The influence of problem features and individual differences on strategic performance in simple arithmetic

Abstract

454Strategic performance of adults on cognitive problems consists of two main components. To solve a cognitive problem, people first have to choose the most appropriate strategy to solve it (i.e., strategy selection). Next, they have to execute the chosen strategy with reasonable speed and accuracy (i.e., strategy efficiency). For a long time, researchers studying mental arithmetic assumed that adults used only memory retrieval to solve simple arithmetic problems such as 8 3 or 5 4 (see, e.g., Ashcraft, 1987Ashcraft, , 1992Ashcraft, , 1995Campbell, 1987aCampbell, , 1995Campbell & Oliphant, 1992;Lebiere & Anderson, 1998;McCloskey, 1992;Siegler, 1989;Widaman & Little, 1992). Fairly recently however, LeFevre and colleagues ; see also Baroody, 1994;Geary, Frensch, & Wiley, 1993;Geary & Wiley, 1991) showed that even skilled adults still make substantial use of procedures such as counting (e.g., 6 3 6 1 1 1) and transformation (e.g., 7 5 7 3 2) when solving simple arithmetic problems. It is clear that retrieval and nonretrieval (i.e., procedural) strategies differ in their efficiency, since retrieval is generally much faster (i.e., more efficient) than any procedural strategy. Although people may adopt other strategies to solve arithmetic problems (such as using a calculator), the present study investigated mental arithmetic and thus focused on the two broad kinds of strategy mentioned above-retrieval and procedural.Both strategy selection and strategy efficiency may depend on factors such as problem features (e.g., operation, problem size) and individual differences 1 (e.g., arithmetic skill, arithmetic practice). Although models have been proposed in which such experiential factors are the main determinants of mental representation, acquisition, and performance (see, e.g., Ashcraft, 1987;Campbell & Graham, 1985;Siegler, 1988;Siegler & Shipley, 1995), there are very few direct comparisons of the simple arithmetic performance of adults who differ in their mathematical education, arithmetic skill, or arithmetic practice (see also LeFevre & Liu, 1997). Moreover, up until now, no study has investigated the effects of these factors in strategy selection and strategy efficiency separately. The present study therefore examined the effects of features that differed across problems and across individuals on strategic performance of simple arithmetic. Problem FeaturesAlthough adults rely on both retrieval and procedural strategies for the entire domain of elementary arithmetic (i.e., the four basic operations; see, e.g., Campbell & Xue, 2001), they adjust their strategy selection according to the operation involved. In solving subtraction and division problems, for example, adults rely more heavily on procedural strategies than they do when solving either addition or multiplication problems, for which retrieval strategies are predominantly used (Campbell & Xue, 2001;Seyler, Kirk, & Ashcraft, 2003). Furthermore, adults use direct retrieval to solve multiplication problems even more frequently than they do to solve addition prob...

Practice effects on strategy selection and strategy efficiency in simple mental arithmetic

“…Comparable eVects have been observed in a previous study (Imbo, Vandierendonck, & Rosseel, 2007), in which arithmetic experience inXuenced strategy selection and strategy eYciency for multiplication problems only. There are several possible explanations for this eVect.…”

Four and twenty blackbirds: how transcoding ability mediates the relationship between visuospatial working memory and math in a language with inversion

“…Problem size, or the value of the number, is a strong predictor of difficulty in many mathematical domains (Ashcraft & Guillaume, 2009;Campbell & Graham, 1985;Imbo, Vandierendonck, & rosseel, 2007;Parkman, 1972). In one study a problem size effect has also been demonstrated for transcoding: response latency was longer for larger numbers than for smaller numbers, even when the number of digits was identical (van Loosbroek et al, 2009).…”

Switch costs and the operand-recognition paradigm

“…For many years, the problem-size effect in adult performance was assumed to reflect slower and more error-prone retrieval processes for large problems, presumably because large problems are encountered less often (Ashcraft 1995). More recently, researchers have concluded that the problem-size effect in adults substantially reflects greater use of procedural strategies (e.g., counting, decomposition) for large problems (e.g., Campbell and Xue 2001;LeFevre et al 1996;Imbo et al 2007). Measurement of strategies in these studies has relied predominantly on verbal self-reports.…”