When Three Heads Are Better Than Two

The present study investigated the effects of both group size and heterogeneity in relevant math skill on collaborative problem solving. Overall, triads demonstrated better reasoning and more effective cryptarithmetic problem solving than dyads and singletons. Importantly, triads outperformed the best individuals in a nominal groups analysis. Triads were also better able than dyads to take advantage of heterogeneity in math skill. The results suggest that some specific advantages of group collaboration may be more likely to be realized in triads than dyads, and that triads may be an optimal group size when critical evaluation and reasoning are required for a task. What Are The Advantages of Collaboration? One popular reason why people believe groups should be more effective, flexible and innovative at problem solving is the assumption that each group member brings to the task a slightly different set of task-relevant knowledge and skills. Through discussion, the knowledge and skills of each member can become available for all, giving each member a larger pool of ideas to draw from. Especially if members possess different backgrounds, group problem solving will give people a greater opportunity for novel associations, strategies and operations. Exposure to diverse viewpoints may increase both the quantity and quality of idea generation in a group context (Hoffman, Harburg & Maier, 1962; Maier, 1962; Nemeth, 1986; Paulus & Yang, 2000, Stasser, Stewart, & Wittenbaum, 1995). There are a few studies in the cognitive science literature that have explored the idea that diversity and collaboration may be important for successful and innovative scientific discovery. For example, in an investigation of several molecular biology laboratories, Dunbar (1997) has reported that the diversity of a group can be very important. When scientists in a laboratory are from diverse backgrounds, they are better able to generate alternative hypotheses and analogies in the face of unexpected findings, which can in turn lead to scientific breakthroughs. In an attempt to examine this phenomena in an experimental context, Wiley and Jolly (2003) examined collaborative performance on a creative problem solving task where prior knowledge has been shown to be related to fixation and an inability to come to solution (Wiley, 1998). Comparisons of observed versus expected outcomes (based on combinations of individual base rates) indicated that only the mixed knowledge pairs with one high knowledge member and one low knowledge member performed significantly better than would be predicted using base rates. The high knowledge pairs also tended to do better than would be expected, but this did not reach significance. The low knowledge pairs did significantly worse than would be expected based on past performance of individual low knowledge participants. This result shows specific advantages for experts collaborating when their prior knowledge may lead them into fixation on unpromising solution paths, and that experts may sometimes need the assistance of novices in order to be most effective, flexible or innovative in their problem solving. However, it is also the case that collaboration does not always lead to superior outcomes (Hill, 1982; Taylor, Berry & Block, 1958; Salomon & Globerson, 1989; Steiner, 1972; Stroebe & Diehl, 1984). In another study on collaborative argumentation, we found disadvantages to students working in dyads (Wiley & Bailey, 2006). Instead of acting as critical evaluators of information and pushing the reasoning to a higher level, we found pairs of students engaging in a lot of passive acceptance of each others’ statements. This highlights the need to examine the many possible advantages of collaboration, and under which specific contexts hypothetical advantages may be most likely to occur. In the case of the present study, we were interested in both the size of the group and the heterogeneity of math skills within the group as possible determinants of benefits from collaboration.