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Articles

Involvement of working memory in mental multiplication in Chinese elementary students

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Pages 380-390 | Received 02 Apr 2015, Accepted 02 Aug 2015, Published online: 16 Sep 2016

References

  • Ashcraft, M. H. (1995). Cognitive psychology and simple arithmetic: A review and summary of new directions. Mathematical Cognition, 1, 3–34.
  • 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, the Netherlands: Elsevier Science.
  • Ashcraft, M. H., & Kirk, E. P. (2001). The relationships among working memory, math anxiety, and performance. Journal of Experimental Psychology: General, 130, 224–237.
  • Baddeley, A. D. (1992). Working memory. Science, 255, 556–559.
  • Baddeley, A. D. (1996). Exploring the central executive. The Quarterly Journal of Experimental Psychology, 49A, 5–28.
  • Baddeley, A. D. (2003). Working memory: Looking back and looking forward. Nature Reviews Neuroscience, 4, 829–839.
  • Baddeley, A. D., & Hitch, G. (1974). Working memory. Psychology of Learning and Motivation, 8, 47–89.
  • Baddeley, A. D., Lewis, V., Eldridge, M., & Thomson, N. (1984). Attention and retrieval from long-term memory. Journal of Experimental Psychology: General, 113, 518–540.
  • Bryk, A. S., & Raudenbush, S. W. (1992). Hierarchical linear model: Application and data analysis methods. Newbury Park, CA: Sage.
  • Chang, L. (2003). Variable effects of children's aggression, social withdrawal, and prosocial leadership as functions of teacher beliefs and behaviors. Child Development, 74, 535–548.
  • Chang, L. (2004). The role of classroom norms in contextualizing the relations of children's social behaviors to peer acceptance. Developmental Psychology, 40, 691–702.
  • Chen, Y.-H., & Wang, M.-Y. (2006). The influence of working memory span on children's arithmetical cognitive strategies. Psychological Development and Education, 2, 29–35.
  • Conway, A. R. A., & Engle, R. W. (1994). Working memory and retrieval: A resource-dependent inhibition model. Journal of Experimental Psychology: General, 123, 354–373.
  • Cowan, N. (1999). An embedded-processes model of working memory. In A. Miyake & P. Shah (Eds.), Models of working memory: Mechanisms of active maintenance and executive control (pp. 62–101). New York, NY: Cambridge University Press.
  • Daneman, M., & Carpenter, A. (1980). Individual differences in working memory and reading. Journal of Verbal Learning and Verbal Behavior, 19, 450–466.
  • De Rammelaere, S., Stuyvea, E., & Vandierendonck, A. (1999). The contribution of working memory resources in the verification of simple mental arithmetic sums. Psychological Research, 62, 72–77.
  • De Rammelaere, S., Stuyvea, E., & Vandierendonck, A. (2001). Verifying simple arithmetic sums and products: Are the phonological loop and the central executive involved? Memory and Cognition, 29, 267–273.
  • Dehaene, S. (1992). Varieties of numerical abilities. Cognition, 44, 1–42.
  • Dehaene, S., Spelke, E., Pinel, P., Stanescu, R., & Tsivkin, S. (1999). Sources of mathematical thinking: Behavioral and brain-imagining evidence. Science, New Series, 284, 970–974.
  • DeStefano, D., & LeFevre, J.-A. (2004). The role of working memory in mental arithmetic. European Journal of Cognitive Psychology, 16, 353–386.
  • Flanagan, D. P., & Kaufman, A. S. (2009). Introduction and overview. In A. S. Kaufman & N. L. Kaufman (Eds.), Essentials of WISC-IV assessment (2nd ed., pp. 2–51). Hoboken, NJ: Wiley.
  • Fuchs, L. S., Compton, D. L., Fuchs, D., Paulsen, K., & Bryant, J. D. (2005). The prevention, identification, and cognitive determinants of math difficulty. Journal of Educational Psychology, 97, 493–513.
  • Furst, A. J., & Hitch, G. J. (2000). Separate roles for executive and phonological components of working memory in mental arithmetic. Memory & Cognition, 28, 774–782.
