The roles of the central executive and visuospatial storage in mental arithmetic: A comparison across strategies

REFERENCES

• Ashcraft, M. H. (1992). Cognitive arithmetic: A review of data and theory. Cognition, 44(1–2), 75–106. doi: 10.1016/0010-0277(92)90051-I
   PubMed Web of Science ®Google Scholar
• Baddeley, A. D. (1996). Exploring the central executive. The Quarterly Journal of Experimental Psychology section A: Human Experimental Psychology, 49(1), 5–28. doi: 10.1080/713755608
   Web of Science ®Google Scholar
• Baddeley, A. D. (2000). The episodic buffer: A new component of working memory? Trends in Cognitive Sciences, 4, 417–423. doi: 10.1016/S1364-6613(00)01538-2
   PubMed Web of Science ®Google Scholar
• Baddeley, A. D. (2003). Working memory: Looking back and looking forward. Nature Reviews Neuroscience, 4, 829–839. doi: 10.1038/nrn1201
   PubMed Web of Science ®Google Scholar
• Baddeley, A. D., & Hitch, G. J. (1974). Working memory. In G. A. Bower (Ed.), Recent advances in learning and motivation (Vol. 8, pp. 47–90). New York: Academic Press.
   Google Scholar
• Bull, R., Espy, K., & Wiebe, S. A. (2008). Short-term memory, working memory, and executive functioning in pre-schoolers: Longitudinal predictors of mathematical achievement at age 7 years. Developmental Neuropsychology, 33, 205–228. doi: 10.1080/87565640801982312
   PubMed Web of Science ®Google Scholar
• Bull, R., Johnston, R. S., & Roy, J. A. (1999). Exploring the roles of the visual-spatial sketch pad and central executive in children's arithmetic skills: Views from cognition and developmental neuropsychology. Developmental Neuropsychology, 15(3), 421–442. doi: 10.1080/87565649909540759
   Web of Science ®Google Scholar
• Campbell, J. I. D. (1995). Mechanisms of number-fact retrieval: A modified network-interference theory and simulation. Mathematical Cognition, 1, 121–164.
   Google Scholar
• Campbell, J. I. D., & Austin, S. (2002). Effects of response time deadlines on adults’ strategy choices for simple addition. Memory and Cognition, 30(6), 988–994. doi: 10.3758/BF03195782
   PubMed Web of Science ®Google Scholar
• Campbell, J. I. D., & Tarling, D. P. M. (1996). Retrieval processes in arithmetic production and verification. Memory and Cognition, 24(2), 156–172. doi: 10.3758/BF03200878
   PubMed Web of Science ®Google Scholar
• Dehaene, S. (1992). Varieties of numerical abilities. Cognition, 44, 1–42. doi: 10.1016/0010-0277(92)90049-N
   PubMed Web of Science ®Google Scholar
• Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and number magnitude. Journal of Experimental Psychology: General, 122(3), 371–396. doi: 10.1037/0096-3445.122.3.371
   Web of Science ®Google Scholar
• De Hevia, M. D., Vallar, G., & Girelli, L. (2008). Visualizing numbers in the mind's eye: The role of visuo-spatial processes in numerical abilities. Neuroscience and Biobehavioural Reviews, 32, 1361–1372. doi: 10.1016/j.neubiorev.2008.05.015
   PubMed Web of Science ®Google Scholar
• 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. doi: 10.1007/s004260050041
   Web of Science ®Google Scholar
• De Stefano, D., & LeFevre, J-A. (2004). The role of working memory in mental arithmetic. European Journal of Cognitive Psychology, 16(3), 353–386. doi: 10.1080/09541440244000328
   Google Scholar
• Dumontheil, I., & Klingberg, T. (2012). Brain activity during a visuospatial working memory task predicts arithmetical performance 2 years later. Cerebral Cortex, 22, 1078–1085. doi: 10.1093/cercor/bhr175
   PubMed Web of Science ®Google Scholar
• Fürst, A. J., & Hitch, G. J. (2000). Separate roles for executive and phonological components of working memory in mental arithmetic. Memory and Cognition, 28, 774–782. doi: 10.3758/BF03198412
   PubMed Web of Science ®Google Scholar
• Gilmore, C., Attridge, N., Clayton, S., Cragg, L., Johnson, S., Marlow, N., … Inglis, M. (2013). Individual differences in inhibitory control, not non-verbal number acuity, correlate with mathematics achievement. PLoS ONE, 8(6), e67374. doi: 10.1371/journal.pone.0067374
   PubMed Web of Science ®Google Scholar
• Hanich, L. B., Jordan, N. C., Kaplan, D., & Dick, J. (2001). Performance across different areas of mathematical cognition in children with learning difficulties. Journal of Educational Psychology, 93, 615–626. doi: 10.1037/0022-0663.93.3.615
   Web of Science ®Google Scholar
• Heathcote, D. (1994). The role of visuo-spatial working memory in the mental addition of multi-digit addends. Current Psychology of Cognition, 13, 207–245.
