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Research Progress and Prospect of Abacus Knowledge System
2022-02-08 10:35 Hits:175 Source:WAAMA

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Dr. Niu Teng, Abacus and Mental Arithmetic Research Center of Chinese Academy of Fiscal Sciences

 

 

Chinese Abacus Skill is a representative of excellent traditional Chinese culture with a history of more than 1,800 years. Nowadays, although the calculation function of abacus has been replaced by computers and abacus has gradually withdrawn from China's national curriculum system, its scientific, cultural and educational value is enduring. In 2008, abacus was included into the second-batch list of national intangible cultural heritages. On December 4, 2013, Chinese Zhusuan was successfully inscribed on the Representative List of the Intangible Cultural Heritage of Humanity. UNESCO acknowledged and applauded that Chinese Abacus Skill provided “an alternative knowledge system” for the world and was “an example of adaptability to contemporary needs”. Since then, albeit gradual attention from experts and scholars gradually to the thinking and exploration of the abacus knowledge system and other related issues, the overall research progress is relatively slow and few breakthroughs have been made in recent years. In order to attract wider attention, in 2020, the Chinese Abacus and Mental Arithmetic Association, as the protection unit of the national abacus project, held two important academic seminars on “abacus knowledge system. Participating experts exchanged views on the connotation and value of the abacus knowledge system from different perspectives, achieving many results and laying a foundation for in-depth, comprehensive and multi-angle thinking and discussion of the abacus knowledge system in the future. To further study the abacus knowledge system in a systematic and deep way, it’s necessary to comprehensively clarify the existing research results and reflect on and summarize the existing problems in the research so as to point out the direction and focus of future research.

 

 I. Clarify the Connotation of Abacus Knowledge System

 Cihai interprets the “system” as follows: “A number of things are related to and constrain each other, thus constituting a whole” [1]. How to define the connotation of the “abacus knowledge system” is one of the relatively basic research topics in theoretical research of the abacus knowledge system, and also one of the recent issues of key concern by many people. As their research perspectives and starting points vary, scholars have different views on the connotation of the abacus knowledge system, including both narrow interpretations and relatively broad understandings.

 Liu Qinying compared manual computation and abacus from the perspective of the disciplinary knowledge system. She holds that, the knowledge system of manual computation is the algorithmic system of western mathematics--mathematical education, while abacus knowledge system is the algorithmic system of traditional Chinese mathematics--mathematical education [2]. With mathematical history and the abacus knowledge structure as the starting point, Dr. Niu Teng stated that the abacus knowledge system is a whole composed of abacus, calculation formula, algorithm and operational rules that are related to and constrain each other [3]. Its self-consistency is mainly based on the scientific and unified abacus structure, arithmetic formula and operational rules, among others. From the perspective of contemporary mathematics with excellent genes, Guo Qishu points out that the abacus knowledge system is a holistic knowledge network system composed of a “mathematical enlightenment and basic knowledge structure system constructed by the original meaning of abacus and the use of abacus genes”--a result of mathematics with excellent genes, textbooks, core mathematical literacy and brain potential development [4]. According to Guo Shirong, in terms of its connotation, the abacus knowledge system includes “calculation tool abacus, formula system, practice and operational rules, algorithm and arithmetic design”, and is extended to cover the “additional function, value, function and significance of abacus” [5].

 It can be seen from the studies above that the abacus knowledge system contains many contents, of which the most basic is its hardware and software systems, namely abacus, formula, algorithm, etc. In addition, it also includes abacus education, calculation method of abacus and mental arithmetic, formula, education and functional value, which are a key component of the abacus knowledge system. Definitions of the abacus knowledge system above can be regarded as a high generalization of its related contents. However, due to different research perspectives and focuses of scholars, a unified understanding of the connotation of the abacus knowledge system has not formed, which inevitably leads to inconsistent knowledge structures.

 

 II. Analysis on the Content, Method of Thinking and Connotation of Abacus Knowledge System

 We have currently gained a basic understanding of general contents covered by the abacus knowledge system. Existing researches focus more on one or several aspects of the abacus knowledge system, such as the abacus structure, the history of abacus and abacus and mental arithmetic, abacus formula and various algorithms, as well as the teaching methods of abacus and abacus and mental arithmetic. Many researches have been conducted in these areas, with certain results, which will not be detailed here.

