Calculation methods and arithmetical accuracy from grades 3 - 8: Algorithmic approaches are less accurate than number-based yet increasingly preferred

Number-based strategies (NS), i.e. the strategies with the fewest and simplest calculation steps, are considered easier than the standard algorithm (SA) and could therefore be expected to yield higher accuracy in items designed to elicit such methods (Hickendorff, 2018). However, research on strategy efficiency in multi-digit arithmetic shows somewhat inconsistent results (Hickendorff et al, 2019).

In this study we investigated effect of arithmetic operation and grade on proportional use and accuracy of SA and NS in Danish students. Students from 3rd (749), 6th (731) and 8th (818) grade solved three or four items in multi-digit addition, subtraction and multiplication (3rd grade only addition and subtraction) in a free-choice setting. For each solved item the method was categorised as SA, NS or other (the latter excluded in this analysis), and the answer was scored as correct or wrong.

Across all grades, NS was more accurate than SA (NS vs. SA for 3rd grade [proportion+/-95%CI]: 0.68+/-0.05 vs. 0.85+/-0.07; 8th grade: 0.86+/-0.05 vs. 0.94+/-0.02). Accuracy differed between operations with addition and multiplication showing highest and subtraction lowest accuracy. For all operations, NS outperformed SA on accuracy. Despite lower accuracy of SA, proportional use of SA increased from 3rd (0.78) to 8th (0.87) grade. Hence, the reason for students valuing SA over NA increasingly with age must be rooted in other (yet unidentified) reasons than experience of computational accuracy per se.