Neighborhood consistency and memory for number facts

Verguts and Fias (Memory & Cognition 33:1-16, 2005a) proposed a new model of memory for simple multiplication facts ( $ 2 \times 3 = 6 $ ; $ 8 \times 7 = 56 $ ) in which learning and performance is governed by the consistency of a problem’s correct product with neighboring products in the times table. In the present study, to directly investigate effects of neighborhood consistency, participants memorized a set of 16 novel “pound” arithmetic equations. The pound arithmetic table included eight tie equations with repeated operands (e.g., 4 # 4 = 29) and eight nontie equations (e.g., 5 # 4 = 39). In the consistent problem set, tie and nontie answers in adjacent columns and rows shared a common decade or unit value. In the inconsistent problem set, neighboring tie and nontie problems did not share a common decade or unit. Across 14 study–test blocks, memorization of the pound arithmetic table presented a robust effect of neighborhood consistency, with the rate of learning nearly doubling that of the inconsistent condition. An analysis of error types showed that consistency fostered the development of a categorical structure based on problem operands and that tie problems were encoded as a distinct subcategory of problems. There was also a substantial learning advantage for tie problems relative to nonties both with consistent and inconsistent neighbors. The results indicate that neighborhood consistency can have a major impact on memory for number facts.     

Simple addition and multiplication: No comparison

Some models of memory for arithmetic facts (e.g., 5+2=7, 6×7=42) assume that only the max-left order is stored in memory (e.g., 5+2=7 is stored but not 2+5=7). These models further assume an initial comparison of the two operands so that either operand order (5+2 or 2+5) can be mapped to the common internal representation. We sought evidence of number comparison in simple addition and multiplication by manipulating size congruity. In number comparison tasks, performance costs occur when the physical and numerical size of numerals are incongruent (8 3) relative to when they are congruent (8 3). Sixty-four volunteers completed a number comparison task, an addition task, and a multiplication task with both size congruent and size incongruent stimuli. The comparison task demonstrated that our stimuli were capable of producing robust size congruity and split effects. In the addition and multiplication task, however, we were unable to detect any of the RT signatures of comparison or reordering processes despite ample statistical power: Specifically, there was no evidence of size congruity, split, or order effects in either the addition or multiplication data. We conclude that our participants did not routinely engage a comparison operation and did not consistently reorder the operands to a preferred orientation.     

The tie effect in simple arithmetic: An access-based account

Simple arithmetic problems with repeated operands (i.e., ties such as 4 + 4, 6 x 6, 10 - 5, or 49 / 7) are solved more quickly and accurately than similar nontie problems (e.g., 4 + 5, 6 x 7, 10 - 6, or 48 / 6). Further, as compared with nonties, ties show small or nonexistent problem-size effects (whereby problems with smaller operands such as 2 + 3 are solved more quickly and accurately than problems with larger operands such as 8 + 9). Blankenberger (2001) proposed that the tie advantage occurred because repetition of the same physical stimulus resulted in faster encoding of tie than of nontie problems. Alternatively, ties may be easier to solve than nonties because of differences in accessibility in memory or differences in the solution processes. Adults solved addition and multiplication (Experiment 1) or subtraction and division (Experiment 2) problems in four two pure formats (e.g., 4 + 4, FOUR + FOUR) and two mixed formats (e.g., 4 + FOUR, and FOUR + 4). Tie advantages were reduced in mixed formats, as compared with pure formats, but the tie x problem-size interaction persisted across formats. These findings support the view that tie effects are strongly related to memory access and are influenced only moderately by encoding factors.     

Semantic memory and verbal working memory correlates of N400 to subordinate homographs

N400 is an event-related brain potential that indexes operations in semantic memory conceptual space, whether elicited by language or some other representation (e.g., drawings). Language models typically propose three stages: lexical access or orthographic- and phonological-level analysis; lexical selection or word-level meaning and associate activation; and lexical integration, sentence- and discourse-level operations. The exact stage that N400 reflects is unknown, although opinion favors lexical integration over lexical selection. Surprisingly, little research has assessed relationships between neuropsychological measures of semantic memory fund of information or verbal working memory capacity and N400. Subjects performed a homograph disambiguation comprehension task with minimal working memory load. Short sentences read: The noun was adjective/verb. The nouns were either homographs or unambiguous. The adjective/verb was disambiguating for the homograph, and congruent or incongruent for the unambiguous noun. The primary noun of interest was the subordinate homograph. Comprehension of the subordinate meaning should correlate with semantic memory stores, reflecting greater knowledge. If N400 primarily reflects lexical access operations, it should also correlate with measures of semantic knowledge. If N400 reflects lexical integration, it should correlate with measures of working memory capacity. Comprehension errors were associated with semantic memory stores, but not working memory capacity. N400 was related to working memory capacity, but not semantic knowledge, suggesting that N400 primarily reflects late-stage working memory operations. N400 to subordinate disambiguating words was larger with greater working memory capacity, and thus may index the absolute capacity of working memory rather than difficulty in contextual integration.     