  • Grant, J. D., & Dagenbach, D. (2000). Further considerations regarding inhibitory processes, working memory, and cognitive aging. The American Journal of Psychology, 113, 69–94.
  • Heathcote, D. (1994). The role of visuo-spatial working memory in the mental addition of multidigit addends. Current Psychology of Cognition, 13, 207–245.
  • Hecht, S. A. (2002). Counting on working memory in simple arithmetic when counting is used for problem solving. Memory and Cognition, 30, 447–455.
  • Imbo, I., & Vandierendonck, A. (2007). Do multiplication and division strategies rely on executive and phonological working memory resources? Memory and Cognition, 35, 1759–1771.
  • Kaye, D. B., de Winstanley, P., Chen, Q., & Bonnefil, V. (1989). Development of efficient arithmetic computation. Journal of Educational Psychology, 81, 467–480.
  • Kouba, V. L. (1989). Children's solution strategies for equivalent set multiplication and division word problems. Journal for Research in Mathematics Education, 20, 147–158.
  • Krajewski, K., & Schneider, W. (2009). Exploring the impact of phonological awareness, visual-spatial working memory, and preschool quantity-number competencies on mathematics achievement in elementary school: Findings from a 3-year longitudinal study. Journal of Experimental Child Psychology, 103, 516–531.
  • Kulak, A. (1993). Spatial processing and arithmetic performance (Unpublished doctoral dissertation). Carleton University, Ottawa, Ontario, Canada.
  • Lee, K., & Kang, S. (2002). Arithmetic operation and working memory: Differential suppression in dual tasks. Cognition, 83, B63–B68.
  • LeFevre, J. (1998). Interactions among encoding, calculation, and production processes in the multiplication performance of Chinese-speaking adults. Mathematical Cognition, 4, 47–65.
  • LeFevre, J., Lei, Q., Smith-Chant, B., & Mullins, D. (2001). Multiplication by eye and by ear for Chinese-speaking and English-speaking adults. Canadian Journal of Experimental Psychology, 55, 277–284.
  • LeFevre, J., & Liu, J. (1997). The role of experience in numerical skill: Multiplication performance in adults from Canada and China. Mathematical Cognition, 3, 31–62.
  • Lemaire, P., & Siegler, R. S. (1995). Four aspects of strategic change: Contributions to children's learning of multiplication. Journal of Experimental Psychology: General, 124, 83–97.
  • Liu, F., Geary, D. C., Bow-Thomas, C. C., & Siegler, R. S. (1994). Influences of numerical memory span on strategy choices in addition: A comparative study of numerical skill differences between Chinese and American children. Psychological Science, 17, 21–27.
  • Logie, R. H., Gilhooly, K. J., & Wynn, V. (1994). Counting on working memory in mental arithmetic. Memory and Cognition, 22, 395–410.
  • Lyon, G. R., & Krasnegor, N. A. (Eds.). (1996). Attention, memory, and executive function. Baltimore, MD: Brookes.
  • Meyer, M. L., Salimpoor, V. N., Wu, S. S., Geary, D. C., & Menon, V. (2010). Differential contribution of specific working memory components to mathematics achievement in 2nd and 3rd graders. Learning and Individual Differences, 20, 101–109.
  • Miller, G. A., Galanter, E., & Pribram, H. K. (1960). Plans and the structure of behavior. New York, NY: Holt, Rinehart, & Winston.
  • Miyake, A., Friedman, N. P., Emerson, M. J., Witzki, A. H., Howerter, A., & Wager, T. D. (2000). The unity and diversity of executive functions and their contributions to complex “frontal lobe” tasks: A latent variable analysis. Cognitive Psychology, 41, 49–100.
  • Morris, N., & Jones, D. M. (1990). Memory updating in working memory: The role of the central executive. British Journal of Psychology, 81, 111–121.
  • Mulligan, J. T., & Mitchelmore, M. C. (1997). Young children's intuitive models of multiplication and division. Journal for Research in Mathematics Education, 28, 309–330.
