One-third is three-quarters of one-half

Peter Gould; Lynne Outhred; Michael Mitchelmore

One-third is three-quarters of one-half

Peter Gould, Lynne Outhred, Michael Mitchelmore

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

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Abstract

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 language	English
Title of host publication	Identities, cultures and learning spaces
Subtitle of host publication	proceedings of the 29th annual conference of the Mathematics Education Research Group of Australasia, held at Rydges Lakeside Hotel, Canberra, 1-5 July 2006
Editors	Peter Grootenboer, Robyn Zevenbergen, Mohan Chinnappan
Place of Publication	Adelaide, S. Aust.
Publisher	MERGA
Pages	262-269
Number of pages	8
ISBN (Print)	1920846123
Publication status	Published - 2006
Event	Mathematics Education Research Group of Australasia Conference (29th : 2006) - Canberra, ACT Duration: 1 Jul 2006 → 5 Jul 2006

Conference

Conference	Mathematics Education Research Group of Australasia Conference (29th : 2006)
City	Canberra, ACT
Period	1/07/06 → 5/07/06

Bibliographical note

Copyright Mathematics Education Research Group of Australasia Incorporated. Original published at http://www.merga.net.au/node/38?year=2006. 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 http://www.merga.net.au

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Publisher version (open access)Final published version, 273 KBLicence: Unspecified

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Gould, P., Outhred, L., & Mitchelmore, M. (2006). One-third is three-quarters of one-half. In P. Grootenboer, R. Zevenbergen, & M. Chinnappan (Eds.), Identities, cultures and learning spaces: proceedings of the 29th annual conference of the Mathematics Education Research Group of Australasia, held at Rydges Lakeside Hotel, Canberra, 1-5 July 2006 (pp. 262-269). MERGA.

Gould, Peter ; Outhred, Lynne ; Mitchelmore, Michael. / One-third is three-quarters of one-half. Identities, cultures and learning spaces: proceedings of the 29th annual conference of the Mathematics Education Research Group of Australasia, held at Rydges Lakeside Hotel, Canberra, 1-5 July 2006. editor / Peter Grootenboer ; Robyn Zevenbergen ; Mohan Chinnappan. Adelaide, S. Aust. : MERGA, 2006. pp. 262-269

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title = "One-third is three-quarters of one-half",

abstract = "This paper reports on part of a larger cross-sectional study of the development of students{\textquoteright} 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{\textquoteright} concept images and it is argued that the “number of pieces” interpretation is a common response to regional models of fractions.",

author = "Peter Gould and Lynne Outhred and Michael Mitchelmore",

note = "Copyright Mathematics Education Research Group of Australasia Incorporated. Original published at http://www.merga.net.au/node/38?year=2006. 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 http://www.merga.net.au; Mathematics Education Research Group of Australasia Conference (29th : 2006) ; Conference date: 01-07-2006 Through 05-07-2006",

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language = "English",

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Gould, P, Outhred, L & Mitchelmore, M 2006, One-third is three-quarters of one-half. in P Grootenboer, R Zevenbergen & M Chinnappan (eds), Identities, cultures and learning spaces: proceedings of the 29th annual conference of the Mathematics Education Research Group of Australasia, held at Rydges Lakeside Hotel, Canberra, 1-5 July 2006. MERGA, Adelaide, S. Aust., pp. 262-269, Mathematics Education Research Group of Australasia Conference (29th : 2006), Canberra, ACT, 1/07/06.

One-third is three-quarters of one-half. / Gould, Peter; Outhred, Lynne; Mitchelmore, Michael.
Identities, cultures and learning spaces: proceedings of the 29th annual conference of the Mathematics Education Research Group of Australasia, held at Rydges Lakeside Hotel, Canberra, 1-5 July 2006. ed. / Peter Grootenboer; Robyn Zevenbergen; Mohan Chinnappan. Adelaide, S. Aust.: MERGA, 2006. p. 262-269.

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

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T1 - One-third is three-quarters of one-half

AU - Gould, Peter

AU - Outhred, Lynne

AU - Mitchelmore, Michael

N1 - Copyright Mathematics Education Research Group of Australasia Incorporated. Original published at http://www.merga.net.au/node/38?year=2006. 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 http://www.merga.net.au

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

M3 - Conference proceeding contribution

SN - 1920846123

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BT - Identities, cultures and learning spaces

A2 - Grootenboer, Peter

A2 - Zevenbergen, Robyn

A2 - Chinnappan, Mohan

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T2 - Mathematics Education Research Group of Australasia Conference (29th : 2006)

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ER -

Gould P, Outhred L, Mitchelmore M. One-third is three-quarters of one-half. In Grootenboer P, Zevenbergen R, Chinnappan M, editors, Identities, cultures and learning spaces: proceedings of the 29th annual conference of the Mathematics Education Research Group of Australasia, held at Rydges Lakeside Hotel, Canberra, 1-5 July 2006. Adelaide, S. Aust.: MERGA. 2006. p. 262-269

One-third is three-quarters of one-half

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