Special education students’ use of indirect addition in solving subtraction problems up to 100—A proof of the didactical potential of an ignored procedure

Abstract

In this study, we examined special education students' use of indirect addition (subtraction by adding on) for solving two-digit subtraction problems. Fifty-six students (8-to 12-year-olds), with a mathematical level of end grade 2, participated in the study. They were given a computer-based test on subtraction with different types of problems. Although most students had not been taught indirect addition for solving subtraction problems, they frequently applied this procedure spontaneously. The item characteristics were the main prompt for using indirect addition. Context problems that reflect an addingon situation and problems that have a small difference between the minuend and subtrahend most strongly elicited the use of the indirect addition procedure. Moreover, indirect addition was identified as a highly successful procedure for special education students, and the best predictor of a correct answer was found in combination with a stringing strategy.

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

“…The finding that children with higher mathematical achievement levels used shortcut strategies more often than their lower achieving peers supports this idea. Moreover, they add to the body of literature questioning the desirability and feasibility of striving for adaptivity and flexibility for low mathematics achievers (e.g., Fagginger Auer et al 2016a; Torbeyns et al 2006), although there are studies showing promising results (e.g., Peltenburg et al 2012). Several scholars argue that low mathematics achievers might benefit from instruction in a single strategy instead of multiple strategies ( Further research into the levels of flexibility and adaptivity low mathematical achievers can obtain in different domains and under different (instructional) conditions are necessary, to provide insights into the feasibility of fostering flexibility and adaptivity for students of all levels of mathematical competence.…”

“…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).…”

Sum and difference compensation strategy as a calculus strategy

“…Коришћење само једног поступка при решавању задатака са са-бирањем и одузимањем спречава развој мате-матичке писмености ученика (Peltenburg et al, 2012). Карпентер и сарадници (Carpenter et al, 1998) наводе да и стандардни алгоритми и ал-тернативне стратегије комплексни задатак ра-чунања деле у кораке, на једноставније елемен-те над којима се врше операције са доступним знањем процедура.…”

Freudenthal’s Work Continues

“…In this project I cooperate with my PhD student Marjolijn Peltenburg and with Alexander Robitzsch. Here, I will discuss one sub-study of this project in which we investigated SE students' ability to apply alternative methods for solving subtraction problems up to 100 (Peltenburg et al 2012). The starting point of this study was the strong belief in circles of SE educators and psychologists in the Netherlands, but also in other countries, that students who have low scores in mathematics cannot handle alternative calculation methods.…”

“…Solving subtraction problems by adding on (see details in Peltenburg et al 2012; Van den Heuvel-Panhuizen 2012)-The methods that can be applied for carrying out subtractions up to 100 can be described from two perspectives (see Fig. 1).…”