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Characteristics of teaching and learning single-digit whole number multiplication in china: the case of the nine-times table

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Abstract

This study investigates the teaching and learning of single-digit whole number multiplication in China. Analysis of data from documents, classroom teaching, and semi-structured interviews revealed three salient characteristics of emphasizing oral calculation, calculation speed, and understanding across standards, textbook and classroom practices. It also showed how mathematics teachers enact these features in their teaching practice to help students develop their computational skills. The study particularly elaborates the role played by the nine-times table, or Chengfa Kou Jue Table (CKJ Table) in teaching practices, as well as how teachers treat memorization of CKJ and how understanding of operations contributes to their better understanding the relationship between the two in the teaching process.

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References

  • Artigue, M., de Shalit, E., & Ralston, A. (2006). Controversial issues in K-12 mathematical education. In Proceedings of the international congress of mathematicians (pp. 1645–1662). Madrid.

  • Arzarello, F., Azrou, N., Bussi, M. G. B., Xu, H. S., & Man, K. S. (2018). Tradition in whole number arithmetic. In M. G. B. Bussi & X. H. Sun (Eds.), Building the foundation: Whole numbers in the primary grades (pp. 343–373). New York: Springer.

    Chapter  Google Scholar 

  • Baroody, A. J. (2003). The development of adaptive expertise and flexibility: The integration of conceptual and procedural knowledge. In A. J. Baroody & A. Dowker (Eds.), The development of arithmetic concepts and skills: Constructing adaptive expertise (pp. 1–33). Abingdon: Routledge.

    Google Scholar 

  • Baroody, A. J., & Dowker, A. (Eds.). (2013). The development of arithmetic concepts and skills: Constructive adaptive expertise. Abingdon: Routledge.

    Google Scholar 

  • Baroody, A. J., & Ginsburg, H. P. (1986). The relationship between initial meaningful and mechanical knowledge of arithmetic. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 75–112). Hillsdale: Lawrence Erlbaum Associates.

    Google Scholar 

  • Bussi, M. G. B., Inprasitha, M., Arzarello, F., Bass, H., Kortenkamp, U., Ladel, S., Lajoie, C., Ni, Y., Tottmann, T., Sarungi, V., Soury-Lavergne, S., & Young-Loveridge, J. (2018). Aspects that affect whole number learning: Cultural artefacts and mathematical tasks. In M. G. B. Bussi & X. H. Sun (Eds.), Building the foundation: Whole numbers in the primary grades (pp. 181–226). New York: Springer.

    Chapter  Google Scholar 

  • Bussi, M. G. B., & Sun, X. H. (2018). Building the foundation: Whole numbers in the primary grades. New York: Springer.

    Book  Google Scholar 

  • Cai, J. (2002). Assessing and understanding U.S. and Chinese students’ mathematical thinking. ZDM, 34(6), 278–290.

    Google Scholar 

  • Campbell, J., & Robert, N. (2008). Bidirectional associations in multiplication memory: Conditions of negative and positive transfer. Journal of Experimental Psychology/ Learning, Memory and Cognition, 34(3), 546–555. https://doi.org/10.1037/0278-7393.34.3.546.

    Article  Google Scholar 

  • Campbell, J. I. D., & Xue, Q. (2001). Cognitive arithmetic across cultures. Journal of Experimental Psychology, 130(2), 299.

    Article  Google Scholar 

  • Cao, Y., & Leung, F. K. (Eds.). (2018). The 21st century mathematics education in China. New York: Springer.

    Google Scholar 

  • Cao, Y., Li, X., & Zuo, H. (2015). Characteristics of multiplication teaching of whole numbers in China: The application of the nine-times table. In X. Sun, B. Kaur, & J. Novotna (Eds.), Conference proceedings of the ICMI study 23: Primary mathematics study on whole numbers (pp. 423–430). Macao, China.

  • Cao, Y., & Wu, L. (2016). International comparative study on secondary school mathematics textbook of six countries focusing on content of algebra. Shanghai: Shanghai Education Press.

    Google Scholar 

  • Denzin, N. (1970). Strategies of multiple triangulation. In N. Denzin (Ed.), The research act in sociology: a theoretical introduction to sociological method (pp. 297–313). New York: McGraw-Hill.

    Google Scholar 

  • Flick, U. (2007). Qualitative Sozialforschung: Eine Eindührung. Reinbek bei Hamburg: Rowohlt.

    Google Scholar 

  • Geary, D. C. (1994). Children’s mathematical development: Research and practical applications. Washington, DC: American Psychological Association.

    Book  Google Scholar 

  • Ho, C. S. H., & Fuson, K. C. (1998). Children’s knowledge of teen quantities as tens and ones: Comparisons of Chinese, British, and American kindergartners. Journal of Educational Psychology, 90(3), 536.

