Discriminant validity and interrelations of conceptual and procedural knowledge in fractions and algebra: Evidence from confirmatory factor analysis

BACKGROUND: Conceptual and procedural knowledge are two distinct types of mathematical knowledge. Measuring them with sufficient discriminant validity is challenging because they are typically highly correlated. Prior studies have demonstrated discriminant validity of paper-and-pencil measures separately for fractions and algebra. However, whether such measures can distinguish between the two knowledge types within a single sample of students instructed in both domains, and how the four constructs interrelate, remains unclear. AIMS: This study tested the discriminant validity of conceptual and procedural knowledge measures of fractions and algebra in a single sample of students instructed in both domains and examined the full pattern of intercorrelations to clarify which knowledge types underlie the well-established fraction-algebra link. SAMPLE: Participants were 571 German middle-school students (M = 14.91 years). METHODS: Conceptual and procedural knowledge in both domains was assessed using adapted paper-and-pencil tests. Confirmatory factor analysis was used to evaluate the discriminant validity of the measures and to examine the intercorrelations among the four constructs. RESULTS: A four-factor model showed the best fit, indicating empirical separability of the four constructs. Conceptual and procedural knowledge were highly correlated within each domain (fractions and algebra). Descriptively, cross-domain correlations were stronger for corresponding knowledge types (e.g., conceptual-conceptual) than for non-corresponding types (e.g., conceptual-procedural), and stronger for the conceptual-conceptual than the procedural-procedural link. CONCLUSION: The findings contribute to discussions about the discriminant validity and measurability of conceptual and procedural knowledge and offer a more differentiated view of how specific types of knowledge link fractions and algebra.