Distinguishing adaptive from routine expertise with rational number arithmetic

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 andperson-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 thismeasure also predicted later algebra knowledge. Thefindings suggest that it is possible to distinguish adaptiveexpertise from routine expertise with rational numbers and that this distinction is important to consider inresearch on mathematical development.