Short-term memory processes in counting

Four experiments examined the memory processes used to maintain location in a counting sequence. In Experiment 1, subjects who rapidly counted forward omitted many repeated-digit numbers (e.g., 77), as found previously with backward counting. Subjects in Experiment 2 counted backward with normal auditory feedback or with headphones through which white noise was channeled. In both cases, repeated-digit errors predominated, suggesting that the contents of short-term memory, rather than auditory sensory memory, are checked during counting. In Experiment 3, subjects silently wrote counting responses, and the omission errors resembled those in vocal counting. Repetition errors were also found and attributed to phonological recoding failures. Articulatory suppression in Experiment 4 greatly increased the number of repetition errors in the written counting task. A model of the counting process was proposed according to which subjects keep track of their location in the counting sequence by monitoring phonologically coded short-term memory representations of the numbers.     

Perceptual grouping in audition

The present experiments evaluated the effect of relative frequency as a determinant of the figure-ground organization of sequences of auditory tones. Observers counted sequences of 20 ms tones that were presented at the same frequency or that alternated between two different frequencies. The alternating tones differed in frequency by one whole tone, seven tones, or nineteen tones. Counting accuracy increased with increases in the silent interval between the tones. When the alternating tones differed by seven or nineteen tones, counting was disrupted at rates of presentation of eight tones per second or slower. In contrast to this decrement in the counting of tones that alternated by over an octave, very little decrement was observed when the tones alternated by just one whole tone. The best subjects counted these alternating tones more accurately than the tones presented at the same frequency. The poorest subjects showed a small decrement even when the tones alternated by just one whole tone. The results were discussed in terms of determinants of figure-ground organization in auditory information processing.     

节律性时间期待效应不受注意控制的影响

采用双任务范式探讨当听觉节律刺激序列以较慢速度呈现时,其诱导产生的时间期待效应是否受到同时进行的视觉工作记忆任务的影响。结果发现,无论目标刺激是呈现在听觉通道还是视觉通道,双任务和单任务条件下目标刺激出现在规律听觉刺激序列之后被试的反应时均快于目标出现在非规律听觉刺激序列之后,即节律性刺激序列诱导产生的时间期待效应不受工作记忆任务的影响。该结果表明节律性时间期待效应不受注意控制的影响。     

Preschoolers' counting: principles before skill

Three- to 5-year-old children participated in one of 4 counting experiments. On the assumption that performance demands can mask the young child's implicit knowledge of the counting principles, 3 separate experiments assessed a child's ability to detect errors in a puppet's application of the one-one, stable-order and cardinal count principles. In a fourth experiment children counted in different conditions designed to vary performance demands. Since children in the errror-detection experiments did not have to do the counting, we predicted excellent performance even on set sizes beyond the range a young child counts accurately. That they did well on these experiments supports the view that errors in counting—at least for set sizes up to 20—reflect performance demands and not the absence of implicit knowledge of the counting principles. In the final experiment, where children did the counting themselves, set size did affect their success. So did some variations in conditions, the most difficult of which was the one where children had to count 3-dimensional objects which were under a plexiglass cover. We expected that this condition would interfere with the child's tendency to point and touch objects in order to keep separate items which have been counted from those which have not been counted.     

Miscounting suicides

A review of research on the classification and counting of deaths reveals little hard evidence supporting claims that suicides are seriously underreported in the United States. The literature contains hints that much of what underreporting does occur is counterbalanced by "overcounting" (i.e., erroneous certifications of false suicides). An analysis of detailed cause-of-death mortality data for the United States indicates that the maximum likely undercount possible, using generous assumptions concerning misclassification frequency and leaving aside the issue of overcounts, was about 26% for 1980. The maximum likely net undercount, taking compensating overcounts into account, is estimated to be under 10%.     

Infants recognize counting as numerically relevant

Children do not understand the meanings of count words like “two” and “three” until the preschool years. But even before knowing the meanings of these individual words, might they recognize that counting is “about” the dimension of number? Here in five experiments, we asked whether infants already associate counting with quantities. We measured 14‐ and 18‐month olds’ ability to remember different numbers of hidden objects that either were or were not counted by an experimenter before hiding. As in previous research, we found that infants failed to differentiate four hidden objects from two when the objects were not counted—suggesting an upper limit on the number of individual objects they could represent in working memory. However, infants succeeded when the objects were simply counted aloud before hiding. We found that counting also helped infants differentiate four hidden objects from six (a 2:3 ratio), but not three hidden objects from four (a 3:4 ratio), suggesting that counting helped infants represent the arrays’ approximate cardinalities. Hence counting directs infants’ attention to numerical aspects of the world, showing that they recognize counting as numerically relevant years before acquiring the meanings of number words.     

