Adults’ use of subtraction by addition

Abstract

The present study investigates adults' use of addition to solve two-digit subtractions. Inspired by research on single-digit arithmetic, we first examined regression models in which different problem characteristics predicted participants' reaction times. Second, we compared performance on two-digit subtractions presented in 2 presentation formats, i.e., the standard subtraction format (81-37=.) and an addition format (37+.=81). Both methods lead to the conclusion that the participants switched between direct subtraction and subtraction by addition depending on the relative size of the subtrahend: If the subtrahend was smaller than the difference, direct subtraction was mainly used; if the subtrahend was larger than the difference, subtraction by addition was the dominant strategy. However, this performance pattern was only observed when the distance between the subtrahend and the difference was large; when the subtrahend and the difference were close to each other, there was no subtrahend-dependent selection of direct subtraction vs. subtraction by addition. These data indicate that theoretical models of people's strategy choices in subtraction should include the relative size of the subtrahend as an important factor in the strategy selection process.

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

“…81−79=. ), since subtracting a larger subtrahend requires more and/or larger calculation steps (Peters, De Smedt, Torbeyns, Ghesquière, & Verschaffel, 2010b;Woods et al, 1975). However, the observed reaction time patterns argue against this interpretation: Problems with a relatively large subtrahend were solved significantly faster than problems with a medium-sized subtrahend.…”

“…We adopted the regression-based approach that Groen and Poll (1973) and Woods et al (1975) used in the number domain up to 10, an approach that we have already successfully applied for analysing adults' strategy use on two-digit subtractions (Peters et al, 2010b). We predicted the reaction times of all 32 possible large non-tie single-digit subtractions presented in subtraction format, by calculating three regression models which represent different strategy use patterns (see Woods et al, 1975): the consistent use of direct subtraction, the consistent use of subtraction by addition and the flexible switching between both strategies based on the size of the subtrahend.…”

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

“…While previous studies have shown that adults use the subtraction by addition strategy frequently, efficiently (i.e., fast and accurately), and flexibly (i.e., mainly, but not exclusively on problems with a relatively large subtrahend) (Peters, De Smedt, Torbeyns, Ghesquière, & Verschaffel, ,; Torbeyns, De Smedt, Peters, Ghesquière, & Verschaffel, ; Torbeyns, Ghesquière, et al ., ), well‐documented evidence on primary school children's self‐reported use of the subtraction by addition strategy when mentally solving two‐digit subtraction problems is limited (Blöte et al ., ; De Smedt et al ., ; Selter, ; Torbeyns et al ., ). For example, Torbeyns et al .…”

“…This observation asks for the application of other methods of inferring participants' strategy use that do not rely on verbal reports. Two such methods have already been successfully used in both single‐ and multi‐digit arithmetic with children and/or adults: the regression‐based approach (Groen & Poll, ; Woods et al ., ) and the manipulation of presentation formats (Campbell, ; Peters et al ., ,b).…”

“…and the (unusual) addition format ( S + . = M ) (see also Campbell, ; Peters et al ., ,b). Following Campbell (), it can be hypothesized that if subtractions are solved by addition, problems presented in the addition format (e.g., 79 + .…”