Imagining the Density of Fractions
Creators: name: Schmeelk, Suzanna
name: Horwitz, Kenneth
Publisher: name: No Publisher Supplied
Year: 2014

description: This VMC Analytic focuses on a set of activities taken from a yearlong study designed to investigate how 4th grade students build fraction ideas (Schmeelk, 2010). The activities on this day of November 1, 1993 examine the placement of unit fractions on a number line segment between 0 and 1.This Analytic focuses on the November 1, 1993 session with fourth graders in a Colts Neck, New Jersey classroom as students are asked to extend their notions of fraction with rods as operator to the idea of fraction as number. In this session, the students are challenged to order unit fractions ½, 1/3 … 1/10 on a number line segment between 0 and 1. Notice how students use a variety of representations to reason about the placement of fractions – from gestures, to drawings to line segment. Notice, too, how they fold back to earlier models with rods, as represented in rod-model drawings.  The events in this analytic come from the 15th of 44 recorded sessions of the fraction intervention. Prior to this session, students were engaged in building models with Cuisenaire rods to identify number names for the various fractions in relation to the particular rod that was given the number name 1. References:Bulgar, S. (2002).  Through a teacher’s lens: Children’s constructions of division of fractions. Unpublished doctorial dissertation, Rutgers, The State University of New Jersey, New Brunswick.Maher, C. A., Palius, M. F., Maher, J. A. &amp; Sigley, R. (2012). Teachers’ identification of children’s upper and lower bound reasoning. . In L. R. Van Zoest, J. J. Lo, &amp; J. L. Kratky (Eds.), Proceedings of the 34th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, 460-467. Kalamazoo, MI: Western Michigan University.Mueller, M., Yankelewitz, D. &amp; Maher, C. (2010). Promoting student reasoning through careful task design: A comparison of three studies. International Journal for Studies in Mathematics Education, 3(1), 135-16.National Governors Association Center for Best Practices, C. o. (2010). Common Core State Standards for Mathematics. National Governors Association Center for Best Practices, Council of Chief State School Officers, Washington D.CReynolds, S. L. (2005).  A study of fourth grades students’ exploration into comparing fractions. Unpublished doctorial dissertation, Rutgers, The State University of New Jersey, New Brunswick.Rowland, T. (2002). Proofs in number theory: History and heresy. In Proceedings of the twenty-sixth annual meeting of the international group for the psychologyof mathematics education Vol. I, Norwich, England, (pp. 230–235).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.Steencken, E. P. (2001).  Studying fourth graders’ representations of fraction ideas. Unpublished doctorial dissertation, Rutgers, The State University of New Jersey, New Brunswick.Yankelewitz, Y., Mary Mueller and Carolyn A. Maher. (2010). A task that elicits reasoning: A dual analysis. Journal of Mathematical Behavior, 29, 76-85.Yankelewitz, D. (2009) The development of mathematical reasoning in elementary school students’ exploration of fraction ideas. Unpublished doctoral dissertation, Rutgers, The State University of New Jersey, New Brunswick.