Developing mathematics understanding and abstraction : the case of equivalence in the elementary years

Warren, Elizabeth & Cooper, Thomas J. (2009) Developing mathematics understanding and abstraction : the case of equivalence in the elementary years. Mathematics Education Research Journal, 21(2), pp. 76-95.

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Generalising arithmetic structures is seen as a key to developing algebraic understanding. Many adolescent students begin secondary school with a poor understanding of the structure of arithmetic. This paper presents a theory for a teaching/learning trajectory designed to build mathematical understanding and abstraction in the elementary school context. The particular focus is on the use of models and representations to construct an understanding of equivalence. The results of a longitudinal intervention study with five elementary schools, following 220 students as they progressed from Year 2 to Year 6, informed the development of this theory. Data were gathered from multiple sources including interviews, videos of classroom teaching, and pre-and post-tests. Data reduction resulted in the development of nine conjectures representing a growth in integration of models and representations. These conjectures formed the basis of the theory.

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ID Code: 28113
Item Type: Journal Article
Refereed: Yes
Keywords: generalising, equivalence and equations, early algebra, algebraic thinking, arithmetic structures
DOI: 10.1007/BF03217546
ISSN: 1033-2170
Subjects: Australian and New Zealand Standard Research Classification > EDUCATION (130000) > CURRICULUM AND PEDAGOGY (130200) > Mathematics and Numeracy Curriculum and Pedagogy (130208)
Divisions: Current > Research Centres > Office of Education Research
Current > Schools > School of Teacher Education & Leadership
Current > QUT Faculties and Divisions > Faculty of Education
Copyright Owner: Copyright 2009 Springer
Copyright Statement: The definitive version is available on
Deposited On: 06 Dec 2009 22:52
Last Modified: 28 Mar 2013 08:54

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