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Teaching prospective teachers about fractions: historical and pedagogical perspectives

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Abstract

Research shows that students, and sometimes teachers, have trouble with fractions, especially conceiving of fractions as numbers that extend the whole number system. This paper explores how fractions are addressed in undergraduate mathematics courses for prospective elementary teachers (PSTs). In particular, we explore how, and whether, the instructors of these courses address fractions as an extension of the whole number system and fractions as numbers in their classrooms. Using a framework consisting of four approaches to the development of fractions found in history, we analyze fraction lessons videotaped in six mathematics classes for PSTs. Historically, the first two approaches—part–whole and measurement—focus on fractions as parts of wholes rather than numbers, and the last two approaches—division and set theory—formalize fractions as numbers. Our results show that the instructors only implicitly addressed fraction-as-number and the extension of fractions from whole numbers, although most of them mentioned or emphasized these aspects of fractions during interviews.

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Notes

  1. This development was preceded by many centuries of work by mathematicians who struggled with the notation for fractions and with developing algorithms for operations with fractions. Attempts to integrate fractions into the number system finally led to the formalization of decimal fractions by Stevin in the seventeenth century (Smith, 1925).

  2. A divisible remainder occurs when an object can be divided, for example, a candy bar. An indivisible remainder refers to an object that cannot be divided like a school bus or a person. That is, a result can include half a candy bar, but not half a person.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Delaware, 402 Ewing Hall, Newark, DE, 19711, USA

    Jungeun Park

  2. Kaput Center for Research and Innovation in STEM Education, University of Massachusetts Dartmouth, 200 Mill Road, Suite 150B, Fairhaven, MA, 02719, USA

    Beste Güçler

  3. Teacher Education, Michigan State University, 620 Farm Lane #114B, East Lansing, MI, 48824, USA

    Raven McCrory

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  1. Jungeun Park
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  2. Beste Güçler
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  3. Raven McCrory
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Correspondence to Jungeun Park.

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Park, J., Güçler, B. & McCrory, R. Teaching prospective teachers about fractions: historical and pedagogical perspectives. Educ Stud Math 82, 455–479 (2013). https://doi.org/10.1007/s10649-012-9440-8

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