  • Nairne, J. S. (1990). A feature model of immediate memory. Memory and Cognition, 18, 251–269.
  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
  • Neath, I. (2000). Modeling the effects of irrelevant speech on memory. Psychonomic Bulletin & Review, 7, 403–423.
  • Noel, M., Robert, A., & Brysbaert, M (1998). Does language really matter when doing arithmetic? Reply to Campbell (1998). Cognition, 67, 365–374.
  • Noel, M., Seron, X., & Trovarelli, F. (2004). Working memory as a predictor of addition skills and addition strategies in children. Cahiers de Psychologie Cognitive, 22, 3–25.
  • People's Education Press. (2010). Elementary mathematics. Beijing, China: People's Education Press.
  • Rasmussen, C., & Bisanz, J. (2005). Representation and working memory in early arithmetic. Journal of Experimental Child Psychology, 91, 137–157.
  • Sattler, J. M. (2008). Assessment of children: Cognitive foundations (5th ed.). San Diego, CA: Jerome M. Sattler.
  • Schuchardt, K., Maehler, C., & Hasselhorn, M. (2008). Working memory deficits in children with specific learning disorders. Journal of Learning Disabilities, 41, 514–523.
  • Seitz, K., & Schumann-Hengsteler, K. (2000). Mental multiplication and working memory. European Journal of Cognitive Psychology, 12, 552–570.
  • Seitz, K., & Schumann-Hengsteler, K. (2002). Phonological loop and central executive processes in mental addition and multiplication. Psychologische Beitrage, 44, 275–302.
  • Shellenbarger, S. (2014, September 15). The best language for math: Confusing English number words are linked to weaker skills. Wall Street Journal. Retrieved from http://www.wsj.com/articles/the-best-language-for-math-1410304008
  • Smith, E. E., & Jonides, J. (1999). Storage and executive processes in the frontal lobes. Science, 283, 1657–1661.
  • Swanson, H. L. (2006). Cross-sectional and incremental changes in working memory and mathematical problem solving. Journal of Educational Psychology, 98, 265–281.
  • Swanson, H. L., Jerman, O., & Zheng, X. (2008). Growth in working memory and mathematical problem solving in children at risk and not at risk for serious math difficulties. Journal of Educational Psychology, 100, 343–379.
  • Trbovich, P. I., & LeFevre, J. (2003). Phonological and visual-spatial working memory in mental addition. Memory & Cognition, 31, 738–745.
  • Tronsky, L. N. (2005). Strategy use, the development of automaticity, and working memory involvement in complex multiplication. Memory and Cognition, 33, 927–940.
  • Wang, J. (2006). The development characteristics of executive function and its relation with problem solving among primary school children (Unpublished master's thesis). Beijing Normal University, Beijing, P. R. China.
  • Wang, J. (2010). The representation change characteristic of arithmetic word problem solving and its influencing factors on children in primary 5 (Unpublished doctoral dissertation). Beijing Normal University, Beijing, P. R. China.
  • Wu, C.-Z. (2010). The influences of working memory and mathematics anxiety on children's cognitive strategies (Unpublished master's thesis). He Nan University, Kaifeng, P. R. China.
  • Zhang, M., Sui, J., & Fang, W.-J. (2002). Accessing the retrieval capability of visuospatial working memory of students with learning disabilities. Psychological Science, 25, 565–568.
  • Zhao, H. (2007). Characteristics of multidigit multiplication strategy selection in grade 4 primary students and the relations to conceptual knowledge (Unpublished doctoral dissertation). Beijing Normal University, Beijing, P. R. China.
  • Zhao, H., & Chen, Y.-H. (2010). The characteristics of 4th-grade students' multidigit multiplication and their relations to working memory. Psychological Science, 33, 938–941.

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