Capacity and contextual constraints on product activation: Evidence from task-irrelevant fact retrieval

Abstract

Three experiments tested the limiting conditions of multiplication facts retrieval in a number-matching task (LeFevre, Bisanz, & Mrkonjic, 1988). By presenting two digits as cue and by requiring participants to decide whether a subsequent numerical target had been present in the pair, we found interference when the target coincided with the product of the cue digits. This was evidence for obligatory activation of multiplication facts. Also, we showed that multiplication facts retrieval occurred even in the absence of any arithmetic context (i.e., a multiplication sign between the cue digits) and did not require processing resources (i.e., the process met the capacity criterion of automaticity; Jonides, 1981), whereas manipulation of the spatial relation between the two operands (cue digits) negatively affected retrieval. The present work appears to be unique in the context of previous similar studies on mental calculation, which invariably adopted an arithmetic task as the primary demand. We identify this difference as the reason for the failure of all previous studies in revealing independence of multiplication facts from attentional resources. Furthermore, we suggest the application of a contextual definition of automaticity to this kind of retrieval, given the fact that it might depend both on association strength and on contextual setting variables.

The role of response selection and input monitoring in solving simple arithmetical products

“…Nevertheless, our findings constitute an additional support for the idea that response selection is involved in the retrieval of the correct solution from long-term memory. The data are consistent with the idea that the presentation of two numbers of an arithmetic problem results in the automatic activation of the number nodes in an interrelated network of associative links in long-term memory (e.g., Ashcraft, 1992;Campbell, 1987Campbell, , 1995Campbell & Graham, 1985;Collins & Loftus, 1975;Dehaene & Cohen, 1995;Galfano et al, 2004;Galfano et al, 2003;Geary et al, 1986;Le-Fevre et al, 1988;Miller et al, 1984;Rusconi et al, 2004;Siegler, 1988;Siegler & Shrager, 1984;Thibodeau et al, 1996;Verguts & Fias, 2005). Activation then automatically spreads from the presented nodes along associative links to related number nodes, such as the sum or the product.…”

“…Most of the evidence, however, is in favor of the view that response selection is involved in the retrieval of arithmetical sums. According to Ashcraft (1992), arithmetical facts are retrieved from an interrelated network of associative links in long-term memory (see also Collins & Loftus, 1975;Dehaene & Cohen, 1995;Galfano, Mazza, Angrilli, & Umiltà, 2004;Galfano, Rusconi, & Umiltà, 2003;Geary, Widaman, & Little, 1986;LeFevre, Bisanz, & Mrkonjic, 1988;Miller, Perlmutter, & Keating, 1984;Rusconi, Galfano, Speriani, & Umiltà, 2004;Thibodeau, LeFevre, & Bisanz, 1996;Verguts & Fias, 2005). The idea is that the presentation of two numbers of an arithmetic problem results in the automatic activation of the number nodes in the associative network.…”

“…If it is correct that simple sums are solved by automatically activating the possible responses and retrieving the correct answer from these activated responses, it may be expected that concurrent response selection will also impair the calculation of simple multiplications. After all, more than simple sums, simple multiplications are assumed to be solved by retrieving the answers from longterm memory (e.g., Ashcraft, 1992;Campbell, 1987Campbell, , 1995Campbell & Graham, 1985;Collins & Loftus, 1975;Dehaene & Cohen, 1995;Galfano et al, 2004;Galfano et al, 2003;Geary et al, 1986;LeFevre et al, 1988;Miller et al, 1984;Rusconi et al, 2004;Siegler, 1988;Siegler & Shrager, 1984;Thibodeau et al, 1996;Verguts & Fias, 2005).…”

Do multiplication and division strategies rely on executive and phonological working memory resources?

“…Indeed, the presentation of a simple multiplication or division problem does automatically activate several candidate answers in long-term memory (see, e.g., Campbell, 1997;Galfano, Rusconi, & Umiltà, 2003;Rusconi, Galfano, Rebonato, & Umiltà, 2006;Rusconi, Galfano, Speriani, & Umiltà, 2004;Thibodeau, LeFevre, & Bisanz, 1996). After this automatic activation of several associated responses, a deliberate choice of the correct response has to be executed in order to complete the retrieval.…”

The obligatory activation of practiced complex multiplication facts and what it tells us about models of arithmetic processing

“…Number matching stimuli -As noted above, the stimuli for this task were (mostly) modeled after those that have been used in number matching tasks examining the automatic activation of simple multiplication answers (e.g., Galfano et al, 2004;Rusconi et al, 2004). Recall that the number-matching task involves the presentation of two cue numbers followed by a probe number, and participants determine whether the probe number matches one of the cue numbers.…”