Presents data from 2 brain-damaged patients with calculation impairments in support of claims about the cognitive mechanisms underlying simple arithmetic performance. First presented is a model of the functional architecture of the cognitive calculation system based on previous research. This architecture was elaborated through detailed examination of the patterns of spared and impaired performance of the 2 patients. From the patients' performance the following theoretical claims were made: that some arithmetic facts are stored in the form of individual fact representations (eg, 9× 4= 36), whereas other facts are stored in the form of a general rule (eg, 0× N= 0); that arithmetic fact retrieval is mediated by abstract internal representations that are independent of the form in which problems are presented or responses are given; that arithmetic facts and calculation procedures are functionally independent; and that calculation algorithms may include special-case procedures that function to increase the speed or efficiency of problem solving. In conclusion, there was a discussion of several more general issues relevant to the reported research.(PsycINFO Database Record (c) 2016 APA, all rights reserved)