Units of counting: Developmental changes

Insofar as counting is directed toward a definite quantification goal, only items that qualify as valid instances of what is being quantified should be included in the count. Thus, the choice of what to treat as a unit to be counted depends upon one's quantification goals. The present research examined developmental changes in the way children define units for counting. In the first experiment, children were shown arrays of toy animals and asked to count either the number of families or the number of individuals within a family. In the second and third experiments, the stimuli were objects that came apart into two pieces. Children were shown arrays composed of some intact objects and some objects that were separated into their parts, and they were asked either to count the number of wholes or the number of pieces in the entire array. Virtually all the counts children generated were based on some type of common unit, even if it was only defined by physical discreteness. However, marked age differences emerged in children's adaptation of their counting units to what they were asked to count.     

The role of gesture in children's learning to count.

The role of spontaneous gesture was examined in children's counting and in their assessment of counting accuracy. Eighty-five 2-, 3-, and 4-year-olds counted 6 sets of 2-, 4-, and 6-object arrays. In addition, children assessed the counting accuracy of a puppet whose gestures varied as he counted (i.e., gesture matched the number words, gesture mismatched the number words, no gesture at all). Results showed that the correspondence of children's speech and gesture varied systematically across the age groups and that children adhered to the one-to-one correspondence principle in gesture prior to speech. Moreover, children's correspondence of speech and gesture, adherence to the one-to-one principle in gesture, and assessment of the puppet's counting accuracy were related to children's counting accuracy. Findings are discussed in terms of the role that gesture may play in children's understanding of counting.     

Harmonic and rhythmic influences on musical expectancy

The effects of harmony and rhythm on expectancy formation were studied in two experiments. In both studies, we generated musical passages consisting of a melodic line accompanied by four harmonic (chord) events. These sequences varied in their harmonic content, the rhythmic periodicity of the three context chords prior to the final chord, and the ending time of the final chord itself. In Experiment 1, listeners provided ratings for how well the final chord in a chord sequence fit their expectations for what was to come next; analyses revealed subtle changes in ratings as a function of both harmonic and rhythmic variation. Experiment 2 extended these results; listeners made a speeded reaction time judgment on whether the final chord of a sequence belonged with its set of context chords. Analysis of the reaction time data suggested that harmonic and rhythmic variation also influenced the speed of musical processing. These results are interpreted with reference to current models of music cognition, and they highlight the need for rhythmical weighting factors within the psychological representation of tonal/pitch information.     

Coding position in a sequence by rhythmic grouping

It has been suggested that a perceived rhythmic organization may mediate remembering musical and other stimuli. This experiment examined whether or not Ss could register and remember position in a sequence using rhythmic grouping. Sixteen Ss heard tapped sequences 24–63 beats long, accented to encourage grouping by 4s. Ss tapped responses revealing whether or not they remembered the sequence length-the last tap’s position. Significantly more incorrect responses were off by multiples of 4 beats than by adjacent amounts; these frequent errors of whole rhythmic groups of 4 showed that Ss coded sequence length rhythmically. Ss proved 53% accurate over four response conditions, with individual’s scores ranging from 8% to 87%. It was concluded that Ss could count with rhythmic hierarchies, essentially equivalent to counting with a nonstandard number base, to code sequential position.     

Towards an auditory account of speech rhythm: application of a model of the auditory 'primal sketch' to two multi-language corpora

The world's languages display important differences in their rhythmic organization; most particularly, different languages seem to privilege different phonological units (mora, syllable, or stress foot) as their basic rhythmic unit. There is now considerable evidence that such differences have important consequences for crucial aspects of language acquisition and processing. Several questions remain, however, as to what exactly characterizes the rhythmic differences, how they are manifested at an auditory/acoustic level and how listeners, whether adult native speakers or young infants, process rhythmic information. In this paper it is proposed that the crucial determinant of rhythmic organization is the variability in the auditory prominence of phonetic events. In order to test this auditory prominence hypothesis, an auditory model is run on two multi-language data-sets, the first consisting of matched pairs of English and French sentences, and the second consisting of French, Italian, English and Dutch sentences. The model is based on a theory of the auditory primal sketch, and generates a primitive representation of an acoustic signal (the rhythmogram) which yields a crude segmentation of the speech signal and assigns prominence values to the obtained sequence of events. Its performance is compared with that of several recently proposed phonetic measures of vocalic and consonantal variability.     

