Academic journal article Memory & Cognition

Retrieval or Nonretrieval Strategies in Mental Arithmetic? an Operand Recognition Paradigm

Academic journal article Memory & Cognition

Retrieval or Nonretrieval Strategies in Mental Arithmetic? an Operand Recognition Paradigm

Article excerpt

According to LeFevre, Sadesky, and Bisanz (1996), averaging solution latencies in order to study individuals' arithmetic strategies can result in misleading conclusions. Therefore, in addition to classical chronometric data, they collected verbal reports and challenged the assumption that adults rely systematically on retrieval of arithmetic facts from memory to solve simple addition problems. However, Kirk and Ashcraft (2001) questioned the validity of such a methodology and concluded that a more appropriate method has to be found. Thus, we developed an operand recognition paradigm that does not rely on verbal reports or on solution latencies. In accordance with LeFevre et al., we show in a first experiment that adults resort to nonretrieval strategies to solve addition problems involving medium numbers. However, in a second experiment, we show that high-skilled individuals can solve the same problems using a retrieval strategy. The benefits of our paradigm to the study of arithmetic strategies are discussed.

Numerous researchers have indicated that adults solve simple arithmetic problems more or less exclusively by direct retrieval of die answer from a network of associations stored in long-term memory (Ashcraft, 1992, 1995; Campbell, 1995; for a review, see McCloskey, Harley, & Sokol, 1991). It is indeed widely accepted that performance of young children in arithmetic is based on counting or other procedural strategies and that these procedures are gradually replaced by direct memory retrieval (Ashcraft, 1992; Barrouillet & Fayol, 1998; Campbell & Oliphant, 1992; Lemaire, Barrett, Fayol, & Abdi, 1994; Siegler, 1996; Widaman & Little, 1992; Widaman, Little, Geary, & Cormier, 1992; for a review, see Geary, 1994). This fact was first supported by Groen and Parkman (1972) from latency data hi children and adults. The authors showed that for primary school children, response times (RTs) for simple addition problems (e.g., 4+3) increase linearly with the size of the smaller operand. This result was the first to provide evidence for the use of the min strategy by children. This strategy consists in counting on from the larger of the two operands by the number indicated by the smaller of the operands (Carr & Jessup, 1995; Siegler, 1987; Siegler & Crowley, 1994). Adults also show a~significant increase in response latencies as a function of the size of the operands, but this increase is much smaller than that in children. Moreover, unlike in children, adults' RTs form a curvilinear function that is best explained by the square of the sum or the product of the operands than by the size of the operands. These differences between adults and children have been interpreted as evidence that, unlike children, adults use fast and efficient retrieval from memory to solve simple addition problems.

However, LeFevre, Sadesky, and Bisanz (1996) stressed that, as has already been mentioned for children (Siegler, 1987,1989), averaging solution latencies across trials that involve different procedures can result in misleading conclusions about how adults solve problems. These authors note that the researchers who have used the more direct approach of asking participants to report their procedure have challenged the strong assumption that adults always use retrieval for simple addition problems. For example, Svenson (1985) showed that adults were certain that they had used a retrieval strategy on simple addition problems on only 78% of the trials (for similar results, see also Geary, Frensch, & Wiley, 1993; Geary & Wiley, 1991). Then, to address the issue of how the selection of procedures varies across problems and participants, LeFevre et al. collected trial-by-trial reports of procedure, hi addition to the classical Chronometrie data. The authors concluded that the importance of retrieval had been overemphasized in models of adult performance. Indeed, in the case of addition problems, 81% of their participants had used two or more of the counting, retrieval, and decomposition procedures in order to solve simple problems (i. …

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