Recursive and explicit rules: How can we build student algebraic understanding?

Differing perspectives have been offered about student use of recursive and explicit rules. These include: (a) promoting the use of explicit rules over the use of recursive rules, and (b) encouraging student use of both recursive and explicit rules. This study sought to explore students’ use of recursive and explicit rules by examining the reasoning of 25 sixth-grade students, including a focus on four target students, as they approached tasks in which they were required to develop generalizations while using computer spreadsheets as an instructional tool. The results demonstrate the difficulty that students had moving from the successful use of recursive rules toward explicit rules. In particular, two students abandoned general reasoning, instead focusing on particular values in an attempt to construct explicit rules. It is recommended that students be encouraged to connect recursive and explicit rules as a potential means for constructing successful generalizations.