Using meaningful contexts to promote understanding of pronumerals

Developing a conceptual understanding of elementary algebra has been the focus of a number of recent articles in this journal. Baroudi (2006) advocated problem solving to assist students' transition from arithmetic to algebra, and Shield (2008) described the use of meaningful contexts for developing the concept of function. Samson (2011, 2012) also made use of contexts in order to promote ideas of generalisation and equivalent expressions, while Green (2008, 2009) described the use of spreadsheets for investigating functions and solving equations in meaningful contexts. Although many authors promote the use of meaningful contexts there has been little evidence of any positive effect of such approaches. This article describes approaches to teaching algebra in two recent independent projects, one in Australia and one in New Zealand, both of which made extensive use of meaningful contexts. The three aspects of pronumerals (generalised numbers, variables and unknowns) were taught using real contexts to associate meaning with the pronumeral involved. Both projects demonstrated a positive impact of the approaches on junior secondary students' understandings of pronumerals. These findings suggest that classroom teachers should explore the use of meaningful contexts for teaching algebra.