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 language | English |
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Title of host publication | Proceedings of the 39th Conference of the International Group for the Psychology of Mathematics Education (PME39) |
Editors | Kim Beswick, Tracey Muir, Jill Wells |
Place of Publication | Praha Czech Republic |
Publisher | International Group for the Psychology of Mathematics Education |
Pages | 297 - 304 |
Number of pages | 8 |
Volume | 4 |
Publication status | Published - 2015 |
Event | Annual Conference of the International Group for the Psychology of Mathematics Education 2015 - Hobart, Australia Duration: 13 Jul 2015 → 18 Jul 2015 Conference number: 39th |
Conference
Conference | Annual Conference of the International Group for the Psychology of Mathematics Education 2015 |
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Abbreviated title | PME 2015 |
Country/Territory | Australia |
City | Hobart |
Period | 13/07/15 → 18/07/15 |