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

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.The way people solve symbolically presented single-digit subtraction problems has gained a lot of research attention over the last four decades (e.g. . For a long time, researchers assumed that children move from counting-based strategies over procedural strategies to the (adult way of) direct retrieval of an answer from long-term Educ Stud Math (2012) 79:335-349

Subtraction by addition strategy use in children of varying mathematical achievement level: A choice/no-choice study

“…This finding complements previous results on strategy flexibility in single-digit addition and subtraction, evidencing more flexible strategy choices with increasing experience in the domain (Siegler, 1996(Siegler, , 2000. Moreover, it significantly adds to our understanding of the structures and mechanisms underlying children's strategy choices on multi-digit subtraction problems using an extended definition of strategy flexibility as fitting strategies not only to the numerical characteristics of items (Blöte et al, 2000(Blöte et al, , 2001De Smedt et al, 2010;Heinze et al, 2009;Peters et al, 2012Peters et al, , 2013Selter, 2001;Torbeyns, De Smedt, et al, 2009a, 2009b, but also to individual strategy efficiency competencies (Verschaffel, Luwel, Torbeyns, & Van Dooren, 2009).…”

“…Contrasting previous studies with children, we explicitly mentioned the subtraction by addition strategy as a possible strategy to solve multi-digit subtraction problems at the onset of the interview. As children might have serious difficulties in verbally reporting an untaught arithmetic strategy (e.g., Peters, De Smedt, Torbeyns, Ghesquière, & Verschaffel, 2012, 2013, the demonstration and articulation of this strategy by the experimenter at the beginning of the choice session might have helped children to (adequately) verbally report their subtraction by addition strategy use. Moreover, the explicit communication of subtraction by addition as a possible alternative Subtraction by Addition 226 strategy might have established a socio-mathematical norm that stimulated children to report an available but not explicitly taught strategy (Yackel & Cobb, 1996).…”

Instructional approaches to foster third graders’ adaptive use of strategies: an experimental study on the effects of two learning environments on multi-digit addition and subtraction

“…These findings seem to question the idea that the indirect addition strategy can be self-invented by third graders based on suitable problems. Other studies show that young adults are able to use the indirect addition adaptively (e.g., Peters et al 2010Peters et al , 2012Torbeyns et al 2009e), although we can assume that this strategy was hardly addressed explicitly in their mathematics classroom. Overall, it seems that for the acquisition of advanced strategies, like strategies of the indirect subtraction type or the simplifying type either a continuous and explicit learning environment is necessary or-in case of an implicit learning environment-students need specific individual prerequisites before they can self-invent these strategies.…”

Children's use of addition to solve two‐digit subtraction problems

“…Interestingly, our findings are not in line with Peters et al . (), in which children's use of subtraction by addition was investigated with the same research method, but in the number domain up to 20. In that study, Flemish third‐ to sixth‐grade children consistently used a direct subtraction strategy to solve problems presented in subtraction format, whereas in the current study, children switched between direct subtraction and subtraction by addition according to the numbers in the problem.…”

“…We predicted the reaction times of the 32 problems presented in the subtraction format by three regression models representing different strategy use patterns (see Peters et al, 2012;Woods et al, 1975). As stated before, these three models represented the use of DS-Model, the use of SBA-Model, and switching between both strategies based on the Switch-Model.…”