Abstract
Adults (n = 64) solved single-digit multiplication problems under both speed and accuracy instructions. Half also provided self-reports of their solutions to the problems. The participants with relatively low levels of arithmetic fluency were most influenced by instructional requirements. They responded more slowly and accurately when asked to provide descriptions of their solution procedures, whereas the performance of the participants with high and average levels of arithmetic fluency did not change. Furthermore, the performance of the low-fluency participants was more affected by speed and accuracy demands than was that of the other individuals, but only when the low-fluency participants were also required to provide self-reports. Accordingly, models of mental arithmetic will need to include roles for individual differences and situational factors.
Article PDF
Similar content being viewed by others
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., &Kirk, E. P. (2001). The relationships among working memory, math anxiety, and performance.Journal of Experimental Psychology: General,130, 224–237.
Baroody, A. J. (1984). An evaluation of evidence supporting fact-retrieval models.Learning & Individual Differences,6, 148–156.
Campbell, J. I. D. (1994). Architectures for numerical cognition.Cognition,53, 1–44.
Campbell, J. I. D. (1995). Mechanisms of simple addition and multiplication: A modified network-interference theory and simulation.Mathematical Cognition,1, 121–164.
Campbell, J. I. D., &Fugelsang, J. (2001). Strategy choice for arithmetic verification: Effects of numerical surface form.Cognition,80, B21-B30.
Campbell, J. I. D., &Graham, D. J. (1985). Mental multiplication skill: Structure, process, and acquisition.Canadian Journal of Psychology,39, 338–366.
Campbell, J. I. D., &Oliphant, M. (1992). Representation and retrieval of arithmetic facts: A network-interference model and simulation. In J. I. D. Campbell (Ed.),The nature and origin of mathematical skills (pp. 331–364). Amsterdam: Elsevier.
Campbell, J. I. D., &Timm, J. C. (2000). Adults’ strategy choices for simple addition: Effects of retrieval interference.Psychonomic Bulletin & Review,7, 692–699.
Campbell, J. I. D., &Xue, Q. (2001). Cognitive arithmetic across cultures.Journal of Experimental Psychology: General,130, 299–315.
Cooney, J. B., &Ladd, S. F. (1992). The influence of verbal protocol methods on children’s mental computation.Learning & Individual Differences,4, 237–257.
French, J. W., Ekstrom, R. B., &Price, I. A. (1963).Kit of reference tests for cognitive factors. Princeton, NJ: Educational Testing Service.
Geary, D. C., Frensch, P. A., &Wiley, J. G. (1993). Simple and complex mental subtraction: Strategy choice and speed of processing differences in younger and older adults.Psychology & Aging,8, 242–256.
Geary, D. C., &Wiley, J. G. (1991). Cognitive addition: Strategy choice and speed of processing differences in young and elderly adults.Psychology & Aging,6, 474–483.
Haider, H., &Frensch, P. A. (2002). Why aggregated learning follows the power law of practice when individual learning does not: Comment on Rickard (1997, 1999), Delaney et al. (1998), and Palmeri (1999).Journal of Experimental Psychology: Learning, Memory, & Cognition,28, 392–406.
Hecht, S. A. (1999). Individual solution processes while solving addition and multiplication math facts in adults.Memory & Cognition,27, 1097–1107.
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.
LeFevre, J.-A., Bisanz, J., Daley, K. E., Buffone, L., Greenham, S.L., &Sadesky, G. S. (1996). Multiple routes to solution of single-digit multiplication problems.Journal of Experimental Psychology: General,125, 284–306.
LeFevre, J.-A., &Kulak, A. G. (1994). Individual differences in the obligatory activation of addition facts.Memory & Cognition,22, 188–200.
LeFevre, J.-A., Kulak, A. G., &Heymans, S. L. (1992). Factors influencing the selection of university majors varying in mathematical content.Canadian Journal of Behavioural Science,24, 276–289.
LeFevre, J.-A., &Liu, J. (1997). Numerical cognition: Single-digit multiplication skills of adults from China and Canada.Mathematical Cognition,3, 31–62.
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.
LeFevre, J.-A., Smith-Chant, B. L., Hiscock, K., Daley, K. E., &Morris, J. (2003). Young adults’ strategic choices in simple arithmetic: Implications for the development of mathematical representations. In A. J. Baroody & A. Dowker (Eds.),The development of arithmetic concepts and skills: Recent research and theory (pp. 203–228). Hillsdale, NJ: Erlbaum.
Lemaire, P., &Siegler, R. S. (1995). Four aspects of strategic change: Contributions to children’s learning of multiplication.Journal of Experimental Psychology: General,124, 83–97.
Loftus, G. R., &Masson, M. E. J. (1994). Using confidence intervals in within-subject designs.Psychonomic Bulletin & Review,1, 476–490.
Penner-Wilger, M., Leth-Steensen, C., &LeFevre, J.-A. (2002). Decomposing the problem-size effect: A comparison of response time distributions across cultures.Memory & Cognition,30, 1160–1167.
Russo, J. E., Johnson, E. J., &Stephens, D. L. (1989). The validity of verbal protocols.Memory & Cognition,17, 759–769.
Schunn, C. D., &Reder, L. M. (2001). Another source of individual differences: Strategy adaptivity to changing rates of success.Journal of Experimental Psychology: General,130, 59–76.
Siegler, R. S. (1987). The perils of averaging over strategies: An example from children’s addition.Journal of Experimental Psychology: General,116, 250–264.
Siegler, R. S. (1988a). Individual differences in strategy choices: Good students, not-so-good students, and perfectionists.Child Development,59, 833–851.
Siegler, R. S. (1988b). Strategy choice procedures and the development of multiplication skill.Journal of Experimental Psychology: General,117, 258–275.
Siegler, R. S., &Jenkins, E. A. (1989).How children discover new strategies. Hillsdale, NJ: Erlbaum.
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, E. (1995). Variation, selection and cognitive change. In G. Halford & T. Simon (Eds.),Developing cognitive competence: New approaches to process modelling (pp. 31–76). Hillsdale, NJ: Erlbaum.
Siegler, R. S., &Shrager, J. (1984). Strategy choices in addition and subtraction: How do children know what to do? In C. Sophian (Ed.),The origins of cognitive skills (pp. 229–293). Hillsdale, NJ: Erlbaum.
Svenson, O. (1985). Memory retrieval of answers of simple additions as reflected in response latencies.Acta Psychologica,59, 285–304.
Author information
Authors and Affiliations
Corresponding author
Additional information
This research was supported by the Natural Sciences and Engineering Research Council of Canada through a graduate scholarship to B.L.S.-C. and through a research grant to J.-A.L.
Rights and permissions
About this article
Cite this article
Smith-Chant, B.L., LeFevre, JA. Doing as they are told and telling it like it is: Self-reports in mental arithmetic. Memory & Cognition 31, 516–528 (2003). https://doi.org/10.3758/BF03196093
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.3758/BF03196093