 The components of abacus knowledge system are of course important, but the way of thinking that runs through the system and the uniqueness of the system are more important. Wu Wenjun, a famous mathematician, once stated that there were two central ideas throughout the development history of mathematics. Out of them, one was the axiomatic thought, which originated from ancient Greece and occupied a dominant position in modern mathematics, especially pure mathematics; and the other is the mechanized thought, which runs through ancient Chinese mathematics, and has indelible historical achievements and strong vitality in the future. So did Li Wenlin, saying that ancient Chinese mathematics is obviously algorithmic and mechanized characteristic, and abaci are the unique product of Chinese classical algorithm system. He analyzed the uniqueness of the abacus algorithm system from the perspective of necessary conditions for producing abaci: First, the need for calculation tools; second, the decimal value system and decimal fraction; third, mechanization of the computational process.

 Zheng Liguang and Zheng Yi discussed the functions specific to abacus, such as binary representation of numbers and complementation of internal and external beads, from the point of view that abacus is scientific and universally applicable to change subtraction into addition, thus providing an alternative knowledge system for the world [6]. In the paper entitled From the Perspective that “Abacus Provides an Alternative Knowledge System for the World” -- A Contrastive Study on Basic Mechanisms of the Manual Computation Knowledge System and Abacus Knowledge System, Liu Qinying makes a comparative analysis on the basic mechanism and thinking method of the manual computation knowledge system and the abacus knowledge system, covering their counting methods, computing tools and methods as well as mathematics thoughts and methods, and expounds the unique superiority, development prospect and far-reaching significance of abacus. Based on a contrastive analysis on basic mechanisms, thinking methods, carrier forms and other contents of manual computation and abacus, Guo Qishu states that the abacus knowledge system based on “mathematics with excellent genes” is varying more greatly from the manual computation knowledge system that has been westernized as a whole. The former is able to make mathematics education simple, efficient and modern. On top of that, compared with manual computation, “abacus and abacus and mental arithmetic can also be used for brain potential development, physical fitness, cultural identity activities, etc.”

 In general, in research on the abacus knowledge system, there lacks comprehensive analysis and exploration. For example, researches that emphasize the history of abacus are dominated by those on abaci, the history of abacus and abacus and mental arithmetic, abacus calculation formula and various algorithms; while researches that emphasize the mathematical education are dominated by those on the teaching methods of abacus and abacus and mental arithmetic or on the integration with modern mathematical education. On the other hand, the analysis on the way of thinking and uniqueness of the abacus knowledge system is dominated by mathematical thinking, without thinking and understanding from philosophical and cultural perspectives.

 

 III. Analysis on the Function and Value of Abacus Knowledge System

 Boasting a long history, profound cultural accumulation and rich scientific connotation, abacus is recognized for its scientific and cultural value. It also promotes people to constantly study and explore the creative transformation and innovative forms of abacus--abacus and mental arithmetic, giving abacus and mental arithmetic vital practical significance in recent times. In particular, its educational function has gradually attracted increasing attention. In recent years, some breakthrough results have been produced in the research on brain science and cognitive psychology of abacus and mental arithmetic. To name a few, many existing studies can reveal that abacus and mental arithmetic is a special calculation method that largely depends on visual-spatial representation. Abacus training for certain durations can not only improve children's computing ability, but also have a transfer effect on the learning of other subjects and tap the brain intelligence potential of children. When it comes to abacus education, Jiang Zhifeng found in his latest research results that the core value of abacus and mental arithmetic to develop children's intelligence is clear representation and representation operation, and the mathematical goal of abacus and mental arithmetic courses to cultivate clear representation has great educational value [7].

