Figural Pattern Generalisation
Duncan Samson · 2023
The generalisation of number patterns is a widely used didactic approach to engaging with introductory algebra as well as promoting algebraic reasoning. Presenting such number patterns in a pictorial context allows for a far greater depth of engagement compared with patterns presented purely numerically. While numeric patterns have the danger of becoming superficial ‘pattern spotting’ tasks which can be generalised using basic algorithmic methods, number patterns that are presented pictorially provide a rich context for multiple solution strategies. This has the significant benefit of allowing pupils to develop a variety of equivalent expressions of generality, each of which is visually rooted in the pictorial context. Such an approach has the potential to lead to genuine mathematical exploration, to allow pupils to engage with each other’s ‘ways of seeing’, and thus become appreciative of, and sensitised to, different forms of mathematical sense-making.