Memory & Cognition

, Volume 27, Issue 6, pp 1097–1107 | Cite as

Individual solution processes while solving addition and multiplication math facts in adults

  • Steven Alan HechtEmail author


Contrary to predictions of current solution process models, adults used a variety of procedures other than retrieval to solve addition and multiplication math facts. Predictors assumed to capture retrieval processes posited by such models did account for a substantial proportion of variance in averaged retrieval solution times. But most of the variance in individual participants’ retrieval times remained unaccounted for. Cross-operation associations in patterns of strategy use and retrieval latencies were obtained. Adults with stronger higher level math achievement were more likely to use retrieval, solved math facts faster and less variably, and executed retrieval processes posited by current solution process models faster than participants with less math attainment. The results are explained within the context of the adaptive strategy choice model.


Solution Time Retrieval Process Associative Strength Item Analysis Retrieval Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Ashcraft, M. H. (1992). Cognitive arithmetic: A review of data and theory.Cognition,44, 75–106.PubMedCrossRefGoogle Scholar
  2. 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, North-Holland.CrossRefGoogle Scholar
  3. Baroody, A. J. (1993). Early mental multiplication performance and the role of relational knowledge in mastering combinations involving “two.”Learning & Instruction,3, 93–111.CrossRefGoogle Scholar
  4. Campbell, J. I. D., & Graham, D. J. (1985). Mental multiplication skill: Structure, process, and acquisition.Canadian Journal of Psychology,39, 338–366.CrossRefGoogle Scholar
  5. 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 origins of mathematical skills (pp. 331–364). Amsterdam: Elsevier, North-Holland.CrossRefGoogle Scholar
  6. Cooney, J. B., Swanson, H. L., & Ladd, S. F. (1988). Acquisition of mental multiplication skill: Evidence for the transition between counting and retrieval strategies.Cognition & Instruction,5, 323–345.CrossRefGoogle Scholar
  7. Geary, D. C. (1993). Mathematical disabilities: Cognitive, neuropsychological, and genetic components.Psychological Bulletin,114, 345–362.PubMedCrossRefGoogle Scholar
  8. Geary, D. C., & Widaman, K. F. (1987). Individual differences in cognitive arithmetic.Journal of Experimental Psychology: General,116, 154–171.CrossRefGoogle Scholar
  9. Geary, D. C., & Widaman, K. F. (1992). Numerical cognition: On the convergence of componential and psychometric models.Intelligence,16, 47–80.CrossRefGoogle Scholar
  10. Geary, D. C., Widaman, K. F., & Little, T. D. (1986). Cognitive addition and multiplication: Evidence for a single memory network.Memory & Cognition,14, 478–487.CrossRefGoogle Scholar
  11. 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.CrossRefGoogle Scholar
  12. Hecht, S. A. (1998). Toward an information processing account of individual differences in fraction skills.Journal of Educational Psychology,90, 1–18.CrossRefGoogle Scholar
  13. Kail, R., & Salthouse, T. A. (1994). Processing speed as a mental capacity.Acta Psychologica,86, 199–225.PubMedCrossRefGoogle Scholar
  14. LeFevre, J. A., Bisanz, J., Daley, K. E., Buffone, L., & Sadesky, G. S. (1996). Multiple solution routes to solution of single-digit multiplication problems.Journal of Experimental Psychology: General,125, 284–306.CrossRefGoogle Scholar
  15. 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.CrossRefGoogle Scholar
  16. Lorch, R. F., & Meyers, J. L. (1990). Regression analyses of repeated measures data in cognitive research.Journal of Experimental Psychology: Learning, Memory, & Cognition,16, 149–157.CrossRefGoogle Scholar
  17. McCloskey, M., Harley, W., & Sokol, S. M. (1991). Models of arithmetic fact retrieval: An evaluation in light of findings from normal and brain-damaged participants.Journal of Experimental Psychology: Learning, Memory, & Cognition,17, 377–397.CrossRefGoogle Scholar
  18. Miller, K. F., & Paredes, D. R. (1990). Starting to add worse: Effects of learning to multiply on children’s addition.Cognition,37, 213–242.PubMedCrossRefGoogle Scholar
  19. Miller, K. [F.], Perlmutter, M., & Keating, D. (1984). Cognitive arithmetic: Comparison of operations.Journal of Experimental Psychology: Learning, Memory, & Cognition,10, 46–60.CrossRefGoogle Scholar
  20. Siegler, R. S. (1987). The perils of averaging data over strategies: An example from children’s addition.Journal of Experimental Psychology: General,116, 250–264.CrossRefGoogle Scholar
  21. Siegler, R. S. (1988a). Individual differences in strategy choices: Good students, not-so-good students, and perfectionists.Child Development,59, 833–851.PubMedCrossRefGoogle Scholar
  22. Siegler, R. S. (1988b). Strategy choice procedures and the development of multiplication skill.Journal of Experimental Psychology: General,117, 258–275.CrossRefGoogle Scholar
  23. Siegler, R. S., & Shipley, E. (1995). Variation, selection, and cognitive change. In G. Halford & T. Simon (Eds.),Developing cognitive competence: New approaches to process modeling (pp. 31–76). Hillsdale, NJ: Erlbaum.Google Scholar
  24. Wagner, R. K., Torgesen, J. K., & Rashotte, C. A. (1994). Development of reading-related phonological processing abilities: New evidence of bidirectional causality from a latent variable longitudinal study.Developmental Psychology,30, 73–87.CrossRefGoogle Scholar
  25. Widaman, K. F., & Little, T. D. (1992). The development of skill in mental arithmetic: An individual differences approach. In J. I. D. Campbell (Ed.),The nature and origins of mathematical skills. Amsterdam: Elsevier, North-Holland.Google Scholar
  26. Widaman, K. F., Little, T. D., Geary, D. C., & Cormier, P. (1992). Individual differences in the development of skill in mental addition: Internal and external validation of chronometric models.Learning & Individual Differences,4, 167–213.CrossRefGoogle Scholar

Copyright information

© Psychonomic Society, Inc. 1999

Authors and Affiliations

  1. 1.Division of ScienceFlorida Atlantic UniversityDavie

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