 Some other studies look at its function and value of the abacus knowledge system. Professor Zhou Xinlin shared his understanding of “an alternative knowledge system” from the perspectives of mathematical cognition, mathematical brain and mathematical thinking, and analyzed the necessity and feasibility of the integration of abacus and school education [8]. He said, from the perspective of mathematical thinking and cognition, abacus is called “another knowledge system” as it is non-symbolic, with concrete physical characteristics and situational characteristics. Moreover, based on existing experience, students who receive training in abacus and mental arithmetic have raised their sense of non-symbolic numbers, which in turn improves their performance in symbolic arithmetic. Liu Qinying discussed the scientific nature of abacus and the simplification effect of abacus and mental arithmetic on mathematics enlightenment and basic education from the perspective of knowledge system, such as the simplification of binary representation to four operations and the simplification of bead array figure on geometry.

 Existing studies have abundant discussions on the value and function of abacus and abacus and mental arithmetic, and some progress has been made in both empirical studies and studies based on brain mechanism. However, whether from the historical and cultural deposits or from the current teaching effect, the value and function of this relatively unique knowledge system are far more than that, which still needs further discussion. What’s more, with the emergence and development of abacus and mental arithmetic, a new education system of abacus and abacus and mental arithmetic has been established. However, there is still a lack of systematic research on textbooks of abacus and mental arithmetic, teaching methods, curriculum design, teaching staffing, etc. We should consider how to apply existing theoretical research results to the cultural inheritance of abacus and the education and practice of abacus and mental arithmetic, and give full play to the function and role of abacus and abacus and mental arithmetic, which is of great significance to construct a complete abacus knowledge system and exert the educational value of abacus and mental arithmetic to a greater extent.


 IV. Research Suggestions and Prospects

 In order to further protect intangible cultural heritage, the Chinese government has recently released the Opinions on Further Strengthening the Protection of Intangible Cultural Heritage, which calls for upholding integrity and innovation, respecting the basic connotation of intangible cultural heritage and promoting its contemporary value. It also highlights the need to coordinate and integrate resources, strengthen professional research on state-level intangible cultural heritage and build a sound theoretical research system, which requires us to study and perfect the theoretical system of abacus. As the research on abacus knowledge system is one of the key components of theoretical research, the establishment of a sound knowledge system is conducive to understanding abacus and abacus and mental arithmetic more comprehensively and laying a foundation for better inheritance of the abacus culture.

 Existing research on the abacus knowledge system is relatively scattered, and the research results from one aspect or one side are mostly achieved. However, thanks to the interpretation and research of experts and scholars on different areas, we can gradually see the full picture of the abacus knowledge system, including basic contents and mathematical thinking methods it covers as well as its key value and functions. However, the construction of the knowledge system is definitely a complex process. In addition to defining the connotation of abacus knowledge system, conducting a holistic analysis on the contents of abacus knowledge system and exploring the function and value of abacus and mental arithmetic more comprehensively, we should also focus on addressing some more important issues, which are briefly analyzed below.

 First, we will explore the scientific nature and uniqueness of the abacus knowledge system, including its essential difference with other knowledge systems. The reason why abacus has been developing till now is that its scientific knowledge system has been continuously innovated and improved. One of the proposals submitted by Liu Shangxi, Member of the National Committee of CPPCC and President of Chinese Academy of Fiscal Sciences, at the National People's Congress and the Chinese Political Consultative Conference (NPC&CPPCC) in 2020 is the Proposal on Inclusion of "Another System of Knowledge" into National Basic Education. He points out that UNESCO's recognition of abacus as “an alternative knowledge system” is made based on modern characteristics of abacus, including its science ideas, construction logic and algorithm rules. Therefore, it’s necessary to further clarify and study the scientific nature of the abacus knowledge system, and to connect it with its contemporary value. For example, it is of practical significance for us to further understand and exert the scientific value of abacus and mental arithmetic by deeply exploring the visual representation, psychological process and neural mechanism of abacus and mental arithmetic exercisers and the influence of abacus and mental arithmetic training on brain networks of children, adults and special population [9]. Moreover, in view of respective characteristics of different knowledge systems, there is a need to further figure out essential difference between the abacus knowledge system and rod-arithmetic and manual computation knowledge systems for a deeper understanding of the uniqueness of abacus knowledge system.

