Architectures for numerical cognition

Current theories of numerical cognition differ in assumptions about the componential architecture of number processing and about the extent of notation-specific processes. To investigate these issues, 64 adult subjects were tested on simple addition and multiplication problems presented in Arabic digit or English number-word format. Overall, response times and error rates were much higher with the word format, but more importantly, presentation format interacted with arithmetic operation and problem size. Operation errors (2 + 4 = 8), operand-naming errors (2 + 8 = 8), and operand-intrusion errors (9 x 6 = 36) were each characterized by a different format x operation interaction, and analysis of inter-trial error priming showed selective interference from preceding trials as a function of number format. These types of format-specific retrieval interference and operation-specific effects of format are problematic for models that hypothesize notation-independent memory processes for arithmetic. Furthermore, analyses of operand-naming errors, operand-intrusion errors, and other operand-priming effects, revealed strong interactions of number reading and number-fact retrieval processes; processes that are typically posited to be functionally independent. The results suggest a complex encoding architecture that incorporates notation-dependent activation of addition and multiplication facts, as well as interpenetration of number reading and number-fact retrieval processes.