Four and twenty blackbirds: how transcoding ability mediates the relationship between visuospatial working memory and math in a language with inversion

References

• Alloway, T. P., Gathercole, S. E., & Pickering, S. J. (2006). Verbal and visuospatial short-term and working memory in children: Are they separable? Child Development, 77, 1698–1716. doi:10.1111/j.1467-8624.2006.00968.x
   PubMed Web of Science ®Google Scholar
• Ang, S. Y. & Lee, K. (2008). Central executive involvement in children’s spatial memory. Memory, 16, 918–933. doi:10.1080/09658210802365347
   PubMed Web of Science ®Google Scholar
• Ashcraft, M. H. & Guillaume, M. M. (2009). Mathematical cognition and the problem size effect. In B. H. Ross (Ed.), Psychology of learning and motivation (Vol. 51, pp. 121–151). Amsterdam: Academic Press.
   Google Scholar
• Baddeley, A. (2007). Working memory, thought, and action. Oxford: Oxford University Press.10.1093/acprof:oso/9780198528012.001.0001
   Google Scholar
• Baddeley, A. D. (1992). Working memory. Science, 255, 556–559.10.1126/science.1736359
   PubMed Web of Science ®Google Scholar
• Baddeley, A. D., & Hitch, G. J. (1974). Working memory. In G. H. Bower (Ed.), The psychology of learning and motivation, (Vol. 8, pp. 47–89). New York, NY: Academic Press.
   Google Scholar
• Baddeley, A. D., Thomson, N., & Buchanan, M. (1975). Word length and the structure of short-term memory. Journal of Verbal Learning and Verbal Behavior, 14, 575–589. doi:10.1016/S0022-5371(75)80045-4
   Google Scholar
• Barrouillet, P., Camos, V., Perruchet, P., & Seron, X. (2004). ADAPT: A developmental, asemantic, and procedural model for transcoding from verbal to arabic numerals. Psychological Review, 111, 368. doi:10.1037/0033-295X.111.2.368
   PubMed Web of Science ®Google Scholar
• Bates, D. M. (2010). Mixed-effects modeling with R. Retrieved from http://www.wordlatex.com/static/templates/pdf/book_B.pdf
   Google Scholar
• Bull, R. & Lee, K. (2014). Executive functioning and mathematics achievement. Child Development Perspectives, 8, 36–41. doi:10.1111/cdep.12059
   Web of Science ®Google Scholar
• Camos, V. (2008). Low working memory capacity impedes both efficiency and learning of number transcoding in children. Journal of Experimental Child Psychology, 99, 37–57. doi:10.1016/j.jecp.2007.06.006
   PubMed Web of Science ®Google Scholar
• Campbell, J. I. D. & Graham, D. J. (1985). Mental multiplication skill: Structure, process, and acquisition. Canadian Journal of Psychology/Revue canadienne de psychologie, 39, 338–366. doi:10.1037/h0080065
   Web of Science ®Google Scholar
• Cowan, N., Day, L., Saults, J. S., Keller, T. A., Johnson, T., & Flores, L. (1992). The role of verbal output time in the effects of word length on immediate memory. Journal of Memory and Language, 31, 1–17. doi:10.1016/0749-596X(92)90002-F
   Web of Science ®Google Scholar
• De Smedt, B., Janssen, R., Bouwens, K., Verschaffel, L., Boets, B., & Ghesquière, P. (2009). Working memory and individual differences in mathematics achievement: A longitudinal study from first grade to second grade. Journal of Experimental Child Psychology, 103, 186–201. doi:10.1016/j.jecp.2009.01.004
   PubMed Web of Science ®Google Scholar
• Elo, A. (1978). The rating of chess players, past and present. New York, NY: Arco.