    Article  Google Scholar 

  • Huang, R., Ozel, Z. E. Y., Li, Y., & Rowntree, R. V. (2013). Does classroom instruction stick to textbooks? A case study of fraction division. In Y. Li & G. Lappan (Eds.), Mathematics curriculum in school education (pp. 443–472). New York: Springer.

    Google Scholar 

  • James, W. (2008). Principles of psychology. New York: Dover.

    Google Scholar 

  • Kahn, V. E. (2005). A scenario method of teaching multiplication and division concepts. US20050089830 A1. http://www.freepatentsonline.com/y2005/0089830.html. Accessed 10 Sept 2018.

  • Lampert, M. (1986). Knowing, doing, and teaching multiplication. Cognition & Instruction, 3(4), 305–342.

    Article  Google Scholar 

  • Lefevre, J., & Liu, J. (1997). The role of experience in numerical skill multiplication performance in adults from Canada and China. Mathematical Cognition, 3(1), 31–62.

    Article  Google Scholar 

  • Lin, F., & Kubina, R. Jr. (2005). A preliminary investigation of the relationship between fluency and application for multiplication. Journal of Behavioral Education, 14(2), 73–87. https://doi.org/10.1007/s10864-005-2703-z.

    Article  Google Scholar 

  • Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah: Lawrence Erlbaum Associates.

    Google Scholar 

  • Ministry of Education of the People’s Republic of China (MoE). (2011). 全日制义务教育数学课程标准 (2011年版) (Mathematics curriculum standards for full-time compulsory education [2011 version]). Beijing: Beijing Normal University Press.

    Google Scholar 

  • Mullis, I. V. S. E., & Martin, M. O. E. (2013). TIMSS 2015 Assessment Frameworks. International Association for the Evaluation of Educational Achievement.

  • Ni, Y. (2015). How the Chinese methods produce arithmetic proficiency in children. In X. Sun, B. Kaur, & J. Novotna (Eds.), Conference proceedings of the ICMI study 23: Primary mathematics study on whole numbers (pp. 339–345).Macao, China.

  • Nunes, T., Dorneles, B. V., Lin, P. J., & Rathgeb-Schnierer, E. (2016). Teaching and learning about whole numbers in primary school. New York: Springer.

    Book  Google Scholar 

  • OECD. (2014). “Foreword”. In PISA 2012 results: What students know and can do (Volume I, Revised edition, February 2014): Student performance in mathematics, reading and science. Paris: OECD.

    Google Scholar 

  • Resnick, L. B., & Ford, W. W. (Eds.). (1981). The psychology of mathematics for instruction. Hillsdale: Erlbaum.

    Google Scholar 

  • Rittle-Johnson, B., & Siegler, R. S. (1998). The relation between conceptual and procedural knowledge in learning mathematics: A review. In C. Donlan (Ed.), Studies in developmental psychology: The development of mathematical skills (pp. 75–110). Hove: Psychology.

    Google Scholar 

  • Robitaille, D. F., & Travers, K. J. (1992). International studies of achievement in mathematics. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 687–709). New York/Reston: Macmillan/National Council of Teachers of Mathematics.

    Google Scholar 

  • Silver, E. A., & Kenney, P. A. (2000). Results from the Seventh Mathematics Assessment of the National Assessment of Educational Progress. New York: National Council of Teachers of Mathematics.

    Google Scholar 

  • Steel, S., & Funnell, E. (2001). Learning multiplication facts: A study of children taught by discovery methods in England. Journal of Experimental Child Psychology, 79(1), 37–55.

    Article  Google Scholar 

  • Sun, X. H., & Bussi, M. G. B. (2018). Language and cultural issues in the teaching and learning of WNA. In M. G. B. Bussi & X. H. Sun (Eds.), Building the foundation: Whole numbers in the primary grades (pp. 35–70). New York: Springer.

    Chapter  Google Scholar 

  • Sun, X. H., Kaur, B., & Novotna, J. (Eds.). (2015) Proceeding of ICMI Study 23: Primary mathematics study on whole number. June, 2015, Macao, China.

  • Wang, L., Liu, Q., Du, X., & Liu, J. (2018). Chinese mathematics curriculum reform in the twenty-first century. Chapter 3. In Y. Cao & F. K. Leung (Eds.), The 21st century mathematics education in China. New York: Springer.

    Google Scholar 

  • Woodward, J. (2006). Developing automaticity in multiplication facts: Integrating strategy instruction with timed practice drills. Learning Disability Quarterly, 29(4), 269–289.

    Article  Google Scholar 

  • Zhou, X., Chen, C., Zhang, H., Chen, C., Zhou, R., & Dong, Q. (2007). The operand-order effect in single-digit multiplication: An ERP study of Chinese adults. Neuroscience Letters, 414(1), 41–44.

    Article  Google Scholar 

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Zhang, S., Cao, Y., Wang, L. et al. Characteristics of teaching and learning single-digit whole number multiplication in china: the case of the nine-times table. ZDM Mathematics Education 51, 81–94 (2019). https://doi.org/10.1007/s11858-018-01014-8

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