Multiple number and letter comparison: directionality and accessibility in numeric and alphabetic memories

In 3 experiments, subjects made comparativejudgments on a set of 2 numbers or letters, 3 numbers or letters, or 5 numbers or letters. Numeric and alphabetic serial order memories were contrasted. Three aspects of serial order memory processes were identified: computational complexity, directionality, and accessibility. Computational complexity is the number of algorithmic steps involved in identifying a target. Directional bias is measured as the speed differences in identifying serial targets of equal computational complexity in a stimulus array. Memory accessibility is measured as the numeric and alphabetic serial position effects. Subjects had a slight directional bias favoring backward ordering for single digits but no bias in 2-digit number ordering, in contrast to a strong forward directional advantage in letter ordering. The speed of number access was found to steadily and evenly decrease along the numeric scale, in contrast to a systematic pattern of variations in alphabet access along the alphabetic scale. Finally, the middle item effect (the middle item in a multi-item array is identified most slowly) found in Jou's (1997) multiple-letter comparison study was generalized to numbers.     

Algorithmic solution of arithmetic problems and operands-answer associations in long-term memory

Many developmental models of arithmetic problem solving assume that any algorithmic solution of a given problem results in an association of the two operands and the answer in memory (Logan & Klapp, 1991; Siegler, 1996). In this experiment, adults had to perform either an operation or a comparison on the same pairs of two-digit numbers and then a recognition task. It is shown that unlike comparisons, the algorithmic solution of operations impairs the recognition of operands in adults. Thus, the postulate of a necessary and automatic storage of operands-answer associations in memory when young children solve additions by algorithmic strategies needs to be qualified.     

工作记忆广度：资源限制、记忆消退还是转换机制？

为了检验工作记忆广度有限性的3种假说,即资源限制假说、记忆消退假说和转换机制假说,实验要求被试首先完成一项转换效率任务,然后完成工作记忆广度任务。结果发现,加工负荷对工作记忆广度具有重要影响,保持时间不影响工作记忆广度,转换效率与工作记忆广度也没有显著相关。实验结果支持工作记忆广度受认知资源限制的观点     

The memorial structure of organized sequences

Subjects were asked to memorize a sequence of nine consonants which were grouped into three groups of three letters each (e.g., SBJ FQL ZNG). After learning the sequence, they were presented with single letters, letter pairs, or letter triples and asked to indicate if the probe item appeared in the memorized sequence. The latency results suggest that subjects engage in a linear self-terminating memory search in which the items from one chunk are retrieved from memory as the items from the immediately preceding chunk are being scanned. When the probe consisted of more than one item, the subjects were slowed in their comparison if the letters came from different chunks (e.g., JF vs. FQ in the above illustration), and the number of letters in the probe also influenced the reaction time. Neither of those effects were obtained if all the letters in the probe came from the same chunk, and that would seem to suggest that the probe items from the same chunk were compared in parallel to the letters in the memory item, while items from different chunks were compared serial.     

Stimulus similarity decrements in children's working memory span

Two experiments investigated the impact of the relationship between processing and storage stimuli on the working memory span task performance of children aged 7 and 9 years of age. In Experiment 1, two types of span task were administered (sentence span and operation span), and participants were required to recall either the products of the processing task (sentence-final word, arithmetic total) or a word or digit unrelated to the processing task. Experiment 2 contrasted sentence span and operation span combined with storage of either words or digits, in tasks in which the item to be remembered was not a direct product of the processing task in either condition. In both experiments, memory span was significantly greater when the items to be recalled belonged to a different stimulus category from the material that was processed, so that in sentence span tasks, number recall was superior to word recall, and in operation span tasks, word recall was superior to number recall. Explanations of these findings in terms of similarity-based interference and response competition in working memory are discussed.     

