Educational Studies in Mathematics
, Volume 82, Issue 3, pp 455479
First online:
Teaching prospective teachers about fractions: historical and pedagogical perspectives
 Jungeun ParkAffiliated withDepartment of Mathematical Sciences, University of Delaware Email author
 , Beste GüçlerAffiliated withKaput Center for Research and Innovation in STEM Education, University of Massachusetts Dartmouth
 , Raven McCroryAffiliated withTeacher Education, Michigan State University
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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 fractionasnumber and the extension of fractions from whole numbers, although most of them mentioned or emphasized these aspects of fractions during interviews.
Keywords
Whole numbers Fractions Rational numbers Part–whole Measurement and ratio Division Preservice teacher education Elementary Mathematics K–12 Title
 Teaching prospective teachers about fractions: historical and pedagogical perspectives
 Journal

Educational Studies in Mathematics
Volume 82, Issue 3 , pp 455479
 Cover Date
 201303
 DOI
 10.1007/s1064901294408
 Print ISSN
 00131954
 Online ISSN
 15730816
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 Whole numbers
 Fractions
 Rational numbers
 Part–whole
 Measurement and ratio
 Division
 Preservice teacher education
 Elementary Mathematics
 K–12
 Authors

 Jungeun Park ^{(1)}
 Beste Güçler ^{(2)}
 Raven McCrory ^{(3)}
 Author Affiliations

 1. Department of Mathematical Sciences, University of Delaware, 402 Ewing Hall, Newark, DE, 19711, USA
 2. Kaput Center for Research and Innovation in STEM Education, University of Massachusetts Dartmouth, 200 Mill Road, Suite 150B, Fairhaven, MA, 02719, USA
 3. Teacher Education, Michigan State University, 620 Farm Lane #114B, East Lansing, MI, 48824, USA