Academic journal article Memory & Cognition

The Influence of Problem Features and Individual Differences on Strategic Performance in Simple Arithmetic

Academic journal article Memory & Cognition

The Influence of Problem Features and Individual Differences on Strategic Performance in Simple Arithmetic

Article excerpt

The present study examined the influence of features differing across problems (problem size and operation) and across individuals (gender, amount of daily arithmetic practice, calculator use, and arithmetic skill) on simple arithmetic performance. Regression analyses were used to investigate the role of these variables in both strategy selection and strategy efficiency. Results show that more skilled and highly practiced students used memory retrieval more often and executed their strategies more efficiently than did less skilled and practiced students. Furthermore, calculator use correlated with both retrieval and procedural strategy efficiency but not with strategy selection. Only very small associations with gender were observed, with boys retrieving slightly faster than girls. Implications of the present findings for models of mental arithmetic are discussed.

Strategic 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 as8 + 3 or 5 × 4 (see, e.g., Ashcraft, 1987, 1992, 1995; Campbell, 1987a, 1995; Campbell & Oliphant, 1992; Lebiere & Anderson, 1998; McCloskey, 1992; Siegler, 1989; Widaman & Little, 1992). Fairly recently however, LeFevre and colleagues (LeFevre, Bisanz, etal., 1996; LeFevre, Sadesky, & Bisanz, 1996; 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' (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 Features

Although 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 problems (see, e. …

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