Psychology and Aging 1997, Vol. 12, No- 4, 555-564 Copyright 1997 by the Am Sequential and Coordinative Complexity in Time-Accuracy Functions for Mental Arithmetic Paul Verhaeghen University of Leuven Reinhold Kliegl and Ulrich Mayr University of Potsdam Time-accuracy functions for tasks involving single-digit mental addition and subtraction were de- rived in a sample of 18 younger (mean age —21.7 years) and 16 older adults (mean age = 68.8 years). Sequential complexity was manipulated by varying the number of operations (5 vs. 10); Coordinative complexity was induced by bracketing. Age differences were apparent in the Coordinative conditions, even though no age difference was present in the sequential conditions. This indicates that the age difference under conditions of high Coordinative demands could not be attributed solely to a decline in basic speed of processing. The Age X Complexity interaction was due to larger onset times and lower asymptotic performance by the older adults in the Coordinative conditions but not due to to rate of approach to the asymptote. This implies that Coordinative demands do not differen- tially hurt access from semantic memory in older adults; however, Coordinative demands do have disproportionately negative consequences for computation speed and self-monitoring in older adults. Some of the currently more popular thepries about cognitive aging state that age-related changes in the cognitive system are brought about by a decline in some general mechanism. In the words of Salthouse, Kausler, and Saults (1988), this perspective assumes that age differences in certain cognitive tasks are not due to impairments in task-specific components or strategies, but instead are attribut- able to an age-related reduction in the quantity of some type of general-purpose processing resources considered necessary for ef- ficient functioning in a broad assortment of cognitive tasks (p. 158). Much research over the past few decades has been aimed at identifying age differences in such general factors and the impli- cations of these differences for different aspects of cognition. Paul Verhaeghen, Department of Psychology, Center for Develop- mental Psychology, University of Leuven, Leuven, Belgium; Reinhold Kliegl and Ulrich Mayr, Department of Psychology, University of Pots- dam, Potsdam, Germany. A previous version of this article was presented at the Cognitive Aging Conference, Atlanta, Georgia, April 1996. The present research was conducted while Paul Verhaeghen was on an extended stay as a postdoc- toral researcher for the Belgian National Fund for Scientific Research at the University of Potsdam. The research was funded by Grant INK 12/A1 (Project B3) of the German Research Foundation and was supported by a travel grant from the Belgian National Fund for Scientific Research. We thank Hans Irtel for useful discussions in the early stages of the development of this study, Petra Gruetrner, Anke Demmrich, and Anja Meinke for recruiting and testing the participants, and John Cerella for his comments. Correspondence concerning this article should be addressed to Paul Verhaeghen, who is now at the Department of Psychology, 430 Hunting- ton Hall, Syracuse University, Syracuse, New York 13244-2340; or to Reinhold Kliegl, Department of Psychology, University of Potsdam, Post Office Box 60 15 53, D 14415 Potsdam, Germany. Electronic mail may be sent via Internet either to pverhaeg@psych.syr.edu or to kliegl@ rz.uni-potsdam.de. Mainly two fundamentally distinct types of factors have been advanced to explain adult age differences in complex cognition. The first refers to speed and reliability of basic processing com- ponents. Currently prominent models in cognitive aging that attribute age differences in a large variety of tasks to a basic and unspecific loss in processing speed (Cerella, 1990; Myerson, Hale, Wagstaff, Poon, & Smith, 1990; Salthouse, 1985, 1996) are of this kind. The second possible source of age differences in complex cognition lies in the ability to coordinate basic pro- cessing components into a reliable sequence (Kliegl, Mayr, & Krampe, 1994; Mayr & Kliegl, 1993; Mayr, Kliegl, & Krampe, 1996). In this context, coordination refers to an ensemble of functions such as scheduling of processes or retaining of inter- mediate results that are often associated with operative and stor- age aspects of working memory (Baddeley, 1986; Salthouse, 1992). An important task in cognitive aging research is to deter- mine whether these factors are distinct or not (Baltes, Linden- berger, & Staudinger, in press). In the present article, we report an attempt at dissociating the age-related influences of working memory from those of speed, using the methodological tool of time-accuracy functions and mental arithmetic as the critical domain of functioning. Dissociating Sequential and Coordinative Factors One of the challenges of identifying specific age-related prob- lems with Coordinative functions lies in the fact that the assump- tion of a simple general factor has proven empirically extremely successful. Two lines of research are relevant here. First, psycho- metric research has shown that basic speed of processing is a very important mediator between age and fluid cognition. Summarizing 55 comparisons from seven different studies, Salt- house (1993) found that perceptual speed measures were on the average associated with 74% of the age-related variance in fluid cognition. The association between speed and working memory measures appears to be even higher: 88% on the average in nine studies cited in Salthouse (1992). Moreover, the propor- 555