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Learning Fractions Through Folding in an Elementary Face-to-Face Classroom

Part of the Computer-Supported Collaborative Learning Series book series (CULS,volume 15)

Abstract

This chapter describes a data set used for analysis by Shirouzu, Tausan-Matu, and Chiu and discussion by Lund in the following chapters. The data set consists of a lesson that involves six children studying the multiplication of fractions in a sixth-grade classroom in Japan and their recall of its content after 5 months. The task for the children was to cut out three-fourths of two-thirds of a piece of origami paper and then discuss whether or not their solutions were the same. As a result, the children created eight solutions of five types and reached the conclusion that these solutions were the same, because their area equaled one-half of the whole by the multiplication 2/3 × 3/4. Not all of the children, however, remembered this conclusion in their long-term recall. The three researchers analyzed the interaction that took place during the lesson as well as its relationship to recall in the next three chapters, which are integrated by Lund in her discussion chapter.

Keywords

  • Conceptual Understanding
  • Boundary Object
  • External Resource
  • Fraction Multiplication
  • Cottage Cheese

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  • Barrett, J. E., & Clements, D. H. (2003). Quantifying length: Children’s developing abstractions for measures of linear quantity in one-dimensional and two-dimensional contexts. Cognition and Instruction, 21, 475–520.

    CrossRef  Google Scholar 

  • Brown, J. S., Collins, A., & Duguid, P. (1989). Situated cognition and the culture of learning. Educational Researcher, 18, 32–42.

    CrossRef  Google Scholar 

  • Engle, R. A. (2006). Framing interactions to foster generative learning: A situative explanation of transfer in a community of learners classroom. The Journal of the Learning Sciences, 15, 451–498.

    CrossRef  Google Scholar 

  • Engle, R., & Conant, F. R. (2002). Guiding principles for fostering productive disciplinary engagement: Explaining an emergent argument in community of learners classroom. Cognition and Instruction, 20, 399–483.

    CrossRef  Google Scholar 

  • Hatano, G., & Inagaki, K. (1991). Sharing cognition through collective comprehension activity. In L. B. Resnick, J. M. Levine, & S. D. Teasley (Eds.), Perspectives on socially shared cognition (pp. 331–348). Washington, DC: American Psychological Association.

    CrossRef  Google Scholar 

  • Izsák, A. (2005). “You have to count the squares”: Applying knowledge in pieces to learning rectangular area. The Journal of the Learning Sciences, 14(3), 361–403.

    CrossRef  Google Scholar 

  • Izsák, A. (2008). Mathematical knowledge for teaching fraction multiplication. Cognition and Instruction, 26, 95–143.

    CrossRef  Google Scholar 

  • Lave, J., Murtaugh, M., & de la Rocha, O. (1984). The dialectic of arithmetic in grocery shopping. In B. Rogoff & J. Lave (Eds.), Everyday cognition: Its development in social context (pp. 67–94). Cambridge, MA: The Harvard University Press.

    Google Scholar 

  • Linn, M., Lewis, C., Tsuchida, I., & Songer, N. B. (2000). Beyond fourth-grade science: Why do U.S. and Japanese students diverge? Educational Researcher, 29(3), 4–14.

    CrossRef  Google Scholar 

  • Lobato, J., Burns, A., & Munoz, R. (2003). How “Focusing Phenomena” in the instructional environment support individual students’ generalizations. Mathematical Thinking & Learning, 5, 1–36.

    CrossRef  Google Scholar 

  • Miyake, N. (1986). Constructive interaction and the iterative process of understanding. Cognitive Science, 10, 151–177.

    CrossRef  Google Scholar 

  • Miyake, N. (2008). Conceptual change through collaboration. In S. Vosniadou (Ed.), International handbook of research on conceptual change (pp. 453–478). New York, NY: Routledge.

    Google Scholar 

  • Palinscar, A. S. (1989). Less charted waters. Educational Researcher, 18, 5–7.

    Google Scholar 

  • Pea, R. D. (1993). Practices of distributed intelligence and designs for education. In G. Salomon (Ed.), Distributed cognitions: Psychological and educational considerations (pp. 47–87). Cambridge, MA: Cambridge University Press.

    Google Scholar 

  • Roschelle, J. (1992). Learning by collaborating: Convergent conceptual change. The Journal of the Learning Sciences, 2, 235–276.

    CrossRef  Google Scholar 

  • Salomon, G. (1990). If intelligence is distributed: What about the cultivation of individuals’ abilities? Paper presented at a symposium in American Educational Research Association, Boston.

    Google Scholar 

  • Sato, M. (2006). Challenging for higher learning: Building communities of learners. Tokyo, Japan: Shogakukan [in Japanese].

    Google Scholar 

  • Sherin, M. G. (2002). A balancing act: Developing a discourse community in a mathematics classroom. Journal of Mathematics Teacher Education, 5, 205–233.

    CrossRef  Google Scholar 

  • Shirouzu, H. (2008). Observing the lesson as “outsiders”: Lesson study from learning scientists’ perspective. Proceeding of Annual Meeting of Japanese Association of Educational Psychology, s58–s59. [in Japanese]

    Google Scholar 

  • Star, S. L., & Griesemer, J. R. (1989). Institutional ecology, ‘translations’ and boundary objects: Amateurs and professionals in Berkeley’s Museum of Vertebrate Zoology. Social Studies of Science, 19(3), 387–420.

    CrossRef  Google Scholar 

  • Stigler, J. W., & Hiebert, J. (1999). The teaching gap: Best ideas from the world’s teachers for improving education in the classroom. New York, NY: The Free Press.

    Google Scholar 

  • Strom, D., Kemeny, V., Lehrer, R., & Forman, E. (2001). Visualizing the emergent structure of children’s mathematical argument. Cognitive Science, 25, 733–773.

    CrossRef  Google Scholar 

  • Suthers, D. D. (this volume, Ch. 1). The productive multivocality project: origins and objectives. In D. D. Suthers, K. Lund, C. P. Rosé, C. Teplovs, & N. Law (Eds.), Productive multivocality in the analysis of group interactions, Chapter 1. New York, NY: Springer.

    Google Scholar 

  • Vosniadou, S. (2008). International handbook of research on conceptual change. New York, NY: Routledge.

    Google Scholar 

  • Wineburg, S. S. (1989). Remembrance of theories past. Educational Researcher, 18, 7–10.

    Google Scholar 

  • Wortham, S. (2001). Interactionally situated cognition: A classroom example. Cognitive Science, 25, 37–66.

    CrossRef  Google Scholar 

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Correspondence to Hajime Shirouzu .

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Appendix

Appendix

This section shows the transcript in the form that it was originally shared, with analysts Trausan-Matu and Chiu and discussant Lund (cf. Table 4.5). Section authors use line numbers when referring to their analyses.

Table 4.5 Transcript provided by Shirouzu and shared with analysts and discussant

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Shirouzu, H. (2013). Learning Fractions Through Folding in an Elementary Face-to-Face Classroom. In: Suthers, D., Lund, K., Rosé, C., Teplovs, C., Law, N. (eds) Productive Multivocality in the Analysis of Group Interactions. Computer-Supported Collaborative Learning Series, vol 15. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-8960-3_4

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