Interleaved Learning in Elementary School Mathematics: Effects on the Flexible and Adaptive Use of Subtraction Strategies

摘要

Empirical findings show that students are often not capable of using number-based strategies and the standard written algorithm flexibly and adaptively to solve multi-digit subtraction problems. Previous studies have pointed out that students predominantly use the standard written algorithm after its introduction, regardless of task characteristics. Interleaved practice seems to be a promising approach to foster the flexible and adaptive use of strategies. In comparison to the usual blocked approach, in which strategies are introduced and practiced successively, they are presented intermixed in interleaved learning. Thus, the students have to choose an appropriate strategy on the basis of every task itself, and this leads to drawing comparisons between the different strategies. Previous research has shown inconsistent results regarding the effectivity of interleaving mathematical tasks. However, according to the attentional bias framework, interleaved practice seems to be a promising approach for teaching subtraction strategies to enhance the students’ flexibility and adaptivity. In this study, 236 German third graders were randomly assigned to either an interleaved or blocked condition. In the interleaved condition the comparison processes were supported by prompting the students to compare the strategies (between-comparison), while the students of the blocked approach were encouraged to reflect the adaptivity of a specific strategy for specific subtraction tasks (within-comparison). Both groups were taught to use different number-based strategies (i.e., shortcut strategies and decomposition strategies) and the standard written algorithm for solving three-digit subtraction problems spanning a teaching unit of 14 lessons. The results show that the students of the interleaved condition used the shortcut strategies more frequently than those of the blocked condition, while the students of the interleaved condition applied the decomposition strategies as well as the standard written algorithm less frequently. Furthermore, the students of the interleaved condition had a higher competence in the adaptive use of the shortcut strategies and the standard written algorithm. A subsequent cluster analysis revealed four groups differing in their degree of adaptivity. Being part of clusters with a comparatively high level of adaptivity was positively related to the prior arithmetical achievement and, even more so, to the interleaved teaching approach.