Tracking fraction knowledge development using grade-appropriate assessments

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.