Developing Mathematics Understanding and Abstraction: The case of Equivalence in the Elementary Years

Journal article

Warren, Elizabeth Anne, de Vries, Eva and Cole, Antoinette. (2009). Developing Mathematics Understanding and Abstraction: The case of Equivalence in the Elementary Years. Mathematics Education Research Journal.
AuthorsWarren, Elizabeth Anne, de Vries, Eva and Cole, Antoinette
Abstract

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.

Year2009
JournalMathematics Education Research Journal
PublisherMathematics Education Research Group of Australasia
Open accessOpen access
Page range76 - 95
Research GroupSchool of Education
Place of publicationMelbourne, Australia
EditorsR. Bergami, S. Pucci and A. Schuller
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https://acuresearchbank.acu.edu.au/item/8v6y0/developing-mathematics-understanding-and-abstraction-the-case-of-equivalence-in-the-elementary-years

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Young, Janelle Patricia and Warren, Elizabeth Anne. (2002). Literacy and numeracy in the home: Parents supporting children's learning. In Bill Cope and Mary Kalantzis (Ed.). Learning for the Future: Proceedings of the Learning Conference 2001. Melbourne, Australia: Common Ground Publishing. pp. 369 - 376
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Warren, Elizabeth Anne. (2002). Arithmetic and quasi-variables: A year 2 lesson to introduce algebra in the early years. In A. Cockburn and E. Nardi (Ed.). International Group for the Psychology of Mathematics Education: Proceedings of the 26th Annual Conference. Norwich, England: University of East Anglia. pp. 369 - 376
Children's understanding of 'turn arounds'
Warren, Elizabeth. (2002). Children's understanding of 'turn arounds'. Australian Primary Mathematics Classroom. 7(1), pp. 9 - 13.
Parent and school partnerships in supporting literacy and numeracy
Warren, Elizabeth and Young, Janelle. (2002). Parent and school partnerships in supporting literacy and numeracy. Asia-Pacific Journal of Teacher Education. 30(3), pp. 217 - 228.