Abstract
A dual-task methodology was used to investigate the roles played by executive and phonological aspects of working memory in mental arithmetic. Experiment 1 showed that suppression of articulation impaired the ability to add a pair of briefly presented three-digit numbers. Suppression had no effect when the need to store temporarily was minimized by making the numbers visible throughout calculation. Experiment 2 showed that disrupting executive processes by requiring concurrent performance of a Trails task impaired the ability to add numbers that remained permanently visible. Performance on the Trails task deteriorated as the number of carry operations in the addition increased. Experiment 3 showed that this decline in Trails performance was not simply due to the extra time taken by carrying. These and other features of the results suggest that the carrying component of mental arithmetic places substantial demands on executive processes, whereas the need to retain problem information is met by the phonological loop. The results are consistent with an interpretation of executive processes according to which there is a limit on the capacity to inhibit strongly primed routine operations.
Article PDF
Similar content being viewed by others
References
Adams, J. W., &Hitch, G. J. (1997). Working memory and children’s mental addition.Journal of Experimental Child Psychology,67, 21–38.
Ashcraft, M. H. (1982). The development of mental arithmetic: A chronometric approach.Developmental Review,2, 213–236.
Ashcraft, M. H. (1995). Cognitive psychology and simple arithmetic: A review and summary of new directions.Mathematical Cognition,1, 3–34.
Ashcraft, M. H., Donley, R. D., Halas, M. A., &Vakali, M. (1992). Working memory, automaticity, and problem difficulty. In J. I.D. Campbell (Ed.),The nature and origins of mathematical skills (pp. 301–329). Amsterdam: Elsevier.
Baddeley, A. [D.] (1986).Working memory. Oxford: Oxford University Press.
Baddeley, A. [D.] (1992). Is working memory working? The fifteenth Bartlett Lecture.Quarterly Journal of Experimental Psychology,44A, 1–31.
Baddeley, A. [D.] (1996). Exploring the central executive.Quarterly Journal of Experimental Psychology,49A, 5–28.
Baddeley, A. [D.], Lewis, V., Eldridge, M., &Thomson, N. (1984). Attention and retrieval from long-term memory.Journal of Experimental Psychology: General,113, 518–540.
Baddeley, A. D., &Hitch, G. J. (1974). Working memory. In G. H. Bower (Ed.),The psychology of learning and motivation (Vol. 8, pp. 47–90). New York: Academic Press.
Baddeley, A. D., &Lieberman, K. (1980). Spatial working memory. In R. S. Nickerson (Ed.),Attention and performance VIII (pp. 521–539). Hillsdale, NJ: Erlbaum.
Baddeley, A. D., Thomson, N., &Buchanan, M. (1975). Word length and the structure of short-term memory.Journal of Verbal Learning & Verbal Behavior,14, 575–589.
Butterworth, B., Cipolotti, L., &Warrington, E. K. (1996). Short-term memory impairment and arithmetical ability.Quarterly Journal of Experimental Psychology,49A, 251–262.
Campbell, J. I. D. (1995). Mechanisms of simple addition and multiplication: A modified network-interference theory and simulation.Mathematical Cognition,1, 121–164.
Conway, A. R. A., &Engle, R. W. (1994). Working memory and retrieval: A resource-dependent inhibition model.Journal of Experimental Psychology: General,123, 354–373.
Daneman, M., &Carpenter, P. A. (1980). Individual differences in working memory and reading.Journal of Verbal Learning & Verbal Behavior,19, 450–466.
Dansereau, D. F., &Gregg, L. W. (1966). An information processing analysis of mental multiplication.Psychonomic Science,6, 71–72.
Dehaene, S., &Cohen, L. (1995). Towards an anatomical and functional model of number processing.Mathematical Cognition,1, 83–120.
Deloche, G., &Seron, X. (1987). Numerical transcoding: A general production model. In G. Deloche & X. Seron (Eds.),Mathematical disabilities: A cognitive neuropsychological perspective (pp. 137–170). Hillsdale, NJ: Erlbaum.
Frensch, P. A., &Geary, D. C. (1993). Effects of practice on component processes in complex mental addition.Journal of Experimental Psychology: Learning, Memory, & Cognition,19, 433–456.
Hamilton, J. M. E., &Sanford, A. J. (1978). The symbolic distance effect for alphabetic order judgements: A subjective report and reaction time analysis.Quarterly Journal of Experimental Psychology,30, 33–42.
Hitch, G. J. (1978). The role of short-term working memory in mental arithmetic.Cognitive Psychology,10, 302–323.
Just, M. A., &Carpenter, P. A. (1992). A capacity theory of comprehension: Individual differences in working memory.Psychological Review,99, 122–149.
LeFevre, J.-A., Bisanz, J., &Mrkonjic, L. (1988). Cognitive arithmetic: Evidence for obligatory activation of arithmetic facts.Memory & Cognition,16, 45–53.
LeFevre, J.-A., Sadesky, G. S., &Bisanz, J. (1996). Selection of procedures in mental addition: Reassessing the problem size effect in adults.Journal of Experimental Psychology: Learning, Memory, & Cognition,22, 216–230.
Lemaire, P., Abdi, H., &Fayol, M. (1996). The role of working memory resources in simple cognitive arithmetic.European Journal of Cognitive Psychology,8, 73–103.
Lezak, M. D. (1983).Neuropsychological assessment. New York: Oxford University Press.
Logie, R. H., Gilhooly, K. J., &Wynn, V. (1994). Counting on working memory in arithmetic problem solving.Memory & Cognition,22, 395–410.
McCloskey, M. (1992). Cognitive mechanisms in numerical processing: Evidence from acquired dyscalculia.Cognition,44, 107–157.
Norman, D. A., & Shallice, T. (1980).Attention to action: Willed and automatic control of behavior (Tech. Rep. 99). University of California, San Diego, Center for Human Information Processing.
Shallice, T. (1982). Specific impairments of planning.Philosophical Transactions of the Royal Society of London: Series B,298, 199–209.
Widaman, K. F., Geary, D. C., Cormier, P., &Little, T. D. (1989). A componential model for mental addition.Journal of Experimental Psychology: Learning, Memory, & Cognition,15, 898–919.
Zbrodoff, N. J., &Logan, G. D. (1986). On the autonomy of mental processes: A case study of arithmetic.Journal of Experimental Psychology: General,115, 118–130.
Author information
Authors and Affiliations
Corresponding author
Additional information
A.J.F. was supported by an ESRC research studentship and is grateful to Christian Marendaz of the LPE, Université Pierre Mendès France (Grenoble), for support during preparation of the manuscript.
Rights and permissions
About this article
Cite this article
FÜrst, A.J., Hitch, G.J. Separate roles for executive and phonological components of working memory in mental arithmetic. Memory & Cognition 28, 774–782 (2000). https://doi.org/10.3758/BF03198412
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.3758/BF03198412