How are children's strategy selection and execution related to their executive functions? A choice/no-choice study in multi-step arithmetic

In recent years, an increasing number of studies have examined the association between mathematical abilities and executive functions (EFs). However, it remains unknown via which mechanisms' mathematical performance is associated with EFs. The current study examined the associations of overall task proficiency, strategy selection, and strategy execution when solving multi-step subtraction problems with three EFs (i.e., updating, inhibition, and shifting). With a choice/no-choice design, 150 fifth-graders' (Mage = 10 years, 11 months) direct subtraction (DS; e.g., 712 - 346 = ?; 712 - 300 = 412, 412 - 40 = 372, and 372 - 6 = 366) and subtraction by addition (SBA; e.g., 712 - 346 = ?; 346 + 54 = 400, 400 + 300 = 700, 700 + 12 = 712, and 54 + 300 + 12 = 366) use to solve multi-step subtractions was examined. Participants were offered ten subtractions in one choice condition (free choice between DS and SBA), based on which we obtained data about task proficiency and strategy selection, and in two no-choice conditions (mandatory use of either DS or SBA), which were used to examine strategy execution. The results showed that task proficiency in the choice condition was associated with updating and inhibition but not with shifting. Furthermore, strategy selection was associated with updating but not with inhibition and shifting. Strategy execution was associated with updating but not with inhibition and shifting. The inclusion of separate strategy selection and execution parameters helped to unravel how arithmetic performance and EFs are associated.