Generalising mathematical structure in Years 3-4: A case study of equivalence of expression

Cooper, Thomas J. & Warren, Elizabeth (2008) Generalising mathematical structure in Years 3-4: A case study of equivalence of expression. In Figueras, O., Cortina, J. L., Alatorre, S., Rojano, T., & Sepulveda, A. (Eds.) International Group for the Psychology of Mathematics Education: Proceedings of the Joint Meeting of PME 32 and PME-NA XXX, July 17-21, 2008, Morelia, Mexico.


This paper reports on a section of the Early Algebraic Thinking Project (EATP) which focused on Australian Years 3-4 (age 7-9) students' abilities to generalise mathematical structure in relation to equivalence of expressions (with and without unknowns). It focuses on learning activities involving a sequence of representations to show that change resulting from addition-subtraction requires the performance of the opposite change (subtraction-addition respectively) by the same amount in order to return to the original state (e.g., x=x+p-p or x-q+q in algebraic symbols). It shows that children of this age can generalise this mathematical structure and that effective teaching for generalisation uses creative representation-worksheet partnerships.

Impact and interest:

1 citations in Web of Science®
Search Google Scholar™

Citation counts are sourced monthly from Scopus and Web of Science® citation databases.

These databases contain citations from different subsets of available publications and different time periods and thus the citation count from each is usually different. Some works are not in either database and no count is displayed. Scopus includes citations from articles published in 1996 onwards, and Web of Science® generally from 1980 onwards.

Citations counts from the Google Scholar™ indexing service can be viewed at the linked Google Scholar™ search.

Full-text downloads:

502 since deposited on 24 Nov 2008
15 in the past twelve months

Full-text downloads displays the total number of times this work’s files (e.g., a PDF) have been downloaded from QUT ePrints as well as the number of downloads in the previous 365 days. The count includes downloads for all files if a work has more than one.

ID Code: 15697
Item Type: Conference Paper
Refereed: Yes
Additional URLs:
Keywords: mathematical structure, equivalence of expression, early algebra, generalisation
ISBN: 9786079501310
ISSN: 0771-100X
Subjects: Australian and New Zealand Standard Research Classification > EDUCATION (130000) > CURRICULUM AND PEDAGOGY (130200) > Mathematics and Numeracy Curriculum and Pedagogy (130208)
Australian and New Zealand Standard Research Classification > EDUCATION (130000) > SPECIALIST STUDIES IN EDUCATION (130300) > Learning Sciences (130309)
Divisions: Current > Research Centres > Office of Education Research
Current > QUT Faculties and Divisions > Faculty of Education
Copyright Owner: Copyright 2008 Thomas J. Cooper and Elizabeth Warren
Deposited On: 24 Nov 2008 00:00
Last Modified: 29 Feb 2012 13:44

Export: EndNote | Dublin Core | BibTeX

Repository Staff Only: item control page