes the increase of brain capacity of information storage,so the pressure has been eased.

　　In that case,“abacus mental arithmetic” as a kind of intellectual skills,how could it form? A reasonable explanation is that its formation is gradually transferred from external action to internal operation by abacus and calculation on an abacus or the corresponding activities of the language,so the full “internalization” is formed.The former Soviet Union psychologist Gary puts forward “the formation of mental action by stages” theory,which has better explained the process of internalization.In the point of view from Gary,intellectual action is different from the operation action (external action,practice),but comes from the operation,which is the reflection of operation,whereas the intellectual action is “internalized” by external operation.“Internalized”,that is,the image formation process of internal action,which transfers from external action to internal movement.The internalization of operation needs a series of stages;at different stages,implementation methods have been continuously modified,the image of action itself has occurred qualitative changes.Therefore,internalization of external action is a dynamic process.This view provides theoretical basis for the research of “abacus mental arithmetic” skill.

　　The formation of “abacus mental arithmetic” skill can be briefly summarized as three basic stages:abacus image stage → abacus image operation stage → abacus image internalization stage.In the above-mentioned three phases,abacus image operation stage refers to calculations on the actual abacus according to the law (or formula),this stage is the key moment for the formation of “abacus mental arithmetic” skill.It needs a longer time to plan the exercises;the required time is close to 80% of all the time of the formation of “abacus mental arithmetic” skill,so this stage is quite important in the formation of “abacus mental arithmetic” skill.Teaching content includes a very wide range:fingering exercises,number complement,listening and writing the number,seeing and writing the number to master the abacus addition,subtraction,multiplication and division (using formula rules).Because a large number of exercises make the quick match among enough calculation models in the memory and external stimulus in reality,so the calculation models could be pick up from the memory and needn't be disposal by algorithm,whereas the automatic parallel-processing is formed.It can be seen that the sufficient exercises play important role in improving the automatic and rapid parallel processing.It needs to explain that:“abacus mental arithmetic” skill as an intellectual skill,its formation is actually the accumulation process of the knowledge.It is accumulated by internal hidden cognitive processes,including implicit perception,implicit learning,implicit memory,implicit thinking and other processes.As a result of these unconscious and automatic processing,the time for “abacus mental arithmetic” is greatly reduced.By the learning of “abacus mental arithmetic”,children depend on the intuitive abacus image in the ongoing information process,enhance the extraction and application of the same rules in different scenarios,curtail different scenarios to the same kind of clues,reduce a number of procedures to a functional procedure,and cut short related laws to memory module characterized by abacus image.This kind of “cognitive synthesis” course enables “abacus mental arithmetic” experts to associate in the calculation so that the questions will be solved quickly and accurately.

