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Pre-service teachers’ flexibility with referent units in solving a fraction division problem

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Abstract

This study investigated 111 pre-service teachers’ (PSTs’) flexibility with referent units in solving a fraction division problem using a length model. Participants’ written solutions to a measurement fraction division problem were analyzed in terms of strategies and types of errors, using an inductive content analysis approach. Findings suggest that most PSTs could calculate fraction division and make equivalent fractions procedurally but did not have the quantitative meanings of measurement division with fraction quantities or of making equivalent fractions. Implications are discussed for the improvement of PSTs’ specialized knowledge for teaching fraction division.

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Notes

  1. This ability is related to norming, which is described as “the process of reconceptualzing a system in relation to some fixed unit or standard” (Lamon, 1994, p. 94) – more specifically – identifying the standard unit with which to measure and representing quantities of an object with the unit.

  2. According to Star (2005), deep procedural knowledge is defined as “knowledge of procedures that is associated with comprehension, flexibility, and critical judgment and that is distinct from (but possibly related to) knowledge of concepts” (p. 408).

  3. This is one among many possible ways to help PSTs think about why the invert and multiply strategy works.

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Acknowledgements

An earlier version of this paper was presented at the NIMS (National Institute for Mathematical Sciences) and KSME (The Korean Society of Mathematical Education) International Workshop in 2017.

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  1. Division of Teacher Preparation, Arizona State University, 1050 S. Forest Mall, Tempe, AZ, 85287, USA

    Mi Yeon Lee

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Correspondence to Mi Yeon Lee.

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Lee, M.Y. Pre-service teachers’ flexibility with referent units in solving a fraction division problem. Educ Stud Math 96, 327–348 (2017). https://doi.org/10.1007/s10649-017-9771-6

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