Rethinking the role of algorithms in school mathematics: a conceptual model with focus on cognitive development
Rethinking the role of algorithms in school mathematics: a conceptual model with focus on cognitive development
Starting from the context of mathematics learning in the East and West, this paper discusses the position and role of algorithms within school mathematics and argues that learning of algorithms has suffered from an alleged dichotomy between procedures and understanding, in that algorithms have been associated with low-level cognition. The paper first introduces a broad perspective about algorithms in school mathematics, and then, partially drawing on Bloom’s taxonomy and Säljö’s categorization of learning, proposes a model for the learning of algorithms with focus on students’ cognitive development. The model consists of three cognitive levels: (1) Knowledge and Skills, (2) Understanding and Comprehension, and (3) Evaluation and Construction. The model suggests that the learning of algorithms does not simply imply a low level of cognition, and provides a new perspective and framework to analyse the learning of algorithms. Following the model, we present examples to demonstrate the three levels and discuss related teaching strategies. We propose that the model can be used as an analysis tool to reconceptualize the role of algorithms in school mathematics and pose some questions for further research and scholarly discourse in this direction.
481-492
Fan, Lianghuo
28afe582-cd04-4ddc-9acb-a12494af79e0
Bokhove, Christian
7fc17e5b-9a94-48f3-a387-2ccf60d2d5d8
July 2014
Fan, Lianghuo
28afe582-cd04-4ddc-9acb-a12494af79e0
Bokhove, Christian
7fc17e5b-9a94-48f3-a387-2ccf60d2d5d8
Fan, Lianghuo and Bokhove, Christian
(2014)
Rethinking the role of algorithms in school mathematics: a conceptual model with focus on cognitive development.
ZDM: Mathematics Education, 46 (3), .
(doi:10.1007/s11858-014-0590-2).
Abstract
Starting from the context of mathematics learning in the East and West, this paper discusses the position and role of algorithms within school mathematics and argues that learning of algorithms has suffered from an alleged dichotomy between procedures and understanding, in that algorithms have been associated with low-level cognition. The paper first introduces a broad perspective about algorithms in school mathematics, and then, partially drawing on Bloom’s taxonomy and Säljö’s categorization of learning, proposes a model for the learning of algorithms with focus on students’ cognitive development. The model consists of three cognitive levels: (1) Knowledge and Skills, (2) Understanding and Comprehension, and (3) Evaluation and Construction. The model suggests that the learning of algorithms does not simply imply a low level of cognition, and provides a new perspective and framework to analyse the learning of algorithms. Following the model, we present examples to demonstrate the three levels and discuss related teaching strategies. We propose that the model can be used as an analysis tool to reconceptualize the role of algorithms in school mathematics and pose some questions for further research and scholarly discourse in this direction.
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Accepted/In Press date: 2 February 2014
e-pub ahead of print date: 27 May 2014
Published date: July 2014
Organisations:
Mathematics, Science & Health Education
Identifiers
Local EPrints ID: 364654
URI: http://eprints.soton.ac.uk/id/eprint/364654
ISSN: 1863-9690
PURE UUID: 545aae47-2a3d-4f11-bb2b-03c5bf988f09
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Date deposited: 08 May 2014 09:59
Last modified: 15 Mar 2024 03:44
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