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Children’s use of subtraction by addition on large single-digit subtractions

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Abstract

Subtractions of the type M − S = ? can be solved by various strategies, including subtraction by addition. In this study, we investigated children’s use of subtraction by addition by means of reaction time analyses. We presented 106 third to sixth graders with 32 large non-tie single-digit problems in both subtraction (12 − 9 = .) and addition format (9 + . = 12). We examined the fit of three regression models, which represented the consistent use of direct subtraction, of subtraction by addition and of flexibly switching between both strategies based on the relative size of the subtrahend. Findings revealed that children did not switch flexibly between the two strategies, as adults do, but that they rely on direct subtraction for problems presented in subtraction format and on subtraction by addition for problems in addition format. We end with the major theoretical, methodological and educational implications of these results.

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Notes

  1. Some authors refer to this principle as the complement principle (e.g. Baroody et al., 2009).

  2. Bridging-the-difference does not always imply a subtraction by addition strategy. People can also use the so-called indirect subtraction strategy, in which they determine how much needs to be subtracted from the minuend to get to the subtrahend (e.g. 12 − 9 by 12 − 2 = 10 and 10 − 1 = 9; so the answer is 2 + 1 = 3; De Corte & Verschaffel, 1987). This indirect subtraction strategy may be particularly efficient on problems with relatively large subtrahends (e.g. 12 − 9). However, previous studies on people’s strategy use in subtraction revealed that participants use this strategy only very rarely or not even at all (Beishuizen, Van Putten, & Van Mulken, 1997; De Smedt et al., 2010; Torbeyns et al., 2009a; Van Lieshout, 1997).

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Acknowledgements

Greet Peters is a research assistant for the Research Foundation—Flanders (FWO), Belgium. This research was supported by Grant GOA 2006/01 ‘Developing adaptive expertise in mathematics education’ from the Research Fund K.U.Leuven, Belgium. The authors would like to thank Sara Haling for her assistance during data collection.

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Authors and Affiliations

  1. Centre for Instructional Psychology and Technology, Katholieke Universiteit Leuven, Van den Heuvel Instituut, Dekenstraat 2, 3000, Leuven, Belgium

    Greet Peters, Joke Torbeyns & Lieven Verschaffel

  2. Parenting and Special Education Research Group, Katholieke Universiteit Leuven, Leuven, Belgium

    Bert De Smedt & Pol Ghesquière

  3. GROEP T—Leuven Education College, Leuven, Belgium

    Joke Torbeyns

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  1. Greet Peters
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Correspondence to Greet Peters.

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Peters, G., De Smedt, B., Torbeyns, J. et al. Children’s use of subtraction by addition on large single-digit subtractions. Educ Stud Math 79, 335–349 (2012). https://doi.org/10.1007/s10649-011-9308-3

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