Short term Memory Impairment and Arithmetical Ability

We document the dissociation of preserved calculation skills in a patient with impaired auditory short-term memory. The patient (MRF) had a memory span of three digits. Furthermore, he showed rapid decrement in performance of single digits and letters with both auditory and visual presentation in the Brown-Peterson forgetting task. Analysis of his calculation skills revealed a normal ability to solve auditorily presented multidigit addition and subtraction problems such as 173 + 68 and to execute the Paced Auditory Serial Addition Task (Sampson, 1956, 1958; Gronwall, 1977). In addition, his performance on other tests, including arithmetic manipulation of natural numbers, decimals and fractions, approximation, magnitude, ratio, and percentage, appeared to be normal (Hitch, 1978b). It is argued that these findings require a revision of Baddeley and Hitch's (1974) concept of the function of working memory.     

Cognitive skill acquisition and transfer in younger and older adults.

The acquisition of cognitive skills often depends on 1 of (or a combination of) 2 processes, the execution of an algorithm, and the retrieval of problem instances. This study examined the effects of age and repetition of problem instances on the production and verification of solutions to 2 serially presented sets of alphabet arithmetic problems. Analyses of the parameters derived from power-function fits for individuals revealed age differences favoring young adults in improvement span, learning rate, and asymptote. For both age groups, the beneficial effects of repetitions on 1st-set response times were attributable to algorithmic speedup and to the retrieval of instances, whereas improvements in the speed of 2nd-set response times were attributable primarily to item retrieval.     

Same-different judgments of multiletter strings: insensitivity to positional bias and spacing

Several recent studies of multiletter matching have included pairs of strings that have the same letters in different positions (rearranged pairs). The task can be defined such that these rearranged pairs are correctly classified as different (i.e., subjects respond "same" only if the strings have the same letters in the same positions--the order task) or as same (i.e., subjects respond "same" if the strings have the same letters regardless of their positions--the item task). The order task produces left-to-right serial-position effects, whereas the item task produces U-shaped serial-position effects. Because these differences suggest that subjects may be able to exert strategic control over the comparison process, two sets of experiments were designed to test whether or not subjects can change the relative weightings devoted to the respective serial positions. In Experiments 1 and 2, the probability that a mismatch occurred in the different positions was manipulated. In Experiments 3 and 4, the physical spacing between letters, as well as whether or not the spaces were filled with neutral noise characters, was varied. None of the manipulations had much influence on the serial-position effects. Thus, the distinct serial-position effects for the order and item tasks apparently are mandatory and not due to any voluntary comparison strategy.     

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

The role of executive and phonological working memory resources in simple arithmetic was investigated in two experiments. Participants had to solve simple multiplication problems (e.g., 4 x 8; Experiment 1) or simple division problems (e.g., 42 / 7; Experiment 2) under no-load, phonological-load, and executive-load conditions. The choice/no-choice method was used to investigate strategy execution and strategy selection independently. Results for strategy execution showed that executive working memory resources were involved in direct memory retrieval of both multiplication and division facts. Executive working memory resources were also involved in the use of nonretrieval strategies. Phonological working memory resources, on the other hand, tended to be involved in nonretrieval strategies only. Results for strategy selection showed no effects of working memory load. Finally, correlation analyses showed that both strategy execution and strategy selection correlated with individual-difference variables, such as gender, math anxiety, associative strength, calculator use, arithmetic skill, and math experience.     

Order of report and processing in tachistoscopic recognition

Two groups of 12 Ss were shown tachistoscopically 4 letters and 4 numbers. Within these alpha-numeric sequences, three variables were systematically manipulated: grouping of items, initial item, and familiarity of the letter sequences. One group of Ss reported first letters then numbers from each sequence; the other group reported numbers then letters. The results indicated that grouping, redundancy, and order of report had significant effects on letter accuracy but not on number accuracy. These effects were interpreted in terms of processing, particularly the use of spatial and identity information during recognition.     

The role of phonological and executive working memory resources in simple arithmetic strategies

The current study investigated the role of the central executive and the phonological loop in arithmetic strategies to solve simple addition problems (Experiment 1) and simple subtraction problems (Experiment 2). The choice/no-choice method was used to investigate strategy execution and strategy selection independently. The central executive was involved in both retrieval and procedural strategies, but played a larger role in the latter than in the former. Active phonological processes played a role in procedural strategies only. Passive phonological resources, finally, were only needed when counting was used to solve subtraction problems. No effects of working memory load on strategy selection were observed.     

