Abstract
The role of executive and phonological working memory resources in simple arithmetic was investigated in two experiments. Participants had to solve simple multiplication problems (e.g., 4×8; Experiment 1) or simple division problems (e.g., 42÷7; Experiment 2) under no-load, phonological-load, and executive-load conditions. The choice/no-choice method was used to investigate strategy execution and strategy selection independently. Results for strategy execution showed that executive working memory resources were involved in direct memory retrieval of both multiplication and division facts. Executive working memory resources were also involved in the use of nonretrieval strategies. Phonological working memory resources, on the other hand, tended to be involved in nonretrieval strategies only. Results for strategy selection showed no effects of working memory load. Finally, correlation analyses showed that both strategy execution and strategy selection correlated with individual-difference variables, such as gender, math anxiety, associative strength, calculator use, arithmetic skill, and math experience.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Ashcraft, M. H. (1992). Cognitive arithmetic: A review of data and theory.Cognition,44, 75–106.
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.
Ashcraft, M. H., &Kirk, E. P. (2001). The relationships among working memory, math anxiety, and performance.Journal of Experimental Psychology: General,130, 224–237.
Baddeley, A. D. (1996). Exploring the central executive.Quarterly Journal of Experimental Psychology,49A, 5–28.
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., &Logie, R. H. (1999). Working memory: The multiple-component model. In A. Miyake & P. Shah (Eds.),Models of working memory (pp. 28–61). New York: Cambridge University Press.
Barrouillet, P., Bernardin, S., &Camos, V. (2004). Time constraints and resource sharing in adults’ working memory spans.Journal of Experimental Psychology: General,133, 83–100.
Campbell, J. I. D. (1994). Architectures for numerical cognition.Cognition,53, 1–44.
Campbell, J. I. D. (1997). On the relation between skilled performance of simple division and multiplication.Journal of Experimental Psychology: Learning, Memory, & Cognition,23, 1140–1159.
Campbell, J. I. D., &Gunter, R. (2002). Calculation, culture, and the repeated operand effect.Cognition,86, 71–96.
Campbell, J. I. D., &Xue, Q. (2001). Cognitive arithmetic across cultures.Journal of Experimental Psychology: General,130, 299–315.
Carr, M., &Jessup, D. L. (1997). Gender differences in first-grade mathematics strategy use: Social and metacognitive influences.Journal of Educational Psychology,89, 318–328.
Carr, M., Jessup, D. L., &Fuller, D. (1999). Gender differences in first-grade mathematics strategy use: Parent and teacher contributions.Journal for Research in Mathematics Education,30, 20–46.
Case, R. (1985).Intellectual development: Birth to adulthood. San Diego: Academic Press.
Cowan, N. (1995).Attention and memory: An integrated framework. New York: Oxford University Press.
Dehaene, S. (1997).The number sense. New York: Oxford University Press.
De Rammelaere, S., Stuyven, E., &Vandierendonck, A. (1999). The contribution of working memory resources in the verification of simple arithmetic sums.Psychological Research,62, 72–77.
De Rammelaere, S., Stuyven, E., &Vandierendonck, A. (2001). Verifying simple arithmetic sums and products: Are the phonological loop and the central executive involved?Memory & Cognition,29, 267–273.
De Rammelaere, S., &Vandierendonck, A. (2001). Are executive processes used to solve simple arithmetic production tasks?Current Psychology Letters: Behaviour, Brain, & Cognition,5, 79–89.
Deschuyteneer, M., &Vandierendonck, A. (2005a). Are “input monitoring” and “response selection” involved in solving simple mental arithmetical sums?European Journal of Cognitive Psychology,17, 347–370.
Deschuyteneer, M., &Vandierendonck, A. (2005b). The role of response selection and input monitoring in solving simple arithmetical products.Memory & Cognition,33, 1472–1483.
Deschuyteneer, M., Vandierendonck, A., &Muyllaert, I. (2006). Does solution of mental arithmetic problems such as 2+6 and 3×8 rely on the process of “memory updating”?Experimental Psychology,53, 198–208.
