Routine and adaptive experts: individual characteristics and their impact on multidigit arithmetic strategy flexibility and mathematics achievement

Motivated by a curriculum privileging number-based strategies but national tests highlighting students’ reliance on standard algorithms, this study analyses 2216 Danish grade 3, 6 and 8 students’ solutions to various multidigit arithmetic tasks, each designed to elicit shortcut strategies, against background variables including sex, ethnicity and familial socio-economic status (SES), and outcomes including strategy flexibility, and national tests for both mathematics and reading. Students offering multiple solutions to a task were defined as flexible, while arithmetic experts (defined by accuracy) were distinguished by their use of shortcut strategies; routine experts never used them, while adaptive experts used them in at least one third of all tasks. With respect to mathematics achievement, experts scored 0.86 SD-units higher than non-experts, and within the former, adaptive experts scored 0.49 SD-units higher than routine experts. With respect to reading, experts achieved 0.57 SD-units higher than non-experts, while adaptive experts achieved 0.19 SD-units higher than routine experts. Boys were significantly more adaptive and flexible than girls. The proportion of experts increased from grade 3 to grade 8, whereas the proportion of adaptive experts increased from grade 3 to 6 but then remained constant. Familial SES was significantly higher for experts than for non-experts but not for adaptive experts in relation to routine. Neither quarter of birth nor the existence of older siblings influenced any outcomes, although the proportion of experts was higher for children with Western backgrounds than for children with non-western background. The results suggest a relationship between adaptive expertise, strategy flexibility, and achievement.