Advertisement

The Cognitive Process of Chinese Abacus Arithmetic

  • Pei-Luen Patrick Rau
  • Anping Xie
  • Ziyang Li
  • Cuiling Chen
Article

Abstract

Based on the literature review about abacus arithmetic, this study proposes a model of the cognitive process of Chinese abacus arithmetic. This model describes three methods for solving abacus arithmetic problems: retrieval method, procedure method, and mental arithmetic method and three external factors that affect the choice of those methods: level of expertise, level of difficulty, and type of operation. The experiment in the study invited 36 participants including 12 vocational high-school students as junior experts, 12 ordinary high-school students as novices, and 12 bank clerks as senior experts to validate the 3 × 3 × 2 experiment. The results of this study indicate that (1) the retrieval method, procedure method, and mental arithmetic method are the three main calculation methods of abacus arithmetic, each of them having some variations; (2) experts tend to use the retrieval method, while novices tend to use the mental arithmetic method; (3) the retrieval method and mental arithmetic method are applied more for simple operations and addition problems, while the procedure method is applied more for complicated operations and subtraction problems.

Keywords

Abacus arithmetic Cognitive process Mental arithmetic method Procedure method Retrieval method 

Notes

Acknowledgments

This study was funded by the National Natural Science Foundation of China (grant no. 71188001).

