One-third is three-quarters of one-half

Peter Gould, Lynne Outhred, Michael Mitchelmore

    Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionpeer-review

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    This paper reports on part of a larger cross-sectional study of the development of students’ quantitative concepts of fractions. In total, 1676 students in Years 4–8 were asked a series of questions designed to elicit their concept images of various fractions. Three questions asked the students to construct a regional model (parts of a circle) for one-half, one-third and one-sixth. The initial analysis of the evoked concept image of one-third revealed an unexpectedly high number of responses shading one-quarter of a circle. Further analysis suggested that what appeared to be one-quarter was frequently intended to be one of three parts, confirming that drawings frequently do not “speak for themselves”. Area is not always the intended feature of regional models of fractions in students’ concept images and it is argued that the “number of pieces” interpretation is a common response to regional models of fractions.
    Original languageEnglish
    Title of host publicationIdentities, cultures and learning spaces
    Subtitle of host publicationproceedings of the 29th annual conference of the Mathematics Education Research Group of Australasia, held at Rydges Lakeside Hotel, Canberra, 1-5 July 2006
    EditorsPeter Grootenboer, Robyn Zevenbergen, Mohan Chinnappan
    Place of PublicationAdelaide, S. Aust.
    Number of pages8
    ISBN (Print)1920846123
    Publication statusPublished - 2006
    EventMathematics Education Research Group of Australasia Conference (29th : 2006) - Canberra, ACT
    Duration: 1 Jul 20065 Jul 2006


    ConferenceMathematics Education Research Group of Australasia Conference (29th : 2006)
    CityCanberra, ACT

    Bibliographical note

    Copyright Mathematics Education Research Group of Australasia Incorporated. Original published at Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further reproduction rights please contact the publisher at


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