한국수학교육학회지시리즈D:수학교육연구 (Research in Mathematical Education)

  • 제15권1호
  • /
  • Pages.45-57
  • /
  • 2011
  • /
  • 1226-6191(pISSN)
  • /
  • 2287-9943(eISSN)
한국수학교육학회 (Korean Society of Mathematical Education)
권호 표지
DOI QR코드

DOI QR Code

Mathematical Thinking through Different Representations and Analogy

  • 투고 : 2011.02.13
  • 심사 : 2011.03.25
  • 발행 : 2011.03.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

Mathematical thinking is a core element in mathematics education and classroom learning. This paper wish to investigate how primary four (grade 4) students develop their mathematical thinking through working on tasks in multiplication where greatest products of multiplication are required. The tasks include the format of many digit times one digit, 2 digits times 2 digits up to 3 digits times 3 digits. It is found that the process of mathematical thinking of students depends on their own representation in obtaining the product. And the solution is obtained through a pattern/analogy and "pattern plus analogy" process. This specific learning process provides data for understanding structure and mapping in problem solving. The result shows that analogy allows successful extension of solution structure in the tasks.

키워드

참고문헌

  1. Ambrose, R.; Baek, J.-M.; Carpenter, T. (2003). Children's Invention of Multidigit Multiplication and Division Algorithms. In: A. J. Baroody and A. Dowker (Eds), The development of arithmetic concepts and skills: constructing adaptive expertise (pp. 305-336). Mahwah, NJ: Lawrence Erlbaum Associates. ME 2003c.02302
  2. Bruner, J. S. (1960). The Process of Education. Cambridge, Mass.: Harvard University Press / New York: Vintage Books.
  3. Cheng, C. C. L. (2008). From counting to mathematical structure. J. Korea Soc. Math. Educ. Ser. D 12(2), 127-142. ME 2008f.00094
  4. Cheng, C. C. L. (2010). Mathematical thinking and developing mathematical structure. J. Korea Soc. Math. Educ. Ser. D 14(1), 33-50. ME 2010f.00626
  5. English, L. D. (1997). Mathematical Reasoning. Analogies, Metaphors, and Images. Mahwah, NJ: Lawrence Erlbaum Associates, Publishers. ME 1997f.03923
  6. English, L. D. & Halford, G. S. (1995). Mathematics Education: Models and Processes. Mahwah, NJ: Lawrence Erlbaum Associates, Publishers. ME 1996c.01527
  7. Gentner, D. (1983). Structural mapping: A theoretical framework for analogy. Cognitive Science 7. 155-170. https://doi.org/10.1207/s15516709cog0702_3
  8. Halford, G. S. (1993). Children's understanding: The development of mental models. Hillsdale, NJ: Lawrence Erlbaum Associates.
  9. Reid, D. A. (2002). Conjecturing and Refutations in Grade 5 Mathematics. J. Res. Math. Educ. 33(1), 5-29. ME 2002e.04028 https://doi.org/10.2307/749867
  10. Treffers, A. & Beishuizen, M. (1999). Realistic Mathematics Education in the Netherlands. In: I. Thompson (Ed.), Issues in Teaching Numeracy in Primary Schools (pp. 27-38). Milton Keynes, UK: Open University Press.
  11. Vosniadou, S. (1989). Anaolgical reasoning as a mechanism in knowledge acquisition: A developmental perspective. In: S. Vosniadou & A. Ortony (Eds.), Similarity and analogical reasoning (pp. 413-437). Cambridge, England: Cambridge University Press.