 Second, we will analyze and study the origin and development process of the abacus knowledge system while taking into account the development trajectory of traditional Chinese mathematics. It’s generally believed that the abacus algorithm is inherited from the rod-arithmetic algorithm, with its own development and improvement process and different characteristics in different historical periods. For instance, every historical period of abacus development from abacus emergence, development of abacus and calculations in parallel, abacus as the main method of calculation after phasing out rod-arithmetic, combination of abacus, manual computation and oral arithmetic to abacus and mental arithmetic also features different compositions of the knowledge system. Therefore, in terms of its historical development, the abacus knowledge system has also experienced a process of continuous development and reform. It’s necessary to analyze the composition and development process of the abacus knowledge system and clarify the evolution and development of the abacus knowledge system, while taking into account the development trajectory of traditional Chinese mathematics.

 Third, we will discuss the entire composition and characteristics of the abacus knowledge system from multiple dimensions of philosophy, culture, education, etc. Boasting a long history and profound cultural deposits, Chinese Abacus Skill is subject to comprehensive and profound impact of Chinese philosophy and traditional culture in the process of generation and development. At the same time, the emergence and development of abacus and mental arithmetic can be said to be a new discovery in science. In addition to giving birth to new concepts and theories, the fundamental change of the abacus knowledge system also takes place. The fundamental reform of the abacus theory system and of the scientific thinking mode and teaching method enriches the system’s scientific connotation and enhances its realistic significance in contemporary society. The stories above tell that, the process from abacus generation to its transformation into abacus and mental arithmetic is affected by many factors such as philosophy, culture and education. Therefore, while evaluating and interpreting the abacus knowledge system from a modern perspective and thought, we should also interpret the abacus knowledge system from traditional philosophy, culture and education so that it can be promoted to the world and become an important component of world culture. This can also help us deeply understand the cultural attribute of abacus, and take a new look at the composition and characteristics of the abacus knowledge system.

 

 References:

 [1] Cihai Editorial Board. Cihai [M]. Shanghai: Shanghai Lexicographical Publishing House, 1997.

 [2] Liu Qinying. From the Perspective that “Abacus Provides an Alternative Knowledge System for the World” -- A Contrastive Study on Basic Mechanisms of the Manual Computation Knowledge System and Abacus Knowledge System [J]. Abacus and Abacus and Mental Arithmetic, 2018(2):48-52.

 [3] Niu Teng. Analyze the Formation and Development of Abacus Knowledge System Based on Historical Data of Mathematics in Ming and Qing Dynasties [J]. Research on Abacus and Mental Arithmetic, 2021(1):38-44.

 [4] Guo Qishu. Abacus, Another System of Knowledge in the World, its Significance and Function in Contemporary Times [J]. Research on Abacus and Mental Arithmetic, 2021(1):12-21.

 [5] Guo Shirong. Issues on the Knowledge System and Development of Chinese Abacus Skill [J]. Research on Abacus and Mental Arithmetic, 2021(1):1-6.

 [6] Zheng Liguang, Zheng Yi. Abacus Provides Another Knowledge System for the World -- On the Scientific Nature of Abacus Operation Subtraction to Addition [J]. Abacus and Abacus and Mental Arithmetic, 2020(4):20-23.

 [7] Jiang Zhifeng. The Teaching Goal of Abacus and Mental Arithmetic to Foster Clear Representation Has Significant Educational Value [J]. Abacus and Abacus and Mental Arithmetic, 2021(2):3-5.

 [8] Zhou Xinlin. Chinese Abacus Skill As Another Knowledge System: Non-symbolic arithmetic [J]. Abacus and Abacus and Mental Arithmetic, 2021(3):6-8.

 [9] Chen Feiyan. An Overview of Research on Abacus and Mental Arithmetic [J]. Abacus and Abacus and Mental Arithmetic, 2018(6):13-21.

 

(About the Author: Niu Teng, Doctor of Science of the University of Chinese Academy of Sciences. In 2017-2020, she worked as a postdoctoral fellow at the Chinese Academy of Fiscal Sciences. She is now working at Abacus and Mental Arithmetic Research Center of Chinese Academy of Fiscal Sciences, and engaged in research in the fields of the history of abacus and the education and teaching of abacus and abacus and mental arithmetic. She currently serves as Academic Secretary of the Abacus and Abacus and Mental Arithmetic Academic Research Department, Chinese Abacus and Mental Arithmetic Association.)