   Google Scholar
• Fisk, J. E. & Sharp, C. A. (2003). The role of the executive system in visuo-spatial memory functioning. Brain and Cognition, 52, 364–381. doi:10.1016/S0278-2626(03)00183-0
   PubMed Web of Science ®Google Scholar
• Friso-Van den Bos, I., van der Ven, S. H. G., Kroesbergen, E. H., & van Luit, J. E. H. (2013). Working memory and mathematics in primary school children: A meta-analysis. Educational Research Review, 10, 29–44. doi:10.1016/j.edurev.2013.05.003
   Web of Science ®Google Scholar
• Gathercole, S. E., Pickering, S. J., Ambridge, B., & Wearing, H. (2004). The structure of working memory from 4 to 15 years of age. Developmental Psychology, 40, 177–190. doi:10.1037/0012-1649.40.2.177
   PubMed Web of Science ®Google Scholar
• Geary, D. C., Bow-Thomas, C. C., Liu, F., & Siegler, R. S. (1996). Development of arithmetical competencies in Chinese and American children: Influence of age, language, and schooling. Child Development, 67, 2022–2044. doi:10.2307/1131607
   PubMed Web of Science ®Google Scholar
• Göbel, S. M., Moeller, K., Pixner, S., Kaufmann, L., & Nuerk, H.-C. (2014). Language affects symbolic arithmetic in children: The case of number word inversion. Journal of Experimental Child Psychology, 119, 17–25. doi:10.1016/j.jecp.2013.10.001
   PubMed Web of Science ®Google Scholar
• Helmreich, I., Zuber, J., Pixner, S., Kaufmann, L., Nuerk, H.-C., & Moeller, K. (2011). Language effects on children's nonverbal number line estimations. Journal of Cross-Cultural Psychology, 42, 598–613. doi:10.1177/0022022111406026
   Web of Science ®Google Scholar
• Holmes, J. & Adams, J. W. (2006). Working memory and children’s mathematical skills: Implications for mathematical development and mathematics curricula. Educational Psychology, 26, 339–366. doi:10.1080/01443410500341056
   Google Scholar
• Huizinga, M., Dolan, C. V., & van der Molen, M. W. (2006). Age-related change in executive function: Developmental trends and a latent variable analysis. Neuropsychologia, 44, 2017–2036. doi:10.1016/j.neuropsychologia.2006.01.010
   PubMed Web of Science ®Google Scholar
• Imbo, I., Vanden Bulcke, C., & Fias, W. (2014). Sixty-four or four-and-sixty? The influence of language and working memory on children’s number transcoding. Frontiers in Psychology, 5, 1–10. doi:10.3389/fpsyg.2014.00313
   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, 454–463. doi:10.3758/bf03193285
   PubMed Web of Science ®Google Scholar
• Jahr, E. H. (1989). Language planning and language change. In L. E. Breivik & E. H. Jahr (Eds.), Trends in linguistics. Studies and monographs (Vol. 43, pp. 99–113). New York, NY: Mouton de Gruyter.
   Google Scholar
• Janssen, J., Scheltens, F., & Kraemer, J.-M. (2005). Leerling-en onderwijsvolgsysteem rekenen-wiskunde [Student and education tracking system arithmetic-mathematics]. Arnhem, The Netherlands: Cito.
   Google Scholar
• Kessels, R. P. C., van den Berg, E., Ruis, C., & Brands, A. M. A. (2008). The backward span of the corsi block-tapping task and its association with the WAIS-III digit span. Assessment, 15, 426–434. doi:10.1177/1073191108315611
   PubMed Web of Science ®Google Scholar
• Klinkenberg, S., Straatemeier, M., & Van der Maas, H. L. J. (2011). Computer adaptive practice of Maths ability using a new item response model for on the fly ability and difficulty estimation. Computers & Education, 57, 1813–1824. doi:10.1016/j.compedu.2011.02.003
   Web of Science ®Google Scholar
• Krinzinger, H., Gregoire, J., Desoete, A., Kaufmann, L., Nuerk, H.-C., & Willmes, K. (2011). Differential language effects on numerical skills in second grade. Journal of Cross-Cultural Psychology, 42, 614–629. doi:10.1177/0022022111406252
   Web of Science ®Google Scholar
• Maris, G. & Van der Maas, H. (2012). Speed-accuracy response models: Scoring rules based on response time and accuracy. Psychometrika, 77, 615–633. doi:10.1007/s11336-012-9288-y
   Web of Science ®Google Scholar
• Moeller, K., Pixner, S., Zuber, J., Kaufmann, L., & Nuerk, H. C. (2011). Early place-value understanding as a precursor for later arithmetic performance – A longitudinal study on numerical development. Research in Developmental Disabilities, 32, 1837–1851. doi:10.1016/j.ridd.2011.03.012
   PubMed Web of Science ®Google Scholar
• Moura, R., Wood, G., Pinheiro-Chagas, P., Lonnemann, J., Krinzinger, H., Willmes, K., & Haase, V. G. (2013). Transcoding abilities in typical and atypical mathematics achievers: The role of working memory and procedural and lexical competencies. Journal of Experimental Child Psychology, 116, 707–727. doi:10.1016/j.jecp.2013.07.008
   PubMed Web of Science ®Google Scholar
• Mullis, I. V. S., Martin, M. O., Foy, P., & Arora, A. (2012). The TIMSS 2011 international results in mathematics. Boston, MA: International Association for the Evaluation of Educational Achievement.
