한국수학교육학회지시리즈D:수학교육연구 (Research in Mathematical Education)

  • 제24권1호
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  • Pages.1-27
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  • 2021
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  • 1226-6191(pISSN)
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  • 2287-9943(eISSN)
한국수학교육학회 (Korean Society of Mathematical Education)
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Where's the Procedural Fluency?: U.S. Fifth Graders' Demonstration of the Standard Multiplication Algorithm

  • Colen, Yong S. (Indiana University of Pennsylvania) ;
  • Colen, Jung (Chadron State College)
  • 투고 : 2021.01.19
  • 심사 : 2021.03.30
  • 발행 : 2021.03.31
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초록

For elementary school children, learning the standard multiplication algorithm with accuracy, clarity, consistency, and efficiency is a daunting task. Nonetheless, what should be our expectation in procedural fluency, for example, in finding the product of 25 and 37 among fifth grade students? Collectively, has the mathematics education community emphasized the value of conceptual understanding to the detriment of procedural fluency? In addition to examining these questions, we survey multiplication algorithms throughout history and in textbooks and reconceptualize the standard multiplication algorithm by using a new tool called the Multiplication Aid Template.

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참고문헌

  1. Beckmann, S. (2018). Mathematics for elementary teachers with activities (5th ed.). Pearson Education, Inc.
  2. Bell, M., Bell, J., Bretzlauf, J., Dillard, Flanders, J., Hartfield, R., Issacs, A., Leslie, D., McBride, J., Pitvorec, K., & Saecker, P. (2012a). Everyday mathematics: Student reference book (grade 4). Chicago: The McGraw-Hill Companies, Inc.
  3. Bell, M., Bretzlauf, J., Dillard, A., Hartfield, R., Issacs, A., Maxcy, R., McBride, J., Pitvorec, K., Saecker, P., Balfanz, R., Carroll, W., & Sconiers, S. (2012b). Everyday mathematics: Teacher's lesson guide: vol. 1 (grade 4). Chicago: The McGraw-Hill Companies, Inc.
  4. Billstein, R., Boschmans, B., Libeskind, S., & Lott, J. (2020). A Problem solving approach to mathematics for elementary school teachers (13th ed.) Pearson Education, Inc.
  5. Fuson, K. C. (1986). Roles of representation and verbalization in the teaching of multi-digit addition and subtraction. European Journal of Psychology of Education, 1(2), 35-56. https://doi.org/10.1007/bf03172568
  6. Fuson, K. C., & Briars, D. J. (1990). Using a base-ten blocks learning/teaching approach for first-and second-grade place-value and multidigit addition and subtraction. Journal for Research in Mathematics Education, 21(3), 180-206. https://doi.org/10.2307/749373
  7. Kamii, C. (1989). Young children continue to reinvent arithmetic, 2nd grade. New York: Teachers College Press. [This book has been replaced by a 2nd edition published in 2004.]
  8. Korean Ministry of Education (2014a). Mathematics in Grade 3, Volume 2: Teacher's Guide.
  9. Korean Ministry of Education (2014b). Mathematics in Grade 4, Volume 1: Teacher's Guide.
  10. National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.
  11. National Council of Teachers of Mathematics. (1991). Professional teaching standards. Reston, VA: Author.
  12. National Council of Teachers of Mathematics. (1995). Assessment standards. Reston, VA: Author.
  13. National Council of Teachers of Mathematics. (2000). Executive Summary Principles and Standards for School Mathematics. Reston, VA: Author.
  14. National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for mathematics initiatives. Washington, DC: Authors.
  15. Smith, D. E. (1919). Number stories of long ago. Boston: Ginn and Company.