Boon Liang Chua, Celia Hoyles
This paper reports how a group of prospective secondary school teachers in Singapore solved a quadratic generalising task. The findings show that the teachers were capable of deriving multiple equivalent expressions for the task. Three approaches were used to work out the rule: numerical, figural and pragmatic, with the last two being more predominant. It was also found that the same expression could be obtained from different visual representations, and conversely, the same visual representation could also produce different expressions.