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Bivariate Developmental Relations between Calculations and Word Problems: A Latent Change Approach.

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  • 1Vanderbilt University, 228 Peabody College, Nashville, TN 37203, USA.

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Mathematical development in calculations and word problems shows distinct but related growth patterns. These cognitive skills develop independently, influenced by shared external factors rather than direct prediction.

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Area of Science:

  • Cognitive Development
  • Educational Psychology
  • Mathematics Education

Background:

  • Mathematical cognition involves distinct skills like calculations and word problems.
  • Understanding the developmental relationship between these skills is crucial for effective pedagogy.

Purpose of the Study:

  • To examine the developmental relationship between calculations and word problems in children.
  • To determine if performance or growth in one domain predicts the other.

Main Methods:

  • Longitudinal study tracking 328 children (grades 2-3) over three assessment points.
  • Latent change score models were used to analyze developmental trajectories.
  • Bivariate models assessed the predictive relationship between calculation and word-problem development.

Main Results:

  • A dual change model best described independent, slowing growth in both calculations and word problems.
  • Neither prior performance nor growth in calculations predicted subsequent word-problem development, and vice versa.
  • Development in both domains appears related through shared external factors, not direct influence.

Conclusions:

  • Calculation and word-problem skills develop along separate trajectories during early elementary school.
  • The relationship between these mathematical skills is indirect, mediated by common underlying factors.
  • Findings suggest targeted interventions may be needed for each skill domain separately.