Multiplication Number Facts: Modeling Human Performance with Connections Networks

Three connectionist models of human performance on simple multiplication number facts, commonly called \times tables," are reviewed. Also, human data from normal subjects and brain-damaged patients, which constrain these models, are presented. These human data include the problem size eeect, error eeects, priming eeects, use of strategies and rules, and number representation. The connectionist models presented are: a simple auto-associator (J.A. Anderson's Brain-State-in-a-Box), a standard back-propagation model, and McCloskey and Lindemann's mathnet. The review of human data and connectionist models of memory retrieval provides some insight into the strengths of, diierences between , and challenges for, this approach to computational modeling. Particular attention is paid to the representation of number used by these models, and a related ability to generalize learning.