　　On the information processing model flow of “abacus mental arithmetic”,we have made scientific analysis in the article “Theory Demonstration on Teaching Experimental Effect of Abacus Mental Arithmetic” (Please see the third publication of “Educational Research”,1993).According to the latest research results,the further analysis shall be made here;many theories of the brain information processing have respectively analyze the types and nature of brain information processing from different perspectives,for example:controlled processing and automatic processing theory,serial processing and parallel processing theory.The use of these theories could “read” the cognitive processing mechanism from the cognitive processing and cognitive processing mode.Two processing theories,“controlled processing and automatic processing”,indicate the brain information processing.Theoretically,the whole thinking process of “abacus mental arithmetic” could be generally divided into seven steps.1 Information input → 2 Pattern recognition → 3 Extraction rules → 4 Selection strategy → 5 Calculation → 6 Number of solutions → 7 Output information.We have used an example of a multi-digit multiplication.In theory,to count 25137 × 241,it needs to break down by distribution law of multiplication and applies three times of multiplication rules and three times of addition rules;additionally,the pattern recognition and abacus number translation shall be carried out;but if one “abacus mental arithmetic” expert only takes several seconds to calculate the results,so it is sure that not every step is carried out under the ideology,quite a number of steps can be completed by automatic processing.To the “abacus mental arithmetic” experts,their information process in the brain are changed from “controlled processing” to “automatic processing”.After long-term practice,the operation can be fully skilled.The original task needs controlled processing in the brain,but it gradually changes into automatic completion;when the same task being implemented,the automatic processing will be carried out in the brain.Two processing methods' theories,“serial processing and parallel processing”,are used to describe the way of the brain information processing.To “abacus mental arithmetic” experts,their processing modes may not be a single serial number of processing unit,some of them may be several units of the “block” processing,while others are a number of parallel “block” processing.In the research,we also find that the “abacus mental arithmetic” experts who have do a large number of exercises have remembered a lot of answers of quite a few calculations,so when they answer the questions,they could directly extract the answers from the memory,but it does not rule out the occasional use of count strategies.Count is an operation mode,which obtained at the early stage of “abacus mental arithmetic” skill;when children solve the questions at the early stage,they will use to count.But after a large number of exercises,the count mode will be reduced,whereas the memory extraction will be increased.However,at that time,the speed and accuracy depend on the associated intensity between the numbers and answers as well as the interference degree.Therefore,to complete “abacus mental arithmetic” operation needs two types of strategies.One is directly extracted from the memory,and the other is based on the calculation procedures of certain rules.For many cognitive tasks,“abacus mental arithmetic” experts usually take mixed strategy rather than a single strategy to solve the question;they often take most effective solution strategies to the corresponding subject.But,generally speaking,the development of “abacus mental arithmetic” skill represents that the count strategy is less used,whereas the use of extraction process is increased.This point accords with the general processing strategy.From the test results between Chinese people and white adult in Canada for mathematical calculations,Campell,et al.find the marks from Chinese people are much higher than that of the white adult;moreover,these China people often calculate through direct extraction from the mathematical facts in their memory.

　　“Abacus mental arithmetic” as a unique skill of calculation,how does the relation between the “abacus mental arithmetic” and the right and left brain? If we could understand the functional orientation of “abacus mental arithmetic” skill in the brain,it will help unclose the psychological mechanism of “abacus mental arithmetic”.Many studies have found that the right brain of “abacus mental arithmetic” expert is more excellent than the left brain to carry out mental arithmetic.For instance,Kimiko and Kawano divided 35 pupils into primary,middle and senior groups to observe,they measured the β-wave when each pupil had rest and carried the “abacus mental arithmetic”,and found that as to the pupils who had relatively poor ability,their left brain rear produced β-wave to control logic function,whereas as to the pupils who were in middle and senior groups produced β-wave to control emotional function.From that,we can see that the abacus promotes the function of right brain and develops the creative thinking.Another study also found that the right and left brain play important role in the formation of abacus image,but the right brain is more conducive to operate the image than the left brain.It could be believed that,the formation of “abacus mental arithmetic” needs the coordination of right brain and left brain,especially the participation of right brain.Abacus mental arithmetic needs to confirm the number identification,extract the arithmetic facts,temporarily store the intermediate results,and operate the mental representation and other multiple cognitive functions.According to the progress of brain science research,we also believe that “abacus mental arithmetic” is the collaborative activity of the brain and cerebellum.At the early stage of the formation of “abacus mental arithmetic” skill,the brain must carry out conscious endeavor,whereas in the process of skill formation,cerebellum creates the models to imitate the brain.The production process of this model is realized by repeated practice.Once the cerebellum forms the thinking model,people could automatically and unconsciously think.Therefore,we presume that the formation of “abacus mental arithmetic” skill is the result of “whole brain coordination and participation”.Of course,the relation between “abacus mental arithmetic” and the brain still needs to be further researched.It is gratifying that the continuous development and improvement of functional magnetic resonance imaging,positron emission tomography and other brain functional imaging technologies have provided a broad space to the research on the subject of “abacus mental arithmetic” and the brain.

　　Chapter Three:Is it credible that “abacus mental arithmetic” could develop children's potential to a large extent?

