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 on 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.