Does Group Composition Affect Learning by Invention?

Schwartz and Martin ("Cogn Instr" 22:129-184, 2004) as well as Kapur ("Instr Sci", this issue, 2012) have found that students can be better prepared to learn about mathematical formulas when they try to invent them in small groups before receiving the canonical formula from a lesson. The purpose of the present research was to investigate how the effectiveness of invention activities may be mediated by composition of the small groups in terms of their mathematical skills. In two studies, small groups of undergraduates engaged in an "inventing standard deviation" task. Results suggested that groups may need at least one member with high math ability to take advantage of "learning by invention". Groups consisting of both high and low math ability members generated a broader range of solution attempts during the invention task, and this seemed to be related to better uptake of the standard deviation formula from a later lesson.