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Empirical Article

Toys or Math Tools: Do Children’s Views of Manipulatives Affect Their Learning?

References

  • Alibali, M. W., Knuth, E. J., Hattikudur, S., McNeil, N. M., & Stephens, A. C. (2007). A longitudinal examination of middle school students’ understanding of the equals sign and equivalent equations. Mathematical Thinking and Learning, 9(3), 221–247. doi:10.1080/10986060701360902
  • Brown, M. C., McNeil, N. M., & Glenberg, A. M. (2009). Using concreteness in education: Real problems, potential solutions. Child Development Perspectives, 3(3), 160–164. doi:10.1111/j.1750-8606.2009.00098.x
  • Brown, S. A., & Alibali, M. W. (2018). Promoting strategy change: Mere exposure to alternative strategies helps, but feedback can hurt. Journal of Cognition and Development, 19(3), 301–324. doi:10.1080/15248372.2018.1477778
  • Bruner, J. S. (1966). Toward a theory of instruction. Cambridge, MA: Belknap Press.
  • 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(2), 380–400. doi:10.1037/a0031084
  • Cook, S. W., Friedman, H. S., Duggan, K. A., Cui, J., & Popescu, V. (2017). Hand gesture and mathematics learning: Lessons from an avatar. Cognitive Science, 41(2), 518–535. doi:10.1111/cogs.12344
  • DeLoache, J. S. (1987). Rapid change in the symbolic functioning of very young children. Science, 238(4833), 1556–1557. doi:10.1126/science.2446392
  • DeLoache, J. S. (1989a). Young children’s understanding of the correspondence between a scale model and a larger space. Cognitive Development, 4(2), 121–139. doi:10.1016/0885-2014(89)90012-9
  • DeLoache, J. S. (1989b). The development of representation in young children. Advances in Child Development and Behavior, 22, 2–39.
  • DeLoache, J. S. (2000). Dual representation and young children’s use of scale models. Child Development, 71(2), 329–338. doi:10.1111/1467-8624.00148
  • DeLoache, J. S. (2004). Becoming symbol-minded. TRENDS in Cognitive Science, 8(2), 66–70. doi:10.1016/j.tics.2003.12.004
  • DeLoache, J. S., & Marzolf, D. P. (1992). When a picture is not worth a thousand words: Young children’s understanding of pictures and models. Cognitive Development, 7(3), 317–329. doi:10.1016/0885-2014(92)90019-N
  • Donovan, A. M., & Alibali, M. W. (in press). Manipulatives and mathematics learning: The role of perceptual and interactive features. In S. Macrine & J. Fugate (Eds.), Movement matters: How embodied cognition informs teaching and learning. Cambridge, MA: MIT Press.
  • Donovan, A. M., Alibali, M. W., & Waters, B. (2016). Gesture and embodiment in mathematical learning: Do actions leave a legacy in gesture? Paper presented at the meeting of the International Society for Gesture Studies, Paris, France.
  • Donovan, A. M., & Fyfe, E. R., (under review). Connecting concrete objects and abstract symbols promotes children’s mathematics learning.
  • Donovan, A. G., & Donovan, A. M. (2021). Buckets and beanbags child image. Retrieved from https://osf.io/exbru/
  • Falkner, K. P., Levi, L., & Carpenter, T. P. (1999). Children’s understanding of equality: A foundation for algebra. Teaching Children Mathematics, 6(4), 56–60. doi:10.5951/TCM.6.4.0232
  • Furman, C. E. (2017). Making sense with manipulatives: Developing mathematical experiences for early childhood teachers. Education & Culture, 33(2), 67–86. doi:10.5703/educationculture.33.2.0067
  • Givvin, K., Stigler, J. W., & Thompson, B. (2011). What community college developmental mathematics students understand about mathematics. Part II: The interviews. MathAMATYC Educator, 2, 4–18.
  • Glenberg, A. M., Jaworski, B., Rischal, M., & Levin, J. (2007). What brains are for: Action, meaning, and reading comprehension. In D. S. McNamara (Ed.), Reading comprehension strategies: Theories, interventions, and technologies (pp. 221–240). Mahwah, NJ, US: Lawrence Erlbaum Associates Publishers.
  • Hattikudur, S., & Alibali, M. W. (2010). Learning about the equal sign: Does comparing with inequality symbols help? Journal of Experimental Child Psychology, 107(1), 15–30. doi:10.1016/j.jecp.2010.03.004