DeStefano, D., &LeFevre, J.-A. (2004). The role of working memory in mental arithmetic.European Journal of Cognitive Psychology,16, 353–386.
Engle, R. W., Kane, M. J., &Tuholski, S. W. (1999). Individual differences in working memory capacity and what they tell us about controlled attention, general fluid intelligence, and functions of the prefrontal cortex. In A. Miyake & P. Shah (Eds.),Models of working memory: Mechanisms of active maintenance and executive control (pp. 102–134). Cambridge: Cambridge University Press.
Ericsson, K. A., &Kintsch, W. (1995). Long-term working memory.Psychological Review,102, 211–245.
Faust, M. W., Ashcraft, M. H., &Fleck, D. E. (1996). Mathematics anxiety effects in simple and complex addition.Mathematical Cognition,2, 25–62.
Fennema, E., Carpenter, T. P., Jacobs, V. R., Franke, M. L., &Levi, L. W. (1998). A longitudinal study of gender differences in young children’s mathematical thinking.Educational Researcher,27, 6–11.
French, J. W., Ekstrom, R. B., &Price, L. A. (1963).Kit of reference tests for cognitive factors. Princeton, NJ: Educational Testing Service.
Fürst, A. J., &Hitch, G. J. (2000). Separate roles for executive and phonological components of working memory in mental arithmetic.Memory & Cognition,28, 774–782.
Galfano, G., Rusconi, E., &Umiltà, C. (2003). Automatic activation of multiplication facts: Evidence from the nodes adjacent to the product.Quarterly Journal of Experimental Psychology,56A, 31–61.
Geary, D. C., Saults, S. J., Liu, F., &Hoard, M. K. (2000). Sex differences in spatial cognition, computational fluency, and arithmetical reasoning.Journal of Experimental Child Psychology,77, 337–353.
Geary, D. C., &Widaman, K. F. (1992). Numerical cognition: On the convergence of componential and psychometric models.Intelligence,16, 47–80.
Gilles, P. Y., Masse, C., &Lemaire, P. (2001). Individual differences in arithmetic strategy use.Année Psychologique,101, 9–32.
Hecht, S. A. (1999). Individual solution processes while solving addition and multiplication math facts in adults.Memory & Cognition,27, 1097–1107.
Hecht, S. A. (2002). Counting on working memory in simple arithmetic when counting is used for problem solving.Memory & Cognition,30, 447–455.
Hitch, G. J. (1978). Role of short-term memory in mental arithmetic.Cognitive Psychology,10, 302–323.
Imbo, I., & Vandierendonck, A. (in press). The role of the phonological loop and the central executive in simple-arithmetic strategies.European Journal of Cognitive Psychology.
Imbo, I., Vandierendonck, A., &De Rammelaere, S. (2007). The role of working memory in the carry operation of mental arithmetic: Number and value of the carry.Quarterly Journal of Experimental Psychology,60, 708–731.
Imbo, I., Vandierendonck, A., & Rosseel, Y. (in press). The influence of problem features and individual differences on strategic performance in simple arithmetic.Memory & Cognition.
Imbo, I., Vandierendonck, A., &Vergauwe, E. (2007). The role of working memory in carrying and borrowing.Psychological Research,71, 467–483.
Kaufmann, L. (2002). More evidence for the role of the central executive in retrieving arithmetic facts: A case study of severe developmental dyscalculia.Journal of Clinical & Experimental Neuropsychology,24, 302–310.
Kaufmann, L., Lochy, A., Drexler, A., &Semenza, C. (2003). Deficient arithmetic fact retrieval—Storage or access problem? A case study.Neuropsychologia,42, 482–496.
Kirk, E. P., &Ashcraft, M. H. (2001). Telling stories: The perils and promise of using verbal reports to study math strategies.Journal of Experimental Psychology: Learning, Memory, & Cognition,27, 157–175.
Lee, K.-M., &Kang, S.-Y. (2002). Arithmetic operation and working memory: Differential suppression in dual tasks.Cognition,83, B63-B68.
