Abstract
This chapter focuses on number line segment activities taken from one session of the year-long intervention investigating how 4th grade students build fraction ideas (Schmeelk, 2010). The videotapes of the session provide data for a narrative that has been partitioned into an analytic, entitled “Imagining the Density of Fractions.” This analytic provides illustrations of the students ordering fractions on a number line segment between zero and one based on their rod models.
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References
Common Core State Standards Initiative (CCSSI). (2010). National Governors Association (NGA) and the Council of Chief State School Officers.
Fosnot, C., & Dolk, M. (2001). Young mathematicians at work. Portsmouth, NH: Heinemann Publishers.
Goldin, G. (2003). Representation in school mathematics: A unifying research perspective. In J. Kilpatrick, W. G. Martin & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 275–285). Reston, VA: National Council of Teachers of Mathematics.
Kasner, E., & Newman, J. (1949). Mathematics and the imagination. Mineola, NY: Dover Publications.
Mueller, M., Yankelewitz, D., & Maher, C. (2010). Promoting student reasoning through careful task design: A comparison of three studies. International Journal for Studies in Mathematics Education, 3(Transcript line 1), 135–156.
Pirie, S., & Kieren, T. (1992). Watching Sandy’s understanding grow. Journal of Mathematical Behavior, 11, 243–257.
Pirie, S., & Kieren, T. (1994a). Growth in mathematical understanding: How can we characterize it and how can we represent it? In P. Cobb (Ed.), Learning mathematics: Constructivist and interventionist theories of mathematical development (pp. 61–86). Dordrecht, NL: Kluwer.
Pirie, S., & Kieren, T. (1994b). Growth in mathematical understanding: How can we characterize it and how can we represent it? Educational Studies in Mathematics, 26(2–3), 165–190.
Schmeelk, S. (2010). An investigation of fourth grade students growing understanding of rational numbers (Unpublished doctoral dissertation). Rutgers, The State University of New Jersey, New Brunswick, NJ.
Simon, M. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26, 114–145.
Yankelewitz, Y., Mueller, M., & Maher, C. A. (2010). A task that elicits reasoning: A dual analysis. Journal of Mathematical Behavior, 29, 76–85.
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Schmeelk, S. (2017). From Rod Models to Line Segments. In: Maher, C.A., Yankelewitz, D. (eds) Children’s Reasoning While Building Fraction Ideas. Mathematics Teaching and Learning. SensePublishers, Rotterdam. https://doi.org/10.1007/978-94-6351-008-0_15
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DOI: https://doi.org/10.1007/978-94-6351-008-0_15
Publisher Name: SensePublishers, Rotterdam
Online ISBN: 978-94-6351-008-0
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