Conceptual explanations and understanding fraction comparisons

Abstract

Explanations are used as indicators of understanding in mathematics, and conceptual explanations are often taken to signal deeper understanding of a domain than more superficial explanations. However, students who are able to produce a conceptual explanation in one problem or context may not be able to extend that understanding more generally. In this study we challenge the notion that conceptual explanations indicate general understanding by showing that – although conceptual explanations are strongly associated with correct answers – they are not employed equally across different contexts, and the highest performing students tend to use more general explanations, which may or may not be conceptual. Overall, our results suggest that explanations of fraction magnitudes follow a learning trajectory reflected in students’ accuracy and explanations: weak students focus on concrete, non-conceptual features, stronger students use concepts to explain their answers, and the highest performers tend to use general (but not necessarily conceptual) rules.