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Individual versus collaborative problem solving: divergent outcomes depending on task complexity

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Abstract

Many studies have tested external supports for promoting productive collaboration, but relatively few have examined what features characterize naturally productive collaborative tasks. Two lines of research have come to distinct conclusions on the primary task feature associated with productive collaboration: demonstrability versus complexity. This study examined the problem-solving performance of 110 seventh grade students on a demonstrable mathematical task, including 69 in three traditional math classrooms (for whom the task was complex) and 41 in two accelerated math classrooms (for whom the task was not complex). Students were further assigned to one of four conditions split by two factors: grouping (individual versus dyad) and number of problems (one or two). For the accelerated math classes, individuals performed significantly better than dyads. For the traditional math classes, dyads performed significantly better than individuals and exceeded the truth-wins criterion (a theoretical maximum indicating how individuals would perform if they shared knowledge perfectly). A complex-demonstrable task framework is proposed for characterizing naturally productive collaborative tasks.

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Notes

  1. The calculation for the expected group performance is based on the work of Lorge and Solomon (1955). Since we know the proportion of individuals that could solve the husband and wives problem (14 %), we can calculate the probability that groups from this population will have at least one person that can find the correct answer to the problem. The easiest way to do this is to find the probability that the group contains no one that can solve the problem and subtract from one (e.g., if there is a 10 % chance no one in a group can solve the problem, then there is a 90 % chance that at least one person can). If Q is the proportion of individuals who cannot solve the problem, the probability that a group of size n contains no one that can solve the problem is Qn. In the husband and wives problem the group size is 4 and the proportion of individuals that cannot solve the problem is Q = (1−0.14) = 0.86. Thus, the probability that the four-person group contains at least one individuals that can solve the problem is 1−0.864 ~45%.

  2. The degrees of freedom are adjusted due to heterogeneity of variance between conditions. The unadjusted results are similar, t(108) = 3.238, p = .002.

  3. Results of all analyses were the same with or without the Pretest score entered as a covariate.

  4. This does not include four groups of three traditional math students (all of whom also found at least one solution to the problem). The proportion would have been even greater, 19 out of 21, had the triads been included.

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Acknowledgments

This work was supported in part by a Kinley Trust research grant to David Sears. Any opinions, findings, and conclusions or recommendations expressed in this work are those of the authors and do not necessarily reflect the views of the Kinley Trust. Both authors contributed equally to this manuscript. They would like to thank the principal, teacher, and students for making this research possible. Additional thanks go to Jammie Chang, James Greenan, and anonymous reviewers for their feedback on this work.

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  1. Purdue University, 5130 BRNG Hall, 100 N. University St, West Lafayette, IN, 47907, USA

    David A. Sears & James Michael Reagin

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Correspondence to David A. Sears.

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Sears, D.A., Reagin, J.M. Individual versus collaborative problem solving: divergent outcomes depending on task complexity. Instr Sci 41, 1153–1172 (2013). https://doi.org/10.1007/s11251-013-9271-8

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