The Role of abstraction in learning about rates of change

Ibrahim Hassan; Michael Mitchelmore

The Role of abstraction in learning about rates of change

Ibrahim Hassan, Michael Mitchelmore

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

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Abstract

Fourteen Year 11 advanced mathematics students participated in individual teaching interviews designed to investigate how they learnt various rate of change concepts. The theoretical framework compared two models of abstraction: the empirical abstraction model of Mitchelmore and White and the nested RBC model of Hershkowitz, Schwarz, and Dreyfus. Examples of learning were found that fitted the nested RBC model, but none that fitted the empirical abstraction model. It was concluded that the nested RBC model is valuable for understanding student learning of the concepts of average and instantaneous rate of change, but that empirical abstraction is likely to be more valuable in understanding how students develop a global concept of rate of change earlier.

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
Editors	Peter Grootenboer, Robyn Zevenbergen, Mohan Chinnappan
Place of Publication	Adelaide, S. Aust.
Publisher	MERGA
Pages	278-285
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, 106 KBLicence: Unspecified

Cite this

@inproceedings{017afe910389485787e9f14b84777415,

title = "The Role of abstraction in learning about rates of change",

abstract = "Fourteen Year 11 advanced mathematics students participated in individual teaching interviews designed to investigate how they learnt various rate of change concepts. The theoretical framework compared two models of abstraction: the empirical abstraction model of Mitchelmore and White and the nested RBC model of Hershkowitz, Schwarz, and Dreyfus. Examples of learning were found that fitted the nested RBC model, but none that fitted the empirical abstraction model. It was concluded that the nested RBC model is valuable for understanding student learning of the concepts of average and instantaneous rate of change, but that empirical abstraction is likely to be more valuable in understanding how students develop a global concept of rate of change earlier.",

author = "Ibrahim Hassan 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",

year = "2006",

language = "English",

isbn = "1920846123",

pages = "278--285",

editor = "Peter Grootenboer and Robyn Zevenbergen and Mohan Chinnappan",

booktitle = "Identities cultures and learning spaces",

publisher = "MERGA",

address = "Australia",

}

Hassan, I & Mitchelmore, M 2006, The Role of abstraction in learning about rates of change. 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. MERGA, Adelaide, S. Aust., pp. 278-285, Mathematics Education Research Group of Australasia Conference (29th : 2006), Canberra, ACT, 1/07/06.

The Role of abstraction in learning about rates of change. / Hassan, Ibrahim; Mitchelmore, Michael.
Identities cultures and learning spaces: proceedings of the 29th annual conference of the Mathematics Education Research Group of Australasia. ed. / Peter Grootenboer; Robyn Zevenbergen; Mohan Chinnappan. Adelaide, S. Aust.: MERGA, 2006. p. 278-285.

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

TY - GEN

T1 - The Role of abstraction in learning about rates of change

AU - Hassan, Ibrahim

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 - Fourteen Year 11 advanced mathematics students participated in individual teaching interviews designed to investigate how they learnt various rate of change concepts. The theoretical framework compared two models of abstraction: the empirical abstraction model of Mitchelmore and White and the nested RBC model of Hershkowitz, Schwarz, and Dreyfus. Examples of learning were found that fitted the nested RBC model, but none that fitted the empirical abstraction model. It was concluded that the nested RBC model is valuable for understanding student learning of the concepts of average and instantaneous rate of change, but that empirical abstraction is likely to be more valuable in understanding how students develop a global concept of rate of change earlier.

AB - Fourteen Year 11 advanced mathematics students participated in individual teaching interviews designed to investigate how they learnt various rate of change concepts. The theoretical framework compared two models of abstraction: the empirical abstraction model of Mitchelmore and White and the nested RBC model of Hershkowitz, Schwarz, and Dreyfus. Examples of learning were found that fitted the nested RBC model, but none that fitted the empirical abstraction model. It was concluded that the nested RBC model is valuable for understanding student learning of the concepts of average and instantaneous rate of change, but that empirical abstraction is likely to be more valuable in understanding how students develop a global concept of rate of change earlier.

M3 - Conference proceeding contribution

SN - 1920846123

SP - 278

EP - 285

BT - Identities cultures and learning spaces

A2 - Grootenboer, Peter

A2 - Zevenbergen, Robyn

A2 - Chinnappan, Mohan

PB - MERGA

CY - Adelaide, S. Aust.

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

Y2 - 1 July 2006 through 5 July 2006

ER -

The Role of abstraction in learning about rates of change

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