Effects of multiplication practice on product verification: Integrated structures model or retrieval-induced forgetting?

Abstract

324Manly and Spoehr (1999) proposed the integrated structures model (ISM) of multiplication fact representation. According to the ISM, multiplication problems activate three distinct representations in memory: a whole facts representation (e.g., 2 3 7 5 14), an analog code representing the approximate magnitude of the product, and an operand multiples representation consisting of the multiples of the problems operands (e.g., 2 3 7 5 14 activates the operand multiples of 2, 4, 6, 8, . . . and 7, 14, 21, 28 . . .). The three codes are activated simultaneously, and collectively they mediate retrieval of multiplication facts.In this article, we will focus on the evidence presented by Manly and Spoehr (1999) in connectionwith the operand multiples representation. Specifically, it is assumed in the ISM that the operand multiples representation is strengthened when a problem (e.g., 4 3 5 5 20) is practiced and that this leads to increased interference when the strengthened multiples are tested later in a true-false verification task. For example, deciding that 4 3 6 5 16 is false should be more difficult following practice on 4 3 5 because the 4-multiple 16 would be strengthened during practice and become a stronger lure in the context of a false equation. Their experiments appeared to confirm this prediction.Although Manly and Spoehr's (1999) results supported ISM predictions regarding operand multiples, their results are surprising when viewed from a different perspective.Specifically, Manly and Spoehr's practice-test multiplication paradigm is conceptually quite similar to the paradigms developed by M. C. Anderson and colleagues (M. C. Anderson, Bjork, & Bjork, 1994;M. C. Anderson & McCulloch, 1999) to investigate retrieval-induced forgetting (RIF). Specifically, M. C. Anderson and colleagues have shown that repeated cued-retrieval practice on a subset of previously studied items interferes with cued retrieval of semantically related unpracticed items. Thus, in contrast to the predictions of the ISM, the RIF effect suggests that repeatedly practicing specific facts should lead to the suppression of related facts, rather than to the strengthening of them. In the present article, we present evidence that practicing multiplicationfacts does produce RIF and that Manly and Spoehr's evidence for the strengthening of related facts occurred because of a confounding of opposing factors in their stimuli. We will begin by reviewing Manly and Spoehr's paradigm in some detail, and then we will turn to the rationale and design of our experiment. Manly and Spoehr's (1999) Test of the Operand Multiples AssumptionTo test their assumptions regarding operand multiples representations, Manly and Spoehr (1999) used a multiplication verification task (e.g., 2 3 7 5 21, true or false?). Their main interest was a well-established phenomenon called the lure effect (Campbell & Tarling, 1996;Stazyk, Ashcraft, & Hamann, 1982;Winkelman & Schmidt, 1974): When a presented false answer is a multiple of one of the problem's operands (a related lure...

A progress report on the inhibitory account of retrieval-induced forgetting

“…The finding has proven to be highly robust and general, emerging in many contexts and with a variety of materials (e.g., with factual propositions, M. C. Anderson & Bell, 2001;Gómez-Ariza, Lechuga, Pelegrina, & Bajo, 2005;Macrae & MacLeod, 1999;phonological categories, Bajo, Gómez-Ariza, Fernandez, & Marful, 2006;text passages, Carroll, Campbell-Ratcliffe, Murnane, & Perfect, 2007;Chan, McDermott, & Roediger, 2006;Little, Storm, & Bjork, 2011;visuospatial materials, Ciranni & Shimamura, 1999; language selection, Levy, McVeigh, Marful, & Anderson, 2007; arithmetic facts, Phenix & Campbell, 2004; eyewitness memory, Garcia-Bajos, Migueles, & Anderson, 2009;M. D. MacLeod, 2002;Saunders & MacLeod, 2002;Shaw, Bjork, & Handal, 1995;mental imagery, Saunders, Fernandes, & Kosnes, 2009; creative problem solving, Storm, Angello, & Bjork, 2011;autobiographical memory, Barnier, Hung, & Conway, 2004;and social contexts, Dunn & Spellman, 2003;Storm, Bjork, & Bjork, 2005).…”

Identical elements model of arithmetic memory: Extension to addition and subtraction

“…One of these concerns how problems are functionally related to each other in memory and how the network of related facts is processed (i.e., specific assumptions about excitatory and inhibitory processes). The IE model leads one to think of each arithmetic fact as an isolated entity, but it is well established that processing one problem has effects on other, related problems (Ashcraft, 1992(Ashcraft, , 1995Campbell, 1987Campbell, , 1997Campbell & Timm, 2000;Manly & Spoehr, 1999;Phenix & Campbell, 2004). For example, Phenix and Campbell demonstrated that repeatedly practicing a multiplication problem facilitated retrieval of the correct product, as was expected, but also reduced the accessibility of other multiples of the factors.…”

Semantic integration as a boundary condition on inhibitory processes in episodic retrieval.

“…To focus retrieval on the target, inhibition is thought to suppress competing traces, with the lingering effects causing difficulties in recalling those competitors. This phenomenon, known as retrieval-induced forgetting (RIF), has been observed in many contexts, including episodic memory (e.g., Anderson, Bjork, & Bjork, 1994;Ciranni & Shimamura, 1999), semantic memory (Blaxton & Neely, 1983;Johnson & Anderson, 2004), memory for word meaning (Johnson & Anderson, 2004;Shivde & Anderson, 2001), memory for factual knowledge (Anderson & Bell, 2001;Gómez-Ariza, Lechuga, Pelegrina, & Bajo, 2005;Macrae & MacLeod, 1999;Phenix & Campbell, 2004), autobiographical memory (Barnier, Hung, & Conway, 2004;Harris, Sharman, Barnier, & Moulds, 2010), eyewitness memory (Garcia-Bajos, Migueles, & Anderson, 2009;MacLeod, 2002;Migueles & Garcia-Bajos, 2006;Shaw, Bjork, & Handal, 1995), visuo-spatial memory (Ciranni & Shimamura, 1999), and even memory for phonological information retrieved during language production (Levy, McVeigh, Marful, & Anderson, 2007). RIF, thus, is a general factor contributing to memory lapses in a broad range of contexts.…”