　　Some people said that except that race results from a small number of top abacus fiends,that is,“prodigies”,were applauded,it was hard to believe that such an experiment brought a good harvest to a large extent from ordinary rural schools.From the research in Minghe Primary School in Cixi City Zhejiang,we found the emergence of many “prodigies” which was firstly in the form of hobby group to carry out a small-scale experiment (to attract 17 students from different grades to participate in it).After two years of practice,the students in the hobby group all achieved fairly good results in all respects,especially because these students who did not participate in abacus mental arithmetic training had the tendency to focus on a few subjects.Their learning interest and calculation ability were generally improved,while their think became more vivacious.So in autumn 1988,the school selected from the first year students to organize the experiment of repeated teaching for “abacus mental arithmetic”,from point to surface and gradually expanded the scope of the feasible testing,focused on improving rural education quality at a large extent and promoting all-round development of students.Now this been extended to the entire urban and rural areas in Cixi City and many schools inside and outside the province.After years of experiments,how does the effectiveness of it? Two conclusions of our study report (see the third publication “Educational Research”,1993) are noticeable.

　　Firstly,the abacus mental arithmetic teaching could be carried out in ordinary rural primary schools (no requirement on special conditions),whereas the reaching shall be assumed by ordinary teachers in rural areas (no requirement on high academic qualifications but they must have the spirit of responsibility and dedication),which should be implemented to ordinary classes and students (no requirement on IQ or high marks).It does not require other disciplines making way for it,whereas other work in the school shall not be subject to it.Only for understanding and support,people can quickly obtain better teaching results than the expectation.

　　Secondly,because of abacus mental arithmetic teaching and training,children gradually master the abacus skills and proficiency,which could really give positive impact on their quality and school atmosphere.“It effectively increases the cognitive level and intellectual level of the students.It could enhance the calculation ability of the students and raise the mathematical level of the students,which will help students cultivate scientific knowledge learning,cultural interest and self-confidence,effectively improve the efficiency of student learning in peacetime,improve the habit of thinking so that they will be smart.Moreover,it also plays positive role in the school teaching and educational process to alleviate students' heavy burden of schoolwork,improve the confidence from teachers to students' learning ability,exert the leading role of teachers in teaching process,etc.In 1991,Cixi City once again invited experts and professors to organize a high-level expert group,the expert group identified the teaching of the abacus mental arithmetic (not just Minghe Primary School),conclusion is the same and fully recognized.

　　Some people put forward that this result is based on the fatigue of students and teachers,which is at the expense of hard-working.They believe that when training,the students shall highly concentrate,whereas the training volume is great.The long training will affect the physical and mental development of the students.A large number of training with high-strung nerve certainly hinder the healthy development of students,but the abacus mental arithmetic training could be scattered in extra-curricular class or out of school.There is no need to carry out too much training for one time.In class training,considering that this kind of teaching is more trouble,the training time is often completed in a matter of minutes.The survey from experimental classes and hobby groups,students are very active and do not appear to have over-fatigue,which are better than students in physical development from regular classes.As to teachers,those who never touch abacus mental arithmetic will feel troubled,but to those who master abacus mental arithmetic teaching method,their hardship might not be so great,as extra-curricular work can be greatly reduced,many schoolwork could be finished and revised in the class.Teachers could focus their energy on teaching plan and research.To increase density of 40-minute class is quite necessary,which is also the study orientation for other teachers.Any work shall pay attention to the efficiency,of course,education is no exception.However,to the teachers who have not fully grasped the abacus mental arithmetic shall spend a lot of effort at the initial stage.

　　In short,abacus mental arithmetic,this wonderful work in the teaching reform,at least has been fully affirmed by the community in the Zhejiang Province,people are delighted to compare “abacus,this is the rediscover of national jewelry”.Zhejiang Provincial CPC Committee,the provincial government issued the call to the province,“to build Zhejiang into abacus village”.“Integration of the three arithmetic methods” obtains a new strong impetus abacus,while the impact of “abacus mental arithmetic” teaching has been rapidly expanded,from province to province,number of teachers who have been dispatched to participate in training center of our province has been thousands,except the number from 11 cities and places in Zhejiang,they are all from 26 provinces,autonomous regions and municipalities.It could be said that it is not accidental for the abacus mental arithmetic to root and develop rapidly in Zhejiang.Therefore,great achievements of the experimental results are not hard to believe,but basically credible.

　　Chapter Four:Whether it is necessary and feasible to melt theabacus mental arithmetic into new courses?

