Fraction Conceptual and Procedural Knowledge: Validity of Equivalence Judgment as an Indicator, Mediating Role of Procedural Knowledge, and Latent Profile Classification of Students

Research Hypotheses:Fraction equivalence judgment serves as a valid measure of Fraction Conceptual Knowledge (FCK)Fraction Procedural Knowledge (FPK) mediates the relationship between FCK and General Mathematics Achievement (GMA)Students can be classified into distinct profiles based on FCK, FPK, and GMAData and Methods:282 students (grades 6-8) completed:Computer-based FCK tasks (number line estimation, fraction comparison, equivalence judgment)Paper-based FPK test (fraction arithmetic operations)Standardized mathematics exam for GMAKey Findings:Confirmatory Factor Analysis showed good model fit when including equivalence tasks in FCK measurement (CFI=1, TLI=1.013)Structural Equation Modeling revealed partial mediation:Direct effect of FCK on GMA: β=0.525Indirect effect through FPK: β=0.108Latent Profile Analysis identified three classes:Low-achieving (4.6%): weak in all three areasHigh-achieving (62.4%): strong in all areasConcept-strong (33.0%): high FCK but moderate FPK and low GMAInterpretation and Application:Understanding fraction equivalence is crucial for conceptual knowledgeProcedural knowledge enables transformation of conceptual understanding into mathematical achievementDifferentiated instruction needed:Low-achievers need both conceptual and procedural supportConcept-strong students require procedural skill developmentData Value:This multi-method study reveals the complex structure of fraction knowledge and provides empirical evidence for personalized mathematics instruction based on students' knowledge profiles.