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Articles

Grounding the Symbols for Place Value: Evidence From Training and Long-Term Exposure to Base-10 Models

References

  • Allison, P. D. (1990). Change scores as dependent variables in regression analysis. Sociological Methodology, 20, 93–114. doi:10.2307/271083
  • Ball, D. L. (1992). Magical hopes: Manipulatives and the reform of math education. American Educator, 16(2), 14–18, 46–47.
  • Barsalou, L. B. (2008). Grounded cognition. Annual Review of Psychology, 59, 617–645. doi:10.1146/annurev.psych.59.103006.093639
  • Bassok, M., & Medin, D. L. (1997). Birds of a feather flock together: Similarity judgments with semantically rich stimuli. Journal of Memory and Language, 36, 311–336. doi:10.1006/jmla.1996.2492
  • Bassok, M., Wu, L., & Olseth, L. K. (1995). Judging a book by its cover: Interpretative effects of content on problem solving transfer. Memory & Cognition, 23, 354–367. doi:10.3758/BF03197236
  • Bednarz, N., & Janvier, B. (1982). The understanding of numeration in primary school. Educational Studies in Mathematics, 13, 33–57. doi:10.1007/BF00305497
  • Blair, C., & Razza, R. P. (2007). Relating effortful control, executive function, and false belief understanding to emerging math and literacy ability in kindergarten. Child Development, 78, 647–663. doi:10.1111/cdev.2007.78.issue-2
  • Booth, J., L. & Siegler, R.S. (2006). Developmental and individual differences in pure numerical estimation. Developmental Psychology, 41, 189–201. doi:10.1037/0012-1649.6.189
  • Bornstein, M. H., Haynes, M. O., & Painter, K. M. (1998). Sources of child vocabulary competence: A multivariate model. Journal of Child Language, 25, 367–393. doi:10.1017/S0305000998003456
  • Bruner, J. S., Oliver, R. R., & Greenfield, P. M. (1966). Studies in cognitive growth. New York, NY: Wiley.
  • Bull, R., & Scerif, G. (2001). Executive functioning as a predictor of children’s mathematics ability: Inhibition, switching, and working memory. Developmental Neuropsychology, 19, 273–293. doi:10.1207/S15326942DN1903_3
  • Byrge, L., Smith, L. B., & Mix, K. S. (2014). Beginnings of place value: How preschoolers write three-digit numbers. Child Development, 85, 437–443. doi:10.1111/cdev.12162
  • Carbonneau, K. J., Marley, S. C., & Selig, J. P. (2013). A meta-analysis of the efficacy of teaching mathematics with concrete manipulatives. Journal of Educational Psychology, 105, 380–400. doi:10.1037/a0031084
  • Cauley, K. M. (1988). Construction of logical knowledge: Study of borrowing in subtraction. Journal of Educational Psychology, 80, 202–205. doi:10.1037/0022-0663.80.2.202
  • Clark, C. A. C., Pritchard, V. E., & Woodward, L. J. (2010). Preschool executive functioning abilities predict early mathematics achievement. Developmental Psychology, 48, 1176–1191. doi:101037/a0019672
  • Cobb, P., & Wheatley, G. (1988). Children’s initial understandings of ten. Focus on Learning Problems in Mathematics, 10(3), 1–28.
  • Dohrmann, K. R., Nishida, T. K., Gartner, A., Lipsky, D. K., & Grimm, K. J. (2007). High school outcomes for students in a public Montessori program. Journal of Research in Childhood Education, 22, 205–217. doi:10.1080/02568540709594622
  • Faul, F., Erdfelder, E., Buchner, A., & Lang, A.-G. (2009). Statistical power analyses using G*Power 3.1: Tests for correlation and regression analyses. Behavior Research Methods, 41, 1149–1160. doi:10.3758/BRM.41.4.1149
  • Fuson, K. C. (1986). Roles of representation and verbalization in the teaching of multi-digit addition and subtraction. European Journal of Psychology of Education, 1, 35–56. doi:10.1007/BF03172568
  • Fuson, K. C. (1988). Children’s counting and concepts of number. New York, NY: Springer-Verlag.
