From fractions to algebra: Cross-domain predictive relationships between conceptual and procedural knowledge and the potential mediating role of relational and proportional reasoning.

Autor/inn/en	D'Erchie, Michael; Forsmann, Claire L.; Schneider, Michael; Obersteiner, Andreas
Titel	From fractions to algebra: Cross-domain predictive relationships between conceptual and procedural knowledge and the potential mediating role of relational and proportional reasoning. Gefälligkeitsübersetzung: Von Brüchen zur Algebra: Domänenübergreifende prädiktive Beziehungen zwischen konzeptuellem und prozeduralem Wissen und die potenzielle vermittelnde Rolle des relationalen und proportionalen Denkens.
Quelle	In: The journal of educational psychology, 118 (2025) 5, S. 703-719Infoseite zur Zeitschrift PDF als Volltext Link als defekt meldenVerfügbarkeit
Sprache	englisch
Dokumenttyp	online; Zeitschriftenaufsatz
ISSN	1939-2176
DOI	10.1037/edu0001002
Schlagwörter	Denken; Schlussfolgerung; Sekundarbereich; Schüler; Schülerin; Deklaratives Wissen; Prozedurales Wissen; Algebra; Mathematik; Mathematische Kompetenz; Leistung
Abstract	Students? fraction knowledge predicts their later algebra knowledge. In both domains, conceptual and procedural knowledge are empirically distinguishable constructs, yet how conceptual and procedural fraction knowledge predicts conceptual and procedural algebra knowledge is unclear. Furthermore, although theoretical arguments exist regarding potential mediators that could reveal pathways from fractions to algebra, there is a lack of empirical testing of these mediators using mediation models. This longitudinal study addresses these two gaps. We assessed 357 German middle-school students on their conceptual and procedural knowledge of fractions and algebra, alongside potential mediators, including whole number sense, relational and proportional reasoning, and whole-number arithmetic fluency. The study provides three key findings: First, for both fractions and algebra, confirmatory factor analysis supported a two-factor model distinguishing between conceptual and procedural knowledge over a one-factor model, supporting the empirical separability of conceptual and procedural knowledge within each domain. Second, conceptual fraction knowledge predicted conceptual algebra knowledge and procedural fraction knowledge predicted procedural algebra knowledge. Third, significant indirect effects were found in mediation models with relational and proportional reasoning as intermediaries between conceptual fraction and conceptual algebra knowledge, whereas no significant indirect effects were found between procedural fraction and procedural algebra knowledge. The findings contribute to discussions about conceptual and procedural knowledge and their separability, emphasize the importance of both conceptual and procedural fraction knowledge for later algebra knowledge, and provide suggestive evidence regarding potential causal pathways from fractions to algebra via relational and proportional reasoning that should be explored in future experimental research. (ZPID).
Erfasst von	Leibniz-Institut für Psychologie, Trier
Update	2026/3