Bidirectional links in the network of multiplication facts

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.     

Contextual modulation of N400 amplitude to lexically ambiguous words

Though much is known about the N400 component, an event-related EEG potential that is sensitive to semantic manipulations, it is unclear whether modulations of N400 amplitude reflect automatic processing, controlled processing, or both. We examined this issue using a semantic judgment task that manipulated local and global contextual cues. Word triplets (prime-noun-target, e.g., finance-bank-money) were sequentially presented on a computer screen (500 ms duration, 1000 ms stimulus onset asynchrony), in which the second word was a homograph. The first word (prime) created a neutral-, dominant-meaning- or subordinate-meaning-biased "global context," and the third word (target) created a dominant- or subordinate-biased "local context" that was either congruent or incongruent with the "global context" established by the first prime word. Participants were instructed to read all three words but to decide only whether the second and third words were semantically related. Event-related potentials (ERPs), specifically the N400, were recorded to the third terminal word. N400 amplitudes evoked by dominant meaning-related third words incongruent with the globally biased subordinate context (e.g., river-bridge-money) were significantly more negative than dominant endings in neutral contexts (e.g., taxi-bank-money), but not different from unrelated filler triplets. In addition, there was some indication that left hemisphere, temporal-parietal electrode sites were associated with greater N400 negativity for dominant targets in conflicting subordinate global contexts than homologous right hemisphere electrode sites, the latter of which showed significant activation to subordinate meanings in cooperating contexts. Thus, N400 amplitude was more affected by global than local context suggesting that controlled processes may take priority over automatic processes in modulating N400 amplitude, especially for left hemisphere electrode sites.     

Working memory,strategy execution,and strategy selection in mental arithmetic

A total of 72 participants estimated products of complex multiplications of two-digit operands (e.g., 63 × 78), using two strategies that differed in complexity. The simple strategy involved rounding both operands down to the closest decades (e.g., 60 × 70), whereas the complex strategy required rounding both operands up to the closest decades (e.g., 70 × 80). Participants accomplished this estimation task in two conditions: a no-load condition and a working-memory load condition in which executive components of working memory were taxed. The choice/no-choice method was used to obtain unbiased strategy execution and strategy selection data. Results showed that loading working-memory resources led participants to poorer strategy execution. Additionally, participants selected the simple strategy more often under working-memory load. We discuss the implications of the results to further our understanding of variations in strategy selection and execution, as well as our understanding of the impact of working-memory load on arithmetic performance and other cognitive domains.     

Working memory, strategy execution, and strategy selection in mental arithmetic

A total of 72 participants estimated products of complex multiplications of two-digit operands (e.g., 63 × 78), using two strategies that differed in complexity. The simple strategy involved rounding both operands down to the closest decades (e.g., 60 × 70), whereas the complex strategy required rounding both operands up to the closest decades (e.g., 70 × 80). Participants accomplished this estimation task in two conditions: a no-load condition and a working-memory load condition in which executive components of working memory were taxed. The choice/no-choice method was used to obtain unbiased strategy execution and strategy selection data. Results showed that loading working-memory resources led participants to poorer strategy execution. Additionally, participants selected the simple strategy more often under working-memory load. We discuss the implications of the results to further our understanding of variations in strategy selection and execution, as well as our understanding of the impact of working-memory load on arithmetic performance and other cognitive domains.     

Interoperation transfer in Chinese–English bilinguals’ arithmetic

We examined interoperation transfer of practice in adult Chinese-English bilinguals' memory for simple multiplication (6 × 8 = 48) and addition (6 + 8 = 14) facts. The purpose was to determine whether they possessed distinct number-fact representations in both Chinese (L1) and English (L2). Participants repeatedly practiced multiplication problems (e.g., 4 × 5 = ?), answering a subset in L1 and another subset in L2. Then separate groups answered corresponding addition problems (4 + 5 = ?) and control addition problems in either L1 (N = 24) or L2 (N = 24). The results demonstrated language-specific negative transfer of multiplication practice to corresponding addition problems. Specifically, large simple addition problems (sum > 10) presented a significant response time cost (i.e., retrieval-induced forgetting) after their multiplication counterparts were practiced in the same language, relative to practice in the other language. The results indicate that our Chinese-English bilinguals had multiplication and addition facts represented in distinct language-specific memory stores.     

