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...
When a crime has been committed, investigators must obtain as much and as accurate information as possible from witnesses. Initial incomplete interviews may pose a potential cost to unretrieved information. We explored retrieval-induced forgetting (RIF) in children's autobiographical memory for related episodic events. Children experienced four related play sessions across 4 days, followed by word stem retrieval practice of half of the items, and a cued recall task that took place either 15 minutes or 2 hours later. Categorized details were experienced either within a single day or across multiple days. The emergence of RIF was dependent upon the length of delay between practice and test phases and the temporal distribution of the episodic events. Our observations demonstrate that RIF can be a subtle phenomenon whose occurrence depends upon whether the retrieval context supports an environment of retrieval interference.
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