  • Fuson, K. C., & Briars, D. J. (1990). Using a base-ten blocks learning/teaching approach for first- and second-grade place-value and multidigit addition and subtraction. Journal for Research in Mathematics Education, 21, 180–206. doi:10.2307/749373
  • Gentner, D. (2010). Bootstrapping the mind: Analogical processes and symbol systems. Cognitive Science, 34, 752–775. doi:10.1111/cogs.2010.34.issue-5
  • Gentner, D., & Markman, A. B. (1994). Structural alignment in comparison: No difference without similarity. Psychological Science, 4, 152–158. doi:10.1111/j.1467-9280.1994.tb00652.x
  • Gick, M. L., & Holyoak, K. J. (1983). Schema induction and analogical transfer. Cognitive Psychology, 15, 1–38. doi:10.1016/0010-0285(83)90002-6
  • Glenberg, A. M., Gutierrez, T., Levin, J. R., Japuntich, S., & Kaschak, M. P. (2004). Activity and imagined activity can enhance young children’s reading comprehension. Journal of Educational Psychology, 96, 424–436. doi:10.1037/0022-0663.96.3.424
  • Glenberg, A. M., & Robertson, D. A. (2000). Symbol grounding and meaning: A comparison of high-dimensional and embodied theories of meaning. Journal of Memory & Language, 43, 379–401. doi:10.1006/jmla.2000.2714
  • Goldstone, R. L., & Sakamoto, Y. (2003). The transfer of abstract principles governing complex adaptive systems. Cognitive Psychology, 46, 414–466. doi:10.1016/S0010-0285(02)00519-4
  • Hart, B., & Risley, T. R. (1995). Meaningful differences in the everyday experience of young American children. Baltimore, MD: Paul H. Brookes.
  • Ho, C. S. H., & Cheng, F. S. F. (1997). Training in place-value concepts improves children’s addition skills. Contemporary Educational Psychology, 22, 495–506. doi:10.1006/ceps.1997.0947
  • Huttenlocher, J., Haight, W., Bryk, A., Seltzer, M., & Lyons, T. (1991). Early vocabulary growth: Relation to language input and gender. Developmental Psychology, 27, 236–248. doi:10.1037/0012-1649.27.2.236
  • Jesson, D. S. (1983). The development of place value skills in primary and middle school children. Research in Education, 29, 69–79.
  • Kalyuga, S., Ayres, P., Chandler, P., & Sweller, J. (2003). The expertise reversal effect. Educational Psychologist, 38, 23–31. doi:10.1207/S15326985EP3801_4
  • Kamii, C. (1986). Place value: An explanation of its difficulty and educational implications for the primary grades. Journal of Research in Childhood Education, 1, 75–86. doi:10.1080/02568548609594909
  • Kaminski, J. A., & Sloutsky, V. M. (2009). The effect of concreteness on children’s ability to detect common proportion. In N. Taatgen & H. Van Rijn (Eds.), Proceedings of the XXXI Annual Conference of the Cognitive Science Society (pp. 335–340). Mahwah, NJ: Erlbaum.
  • Kaminski, J. A., Sloutsky, V. M., & Heckler, A. F. (2008). Learning theory: The advantage of abstract examples in learning math. Science, 320, 454–455. doi:10.1126/science.1154659
  • Kouba, V. L., Brown, C. A., Carpenter, T. P., Lindquist, M. M., Silver, E. A., & Swafford, J. O. (1988). Results of the fourth NAEP assessment of mathematics: Number, operations, and word problems. The Arithmetic Teacher, 35, 14–19.
  • Kurtz, K. J., Miao, C.-H., & Gentner, D. (2001). Learning by analogical bootstrapping. Journal of the Learning Sciences, 10, 417–446. doi:10.1207/S15327809JLS1004new_2
  • Labinowicz, E. (1985). Learning from children: New beginnings for teaching numerical thinking. Menlo Park, CA: Addison-Wesley.
  • Lakoff, G., & Nunez, R. (2001). Where mathematics comes from: How the embodied mind brings mathematics into being. New York, NY: Basic Books.
  • Laski, E., Ermakova, A., & Vasilyeva, M. (2014). Early use of decomposition for addition and its relation to base-10 knowledge. Journal of Applied Developmental Psychology, 35, 444–454. doi:10.1016/j.appdev.2014.07.002
  • Lillard, A. S. & Else-Quest, N. (2006). The early years: Evaluating Montessori education. Science, 313, 1893–1894. doi:10.1126/science.1132362
  • Lillard, A. S. (2012). Preschool children’s development in classic Montessori, supplemented Montessori, and conventional programs. Journal of School Psychology, 50, 379–401. doi:10.1016/j.jsp.2012.01.001
  • Lillard, P. P. (1997). Montessori in the classroom: A teacher’s account of how children really learn. New York, NY: Schocken.