Orthographically mediated inhibition effects: evidence of activational feedback during visual word recognition

Models of visual word recognition that have adopted an interactive activation framework (e.g., Coltheart, Curtis, Atkins, & Haller, 1993; Grainger & Jacobs, 1996) assume that activation can spread from semantic to orthographic representations via a feedback mechanism during visual word recognition. The present study used a mediated priming paradigm to test whether such feedback exists and, if so, under what conditions. Participants named aloud targets that were preceded either by a semantically related prime (e.g., dog-cat) or by a prime that was related to the target via a mediating word (e.g., cat-[dog]-bog). Direct evidence of activational feedback was obtained in the form of orthographically mediated inhibition effects. These mediated inhibition effects are consistent with activational feedback and support models of visual word recognition that have adopted an interactive activation framework.     

Dissociated developmental trajectories for semantic and phonological false memories

False recognition following presentation of semantically related and phonologically related word lists was evaluated in 8-, 11-, and 13-year-olds. Children heard lists of words that were either semantic (e.g., bed, rest, wake ...) or phonological associates (e.g., pole, bowl, hole ...) of a critical unpresented word (e.g., sleep, roll), respectively. A semantic false memory was defined as false recognition of a semantically related but unpresented word. A phonological false memory was defined as false recognition of a phonologically related but unpresented word. False memories in the two tasks showed opposite developmental trends, increasing with age for semantic relatedness and decreasing with age for phonological relatedness.     

Directed forgetting of trauma cues in adults reporting repressed or recovered memories of childhood sexual abuse

An item-cuing directed forgetting task was used to investigate whether women reporting repressed (n = 13) or recovered (n = 13) memories of childhood sexual abuse (CSA) exhibit an avoidant encoding style (and resultant impaired memory) for trauma cues relative to women reporting no CSA experience (n = 15). All participants viewed intermixed trauma (e.g., molested), positive (e.g., confident), and categorized neutral (e.g., mailbox) words on a computer screen and were instructed either to remember or to forget each word. The results provided no support for the hypothesis that people reporting either repressed or recovered memories of CSA are especially adept at forgetting words related to trauma. These groups recalled words they were instructed to remember more often than words they were instructed to forget regardless of whether they were trauma related.     

Dissociated developmental trajectories for semantic and phonological false memories

False recognition following presentation of semantically related and phonologically related word lists was evaluated in 8-, 11-, and 13-year-olds. Children heard lists of words that were either semantic (e.g., bed, rest, wake …) or phonological associates (e.g., pole, bowl, hole …) of a critical unpresented word (e.g., sleep, roll), respectively. A semantic false memory was defined as false recognition of a semantically related but unpresented word. A phonological false memory was defined as false recognition of a phonologically related but unpresented word. False memories in the two tasks showed opposite developmental trends, increasing with age for semantic relatedness and decreasing with age for phonological relatedness.     

Adults' strategies for simple addition and multiplication: verbal self-reports and the operand recognition paradigm

Accurate measurement of cognitive strategies is important in diverse areas of psychological research. Strategy self-reports are a common measure, but C. Thevenot, M. Fanget, and M. Fayol (2007) proposed a more objective method to distinguish different strategies in the context of mental arithmetic. In their operand recognition paradigm, speed of recognition memory for problem operands after solving a problem indexes strategy (e.g., direct memory retrieval vs. a procedural strategy). Here, in 2 experiments, operand recognition time was the same following simple addition or multiplication, but, consistent with a wide variety of previous research, strategy reports indicated much greater use of procedures (e.g., counting) for addition than multiplication. Operation, problem size (e.g., 2 + 3 vs. 8 + 9), and operand format (digits vs. words) had interactive effects on reported procedure use that were not reflected in recognition performance. Regression analyses suggested that recognition time was influenced at least as much by the relative difficulty of the preceding problem as by the strategy used. The findings indicate that the operand recognition paradigm is not a reliable substitute for strategy reports and highlight the potential impact of difficulty-related carryover effects in sequential cognitive tasks.     

