Exploring early secondary students' algebraic generalisation in geometric context

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Abstract

Exploring multiple representations of a relationship between two variables has been shown to help students learn conceptually about functions in algebra. This paper discusses an investigation of 102 Year 7 students, prior to their study of algebra, which considered their making sense of a linear functional relationship in two geometric contexts - through generalisation of a 2-dimensional figural growing pattern and through representation of its variables on a Cartesian plane. This provided the opportunity to consider how algebraic and geometric understandings might reinforce each other in different representations of the same function. Students used a variety of ways to describe the structure of the figural pattern and 40 were able to use this to create an explicit rule, with over 20 already using a symbolic expression or full equation. Two thirds of the students created an incorrect graphical representation of the relationship and the other third drew either a column or line graph. Implications for middle-school algebra learning are discussed.
Original languageEnglish
Title of host publicationProceedings of the 39th Conference of the International Group for the Psychology of Mathematics Education (PME39)
EditorsKim Beswick, Tracey Muir, Jill Wells
Place of PublicationPraha Czech Republic
PublisherInternational Group for the Psychology of Mathematics Education
Pages297 - 304
Number of pages8
Volume4
Publication statusPublished - 2015
EventAnnual Conference of the International Group for the Psychology of Mathematics Education 2015 - Hobart, Australia
Duration: 13 Jul 201518 Jul 2015
Conference number: 39th

Conference

ConferenceAnnual Conference of the International Group for the Psychology of Mathematics Education 2015
Abbreviated titlePME 2015
CountryAustralia
CityHobart
Period13/07/1518/07/15

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