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.
"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. "
[Show abstract][Hide abstract] ABSTRACT: Many consumers today hold loyalty program points which function as a currency, but are not cash. This paper examines factors that influence consumers' decisions to keep or spend their accumulated points. We found that consumers are more likely to spend points when they can easily anticipate the benefits they can enjoy with the points. Specifically, the decision to spend points is facilitated when it is easier to compute the percentage savings one can get by using the points. This computational ease has effects on point spending beyond that of saving magnitude.
"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). "
[Show abstract][Hide abstract] ABSTRACT: Educated adults solve simple addition problems primarily by direct memory retrieval, as opposed to by counting or other procedural strategies, but they report using retrieval substantially less often with problems in written-word format (four + eight) compared with digit format (4 + 8). It was hypothesized that retrieval efficiency is relatively low with word operands compared with digits and that this promotes a shift to procedural backup strategies. Consistent with this hypothesis, Experiment 1 demonstrated greater word-format costs on retrieval usage for addition than subtraction, which was due to increased counting for addition but not subtraction. Experiment 2 demonstrated greater word-format costs on retrieval for division than multiplication, which was due to increased use of multiplication-fact reference to solve division problems. Format-related strategy shifts away from retrieval reflected both the efficiency of retrieval for a given operation and the availability of viable alternative strategies. The results demonstrate that calculation processes are not abstracted away from problem surface form. The authors propose that retrieval efficiency for arithmetic connects diverse performance and strategy-related effects across key arithmetic factors, including arithmetic operation, numerical size, and numeral format.
Journal of Experimental Psychology Learning Memory and Cognition 08/2009; 35(4):999-1011. DOI:10.1037/a0015829 · 2.86 Impact Factor
"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). "
[Show abstract][Hide abstract] ABSTRACT: In three experiments, we tested the hypothesis that activation of multiplication operand nodes (e.g., 3 and 8) can occur through presentation of their product (e.g., 24). In Experiments 1 and 2 we found activation of the operands when the product was presented as a cue in a number-matching task. In Experiment 3, activation also occurred in a parity-matching task, where the product (24) was not relevant to the parity matching on its operands (3 and 8). We concluded that bidirectional links exist among the operands and their product for multiplication problems and these links can be activated in a purely stimulus-driven manner. We suggest this may constitute the basis for the solution of simple divisions by mediation through the complementary multiplication facts.
Psychological Research 02/2006; 70(1):32-42. DOI:10.1007/s00426-004-0187-4 · 2.47 Impact Factor
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