The transition from algorithm to retrieval in memory-based theories of automaticity

Two memory-based theories of automaticity were compared. The mixture model and the race model both describe automatization as a transition from algorithmic processing to memory retrieval. The mixture model predicts that, with training, the variability of reaction time will initially increase, and later decrease in a concave downward manner, whereas the race model predicts the variability will decrease only in a concave upward manner. The mixture model predicts that using both algorithm and retrieval on a single trial will be slower than using the algorithm alone, whereas the race model predicts the reverse. The experiments used an alphabet arithmetic task, in which subjects verified equations of the form H + 3 = K and made subjective reports of their strategies on individual trials. Both the variability of reaction times and the pattern of reaction times associated with the strategy reports supported the race model.     

Same—differentjudgments of multiletter strings: Insensitivity to positional bias and spacing

Several recent studies of multiletter matching have included pairs of strings that have-the-same letters in different positions (rearranged pairs). The task can be defined such that these rearranged pairs are correctly classified asdifferent (i.e., subjects respond “same” only if the strings have the same letters in the same positions—the order task) or assame (i.e., subjects respond “same” if the strings have the same letters regardless of their positions—the item task). The order task produces left-to-right serial-position effects, whereas the item task produces U-shaped serial position effects. Because these differences suggest that subjects may be able to exert strategic control over the comparison process, two sets of experiments were designed to test whether or not subjects can change the relative weightings devoted to the respective serial positions. In Experiments 1 and 2, the probability that a mismatch occurred in the different positions was manipulated. In Experiments 3 and 4, the physical spacing between letters, as well as whether or not the spaces were filled with neutral noise characters, was varied. None of the manipulations had much influence on the serial-position effects. Thus, the distinct serial-position effects for the order and item tasks apparently are mandatory and not due-to-any voluntary-comparison strategy.     

Attention switching and working memory spans

Barrouillet and Camos () concluded from their developmental study on working memory that when performing complex span tasks, individuals maintain memory items by switching rapidly their attention from processing to storage while performing the concurrent task. Thus, a processing component that would require a continuous attentional focusing should have a highly detrimental effect on span. The present study verifies two predictions issuing from this hypothesis by comparing the classical self‐paced reading and operation span tasks with new computer‐paced tasks in adults. First, any increase in the pace at which the processing component of a working memory span task has to be performed impedes switching and then leads to lower spans. Second, when presented at a fast pace, even simple activities such as reading letters or adding and subtracting 1 to small numbers have an effect on spans as detrimental as complex activities like reading and understanding sentences or solving complex equations.     

Arithmetic split effects reflect strategy selection: an adult age comparative study in addition comparison and verification tasks.

We tested whether split effects in arithmetic (i.e., better performance on large-split problems, like 3 + 8 = 16, than on small-split problems, like 3 + 8 = 12) reflect decision processing or strategy selection. To achieve this end, we tested performance of younger and older adults, matched on arithmetic skills, on two arithmetic tasks: the addition/number comparison task (e.g., 4 + 8, 13; which item is the larger?) and in the inequality verification task (e.g., 4 + 8 < 13; Yes/No?). In both tasks, split between additions and proposed numbers were manipulated. We also manipulated the difficulty of the additions, which represents an index of arithmetic fact calculation (i.e., hard problems, like 6 + 8 < 15, are solved more slowly than easy problems, like 2 + 4 < 07, suggesting that calculation takes longer). Analyses of latencies revealed three main results: First, split effects were of smaller magnitude in older adults compared to younger adults, whatever the type of arithmetic task; second, split effects were of smaller magnitude on easy problems; and third, calculation processes were well maintained in older adults with high level of arithmetic skills. This set of results improves our understanding of cognitive aging and strategy selection in arithmetic.     

Toward a generalized theory of the shift to retrieval in cognitive skill learning

Prior research on cognitive skill learning has shown that algorithmic and direct memory retrieval strategies are not executed in parallel if the algorithm entails a series of long-term memory (LTM) retrieval steps (as in the case, for example, of mental arithmetic). This phenomenon has been hypothesized to reflect a bottleneck in LTM retrieval processes that forces a strategy choice during an early stage of processing. Here, we investigate simple perceptual–motor algorithms that involve no memory retrieval steps, a largely unexplored case in which parallel strategy execution models remain viable. Pronounced strategy interference was again observed, albeit interference that was different in important respects from that observed for LTM retrieval algorithms. It appears that neither parallel nor choice models, as developed to date, are sufficient as a generalized theory of this skill learning phenomenon. Issues central to the development of a more comprehensive theory are discussed.     

