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Are Arithmetic Networks Interdependent In Number-Matching Task?

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Abstract

Addition and multiplication facts are retrieved from a network-like structure, as shown by data from number-matching tasks. Even if several evidences (e.g., cross-operation confusion effect) suggest that these networks are interrelated, the interdependency between addition and multiplication networks could be influenced by the type of task used (e.g., verification task). The present study aimed to investigate whether the addition and multiplication networks were interdependent or separate using a number-matching task. Eighty participants were divided in four groups. The Groups A (x, x, x) and B (+, +, +) performed the task in which only one arithmetic interference effect was implemented through three sessions (pure condition). The Groups C (x, x, +) and D (+, +, x) performed the same task in which the same arithmetic interference effect appeared in the first and second sessions, while a different arithmetic problem was presented in the last session (mixed condition). In the last session, the interference effect in the mixed condition was higher than that in the pure condition. The results argued more for an independency of addition and multiplication networks than for their interdependency.

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References

  • Ashcraft, M. H. (1987). Children’s knowledge of simple arithmetic: a developmental model and simulation. In C. J. Brainerd, R. Kail, & J. Bisanz (Eds.), Formal methods in developmental research (pp. 302–338). New York: Springer-Verlag.

    Google Scholar 

  • Ashcraft, M. H. (1992). Cognitive arithmetic: a review of data and theory. Cognition, 44, 75–106.

    Article  PubMed  Google Scholar 

  • Baroody, A. J. (1983). The development of procedural knowledge: an alternative explanation of chronometric trends of mental arithmetic. Developmental Review, 3, 225–230. doi:10.1016/0273-2297(83)90031-X.

    Article  Google Scholar 

  • Bjorklund, D. F., & Harnishfeger, K. K. (1995). The evolution of inhibition mechanisms and their role in human cognition and behavior. In F. N. Dempster, & C. J. Brainerd (Eds.), Interference and inhibition in cognition (pp. 142–169). San Diego, CA: Academic press.

    Google Scholar 

  • Blankenberger, S. (2001). The arithmetic tie effect is mainly encoding-based. Cognition, 82, B15–B24. doi:10.1016/S0010-0277(01)00140-8.

    Article  PubMed  Google Scholar 

  • Butterworth, B., Zorzi, M., Girelli, L., & Jonckheere, A. R. (2001). Storage and retrieval of addition facts: the role of number comparison. The Quarterly Journal of Experimental Psychology A: Human Experimental Psychology, 54A, 1005–1029. doi:10.1080/02724980143000064.

    Article  Google Scholar 

  • Campbell, J. I. D. (1994). Architectures for numerical cognition. Cognition, 53, 1–44. doi:10.1016/0010-0277(94)90075-2.

    Article  PubMed  Google Scholar 

  • Campbell, J. I. D., & Xue, Q. L. (2001). Cognitive arithmetic across cultures. Journal of Experimental Psychology: General, 130, 299–315. doi:10.1037//0096-3445.130.2.299.

    Article  Google Scholar 

  • Dehaene, S., & Cohen, L. (1997). Cerebral pathways for calculation: double dissociation between rote verbal and quantitative knowledge of arithmetic. Cortex, 33, 219–250. doi:10.1016/S0010-9452(08)70002-9.

    Article  PubMed  Google Scholar 

  • De Visscher, A., & Noël, M.-P. (2013). A case study of arithmetic facts dyscalculia caused by a hypersensitivity-to-interference in memory. Cortex, 49, 50–70. doi:10.1016/j.cortex.2012.01.003.

    Article  PubMed  Google Scholar 

  • Fabbri, M. (2011). Spatial congruency between stimulus presentation and response key arrangements in arithmetic fact retrieval. American Journal of Psychology, 124, 325–340.

    Article  PubMed  Google Scholar 

  • Fabbri, M., Natale, V., & Adan, A. (2008). Effect of time of day on arithmetic fact retrieval in a number-matching task. Acta Psychologica, 127, 485–490. doi:10.1016/j.actpsy.2007.08.011.

    Article  PubMed  Google Scholar 

  • Galfano, G., Penolazzi, B., Vervaeck, I., Angrilli, A., & Umiltà, C. (2009). Event-related brain potentials uncover activation dynamics in the lexicon of multiplication facts. Cortex, 45, 1167–1177. doi:10.1016/j.cortex.2008.09.003.

    Article  PubMed  Google Scholar 

  • 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. doi:10.1080/02724980244000332.

    Article  Google Scholar 

  • Groen, G. J., & Parkman, J. M. (1972). A chronometric analysis of simple addition. Psychological Review, 79, 329–343. doi:10.1037/h0032950.

    Article  Google Scholar 

  • Harnishfeger, K. K. (1995). The development of cognitive inhibition: theories, definitions, and research evidence. In F. N. Dempster, & C. J. Brainerd (Eds.), Interference and inhibition in cognition (pp. 175–204). San Diego, CA: Academic press.

    Chapter  Google Scholar 

  • Howell, D. C. (1997). Statistical methods for psychology. Belmont, CA:Wadsworth Publishing Company.

