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

Abstract

Subtraction problems of the type M - S = ? can be solved with various mental calculation strategies. We investigated fourth- to sixth-graders' use of the subtraction by addition strategy, first by fitting regression models to the reaction times of 32 two-digit subtractions. These models represented three different strategy use patterns: the use of direct subtraction, subtraction by addition, and switching between the two strategies based on the magnitude of the subtrahend. Additionally, we compared performance on problems presented in two presentation formats, i.e., a subtraction format (81 - 37 = .) and an addition format (37 + . = 81). Both methods converged to the conclusion that children of all three grades switched between direct subtraction and subtraction by addition based on the combination of two features of the subtrahend: If the subtrahend was smaller than the difference, direct subtraction was the dominant strategy; if the subtrahend was larger than the difference, subtraction by addition was mainly used. However, this performance pattern was only observed when the numerical distance between subtrahend and difference was large. These findings indicate that theoretical models of children's strategy choices in subtraction should include the nature of the subtrahend as an important factor in strategy selection.

Age-related changes in children’s strategies for solving two-digit addition problems

“…Such schooling effects on age-related changes in arithmetic in general and in two-digit arithmetic (subtraction) problems has been found in numerous previous studies (e.g., Peters et al, 2013;Torbeyns et al, 2009). For two-digit addition problems, because they had just learned columnar retrieval at school during the first and second grades (i.e., a year or two before the present testing), columnar retrieval may be more available for third graders to use.…”

“…However, most studies on complex arithmetic were run on subtraction problems (e.g., Peters et al, 2013;Torbeyns et al, 2009). These previous studies on subtraction problems provided detailed analyses of how children solve subtraction problems.…”

Dutch sixth graders’ use of shortcut strategies in solving multidigit arithmetic problems

“…There is a general consensus that there are three types of mental, 1 number-based solution strategies to solve multidigit addition and subtraction problems: (a) sequential strategies in which the subtrahend is decomposed: e.g., solving 45 − 29 via 45 − 20 = 25; 25 − 9 = 16, (b) decomposition strategies in which both operands are decomposed: e.g., solving 45 − 29 via 40 − 20 = 20; 5 − 9 = − 4; 20 − 4 = 16, and (c) varying (or shortcut) strategies: e.g., the compensation strategy 45 − 29 = 45 − 30 + 1 = 15 + 1 = 16 or the indirect addition strategy (also called subtraction by addition) in which one adds on from the subtrahend: e.g., 29 + 1 = 30; 30 + 15 = 45; so the answer is 1 + 15 = 16 (for overviews, see for instance Beishuizen et al 1997;Heinze et al 2009;Peltenburg et al 2012;Peters et al 2013).…”

“…In the domain of multidigit addition and subtraction, studies with German third graders (Heinze et al 2009;Selter 2001), Dutch second graders (Blöte et al 2001), Flemish second to fourth graders (De Smedt et al 2010;Peters et al 2013;c), and recently, a cross-national study of Dutch and Flemish third to sixth graders showed that students used the shortcut strategies indirect addition, compensation, and other simplifying strategies rather infrequently, usually below 20% (Torbeyns et al 2017). In subtraction problems, compensation strategies seem to be used somewhat more often than indirect addition.…”

Young children's use of derived fact strategies for addition and subtraction

“…The use of derived fact strategies might seem even more important with regard to subtraction than addition, since children are generally less able to retrieve subtraction facts than addition facts (Barouillet et al, 2008), so could benefit more from alternative strategies. Yet it may be more difficult for children to use derived fact strategies for subtraction than addition, both because their relative lack of known facts gives them less of a base from which to use them, and because some derived fact strategies for subtraction, such as the “subtraction by addition” strategy (DeSmedt et al, 2010; Peters et al, 2013) depend on some understanding of the inverse relationship between addition and subtraction, which some studies suggest is difficult for children (see below).…”