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

- 244 Downloads
- 3 Citations

## Abstract

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.

## Keywords

Solution Time Retrieval Process Associative Strength Item Analysis Retrieval Time## Preview

Unable to display preview. Download preview PDF.

## References

- Ashcraft, M. H. (1992). Cognitive arithmetic: A review of data and theory.
*Cognition*,**44**, 75–106.PubMedCrossRefGoogle Scholar - 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 - 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 - Campbell, J. I. D., & Graham, D. J. (1985). Mental multiplication skill: Structure, process, and acquisition.
*Canadian Journal of Psychology*,**39**, 338–366.CrossRefGoogle Scholar - 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 - 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 - Geary, D. C. (1993). Mathematical disabilities: Cognitive, neuropsychological, and genetic components.
*Psychological Bulletin*,**114**, 345–362.PubMedCrossRefGoogle Scholar - Geary, D. C., & Widaman, K. F. (1987). Individual differences in cognitive arithmetic.
*Journal of Experimental Psychology: General*,**116**, 154–171.CrossRefGoogle Scholar - Geary, D. C., & Widaman, K. F. (1992). Numerical cognition: On the convergence of componential and psychometric models.
*Intelligence*,**16**, 47–80.CrossRefGoogle Scholar - 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 - 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 - Hecht, S. A. (1998). Toward an information processing account of individual differences in fraction skills.
*Journal of Educational Psychology*,**90**, 1–18.CrossRefGoogle Scholar - Kail, R., & Salthouse, T. A. (1994). Processing speed as a mental capacity.
*Acta Psychologica*,**86**, 199–225.PubMedCrossRefGoogle Scholar - 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 - 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 - 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 - 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 - 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 - 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 - 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 - Siegler, R. S. (1988a). Individual differences in strategy choices: Good students, not-so-good students, and perfectionists.
*Child Development*,**59**, 833–851.PubMedCrossRefGoogle Scholar - Siegler, R. S. (1988b). Strategy choice procedures and the development of multiplication skill.
*Journal of Experimental Psychology: General*,**117**, 258–275.CrossRefGoogle Scholar - 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 - 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 - 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 - 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