Efficient and flexible strategy use on multi-digit sums: a choice/no-choice study

Abstract

This study analysed children's use of mental computation strategies and standard written algorithms in the domain of multi-digit addition and subtraction, using the choice/no-choice method. Twenty-one Flemish fourth-graders (M _Age =9y10m) solved problem-items that either stimulated the use of mental computation strategies or a standard written algorithm, in one choice and two no-choice conditions. In the choice condition, children could use their preferred strategy on each item. In the two no-choice conditions, they had to solve all items with, respectively, a mental computation strategy (no-choice mental condition) and the standard written algorithm (no-choice written condition). The results revealed that children tended to use the written algorithm on multi-digit sums, even on sums that evoke a mental computation strategy. Moreover, they also used the standard written algorithms with high efficiency and flexibility on sums that elicit a mental computation strategy. We discuss the theoretical, instructional and methodological implications of these results.

Keywords:

• mental computation strategies
• standard written algorithms
• multi-digit addition and subtraction
• choice/no-choice method

Acknowledgements

This research was partially supported by Grant GOA 2012/10 Number sense: analysis and improvement from the Research Fund KU Leuven, Belgium.

Notes

1. As noted by one reviewer and as discussed in Verschaffel et al. (2009), the terms ‘flexibility’ and ‘adaptivity’ are used with different meanings in the international research literature. Surveying the literature, it seems that the term ‘flexibility’ is primarily used to refer to switching (smoothly) between different strategies, whereas the term ‘adaptivity’ puts more emphasis on selecting the most appropriate strategy. In the present article, we use these terms as synonyms, referring to children's ability to switch between different strategies taking into account task and/or individual strategy performance characteristics.

2. As suggested by one reviewer, it would be interesting to explore differences in strategy use between additions and subtractions. Unfortunately, the number of trials in this study was too small to statistically analyse strategy use differences between additions and subtractions. Although our first descriptive analyses did not reveal major differences between the two operations, an investigation of this issue would be worthwhile in future studies in the domain.

3. We first calculated, for each child, the mean frequency with which (s)he used mental computation in the choice condition and the mean accuracy and speed of responding in each no-choice condition, i.e. the mean accuracy and speed of responding in the no-choice mental and the mean accuracy and speed of responding in the no-choice written condition. We next computed, again for each child, the difference in accuracy of responding between the no-choice conditions (mean accuracy no-choice mental condition – mean accuracy no-choice written condition) and the difference in speed between the no-choice conditions (mean speed no-choice mental condition – mean speed no-choice written condition). Finally, we correlated the frequency of mental computation in the choice condition with the accuracy and speed differences between the no-choice conditions, using Pearson correlation coefficients, with child as the unit of analysis.