A complexity theory model in science education problem solving: random walks for working memory and mental capacity.

The present study examines the role of limited human channel capacity from a science education perspective. A model of science problem solving has been previously validated by applying concepts and tools of complexity theory (the working memory, random walk method). The method correlated the subjects' rank-order achievement scores in organic-synthesis chemistry problems with the subjects' working memory capacity. In this work, we apply the same nonlinear approach to a different data set, taken from chemical-equilibrium problem solving. In contrast to the organic-synthesis problems, these problems are algorithmic, require numerical calculations, and have a complex logical structure. As a result, these problems cause deviations from the model, and affect the pattern observed with the nonlinear method. In addition to Baddeley's working memory capacity, the Pascual-Leone's mental (M-) capacity is examined by the same random-walk method. As the complexity of the problem increases, the fractal dimension of the working memory random walk demonstrates a sudden drop, while the fractal dimension of the M-capacity random walk decreases in a linear fashion. A review of the basic features of the two capacities and their relation is included. The method and findings have consequences for problem solving not only in chemistry and science education, but also in other disciplines.

Achievement in chemistry problem-solving as a function of the mobility-fixity dimension.

The present studies explored the relation between students' achievement in chemistry problem-solving and the Mobility-Fixity dimension. Fixity characterizes consistency of function of field-independent subjects in a field-independent fashion, while Mobility provides for variation according to circumstances. The effect of this cognitive variable was examined as a function of the type and the complexity of the problem. Two kinds of problems were used, chemical equilibrium problems with varying mental demand and logical structure, and organic synthesis problems with varying mental demand. The subjects had to carry out different mental tasks, such as manipulation of logical schemata, applying algorithmic procedures, solving nonalgorithmic problems. In all cases, Mobile subjects demonstrated higher achievement than Fixed subjects. The results of this study support the hypothesis that the Mobility-Fixity dimension can serve as a predictor variable of students' performance on chemistry problem-solving.