As an alternative to looking solely at linear functions, a three-lesson learning progression developed for Year 6 students that incorporates triangular numbers to develop children's algebraic thinking is described and evaluated.

When subgoal location was appropriate to the serial pattern, subjects were likely to use a strategy resulting in enhanced rule induction and transfer with increased subgoal density. When subgoal location was not appropriate, subjects tended to use a strategy resulting in considerably reduced role induction and transfer. (Author/PN)