This cat has nine lives? Children's memory for genericity in language

Generic noun phrases ("Birds lay eggs") are important for expressing knowledge about abstract kinds. The authors hypothesized that genericity would be part of gist memory, such that young children would appropriately recall whether sentences were presented as generic or specific. In 4 experiments, preschoolers and college students (N = 280) heard a series of sentences in either generic form (e.g., "Bears climb trees") or specific form (e.g., "This bear climbs trees") and were asked to recall the sentences following a 4-min distractor task. Participants in all age groups correctly distinguished between generic and specific noun phrases (NPs) in their recall, even when forgetting the details of the NP form. Memory for predicate content (e.g., "climb trees") was largely unaffected by genericity, although memory for category labels (e.g., "bear") was at times better for those who heard sentences with generic wording. Overall, these results suggest that generic form is maintained in long-term memory even for young children and thus may serve as the foundation for constructing knowledge about kinds.     

FN400和N400是相同的ERP成分：来自图形材料的证据

本研究通过比较记忆编码阶段语义启动引起的N400效应和提取阶段熟悉性引起的FN400效应的地形图考察图形材料诱发的N400和FN400是否是相同的ERP成分。实验结果发现,语义启动引起的N400效应和熟悉性引起的FN400效应的地形图没有显著差异。这说明图形材料诱发的FN400和N400是相同的ERP成分,两者都反映了语义加工。本研究为FN400效应反映了语义启动而不是熟悉性的观点提供了新的实验证据。     

心算加工中tie effect的加工机制

tie effect主要表现为tie比nontie更快更准确解决,以及tie/nontie与问题大小的交互作用,较大题目的tie比nontie具有更明显的反应时优势,tie的问题大小效应比nontie要小的多。有关tie effect加工机制的解释主要有基于编码的理论和基于结果通达的理论。目前的研究主要通过操作问题呈现方式以及报告加工策略的方法分别考察编码方式及加工策略的影响,今后研究应开拓新的研究范式以加深对其加工机制的认识。     

The locus of self-inhibition in sequential retrieval

Self-inhibition refers to the suppression of a representational node following its use in a sequential task. Two general models of self-inhibition exist in the literature: one that models suppression following activation of a node (Houghton & Tipper, 1994), and one that models suppression following motor production of a node (MacKay, 1986). These two models make opposite predictions for units that are activated but not produced, with the post-activation model predicting interference and the post-production model predicting facilitation. These predictions were tested using operand--answer priming in two mental addition experiments. Addition problems with sums <10 were primed with addition problems that contained the correct sum as one of the operands (e.g., 5 + 8 preceding 3 + 2). Experiment 2 included an additional manipulation of prime-target discriminability to rule out episodic retrieval accounts of the interference effect. Both experiments indicated interference following operand-answer primes relative to control primes, consistent with the predictions of the post-activation model of self-inhibition.     

Retrieval-induced forgetting of arithmetic facts but not rules

Retrieval of a multiplication fact (2×6 =12) can disrupt retrieval of its addition counterpart (2+6=8). We investigated whether this retrieval-induced forgetting effect applies to rule-governed arithmetic facts (i.e., 0×N=0, 1×N=N). Participants (n=40) practised rule-governed multiplication problems (e.g., 1×4, 0×5) and multiplication facts (e.g., 2×3, 4×5) for four blocks and then were tested on the addition counterparts (e.g., 1+4, 0+5, 2+3, 4+5) and control additions. Increased addition response times and errors relative to controls occurred only for problems corresponding to multiplication facts, with no problem-specific effects on addition counterparts of rule-governed multiplications. In contrast, the rule-governed 0+N problems provided evidence of generalisation of practice across items, whereas the fact-based 1+N problems did not. These findings support the theory that elementary arithmetic rules and facts involve distinct memory processes, and confirmed that previous, seemly inconsistent findings of RIF in arithmetic owed to the inclusion or exclusion of rule-governed problems.     

Word learning and individual differences in word learning reflected in event-related potentials

Adults learned the meanings of rare words (e.g., gloaming) and then made meaning judgments on pairs of words. The 1st word was a trained rare word, an untrained rare word, or an untrained familiar word. Event-related potentials distinguished trained rare words from both untrained rare and familiar words, first at 140 ms and again at 400-600 ms after onset of the 1st word. These results may point to an episodic memory effect. The 2nd word produced an N400 that distinguished trained and familiar word pairs that were related in meaning from unrelated word pairs. Skilled comprehenders learned more words than less skilled comprehenders and showed a stronger episodic memory effect at 400-600 ms on the 1st word and a stronger N400 effect on the 2nd word. These results suggest that superior word learning among skilled comprehenders may arise from a stronger episodic trace that includes orthographic and meaning information and illustrate, how an episodic theory of word identification can explain reading skill.