Educational Studies in Mathematics

, Volume 82, Issue 3, pp 455–479 | Cite as

Teaching prospective teachers about fractions: historical and pedagogical perspectives



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.


Whole numbers Fractions Rational numbers Part–whole Measurement and ratio Division Pre-service teacher education Elementary Mathematics K–12 


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Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of DelawareNewarkUSA
  2. 2.Kaput Center for Research and Innovation in STEM EducationUniversity of Massachusetts DartmouthFairhavenUSA
  3. 3.Teacher EducationMichigan State UniversityEast LansingUSA

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