  • Hornburg, C. B., Rieber, M. L., & McNeil, N. M. (2017). An integrative data analysis of gender differences in children’s understanding of mathematical equivalence. Journal of Experimental Child Psychology, 163, 140–150. doi:10.1016/j.jecp.2017.06.002
  • Martin., T., & Schwartz, D. (2005). Physically distributed learning: Adapting and reinterpreting physical environments in the development of fraction concepts. Cognitive Science, 29(4), 587–625. doi:10.1207/s15516709cog0000_15
  • Matthews, P. G., & Fuchs, L. S. (2018). Keys to the gate? Equal sign knowledge at 2nd grade predicts 4th grade algebra competence. Child Development. doi:10.1111/cdev.13144
  • McNeil, N. M. (2007). U-shaped development in math: 7-year-olds outperform 9-year-olds on equivalence problems. Developmental Psychology, 43(3), 687–695. doi:10.1037/0012-1649.43.3.687
  • McNeil, N. M., & Alibali, M. W. (2005a). Why won’t you change your mind? Knowledge of operational patterns hinders learning and performance on equations. Child Development, 76(4), 883–899. doi:10.1111/j.1467-8624.2005.00884.x
  • McNeil, N. M., & Alibali, M. W. (2005b). Knowledge change as a function of mathematics experience: All contexts are not created equal. Journal of Cognition and Development, 6(2), 285–306. doi:10.1207/s15327647jcd0602_6
  • McNeil, N. M., Hornburg, C. B., Devlin, B. L., Carrazza, C., & McKeever, M. O. (2019). Consequences of individual differences in children’s formal understanding of mathematical equivalence. Child Development, 90, 940–956. doi:10.1111/cdev.12948.
  • McNeil, N. M., & Jarvin, L. (2007). When theories don’t add up: Disentangling the manipulatives debate. Theory into Practice, 46(4), 309–316. doi:10.1080/00405840701593899
  • 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(2), 171–184. doi:10.1016/j.learninstruc.2008.03.005
  • Meira, L. (1998). Making sense of instructional devices: The emergence of transparency in mathematical activity. Journal for Research in Mathematics Education, 29(2), 121–142. doi:10.2307/749895
  • Montessori, M. (1912/1964). The Montessori method: Scientific pedagogy as applied to child education in ‘the children’s houses’ with additions and revisions by the author. (A. E. George, Trans.). New York: Schocken Books. ( Original work published 1912; Oxford, England: Bentley).
  • Moyer, P. (2001). Are we having fun yet? How teachers use manipulatives to teach mathematics. Educational Studies in Mathematics, 47(2), 175–197. doi:10.1023/A:1014596316942
  • Osana, H. P., Przednowek, K., Cooperman, A., & Adrien, E. (2018). Encoding effects on first-graders’ use of manipulatives. The Journal of Experimental Education, 86(2), 154–172. doi:10.1080/00220973.2017.1341862
  • Perry, M., Church, R. B., & Goldin-Meadow, S. (1988). Transitional knowledge in the acquisition of concepts. Cognitive Development, 3(4), 359–400. doi:10.1016/0885-2014(88)90021-4
  • Petersen, L. A., & McNeil, N. M. (2013). Effects of perceptually rich manipulatives on preschoolers’ counting performance: Established knowledge counts. Child Development, 84(3), 1020–1033. doi:10.1111/cdev.12028
  • Piaget, J. (1970). Science of education and the psychology of the child. New York, US: Orion Press.
  • Stacey, K., Helme, S., Archer, S., & Condon, C. (2001). The effect of epistemic fidelity and accessibility on teaching with physical materials: A comparison of two models for teaching decimal numeration. Educational Studies in Mathematics, 47(2), 199–221. doi:10.1023/A:1014590319667
  • Suh, J., & Moyer, P. S. (2007). Developing students’ representational fluency using virtual and physical algebra balances. Journal of Computers in Mathematics and Science Teaching, 26(2), 155–173.
  • Uttal, D. H., Schreiber, J. C., & DeLoache, J. S. (1995). Waiting to use a symbol: The effects of delay on children’s use of models. Child Development, 66(6), 1875–1889. doi:10.2307/1131916
  • Yuan, L., & Uttal, D. H. (2017). Analogy lays the foundation for two crucial aspects of symbolic development: Intention and correspondence. Topics in Cognitive Science, 9(3), 738–757. doi:10.1111/tops.12273

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