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ERIC Number: EJ883869
Record Type: Journal
Publication Date: 2009
Pages: 20
Abstractor: As Provided
ISSN: ISSN-1033-2170
Developing Mathematics Understanding and Abstraction: The Case of Equivalence in the Elementary Years
Warren, Elizabeth; Cooper, Tom J.
Mathematics Education Research Journal, v21 n2 p76-95 2009
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 was 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. (Contains 9 figures.)
Mathematics Education Research Group of Australasia. GPO Box 2747, Adelaide SA 5001, Australia. Tel: +61-8-8363-0288; Fax: +61-8-8362-9288; e-mail:; Web site:
Publication Type: Journal Articles; Reports - Evaluative
Education Level: Elementary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Identifiers - Location: Australia