On time differences in searching for letters in words and nonwords: Do they emerge during the initial encoding or the subsequent scan?

Krueger (1970a, 1970b, 1982) has demonstrated that subjects can search for target letters within words faster than they can complete an equivalent search through nonwords, and he further demonstrated that the effect did not arise during the comparison stage. The present study involved three experiments in which the usual word advantage disappeared either when subjects knew where within a display the target item would appear (i.e., it was always the first letter), or when all the component letters were encoded into memory before the task began (i.e., a memory-search task). These data, in conjunction with Krueger's, where interpreted as localizing at least one (and possibly the only) source of the word-nonword difference in this task to the events that occur during the item-to-item transitions subjects make when scanning the letter arrays. That is, these transitions are faster for words than nonwords, and it was suggested that the time difference may emerge because although all the letters from within a word appear to be available in memory before the scan begins, this seems not to be true for consonant arrays. Given that this is the case, part of the word-nonword difference may be attributable to subsequent encoding events that would be needed for the consonant arrays as the scan moves from letter to letter.     

The contributions of strategy use to working memory span: A comparison of strategy assessment methods

In two experiments, we tested whether individual differences in strategy production account for individual differences in performance on a working memory span task. We measured the strategies used during a standard experimenter-paced operation span (OSPAN) task by having participants make both set-by-set reports of strategy use for individual item sets and global reports of strategy use. In Experiment 1, although normatively effective strategies were self-reported on only a small proportion of OSPAN sets, individual differences in effective strategy use correlated with span performance. Experiment 2 replicated this outcome using a sample of 100 participants but, as important, it demonstrated that individual differences in effective strategy use did not mediate the relationship between OSPAN and measures of verbal ability. Discussion focuses on the interpretation of strategy–span relationships and the relative utility of general reports of strategy use versus the set-by-set reports introduced here for the OSPAN task.     

The contributions of strategy use to working memory span: a comparison of strategy assessment methods

In two experiments, we tested whether individual differences in strategy production account for individual differences in performance on a working memory span task. We measured the strategies used during a standard experimenter-paced operation span (OSPAN) task by having participants make both set-by-set reports of strategy use for individual item sets and global reports of strategy use. In Experiment 1, although normatively effective strategies were self-reported on only a small proportion of OSPAN sets, individual differences in effective strategy use correlated with span performance. Experiment 2 replicated this outcome using a sample of 100 participants but, as important, it demonstrated that individual differences in effective strategy use did not mediate the relationship between OSPAN and measures of verbal ability. Discussion focuses on the interpretation of strategy-span relationships and the relative utility of general reports of strategy use versus the set-by-set reports introduced here for the OSPAN task.     

Repeated retrieval practice and item difficulty: Does criterion learning eliminate item difficulty effects?

A wealth of previous research has established that retrieval practice promotes memory, particularly when retrieval is successful. Although successful retrieval promotes memory, it remains unclear whether successful retrieval promotes memory equally well for items of varying difficulty. Will easy items still outperform difficult items on a final test if all items have been correctly recalled equal numbers of times during practice? In two experiments, normatively difficult and easy Lithuanian–English word pairs were learned via test–restudy practice until each item had been correctly recalled a preassigned number of times (from 1 to 11 correct recalls). Despite equating the numbers of successful recalls during practice, performance on a delayed final cued-recall test was lower for difficult than for easy items. Experiment 2 was designed to diagnose whether the disadvantage for difficult items was due to deficits in cue memory, target memory, and/or associative memory. The results revealed a disadvantage for the difficult versus the easy items only on the associative recognition test, with no differences on cue recognition, and even an advantage on target recognition. Although successful retrieval enhanced memory for both difficult and easy items, equating retrieval success during practice did not eliminate normative item difficulty differences.