Distinguishing adaptive from routine expertise with rational number arithmetic. (August 2020) - McMullen, Jake; Hannula-Sormunen, Minna M.; Lehtinen, Erno; Siegler, Robert S.
Abstract: Adaptive expertise is a valued, but under-examined, feature of students' mathematical development (e.g. Hatano & Oura, 2012). The present study investigates the nature of adaptive expertise with rational number arithmetic. We therefore examined 394 7th and 8th graders' rational number knowledge using both variable-centered and person-centered approaches. Performance on a measure of adaptive expertise with rational number arithmetic, the arithmetic sentence production task, appeared to be distinct from more routine features of performance. Even among the top 45% of students, all of whom had strong routine procedural and conceptual knowledge, students varied greatly in their performance the arithmetic sentence production task. Strong performance on this measure also predicted later algebra knowledge. The findings suggest that it is possible to distinguish adaptive expertise from routine expertise with rational numbers and that this distinction is important to consider in research on mathematical development. Highlights: We investigated the nature of adaptive expertise with rational number arithmetic. 394 middle schools completed a battery of rational number measures. Adaptive number knowledge varied among students with high levels of overall rational number knowledge. It is possible to distinguish adaptive expertise from routine expertise with rational number arithmetic.