References

  1. Ashcraft, M. H. (1992). Cognitive arithmetic: A review of data and theory. Cognition, 44(1), 75–106.CrossRefGoogle Scholar
  2. Ashcraft, M. H. & Christy, K. S. (1995). The frequency of arithmetic facts in elementary texts: Addition and multiplication in grades 1–6. Journal for Research in Mathematics Education, 26(5), 396–421.CrossRefGoogle Scholar
  3. Atkinson, R. & Shiffrin, R. (1968). Human memory: A proposed system and its control processes. New York, NY: Academic.Google Scholar
  4. Ball, C. T., Langholtz, H. J., Auble, J. & Sopchak, B. (1998). Resource-allocation strategies: A verbal protocol analysis. Organizational Behavior and Human Decision Processes, 76(1), 70–88.CrossRefGoogle Scholar
  5. Baroody, A. J. (1994). An evaluation of evidence supporting fact-retrieval models. Learning and Individual Differences, 6(1), 1–36.CrossRefGoogle Scholar
  6. Campbell, J. I. D. (1996). Mechanisms of simple addition and multiplication: A modified network-interference theory and simulation. Mathematical Cognition, 1(1), 121–164.Google Scholar
  7. Campbell, J.I.D. & Oliphant, M. (1992). Representation and retrieval of arithmetic facts: A network-interference model and simulation. In J. I. D. Campbell (Ed.). The nature and origin of mathematical skills (pp. 331–364). Amsterdam, The Netherlands: North-Holland, Elsevier Science.Google Scholar
  8. Campbell, J. I. D. & Timm, J. C. (2000). Adults’ strategy choices for simple addition: Effects of retrieval interference. Psychonomic Bulletin & Review, 7(4), 692–699.CrossRefGoogle Scholar
  9. Campbell, J. I. D. & Xue, Q. (2001). Cognitive arithmetic across cultures. Journal of Experimental Psychology: General, 130(2), 299–315.CrossRefGoogle Scholar
  10. Gardner, W. P. & Rogoff, B. (1990). Children’s deliberateness of planning according to task circumstances. Developmental Psychology, 26(1), 480–487.CrossRefGoogle Scholar
  11. Geary, D. C. (1994). Children’s mathematical development: Research and practical applications. Washington, DC: American Psychological Association.CrossRefGoogle Scholar
  12. Geary, D. C. (1996). The problem-size effect in mental addition: Developmental and cross-national trends. Mathematical Cognition, 2(1), 63–94.CrossRefGoogle Scholar
  13. Geary, D. C. & Wiley, J. G. (1991). Cognitive addition: Strategy choice and speed-of-processing differences in young and elderly adults. Psychology and Aging, 6(3), 474–483.CrossRefGoogle Scholar
  14. Hamann, M. S. & Ashcraft, M. H. (1986). Textbook presentations of the basic addition facts. Cognition and Instruction, 3(3), 173–202.CrossRefGoogle Scholar
  15. Hatano, G. (1983). Becoming an expert in mental abacus operation: A case of routine expertise. Advances in Japanese Cognitive Science, 1(1), 141–160.Google Scholar
  16. Hatta, T., Hirose, T., Ikeda, K. & Fukuhara, H. (1989). Digit memory of soroban experts: Evidence of utilization of mental imagery. Applied Cognitive Psychology, 3(1), 23–33.CrossRefGoogle Scholar
  17. Klayman, J. (1985). Children’s decision strategies and their adaptation to task characteristics. Organizational Behavior and Human Decision Processes, 35(2), 179–201.CrossRefGoogle Scholar
  18. Koshmider, J. W. & Ashcraft, M. H. (1991). The development of children’s mental multiplication skills. Journal of Experimental Child Psychology, 51(1), 53–89.CrossRefGoogle Scholar
  19. LeFevre, J. A. & Bisanz, J. (1986). A cognitive analysis of number-series problems: Sources of individual differences in performance. Memory & Cognition, 14(4), 287–298.CrossRefGoogle Scholar
  20. LeFevre, J. A., Sadesky, G. S. & Bisanz, J. (1996). Selection of procedures in mental addition: Reassessing the problem size effect in adults. Journal of Experimental Psychology: Learning, Memory, and Cognition, 22(1), 216–230.Google Scholar
  21. Lemaire, P. & Siegler, R. S. (1995). Four aspects of strategic change: Contributions to children’s learning of multiplication. Journal of Experimental Psychology: General, 124(1), 83–97.CrossRefGoogle Scholar
  22. Li, S. T. (1958). The origin of the abacus and its development. Paper presented at the ACM Annual Conference/Annual Meeting: Preprints of papers presented at the 13th national meeting of the Association for Computing Machinery, Urbana, IL.Google Scholar
  23. Negishi, H., Ueda, K., Kriyama, M., Kato, M., Kawaguchi, H. & Atsumori, H. (2005). Change of mental representation with the expertise of mental abacus. In B. G. Bara, L. Barsalou & M. Bucciarelli (Eds.), Proceedings of the 27th Annual Conference of the Cognitive Science Society, 2005 (pp. 1606–1611). Mahwah, NJ: Erlbaum.Google Scholar
  24. Repovs, G. & Baddeley, A. D. (2006). The multi-component model of working memory: Explorations in experimental cognitive psychology. Neuroscience, 139(1), 5–21.CrossRefGoogle Scholar
  25. Siegler, R. S. (1987). The perils of averaging data over strategies: An example from children’s addition. Journal of Experimental Psychology: General, 116(3), 250–264.CrossRefGoogle Scholar
  26. Siegler, R. S. (1988). Strategy choice procedures and the development of multiplication skill. Journal of Experimental Psychology: General, 117(3), 258–275.CrossRefGoogle Scholar
  27. Siegler, R. S. & Jenkins, E. A. (1989). How children discover new strategies. Hillsdale, MI: Erlbaum.Google Scholar
  28. Siegler, R. S. & Lemaire, P. (1997). Older and younger adults’ strategy choices in multiplication: Testing predictions of ASCM using the choice/no-choice method. Journal of Experimental Psychology: General, 126(1), 71–92.CrossRefGoogle Scholar
  29. Siegler, R. S. & Shipley, C. (1995). Variation, selection, and cognitive change. In T. Simon & G. S. Halford (Eds.), Developing cognitive competence: New approaches to process modeling. Hillsdale, MI: Erlbaum.Google Scholar
  30. Siegler, R. S. & Shrager, J. (1984). Strategy choices in addition and subtraction: How do children know what to do? In C. Sophian (Ed.), Origins of cognitive skills (pp. 229–293). Hillsdale, MI: Erlbaum.Google Scholar
  31. Widaman, K. F., Geary, D. C., Cormier, P. & Little, T. D. (1989). A componential model for mental addition. Journal of Experimental Psychology: Learning, Memory, and Cognition, 15(5), 898–919.Google Scholar

Copyright information

© Ministry of Science and Technology, Taiwan 2015

Authors and Affiliations

  • Pei-Luen Patrick Rau
    • 1
  • Anping Xie
    • 1
  • Ziyang Li
    • 1
  • Cuiling Chen
    • 1
  1. 1.Department of Industrial EngineeringTsinghua UniversityBeijingChina

Personalised recommendations