Stereotypic explanatory bias: Implicit stereotyping as a predictor of discrimination

Two experiments examined whether a measure of implicit stereotyping based on the tendency to explain Black stereotype-incongruent events more often than Black stereotype-congruent events (Stereotypic Explanatory Bias or SEB) is predictive of behavior toward a partner in an interracial interaction. In Experiment 1 SEB predicted White males’ choice to ask stereotypic questions of a Black female (but not a White male or White female) in an interview. In Experiment 2 the type of explanation (internal or external attribution) made for stereotype-inconsistency was examined. Results showed that White participants who made internal attributions for Black stereotype-incongruent behavior were rated more positively and those who made external attributions were rated more negatively by a Black male confederate. These results point to the potential of implicit stereotyping as an important predictor of behavior in an interracial interaction.     

Negative facial expression captures attention and disrupts performance

In two experiments, participants counted features of schematic faces with positive, negative, or neutral emotional expressions. In Experiment 1 it was found that counting features took longer when they were embedded in negative as opposed to positive faces. Experiment 2 replicated the results of Experiment 1 and also demonstrated that more time was required to count features of negative relative to neutral faces. However, in both experiments, when the faces were inverted to reduce holistic face perception, no differences between neutral, positive, and negative faces were observed, even though the feature information in the inverted faces was the same as in the upright faces. We suggest that, relative to neutral and positive faces, negative faces are particularly effective at capturing attention to the global face level and thereby make it difficult to count the local features of faces.     

Learning and discrimination of audiovisual events in human infants: the hierarchical relation between intersensory temporal synchrony and rhythmic pattern cues

This study examined 4- to 10-month-old infants' perception of audio-visual (A-V) temporal synchrony cues in the presence or absence of rhythmic pattern cues. Experiment 1 established that infants of all ages could successfully discriminate between two different audiovisual rhythmic events. Experiment 2 showed that only 10-month-old infants detected a desynchronization of the auditory and visual components of a rhythmical event. Experiment 3 showed that 4- to 8-month-old infants could detect A-V desynchronization but only when the audiovisual event was nonrhythmic. These results show that initially in development infants attend to the overall temporal structure of rhythmic audiovisual events but that later in development they become capable of perceiving the embedded intersensory temporal synchrony relations as well.     

Response latencies in the yes/no detection task: An assessment of two basic models

Two general forms of model for response latency in the yes no signal detection task are described and their predictions examined in the light of experimental data. One model supposes a latency function along the detection axis and the other supposes that a count is made of multiple observation, Experiment I looks at the auditory detection situation with short observation interval, but the results are generally equixocal, although the latency function model gives a simpler interpretation Other results are then discussed, particularly those of Gescheider et al (1969). and it is concluded that an attempt must be made to replicate the results of Carterette et al (1965) for the extended observation interval detection experiment. This is achieved in Experiment II. and the obtained order of mean latencies is then examined in terms of the models The counting model appears by far the more suitable for this situation.     

Using cardinality to compare quantities: the role of social-cognitive conflict in early numeracy

A key question in early number development is how 4- and 5-year-olds learn the roles that counting and cardinal numbers play when comparing quantities. Children who wrongly used length to identify numerosity were assigned to five experimental groups and trained to judge whether a puppet--who sometimes miscounted--created equivalent sets. Over three training sessions, children who were asked to compare sets after they were counted learned to base their judgments on cardinal numbers when the puppet counted accurately by being given feedback. However, only the groups who were also asked to explain either their own or the experimenter's reasoning made progress in identifying the puppet's miscounts. This ability to recognize the importance of counting accuracy for quantitative comparisons predicted whether children would spontaneously count to compare sets on a post-test. The importance of asking children to identify miscounts is discussed alongside the social factors that influence children's recognition of the relationship between procedural counting, cardinality and relative number.     

