Simplifying algebraic expressions

Year: 1999

Author: Cooper, Tom, Williams, Anne, Baturo, Annette

Type of paper: Refereed paper

Developing ideas about the simplification of algebraic expressions (e.g., 5x+2x; 4x2p; 8x+5y+2x- 3y) requires the development of abstract schema (Ohlsson, 1993) for multiplication and addition, as well as the algebraic notion of variable. For example, simplifying by adding of like things applies in arithmetic for whole numbers (e.g., 5 tens + 2 tens = 7 tens, 50+20=70), fractions (e.g., 5 ninths +2 ninths = 7 ninths, 5/9+2/9=7/9), and decimals (e.g., 0.5+0.2=0.7), as well as in algebra (e.g., 5x+2x=7x, where x is any number, a variable). Thus, simplifying by adding of like things is an abstract schema because its meaning lies in the relationships formed between the numbers and variables, rather than in the numbers and variables themselves. A teaching experiment, whose aim was to teach simplification procedures through developing arithmetic principles as abstract schema, was conducted on grade 8 pupils. A variety of activities, including patterns and concrete materials, were employed to highlight the similarities between arithmetic and algebra in the simplification of expressions. This paper describes the activities and their rationale, and discusses the results in terms of the students' responses to the teaching episodes, and the learning exhibited in follow-up interviews.