   Google Scholar
• Hecht, S. A. (2002). Counting on working memory in simple arithmetic when counting is used for problem solving. Memory & Cognition, 30, 447–455. doi: 10.3758/BF03194945
   PubMed Web of Science ®Google Scholar
• Hegarty, M., & Kozhevnikov, M. (1999). Types of visual-spatial representations and mathematical problem solving. Journal of Educational Psychology, 91(4), 684–689. doi: 10.1037/0022-0663.91.4.684
   Web of Science ®Google Scholar
• Imbo, I., Duverne, S., & Lemaire, P. (2007). Working memory, strategy execution, and strategy selection in mental arithmetic. The Quarterly Journal of Experimental Psychology, 60(9), 1246–1264. doi: 10.1080/17470210600943419
   Web of Science ®Google Scholar
• Imbo, I., & LeFevre, J.-A. (2010). The role of phonological and visual working memory in complex arithmetic for Chinese- and Canadian-educated adults. Memory & Cognition, 38(2), 176–185. doi: 10.3758/MC.38.2.176
   PubMed Web of Science ®Google Scholar
• Imbo, I., & Vandierendonck, A. (2007). The development of strategy use in elementary school children: Working memory and individual differences. Journal of Experimental Child Psychology, 96, 284–309. doi: 10.1016/j.jecp.2006.09.001
   PubMed Web of Science ®Google Scholar
• Imbo, I., Vandierendonck, A., & Rosseel, Y. (2007). The influence of problem features and individual differences on strategic performance in simple arithmetic. Memory & Cognition, 35(3), 454–463. doi: 10.3758/BF03193285
   PubMed Web of Science ®Google Scholar
• Jordan, N. C., Hanich, L. B., & Kaplan, D. (2003). A longitudinal study of mathematical competencies in children with specific mathematics difficulties versus children with comorbid mathematics and reading difficulties. Child Development, 74(3), 834–850. doi: 10.1111/1467-8624.00571
   PubMed Web of Science ®Google Scholar
• Lee, K.-M., & Kang, S.-Y. (2002). Arithmetic operation and working memory: Differential suppression in dual tasks. Cognition, 83, B63–B68. doi: 10.1016/S0010-0277(02)00010-0
   PubMed Web of Science ®Google Scholar
• LeFevre, J.-A., DeStefano, D., Coleman, B., & Shanahan, T. (2005). Mathematical cognition and working memory. In J. I. D. Campbell (Ed.), Handbook of mathematical cognition (pp. 361–378). Hove, UK: Psychology Press.
