Experimenting with quasi-variables in the teaching of Algebra

Year: 2002

Author: Williams, Anne, Cooper, Tom

Type of paper: Refereed paper

A teaching experiment with two Year 8 classes facilitated early understandings of algebra by focusing on the meaning of equals, expressions, equations, and the variable x. Activities highlighted the similarities between arithmetic and algebra by developing generalisations in arithmetic that could be applied in algebra. Knowing that an arrangement of numbers such as in 78 - 49 + 49 = 78 is true because the same number is being added and subtracted has been termed quasi-variable understanding (Fujii & Stephens, 2001). This paper focuses on one component of the teaching experiment, the role of quasi-variable worksheets in the development of variable understanding of changes that leave expressions and equations invariant. In particular, the changes were named the doing and undoing of expressions and doing the same thing to both sides of equations. Results showed that these quasi-variable ideas were difficult for students to grasp, but there was evidence that they mediated the development of similar variable understandings.