LeFevre, J.-A., &Bisanz, J. (1986). A cognitive analysis of numberseries problems: Sources of individual differences in performance.Memory & Cognition,14, 287–298.
LeFevre, J.-A., Bisanz, J., Daley, K. E., Buffone, L., Greenham, S. L., &Sadesky, G. S. (1996). Multiple routes to solution of singledigit multiplication problems.Journal of Experimental Psychology: General,125, 284–306.
LeFevre, J.-A., &Morris, J. (1999). More on the relation between division and multiplication in simple arithmetic: Evidence for mediation of division solutions via multiplication.Memory & Cognition,27, 803–812.
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.
Logie, R. H., &Baddeley, A. D. (1987). Cognitive processes in counting.Journal of Experimental Psychology: Learning, Memory, & Cognition,13, 310–326.
Logie, R. H., Gilhooly, K. J., &Wynn, V. (1994). Counting on working memory in arithmetic problem solving.Memory & Cognition,22, 395–410.
Richardson, F. C., &Suinn, R. M. (1972). The Mathematics Anxiety Rating Scale: Psychometric data.Journal of Counseling Psychology,19, 551–554.
Robinson, K. M., Arbuthnott, K. D., &Gibbons, K. A. (2002). Adults’ representations of division facts: A consequence of learning history?Canadian Journal of Experimental Psychology,56, 302–309.
Roussel, J.-L., Fayol, M., &Barrouillet, P. (2002). Procedural vs. direct retrieval strategies in arithmetic: A comparison between additive and multiplicative problem solving.European Journal of Cognitive Psychology,14, 61–104.
Royer, J. M., Tronsky, L. N., Chan, Y., Jackson, S. J., &Marchant, H., III (1999). Math-fact retrieval as the cognitive mechanism underlying gender differences in math test performance.Contemporary Educational Psychology,24, 181–266.
Rusconi, E., Galfano, G., Rebonato, E., &Umiltà, C. (2006). Bidirectional links in the network of multiplication facts.Psychological Research,70, 32–42.
Rusconi, E., Galfano, G., Speriani, V., &Umiltà, C. (2004). Capacity and contextual constraints on product activation: Evidence from task-irrelevant fact retrieval.Quarterly Journal of Experimental Psychology,57A, 1485–1511.
Seitz, K., &Schumann-Hengsteler, R. (2000). Mental multiplication and working memory.European Journal of Cognitive Psychology,12, 552–570.
Seitz, K., &Schumann-Hengsteler, R. (2002). Phonological loop and central executive processes in mental addition and multiplication.Psychologische Beiträge,44, 275–302.
Seyler, D. J., Kirk, E. P., &Ashcraft, M. H. (2003). Elementary subtraction.Journal of Experimental Psychology: Learning, Memory, & Cognition,29, 1339–1352.
Siegler, R. S., &Lemaire, P. (1997). Older and younger adults’ strategy choices in multiplication: Testing predictions of ASCM using the choice/no-choice method.Journal of Experimental Psychology: General,126, 71–92.
Siegler, R. S., &Shipley, C. (1995). Variation, selection, and cognitive change. In T. J. Simon & G. S. Halford (Eds.),Developing cognitive competence: New approaches to process modeling (pp. 31–76). Hillsdale, NJ: Erlbaum.
Szmalec, A., Vandierendonck, A., &Kemps, E. (2005). Response selection involves executive control: Evidence from the selective interference paradigm.Memory & Cognition,33, 531–541.
Thibodeau, M. H., LeFevre, J.-A., &Bisanz, J. (1996). The extension of the interference effect to multiplication.Canadian Journal of Experimental Psychology,50, 393–396.
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
The research reported in this article was supported by Grant 011D07803 of the Special Research Fund at Ghent University to the first author and by Grant 10251101 of the Special Research Fund of Ghent University to the second author.
Rights and permissions
About this article
Cite this article
Imbo, I., Vandierendonck, A. Do multiplication and division strategies rely on executive and phonological working memory resources?. Memory & Cognition 35, 1759–1771 (2007). https://doi.org/10.3758/BF03193508
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.3758/BF03193508