Who Struggles with which Demand? Using Level Models to Understand Interindividual Differences in and Relations Between Facets of Fraction Knowledge

Abstract Dealing with fractions is a central and complex topic in mathematics learning. Existing theoretical models of fraction knowledge and skills describe central knowledge facets and roughly characterize procedural demands. However, it is still unclear how to describe students’ levels of fraction knowledge and skills with explicit reference to the mastered contents and how to understand relations between skill facets using these levels. Based on two datasets with 751 sixth and seventh graders, a structural model with three facets is investigated: knowledge of fraction subconstructs, fraction arithmetic skills, and fraction word problem-solving. These facets build on each other in existing models of fraction knowledge and many fraction curricula. Levels for the three constructs are characterized by more or less prestructured fraction demands and the complexity of numerical information. Linear relations between conceptual and procedural fraction demands are investigated in detail concerning the level descriptions, confirming that conceptual demands show a more substantial contribution to procedural demands than vice versa. Further, the results underline the complexity of fraction word problems demands and that mastering them may require at least the lower levels of knowledge of fraction subconstructs and fraction arithmetic skills. The results provide a basis for learning trajectories and different formative activities in school practice, which may also be relevant for mathematics teacher education.