Selection of procedures in mental subtraction.

Abstract

Adults solved simple subtraction problems (e.g., 16 - 9). Half of the 32 participants provided immediate self-reports of their solution processes on each problem. Performance was analyzed using both traditional descriptive statistics (i.e., means, standard deviations, and percentage of errors) and with statistics derived from fitting the ex-Gaussian distributions to latencies (i.e., mu and tau). The results support the view that ex-Gaussian analyses can be useful in exploring patterns of procedure selection that relate both to characteristics of the stimuli (e.g., problem size) and to characteristics of the participants (e.g., arithmetic skill). More generally, the results provide further evidence that adults use a variety of procedures to solve simple subtraction problems and that these choices are related to patterns of performance on more complex problems that require calculation.

Strategies in subtraction problem solving in children

“…This difference between subtraction and addition has also been found in adults. LeFevre, De Stefano, Penner-Wilger, and Daley's (2006) participants reported retrieval on 82% of easy problems (minuend < 10) but on only 42% of hard problems, results echoing those reported by Campbell and Xue (2001), who observed retrieval on 73 and 42% of easy and hard problems, respectively. For sake of comparison, LeFevre, Sadesky, and Bisanz (1996) reported a retrieval rate of 71% in adults solving the 100 additions with operands from 0 to 9.…”

Negative Numbers in Simple Arithmetic

“…In Negative Numbers -5 particular, the problem-size effect is greater when adults use procedural solutions (such as counting) than when they use memory retrieval to solve problems (LeFevre et al, 1996;Campbell & Fugelsang, 2001;Campbell, Parker, & Doetzel, 2004; Campbell & PennerWilger, 2006). Accordingly, the problem-size effect in subtraction is typically much larger than in addition, because solvers use procedural solutions more frequently (Campbell & Xue, 2001;LeFevre et al, 2006;Seyler et al, 2003). Furthermore, problem-size effects are generally larger in atypical formats than in typical or preferred formats, because atypical formats may cause participants to rely more heavily on procedural solutions (Campbell & Fugelsang, 2001;Campbell & Penner-Wilger, 2006;LeFevre, Shanahan, & DeStefano, 2004;Mauro, LeFevre, & Morris, 2003).…”

“…We hypothesized that arithmetic problems with negative numbers may be processed differently because they usually require subtraction, rather than because of the negative number, per se. Subtraction is slower and more error-prone than addition (Campbell & Xue, 2001;LeFevre, DeStefano, Penner-Wilger, & Daley, 2006;Seyler, Kirk, & Ashcraft, 2003). On this view, the conceptual structure of the problem (i.e., the mental operation that is required) is the critical determinant of processing difficulty rather than the presence of a negative number.…”

“…Accordingly, subtraction problems such as 9 -5 or 14 -9 invoke slower processing and different solution approaches than complementary addition problems such as 5 + 4 or 9 + 5 (Campbell & Xue, 2001;LeFevre et al, 2006). Young adults often report using counting and other multi-step procedures on subtraction problems whereas retrieval from memory is used more frequently in addition (Campbell & Xue, 2001;LeFevre et al, 2006;Seyler et al, 2003). The response-time differences between operations in part reflect these differences in solution approaches (LeFevre et al, 2006;LeFevre, Sadesky, & Bisanz, 1996;Seyler et al, 2003).…”

“…Ganor-Stern and Tzelgov (2008) The most common use of negative signs in arithmetic is in the context of subtraction problems. Accordingly, subtraction problems such as 9 -5 or 14 -9 invoke slower processing and different solution approaches than complementary addition problems such as 5 + 4 or 9 + 5 (Campbell & Xue, 2001;LeFevre et al, 2006). Young adults often report using counting and other multi-step procedures on subtraction problems whereas retrieval from memory is used more frequently in addition (Campbell & Xue, 2001;LeFevre et al, 2006;Seyler et al, 2003).…”