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Are conceptual knowledge and procedural knowledge empirically separable? The case of fractions
Author(s) -
Lenz Katja,
Dreher Anika,
Holzäpfel Lars,
Wittmann Gerald
Publication year - 2020
Publication title -
british journal of educational psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.557
H-Index - 95
eISSN - 2044-8279
pISSN - 0007-0998
DOI - 10.1111/bjep.12333
Subject(s) - psychology , procedural knowledge , cognition , confirmatory factor analysis , test (biology) , empirical research , sample (material) , reliability (semiconductor) , cognitive psychology , conceptual model , scale (ratio) , test validity , psychometrics , social psychology , body of knowledge , developmental psychology , structural equation modeling , knowledge management , computer science , statistics , machine learning , mathematics , database , chemistry , biology , paleontology , power (physics) , chromatography , quantum mechanics , physics , neuroscience
Background Concerning students’ difficulties with fractions, many explanatory approaches are based on the distinction between conceptual knowledge and procedural knowledge. For further research in this field, it is thus crucial to make these constructs accessible to valid measurement. Aims In this study, we aim at developing a test instrument that affords valid measurement of students’ conceptual and procedural fraction knowledge, including in particular empirical validation of this distinction. Sample The data used in this study were from 8th‐ and 9th‐grade students ( N = 235) in Germany. Methods Facilitated by expert discussions, items from previous studies were developed further and assigned to either a conceptual scale or procedural scale. Confirmatory factor analysis was used to investigate the underlying structure of the data including model comparisons (1‐dimensional; conceptual–procedural, verbal–non‐verbal). Further analyses in terms of validation focused on reliability and on correlations of the knowledge types with general cognitive abilities. Results It was found that the theoretically assumed 2‐dimensional model fitted the data best. Correlations of the two knowledge types with general cognitive abilities differed significantly. Furthermore, the latent constructs could be reliably estimated from its indicators. Conclusions Our findings indicate that the empirical separation of conceptual and procedural fraction knowledge is possible: A theoretically grounded test instrument was developed that allows measuring the knowledge types with a sufficient degree of validity. These findings address a research gap that was pointed out repeatedly and gives rise to further research into reasons and remedies for students’ difficulties in dealing with fractions.