Acquisition and use of shortcut strategies by traditionally schooled children

This study aimed at analysing traditionally taught children's acquisition and use of shortcut strategies in the number domain 20-100. One-hundred-ninety-five second, third, and fourth graders of different mathematical achievement levels participated in the study. They were administered two tasks, both consisting of a series of two-digit additions and subtractions that maximally elicit the use of the compensation (45 + 29 = _; 45 + 30 - 1 = 75 - 1 = 74) and indirect addition strategy (71 - 68 = _; 68 + 2 = 70, 70 + 1 = 71, so the answer is 2+1 or 3). In the first task, children were instructed to solve all items as accurately and as fast as possible with their preferred strategy. The second task was to generate at least two different strategies for each item. Results demonstrated that children of all grades and all achievement levels hardly applied the compensation and indirect addition strategy in the first task. Children's strategy reports in the second task revealed that younger and lower achieving children did not apply these strategies because they did not (yet) discover these strategies. By contrast, older and higher achieving children appeared to have acquired these strategies by themselves. Results are interpreted in relation to cognitive psychological and socio-cultural perspectives on children's mathematics learning.