    Google Scholar 

  • Jackson, N., & Coney, J. (2005). Simple arithmetic processing: the question of automaticity. Acta Psychologica, 119, 41–66. doi:10.1016/j.actpsy.2004.10.018.

    Article  PubMed  Google Scholar 

  • LeFevre, J.-A., Bisanz, J., & Mrkonjic, L. (1988). Cognitive arithmetic: evidence for obligatory activation of arithmetic facts. Memory and Cognition, 16, 45–53.

    Article  PubMed  Google Scholar 

  • LeFevre, J.-A., Bisanz, J., Daley, K., Buffone, L., Greenham, S., & Sadesky, G. (1996a). Multiple routes to solution of single-digit multiplication problems. Journal of Experimental Psychology: General, 125, 284–306. doi:10.1037/0096-3445.125.3.284.

    Article  Google Scholar 

  • LeFevre, J.-A., Sadesky, G. S., & Bisanz, J. (1996b). Selection of procedures in mental addition: reassessing the problem size effect in adults. Journal of Experimental Psychology: Learning, Memory, and Cognition, 22, 216–230.

    Google Scholar 

  • Pesenti, M., Depoorter, N., & Seron, X. (2000). Noncommutability of the N + 0 arithmetic rule: a case study of dissociated impairment. Cortex, 36, 445–454. doi:10.1016/S0010-9452(08)70853-0.

    Article  PubMed  Google Scholar 

  • Rickard, T. C. (2005). A revised identical elements model of arithmetic fact representation. Journal of Experimental Psychology: Learning, Memory, and Cognition, 31, 250–257. doi:10.1037/0278-7393.31.2.250.

    PubMed  Google Scholar 

  • Rickard, T. C., Healy, A. F., & Bourne Jr., L. E. (1994). On the cognitive structure of basic arithmetic skills: operation, order, and symbol transfer effects. Journal of Experimental Psychology: Learning, Memory, and Cognition, 20, 1139–1153. doi:10.1037/0278-7393.20.5.1139.

    Google Scholar 

  • Rusconi, E., Galfano, G., Speriani, V., & Umiltà, C. (2004). Capacity and contextual constraints on product activation: evidence from task-irrelevant fact retrieval. The Quarterly Journal of Experimental Psychology. A, 57, 1485–1511. doi:10.1080/02724980343000873.

    Article  Google Scholar 

  • Siegler, R. (1988). Strategy choice procedures and the development of multiplication skill. Journal of Experimental Psychology: General, 117, 258–275.

    Article  Google Scholar 

  • Sokol, S. M., McCloskey, M., Cohen, N. J., & Aliminosa, D. (1991). Cognitive representations and processes in arithmetic: inferences from the performance of brain-damaged subjects. Journal of Experimental Psychology: Learning, Memory, and Cognition, 17, 355–376. doi:10.1037//0278-7393.17.3.355.

    PubMed  Google Scholar 

  • Stazyk, E. H., Ashcraft, M. H., & Hamann, M. S. (1982). A network approach to mental multiplication. Journal of Experimental Psychology: Learning, Memory, and Cognition, 8, 320–335.

    Google Scholar 

  • 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. doi:10.1037/1196-1961.50.4.393.

    Article  PubMed  Google Scholar 

  • Verguts, T., & Fias, W. (2005). Interacting neighbors: a connectionist model of retrieval in single-digit multiplication. Memory & Cognition, 33, 1–16.

    Article  Google Scholar 

  • Winkelman, J., & Schmidt, J. (1974). Associative confusions in mental arithmetic. Journal of Experimental Psychology, 102, 734–736.

    Article  Google Scholar 

  • Zamarian, L., Stadelmann, E., Nürk, H.-C., Gamboz, N., Marksteiner, J., & Delazer, M. (2007). Effects of age and mild cognitive impairment on direct and indirect access to arithmetic knowledge. Neuropsychologia, 45, 1511–1521. doi:10.1016/j.neuropsychologia.2006.11.012.

    Article  PubMed  Google Scholar 

  • Zbrodoff, N. J., & Logan, G. D. (1986). On the autonomy of mental process: a case study of arithmetic. Journal of Experimental Psychology: General, 115, 118–130.

    Article  Google Scholar 

  • Zhou, X. (2011). Operation-specific encoding in single-digit arithmetic. Brain and Cognition, 76, 400–406. doi:10.1016/j.bandc.2011.03.018.

    Article  PubMed  Google Scholar 

Download references

Compliance with Ethical Standards

All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards.

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This study was not supported by any funders.

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The authors declare that they have no conflict of interest.

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  1. Department of Psychology, Second University of Naples, Viale Ellittico, 31, 81100, Caserta (Ce), Italy

    Marco Fabbri

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  1. Marco Fabbri
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Correspondence to Marco Fabbri.

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Fabbri, M. Are Arithmetic Networks Interdependent In Number-Matching Task?. Curr Psychol 35, 149–158 (2016). https://doi.org/10.1007/s12144-015-9377-z

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