  • Lopata, C., Wallace, N. V., & Finn, K. V. (2005). Comparison of academic achievement between Montessori and traditional education programs. Journal of Research in Childhood Education, 20, 5–13. doi:10.1080/02568540509594546
  • McNeil, N. M., Uttal, D. H., Jarvin, L., & Sternberg, R. J. (2009). Should you show me the money? Concrete objects both hurt and help performance on mathematics problems. Learning and Instruction, 19, 171–184. doi:10.1016/j.learninstruc.2008.03.005
  • Miller, K. F., & Stigler, J. W. (1991). Meanings of skill: Effects of abacus expertise on number representation. Cognition and Instruction, 8, 29–67. doi:10.1207/s1532690xci0801_2
  • Mix, K. S., Prather, R. W., Smith, L. B., & Stockton, J. D. (2014). Young children’s interpretation of multidigit number names: From emerging competence to mastery. Child Development, 85, 1306–1319. doi:10.1111/cdev.12197
  • 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
  • National Council of Teachers of Mathematics. (2000). Principals and standards for school mathematics. Reston, VA: Author.
  • National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common core state standards for mathematics. Washington, DC: Authors.
  • Oakes, J. M., & Feldman, H. A. (2001). Statistical power for nonequivalent pretest–posttest designs: The impact of change-score versus ANCOVA models. Evaluation Review, 25, 3–28. doi:10.1177/0193841X0102500101
  • Pan, B. A., Rowe, M. L., Singer, J. D., & Snow, C. E. (2005). Maternal correlates of growth in toddler vocabulary production in low-income families. Child Development, 76, 763–782.
  • Peterson, S. K., Mercer, C. D., & O’Shea, L. (1988). Teaching learning disabled students place value using the concrete to abstract sequence. Learning Disabilities Research, 4, 52–56.
  • Piaget, J. (1951). Play, dreams and imitation in childhood. London, England: Heinemann.
  • Reimer, K., & Moyer, P. S. (2005). Third-graders learn about fractions using virtual manipulatives: A classroom study. Journal of Computers in Mathematics and Science Teaching, 24, 5–25.
  • Resnick, L. B., & Omanson, S. F. (1987). Learning to understand arithmetic. In R. Glaser (Ed.), Advances in instructional psychology (Vol. 3, pp. 41–95). Hillsdale, NJ: Erlbaum.
  • Richland, L. E., & Hansen, J. (2013). Reducing cognitive load in learning by analogy. International Journal of Psychological Studies, 5, 69–80. doi:10.5539/ijps.v5n4p
  • Siegler, R. S., & Booth, J. L. (2004). Development of numerical estimation in young children. Child Development, 75, 428–444. doi:10.1111/cdev.2004.75.issue-2
  • Son, J. Y., Smith, L. B., & Goldstone, R. S. (2011). Connecting instances to promote children’s relational reasoning. Journal of Experimental Child Psychology, 108, 260–277. doi:10.1016/j.jecp.2010.08.011
  • Uttal, D. H., Amaya, M., Maita, M. R., Hand, L. L., Cohen, C. A., O’Doherty, K. & DeLoache, J. S. (2013). It works both ways: Transfer difficulties between manipulatives and written subtraction solutions. Child Development Research, Article ID 216367, doi:10.1155/2013/216367
  • Uttal, D. H., O’Doherty, K., Newland, R., Hand, L. L., & DeLoache, J. (2009). Dual representation and the linking of concrete and symbolic representations. Child Development Perspectives, 3, 156–159. doi:10.1111/j.1750-8606.2009.00097.x
  • Uttal, D. H., Scudder, K. V., & DeLoache, J. S. (1997). Manipulatives as symbols: A new perspective on the use of concrete objects to teach mathematics. Journal of Applied Developmental Psychology, 18, 37–54. doi:10.1016/S0193-3973(97)90013-7
  • Vance, J. H., & Kieren, T. E. (1971). Laboratory settings in mathematics: What does research say to the teacher? The Arithmetic Teacher, 18, 585–589.

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