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Tracking fraction knowledge development using grade-appropriate assessments.

Isabella Starling-Alves1, Xiangyi Liao2, Qi Huang3

  • 1Department of Educational Psychology, University of Nebraska Lincoln, United States.

Journal of Experimental Child Psychology
|February 26, 2026
PubMed
Summary
This summary is machine-generated.

Fraction knowledge develops integratedly, not strictly separated into conceptual and procedural skills. New assessments show significant learning gains from 2nd to 3rd grade, and 5th to 6th grade.

Keywords:
DevelopmentFraction knowledgeFraction knowledge assessmentRational number

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Area of Science:

  • Cognitive Development
  • Educational Psychology
  • Mathematics Education

Background:

  • Fraction knowledge is crucial for mathematical achievement.
  • Its developmental trajectory and the distinction between conceptual and procedural understanding are debated.
  • Existing measures lack psychometric validation across grades.

Purpose of the Study:

  • To develop and evaluate grade-specific Fraction Knowledge Assessments (FKA) for grades 2, 3, 5, and 6.
  • To examine changes in fraction knowledge across adjacent grade transitions.
  • To investigate the relationship between conceptual and procedural fraction knowledge.

Main Methods:

  • An accelerated longitudinal design with 342 children in two cohorts (2nd-3rd and 5th-6th grades).
  • Administration of standardized math and cognitive tests alongside grade-appropriate FKAs over two years.
  • Confirmatory factor analysis and Item Response Theory for psychometric evaluation and cross-grade equating.

Main Results:

  • No strong evidence for a clear separation between conceptual and procedural fraction knowledge; models showed comparable fit.
  • Developmental shifts observed: magnitude items were more discriminative in earlier grades, arithmetic items in later grades.
  • Significant learning gains in both cohorts, with greater improvement from 2nd to 3rd grade than 5th to 6th grade.

Conclusions:

  • Fraction knowledge development appears integrated, challenging strict conceptual-procedural distinctions.
  • Psychometrically linked, grade-appropriate assessments are valuable for tracking developmental changes.
  • Early math achievement and working memory predict later fraction knowledge.