INTRODUCTION
In this study, we examine the development of algebraic reasoning of Ariel, a participant in a 3-year, after-school, informal mathematics program. We focus on Ariel’s engagement with early algebra ideas, particularly his work on the Ladders Problem (Davis, 1964). The task requires that the student construct a rule to predict the number of Cuisenaire rods needed to build a ladder with varying number of rungs. We report Ariel’s problem solving in sessions, fifteen months apart - grade 7 and the end of grade 8 solving the same problem. The research questions guiding this study are: (1) How does Ariel make use of his knowledge of arithmetic and algebra to build his solutions to the Ladders Problem? and (2) What change, if any, was there in Ariel’s problem solving from grade 7 to 8?