Systematic Mathematical Errors and Cognitive Load.

The hypothesis that the intrinsic nature of algebraic bracket tasks causes an uneven distribution of cognitive load during computation was tested in three experiments with grades 8 and 9 students. In Experiment 1, students were given problems which required two successive brackets to be expanded; each bracket required two operations (computations) to be completed. It was discovered that more errors were made during the calculation of the second bracket than the first, and more errors were made during the second operation than the first operation within each bracket. Verbal protocols collected in Experiment 2 indicated that most errors were caused by failures in working memory rather than poorly learned rules. In Experiment 3, a dual-task methodology showed that the cognitive nature of brackets affected working memory performance. It was concluded that the cognitive load experienced by problem solvers on these tasks varied across operations and caused the observed error pattern. Copyright 2001 Academic Press.