　　The facts have proved that the advantages of “abacus mental arithmetic” teaching experiment are prominent in children's mathematics learning,intellectual development and the quality of education.The learning promotion is in the ascendant at home and abroad;in the primary school mathematics education,there has been a century's reform practice,algorithms and teaching have been getting more sophisticated and have been used widely,which embodies our highest achievements in mathematics.At present,the “abacus mental arithmetic” just combines modern mathematics and computer education so as to integrate the Chinese and western mathematical way of thinking.However,it is unfortunate.Some leaders and experts do not understand this.They think it is computer electronic information age.Shall we still need this ancient and backward abacus calculation? Shall the abacus need to be put in the History Museum? A few articles and a few words “dismissed” the abacus from the mathematics teaching in primary schools,which led to national basic education curriculum in primary schools failing to give the rightful place of “abacus mental arithmetic” in mathematics education.All the versions of the new lesson do not absorb the reasonable knowledge structure into mathematics teaching from “abacus mental arithmetic”,so “abacus mental arithmetic” fails to exert its education value.Through many years' investigation and repeated argumentation,we think the experimental results are necessary to integrate into new curriculum in mathematics education.It could be implemented in ordinary class of ordinary school from ordinary teaches to ordinary students,while the desired results of new national curriculum reform could be achieved.

　　One of the reasons is that the Chinese nation should be provided with a set of teaching material and method in line with the situation of the country and Chinese characteristics.“Abacus mental arithmetic” teaching is based on abacus,whereas the abacus is one of China's civil common algorithm,the combination of abacus and mental arithmetic becomes a novel method.This calculation method filled with Chinese characteristics and rooted in Chinese soil will be certainly welcomed by people across the country and be widely used.At the same time,the reform experimental results of Minghe Primary School indicates that the abacus,the representative of the Chinese traditional culture,still has potential to be developed in modern education.“Abacus mental arithmetic” teaching has already begun to be quickly implemented in many places inside and outside our province,this is not a casual thing,but it does include an element for improving quality.In addition,it is quite suitable for China's national conditions and the nature and tasks of education,so it could be spread.The second reason is that the majority of educators have improved the awareness of “abacus mental arithmetic”teaching importance,gradually understand and support the creativity practice of abacus,that is,they hold the cooperation attitude to “abacus mental arithmetic”.On the basis of successful experience in Minghe Primary School and other places,people have proceeded to develop the curriculum and assessment standards,compile temporary teaching materials,improve the teaching and obtain a lot of good results.This is just like the remarks pointed out by Mr.Shen Baiying,our predecessor in education,he said,“Those who do not look at and try but oppose,they no longer criticize when they see the specific results;those who suspect have no comment when the fact proves;those who wait to see successively prepare to experiment when they get the support from leaders.These are the good condition in current teaching reform.”

　　It is clear that in the promotion of mathematics education in primary schools,it is an important work to establish a set of experimental materials not only coinciding with new curriculum of current mathematics but also absorbing the “abacus mental arithmetic”.So far,the textbooks and teaching materials of “abacus mental arithmetic” have been successively published,but these publications can not be categorized into experimental materials of New Curriculum,as they still lack the organic integration with modern mathematical structure,most of them are only regarded as the introduction of mental arithmetic technology.In view of this situation,the specialized personnel and strength shall be organized to make the materials.

　　Abacus and abacus calculation are the treasure of Chinese culture,which is one of the great creations from our ancestors to the culture of mankind.The unique “abacus mental arithmetic” teaching is a creative experiment to carry forward the culture of Chinese nation.We are glad to hear that in 2002,Beijing established the World Abacus Mental Arithmetic Association participated by the representatives from 16 countries and regions,Shanghai Abacus Mental Arithmetic Association also held seminar “to vigorously promote the Chinese abacus culture mechanical thinking” in 2005,to further build the platform for exchange so as to unite the experts and scholars from science history,mathematics history,mathematics education,abacus and other various subjects to tackle the key problems.At the same time,the teaching and reform experiment of abacus mental arithmetic all over the country are deepening,so that the abacus,abacus calculation and abacus mental arithmetic researches have been achieved great progress in both theory and experiment.Therefore,we propose to establish a national expert group for abacus mental arithmetic teaching and reform experiment,so that they could be responsible for integrating abacus mental arithmetic into New Curriculum materials in mathematics education and designing careful experimental program.In this way,abacus mental arithmetic could enter the new curriculum and head into the internationalization.