Effects of Problem Format on Division and Multiplication Performance: Division Facts Are Mediated via Multiplication-Based Representations

Institute of Cognitive Science, Carleton University, Ottawa, Ontario, Canada.
Journal of Experimental Psychology Learning Memory and Cognition (Impact Factor: 2.86). 04/2003; 29(2):163-70. DOI: 10.1037/0278-7393.29.2.163
Source: PubMed


In 2 experiments participants solved division problems presented in multiplication-based formats (e.g., 8 x _ = 72) more quickly than division problems presented in division-based formats (e.g., 72 / 8 = _). In contrast, participants solved multiplication problems presented in a division-based format (e.g., _ / 8 = 9) slowly and made many errors. In both experiments, the advantage for multiplication-based formats on division problems was found only for large problems (i.e., those with products or dividends greater than 25). These findings provide support for the view that large single-digit division facts are mediated via multiplication-based representations and that multiplication is the primary mode of representation for both division and multiplication facts.

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    • "When direct retrieval for division facts fails, people may recast the division problem (e.g., 36 ÷ 4 = __) to multiplication form (e.g., 4 × __ = 36). The solution to the multiplication fact is then accessed and retrieved as the solution to the original division problem (Mauro et al., 2003). These studies in numerical computation suggest that the estimation of percentage savings will be easy when the cash equivalent of the points is a simple, well-learned fraction of the price. "
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    • "The first component is influenced by factors such as familiarity of the surface notation (Metcalfe & Campbell, 2007), problem layout (Campbell, 2008; Mauro et al., 2003), taskswitching costs (e.g., switching from addition to multiplication) and speed-accuracy criteria (Campbell & Austen, 2002). The second component is influenced by factors including problem retrieval strength (which varies both across arithmetic operation and problem size) and performance context (e.g., different presentation formats activate distinct retrieval structures; interference or facilitation from recent primes or problems; Bassok, 2001; Campbell, 1994; Campbell & Metcalfe, 2007). "
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    • "In the present study we tested whether automaticity of retrieval also occurs in the opposite direction, as might be expected in light of the results showing that division is often mediated via multiplication (e.g., Mauro et al., 2003). Several previous studies have demonstrated that the presentation of a product can facilitate or interfere with subsequent processing of its operands (e.g., Campbell, 1987; Meagher & Campbell, 1995; Zbrodoff & Logan, 2000). "
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