Effect of learning on production of duration in variable motor conditions

It has been suggested that increasing proprioceptive feedback and ensuring its consistency from trial to trial favours timing accuracy. The progressive acquisition of a timing performance with isometric and anisometric responses was investigated in conditions of 'inconsistent feedback', with two different methods: counting seconds or not. Subjects gripped the handle of a dynamometer during precisely 5 seconds in 4 randomly distributed conditions: 'Weak' or 'Strong' constant force, 'Slow' or 'Rapid' variable force. A first group produced the durations without counting and a second group counted seconds either mentally or aloud. Learning was examined in 4 successive blocks of trials. Average produced durations did not differ as a function of group, but the variability was reduced when subjects counted seconds. In both groups, the constant force conditions induced more accurate responses than the variable force conditions in the first block of trials. 'Slow' and 'Rapid' conditions were respectively associated with overestimation and under-estimation of response duration. These trends diminished progressively with learning. Both groups yielded sequential effects linked to duration and independent of condition. These data suggest that, whether subjects counted or not, learning was not based on condition-specific proprioceptive feedback. It may involve the elaboration of an internal temporal reference common to all conditions.     

The formation of rhythmic categories and metric priming

Two experiments on categorical rhythm perception are reported, the object of which was to investigate how listeners perceive discrete rhythmic categories while listening to rhythms performed on a continuous time scale. This is studied by considering the space of all temporal patterns (all possible rhythms made up of three intervals) and how they, in perception, are partitioned into categories, ie where the boundaries of these categories are located. This process of categorisation is formalised as the mapping from the continuous space of a series of time intervals to a discrete, symbolic domain of integer-ratio sequences. The methodological framework uses concepts from mathematics and psychology (eg convexity and entropy) that allow precise characterisations of the empirical results. In the first experiment, twenty-nine participants performed an identification task with 66 rhythmic stimuli (a systematic sampling of the performance space). The results show that listeners do not just perceive the time intervals between onsets of sounds as placed in a homogeneous continuum. Instead, they can reliably identify rhythmic categories, as a chronotopic time clumping map reveals. In a second experiment, the effect of metric priming was studied by presenting the same stimuli but preceded with a duple or triple metre subdivision. It is shown that presenting patterns in the context of a metre has a large effect on rhythmic categorisation: the presence of a specific musical metre primes the perception of specific rhythmic patterns.     

Perceptual selectivity is task dependent: The pop-out effect poops out

An attempt was made to determine why evidence for perceptual selectivity based on conceptual category (e.g., digits vs. letters) has been found in some experiments but not in others. Experiments using the partial-report paradigm find no partial-report superiority when the report is cued by category, whereas, in recent visual search studies, evidence for perceptual selectivity has been obtained for arrays containing a single item that was categorically different from the other items (e.g., a digit among letters). Using a search task, Experiment 1 investigated the possibility that the number of categorically different items in the arrays could be a determinant of selectivity. One, two, or three digits and a variable number of letters were presented on each trial, and subjects determined if a particular digit was present. No evidence of selectivity was obtained, even for the one-digit condition. Experiment 2 verified this result, and Experiment 3 extended the failure of selectivity to a search task in which the possible targets differed in color from the distractor items. In Experiment 4, subjects counted the number of digits or red letters in arrays in which black letters were the distractor items. The counting task was used to eliminate the requirement in our previous tasks that the subjects search forspecific items. Evidence was obtained in the counting task for selectivity based on the color difference but not on the categorical difference. The color stimuli used in the counting task were essentially the same as those that did not yield any evidence of selectivity in the search task. The results suggest that task demands are an important determinant of whether or not perceptual selectivity will occur.     

How infants process addition and subtraction events

Three experiments are described that assess 5‐month‐old infants’ processing of addition and subtraction events similar to those reported by Wynn (1992a ). In Experiment 1, prior to each test trial, one group of infants was shown an addition event (1 + 1) while another group was shown a subtraction event (2 ? 1). On test trials, all infants were shown outcomes of 0, 1, 2 and 3. The results seemed to require one of two dual‐process models. One such model assumed that the infants could add and subtract but also had a tendency to look longer when more items were on the stage. The other model assumed that infants had a preference for familiarity along with the tendency to look longer when more items were on the stage. Experiments 2 and 3 examined the assumptions made by these two models. In Experiment 2, infants were given only the test trials they had received in Experiment 1. Thus, no addition and subtraction or familiarity was involved. In Experiment 3 infants were familiarized to either one or two items prior to each test trial, but experienced no actual addition or subtraction. The results of these two experiments support the familiarity plus more items to look at model more than the addition and subtraction plus more items to look at model. Taken together, these three experiments shed doubt on Wynn’s (1992a ) assertion that 5‐month‐old infants can add and subtract. Instead they indicate the importance of familiarity preferences and the fact that one should be cautious before assuming that young infants have sophisticated numerical abilities.