Danish third, sixth and eighth grade students’ strategy adaptivity, strategy flexibility and accuracy when solving multidigit arithmetic tasks

In this paper, the multidigit arithmetic-related strategy adaptivity, strategy flexibility and solution accuracy of Danish compulsory school students is examined. Participants, 749 grade three, 731 grade six and 818 grade eight, were drawn from twenty demographically different schools. Drawing on a tri-phase assessment tool, each student completed a series of tasks designed to elicit shortcut strategies. First, students solved each task by means of their preferred strategy; those using shortcut strategies were construed as adaptive for that task. Second, students solved the same tasks by means of whatever alternative strategies they had available; those offering at least two strategies were construed as flexible for that task. Third, for each task, students were asked to indicate which of their strategies they believed was optimal. Across all grades, students were more flexible than adaptive. Overall, sixth graders exhibited higher levels of flexibility than third graders and marginally lower levels than eighth graders. Sixth graders exhibited higher levels of adaptivity than those in either grade three or grade eight. Students’ accuracy, which improved with maturation, was influenced positively by both adaptivity and flexibility, with flexibility having the greatest influence in grade three and adaptivity in grade six. The findings raise further questions concerning, inter alia, culture’s influence on students’ strategy choices and the interaction of adaptivity, flexibility and maturity on accuracy.