Nonlinear Analysis of the Effect of Working Memory Capacity on Student Performance in Problem Solving

Abstract

We describe a nonlinear approach for studying the effect of working-memory capacity on science problem solving. The tools used are those of complexity theory and are used to test and model the phenomenon of the working-memory overload. The nonlinear method correlates the subjects’ rank-order achievement scores in problem solving with the psychometric variable. From the achievement scores, rank-order sequences of the subjects, according to their scores, were generated, and in the place of each subject, his/her score was then replaced by the value of the cognitive variable. Then the sequence was mapped onto a one-dimensional random-walk model (working-memory random walk) and treated as dynamical flow. For these sequences, the nonlinear correlation exponents (Hurst exponents) were calculated. The null hypothesis was tested with surrogate data. The method is demonstrated with data from achievement scores in chemical equilibrium problems. Problems of various logical structures and mental demands were used. In problems with simpler logical structure and with low mental demand, the Hurst exponent was close to the surrogate value (demonstrating randomness), while sudden increases appeared for more complicated problems (indicating scale invariant long-range correlations). The method provides meaningful results and adds to the understanding of information processing within the frame of science education.