Generalising the pattern rule for visual growth patterns: Actions that support 8 year olds’ thinking

Journal article

Warren, Elizabeth A. and Cooper, Thomas J.. (2007). Generalising the pattern rule for visual growth patterns: Actions that support 8 year olds’ thinking. Educational Studies in Mathematics. 67(2), pp. 171 - 185. https://doi.org/10.1007/s10649-007-9092-2
AuthorsWarren, Elizabeth A. and Cooper, Thomas J.
Abstract

A common approach used for introducing algebra to young adolescents is an exploration of visual growth patterns and expressing these patterns as functions and algebraic expressions. Past research has indicated that many adolescents experience difficulties with this approach. This paper explores teaching actions and thinking that begins to bridge many of these difficulties at an early age. A teaching experiment was conducted with two classes of students with an average age of eight years and six months. From the results it appears that young students are capable not only of thinking about the relationship between two data sets, but also of expressing this relationship in a very abstract form.

Year2007
JournalEducational Studies in Mathematics
Journal citation67 (2), pp. 171 - 185
PublisherSpringer Netherlands
ISSN1573-0816
Digital Object Identifier (DOI)https://doi.org/10.1007/s10649-007-9092-2
Scopus EID2-s2.0-38349184283
Page range171 - 185
Research GroupSchool of Education
Place of publicationNetherlands
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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.