Capitalising on Inherent Ambiguities in Symbolic Expressions of Generality

The exploration of number patterns as a pedagogical approach to introducing algebra has been advocated by many mathematics educators. French (2002) comments that the introduction of algebra through what is potentially a wide range of pattern generalisation activities may be effective in assisting pupils to see algebra as both meaningful and purposeful right from the earliest stages. Generalisation is after all one of the core components of mathematical activity. In addition, from a pedagogic point of view, pattern generalisation activities are a meaningful way of arriving at and exploring algebraically equivalent expressions of generality. The purpose of this article is briefly to explore the generalisation of patterns set in pictorial contexts, with specific focus on the ambiguity inherent in the algebraic expressions as they relate to the pictorial pattern. (Contains 4 figures.)