   Google Scholar
• Logie, R. H., Gilhooly, K. J., & Wynn, V. (1994). Counting on working memory in arithmetic problem solving. Memory & Cognition, 22, 395–410. doi: 10.3758/BF03200866
   PubMed Web of Science ®Google Scholar
• Mix, K. S., & Cheng, Y.-L. (2012). The relation between space and math: Developmental and educational implications. Advances in Child Development and Behavior, 42, 197–243. doi: 10.1016/B978-0-12-394388-0.00006-X
   PubMed Web of Science ®Google Scholar
• Noël, M.-P., Désert, M., Aubrun, A., & Seron, X. (2001). Involvement of short-term memory in complex mental calculation. Memory & Cognition, 29, 34–42. doi: 10.3758/BF03195738
   PubMed Web of Science ®Google Scholar
• Peirce, J. W. (2007). PsychoPy-Psychophysics software in Python. Journal of Neuroscience Methods, 162(1–2), 8–13. doi: 10.1016/j.jneumeth.2006.11.017
   PubMed Web of Science ®Google Scholar
• Pickering, S. J., Gathercole, S. E., Hall, M., & Lloyd, S. A. (2001). Development of memory pattern and path: Further evidence for the fractionation of visuo-spatial memory. The Quarterly Journal of Experimental Psychology, 54A(2), 397–420. doi: 10.1080/713755973
   Web of Science ®Google Scholar
• Raghubar, K. P., Barnes, M. A., & Hecht, S. A. (2010). Working memory and mathematics: A review of developmental, individual difference, and cognitive approaches. Learning and Individual Differences, 20(2), 110–122. doi: 10.1016/j.lindif.2009.10.005
   Web of Science ®Google Scholar
• Reuhkala, M. (2001). Mathematical skills in ninth-graders: Relationship with visuo-spatial abilities and working memory. Educational Psychology, 21(4), 387–399. doi: 10.1080/01443410120090786
   Google Scholar
• Robert, N. D., & LeFevre, J.-A. (2013). Ending up with less: The role of working memory in solving simple subtraction problems with positive and negative answers. Research in Mathematics Education, 15(2), 165–176. doi: 10.1080/14794802.2013.797748
   Google Scholar
• Seron, X., Pesenti, M., Noël, M.-P., Deloche, G., & Cornet, J.-A. (1992). Images of numbers, or “when 98 is upper left and 6 sky blue”. Cognition, 44, 159–196. doi: 10.1016/0010-0277(92)90053-K
   PubMed Web of Science ®Google Scholar
• Seyler, D. J., Kirk, E. P., & Ashcraft, M. H. (2003). Elementary subtraction. Journal of Experimental Psychology: Learning, Memory & Cognition, 29, 1339–1352. doi:10.1037/0278-7393.29.6.1339
   PubMed Web of Science ®Google Scholar
• Siegler, R. S., & Shrager, J. (1984). Strategy choices in addition and subtraction: How do children know what to do. In C. Sophian (Ed.), Origins of cognitive skills (pp. 229–293). Hillsdale, NJ: Erlbaum.
   Google Scholar
• Simmons, F. R., Willis, C., & Adams, A.-M. (2012). Different components of working memory have different relationships with different mathematical skills. Journal of Experimental Child Psychology, 111, 139–155. doi: 10.1016/j.jecp.2011.08.011
   PubMed Web of Science ®Google Scholar
• Towse, J. N., & Neil, D. (1998). Analyzing human random generation behaviour: A review of methods used and a computer program for describing performance. Behaviour, Research Methods, Instruments, & Computers, 30(4), 583–591. doi: 10.3758/BF03209475
   Google Scholar
• Trbovich, P. L., & LeFevre, J.-A. (2003). Phonological and visual working memory in mental addition. Memory & Cognition, 31, 738–745. doi: 10.3758/BF03196112
   PubMed Web of Science ®Google Scholar
• Van Dijck, J.-P., & Fias, W. (2011). A working memory account for spatial–numerical associations. Cognition, 119(1), 114–119. doi: 10.1016/j.cognition.2010.12.013
   PubMed Web of Science ®Google Scholar