The generality of mental addition models: simple and complex addition in a decision-production task

Recently, Widaman, Geary, Cormier, and Little (in press) offered a general componential model for simple and complex addition. In the present study, the generalizability of this model to very complex addition problems and to production task performance was tested. We investigated addition-production performance using a new research paradigm, the decision-production task. The paradigm was used to assess the reaction times of 16 adults to 100 single-digit addition problems (Experiment 1) and to very complex three-digit addition problems (Experiment 2). Generally, the results give evidence for the basic assumptions of the Widaman et al. model. Some of the results, however, demonstrate that short-term memory load factors and strategy choices also have important effects on complex addition-production performance. Furthermore, the results of both experiments indicate that, in production tasks, the nature of the elementary search/compute process can be characterized as a memory-retrieval process and that the decision-production paradigm is a valuable alternative to the classical verbal production paradigm.