   Google Scholar
• Ng, S. S. N. & Rao, N. (2010). Chinese number words, culture, and mathematics learning. Review of Educational Research, 80, 180–206. doi:10.3102/0034654310364764
   Web of Science ®Google Scholar
• Parkman, J. M. (1972). Temporal aspects of simple multiplication and comparison. Journal of Experimental Psychology, 95, 437–444.10.1037/h0033662
   Google Scholar
• Pixner, S., Zuber, J., Heřmanová, V., Kaufmann, L., Nuerk, H. C., & Moeller, K. (2011). One language, two number-word systems and many problems: Numerical cognition in the Czech language. Research in Developmental Disabilities, 32, 2683–2689. doi:10.1016/j.ridd.2011.06.004
   PubMed Web of Science ®Google Scholar
• Power, R. J. D. & Dal Martello, M. F. (1990). The dictation of Italian numerals. Language and Cognitive Processes, 5, 237–254. doi:10.1080/01690969008402106
   Web of Science ®Google Scholar
• Rasmussen, C. & Bisanz, J. (2005). Representation and working memory in early arithmetic. Journal of Experimental Child Psychology, 91, 137–157. doi:10.1016/j.jecp.2005.01.004
   PubMed Web of Science ®Google Scholar
• Seron, X. & Fayol, M. (1994). Number transcoding in children: A functional analysis. British Journal of Developmental Psychology, 12, 281–300. doi:10.1111/j.2044-835X.1994.tb00635.x
   Web of Science ®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
• Tingley, D., Yamamoto, T., Hirose, K., Keele, L., & Imai, K. (2013). Mediation: R package for causal mediation analysis. Retrieved from http://cran.r-project.org/web/packages/mediation/vignettes/mediation.pdf
   Google Scholar
• van der Ven, S. H. G., Kroesbergen, E. H., Boom, J., & Leseman, P. P. M. (2012). The development of executive functions and early mathematics: A dynamic relationship. British Journal of Educational Psychology, 82, 100–119. doi:10.1111/j.2044-8279.2011.02035.x
   PubMed Web of Science ®Google Scholar
• van der Ven, S. H. G., van der Maas, H. L. J., Straatemeier, M., & Jansen, B. R. J. (2013). Visuospatial working memory and mathematical ability at different ages throughout primary school. Learning and Individual Differences, 27, 182–192. doi:10.1016/j.lindif.2013.09.003
   Web of Science ®Google Scholar
• van Loosbroek, E., Dirkx, G. S., Hulstijn, W., & Janssen, F. (2009). When the mental number line involves a delay: The writing of numbers by children of different arithmetical abilities. Journal of Experimental Child Psychology, 102, 26–39.10.1016/j.jecp.2008.07.003
   PubMed Web of Science ®Google Scholar
• Van Luit, J. E. H. & Van der Molen, M. J. (2011). The effectiveness of Korean number naming on insight into numbers in Dutch students with mild intellectual disabilities. Research in Developmental Disabilities, 32, 1941–1947. doi:10.1016/j.ridd.2011.03.028
   PubMed Web of Science ®Google Scholar
• Vandierendonck, A., Kemps, E., Fastame, M. C., & Szmalec, A. (2004). Working memory components of the Corsi blocks task. British Journal of Psychology, 95, 57–79. doi:10.1348/000712604322779460
   PubMed Web of Science ®Google Scholar
• Zuber, J., Pixner, S., Moeller, K., & Nuerk, H.-C. (2009). On the language specificity of basic number processing: Transcoding in a language with inversion and its relation to working memory capacity. Journal of Experimental Child Psychology, 102, 60–77. doi:10.1016/j.jecp.2008.04.003
   PubMed Web of Science ®Google Scholar