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ERIC Number: EJ1101483
Record Type: Journal
Publication Date: 2016-Jun
Pages: 21
Abstractor: As Provided
ISSN: ISSN-1033-2170
Developing Students' Functional Thinking in Algebra through Different Visualisations of a Growing Pattern's Structure
Wilkie, Karina J.; Clarke, Doug M.
Mathematics Education Research Journal, v28 n2 p223-243 Jun 2016
Spatial visualisation of geometric patterns and their generalisation have become a recognised pathway to developing students' functional thinking and understanding of variables in algebra. This design-based research project investigated upper primary students' development of explicit generalisation of functional relationships and their representation descriptively, graphically and symbolically. Ten teachers and their classes were involved in a sequence of tasks involving growing patterns and geometric structures over 1 year. This article focuses on two aspects of the study: visualising the structure of a geometric pattern in different ways and using this to generalise the functional relationship between two quantifiable aspects (variables). It was found that in an initial assessment task (n = 222), students' initial visualisations could be categorised according to different types and some of these were more likely to lead either to recursive or explicit generalisation. In a later task, a small number of students demonstrated the ability to find more than one way to visualise the same geometric structure and thus represent their explicit generalisations as different but equivalent symbolic equations (using pronumerals). Implications for the teaching of functional thinking in middle-school algebra are discussed.
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Publication Type: Journal Articles; Reports - Research
Education Level: Elementary Education; Middle Schools; Secondary Education; Junior High Schools
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A