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Does Conceptual Transparency in Manipulatives Afford Place-Value Understanding in Children at Risk for Mathematics

Anne Lafay1, Helena P Osana2, Joel R Levin3

  • 1Université Savoie Mont-Blanc, CNRS, LPNC UMR 5105, Chambéry, France.

Learning Disability Quarterly : Journal of the Division for Children with Learning Disabilities
|May 11, 2023
PubMed
Summary

Conceptual transparency in manipulatives aids place-value understanding. Making denominations visible, not ones, significantly improves number representation for children, including those at risk for math learning disabilities.

Keywords:
affordanceconceptual transparencymanipulativesmathematics learning disabilitiesplace value

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Area of Science:

  • Cognitive Psychology
  • Educational Psychology
  • Mathematics Education

Background:

  • Place-value understanding is crucial for mathematical development.
  • Manipulatives are commonly used to teach mathematical concepts.
  • The physical design of manipulatives may influence their effectiveness.

Purpose of the Study:

  • To investigate how conceptual transparency in manipulatives affects place-value understanding.
  • To compare the impact of different levels of transparency on number representation.
  • To examine differences between typically developing children and those at risk for mathematics learning disabilities.

Main Methods:

  • Second-grade students were randomly assigned to one of three manipulative conditions: non-transparent (attachable beads), denomination-transparent (pipe cleaners), or fully transparent (string beads).
  • Participants used manipulatives to represent double- and triple-digit numerals.
  • Statistical and descriptive analyses were conducted on their representations.

Main Results:

  • Transparency of denominations, not the ones within denominations, significantly impacted number representation and place-value understanding.
  • Children at risk for mathematics learning disabilities showed greater difficulty with non-transparent manipulatives.
  • The attachable beads condition highlighted disadvantages for at-risk children in interpreting place-value concepts.

Conclusions:

  • The physical transparency of denominations in manipulatives is key for developing place-value understanding.
  • Educational tools should be designed with conceptual transparency in mind, especially for at-risk learners.
  • Further research should explore optimal manipulative designs for diverse learners.