Problem representation: The effects of spatial arrays

Two studies examined how characteristics of spatial arrays contribute to efficient problem representation. Thirty-two adults were presented with information about family relationships in one of two arrays: a hierarchy or a matrix. Their answers to two different sets of questions were timed. The matrix format was superior to the hierarchy for one set of questions only; no differences between the arrays emerged for the other set. The data were interpreted in terms of how the family relationships were mapped onto the arrays; the mapping differences between the arrays affected the number of mental steps needed to solve some questions, but not others. In a second experiment (N=32), the same problem information was remapped onto the arrays, with the mapping relations reversed. As predicted, the pattern of response times exactly reflected the change in mapping. It is proposed that, for spatial arrays, efficiency of problem representation is best understood in terms of the number of mental steps in the problem solution.