This mixed-methods study examines the development of adaptive expertise in second grade students' subtraction understanding. Adaptive expertise involves not only content knowledge but also innovation, habits of mind and ways of organizing content knowledge. This study and its analysis seek to identify evidence of adaptive expertise through a change in student strategy choices, as well as a change in the conversations that took place throughout an instructional intervention.

The foundation of this study is an intervention for a Grade 2 classroom in which extensive subtraction work was situated within a base-ten packing investigation. Data include student work and video from the intervention and assessments from immediately before and after the intervention. Data were also collected from a countywide performance assessment that was administered later in the school year.

The study first looks at the change in student subtraction strategies across the intervention and then compares strategies of the intervention group with that of a control group. The study then examines the conversations that took place during the intervention and identifies opportunities for student development of adaptive expertise. Finally, the analysis identifies a long-term trajectory for adaptive expertise in subtraction.

This research situates the goal of understanding subtraction work within the frame of adaptive expertise. It seeks to help educators identify points early in a trajectory that may help support the development of adaptive expertise. The study concludes with implications and recommendations for mathematics education professionals who are designing curricula, professional development programs and assessments.