Learners’ understanding of the definitions and hierarchical classification of quadrilaterals: towards a theoretical framing
Learners’ understanding of the definitions and hierarchical classification of quadrilaterals: towards a theoretical framing
Defining and classifying quadrilaterals, though an established component of the school mathematics curriculum, appears to be a difficult topic for many learners. The reasons for such difficulties relate to the complexities in learning to analyse the attributes of different quadrilaterals and to distinguish between critical and non-critical aspects. Such learning, if it is to be effective, requires logical deduction, together with suitable interactions between concepts and images. This paper reports on an analysis of data from a total of 263 learners. The main purpose of the paper is to present a theoretical framing that is intended to inform further studies of this important topic within mathematics education research. This theoretical framing relates prototype phenomenon and implicit models to common cognitive paths in the understanding of the relationship between quadrilaterals.
teaching, learning, pedagogy, curriculum, geometry, geometric, geometrical, mathematics, mathematical, quadrilaterals, definitions, hierarchical, theory, deduction, deductive, prototype phenomenon, cognitive paths, understanding, textbooks
0952849848
3-20
Fujita, Taro
8a05b8fc-a1ce-4a7b-9399-3fb00639a3cc
Jones, Keith
ea790452-883e-419b-87c1-cffad17f868f
2007
Fujita, Taro
8a05b8fc-a1ce-4a7b-9399-3fb00639a3cc
Jones, Keith
ea790452-883e-419b-87c1-cffad17f868f
Fujita, Taro and Jones, Keith
(2007)
Learners’ understanding of the definitions and hierarchical classification of quadrilaterals: towards a theoretical framing.
Research in Mathematics Education, 9 (1&2), .
(doi:10.1080/14794800008520167).
Abstract
Defining and classifying quadrilaterals, though an established component of the school mathematics curriculum, appears to be a difficult topic for many learners. The reasons for such difficulties relate to the complexities in learning to analyse the attributes of different quadrilaterals and to distinguish between critical and non-critical aspects. Such learning, if it is to be effective, requires logical deduction, together with suitable interactions between concepts and images. This paper reports on an analysis of data from a total of 263 learners. The main purpose of the paper is to present a theoretical framing that is intended to inform further studies of this important topic within mathematics education research. This theoretical framing relates prototype phenomenon and implicit models to common cognitive paths in the understanding of the relationship between quadrilaterals.
Text
Fujita_Jones_RME_vol9_2007.pdf
- Accepted Manuscript
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Published date: 2007
Additional Information:
Note that, up to volume 9, this journal has one double issue per year; from volume 10 two individual issues per year began to be published. The pagination of this final proof copy is exactly as it appears in the published version. The volume is also available as a book, ISBN: 0953849880
Keywords:
teaching, learning, pedagogy, curriculum, geometry, geometric, geometrical, mathematics, mathematical, quadrilaterals, definitions, hierarchical, theory, deduction, deductive, prototype phenomenon, cognitive paths, understanding, textbooks
Organisations:
Mathematics, Science & Health Education
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Local EPrints ID: 49731
URI: http://eprints.soton.ac.uk/id/eprint/49731
ISBN: 0952849848
ISSN: 1479-4802
PURE UUID: 50d1ea10-8dfb-4939-aa16-f09826dc9dce
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Date deposited: 28 Nov 2007
Last modified: 15 Mar 2024 09:58
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Author:
Taro Fujita
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