Investigating Students’ Attention to Covariation Features of their Constructed Graphs in a Figural Pattern Generalisation Context

Abstract

An important goal in school algebra is to help students notice the covariational nature of functional relationships, how the values of variables change in relation to each other. This study explored 102 Year 7 (12 to 13-year-old) students’ covariational reasoning with their constructed graphs for figural growing patterns they had generalised. A sequence of figural pattern generalisation tasks was incorporated in their school’s linear equations topic, before formal introduction to linear graphs. The aim was to see if or how the students described covariation features of their graph and connected them to their generalisation. Evidence was found for a noticeable increase in both the students’ use of symbolic algebra for their pattern generalisation and knowledge of Cartesian plane graphing conventions, but not for increasing covariational reasoning with their graphs or connections to their generalisation. Possible implications and further research directions on graphing in a pattern generalisation context are discussed.