Single-digit and two-digit Arabic numerals address the same semantic number line.

Many theories about human number representation stress the importance of a central semantic representation that includes the magnitude information of small integer numbers, and that is conceived as an abstract, compressed number line. However, thus far there has been little or no direct evidence that units and teens are represented on the same number line. In two masked priming experiments, we show that single-digit and two-digit Arabic numerals are equally well primed by an Arabic numeral with the same number of digits as by an equally distant Arabic numeral with a different number of digits (e.g. the priming effect of 7 on the target 9 is the same as the priming effect of 11 on the target 9). The finding was obtained both with a number naming task and with a parity judgement task. This is in line with the hypothesis that units and teens are part of a continuous number line.     

Extracting parity and magnitude from Arabic numerals: developmental changes in number processing and mental representation.

Children from Grades 2, 3, 4, 6, and 8 (7.8, 9.2, 9.8, 11.7, and 13. 6 years old, respectively) made speeded, bimanual parity (odd/even) judgments of the Arabic numerals 0-9. Analysis of response times indicated that from fourth grade on, parity information is retrieved directly from memory rather than being extracted by means of a mental calculation strategy. As early as Grade 3, children exhibited the SNARC (Spatial-Numerical Association of Response Codes) effect, where small numbers were responded to faster with the left hand than with the right hand, while the converse held true for large numbers. This finding, previously demonstrated only in adults, confirms that (a) children represent magnitude information in the form of a left-to-right oriented mental number line, and (b) this information is accessed obligatorily even when irrelevant. Finally, although the SNARC effect remained strong at Grade 4, it was attenuated at Grades 6 and 8 by a linguistic effect based on associations between the unmarked adjectives "even" and "right" and between the marked adjectives "odd" and "left." Copyright 1999 Academic Press.     

The development of internal representations of magnitude and their association with Arabic numerals.

Developmental aspects of number concepts were evaluated using participants from the beginning and end of first grade (6-7 years old), third and fifth grades (7-11 years old), and university (22 years old). Participants evaluated the numerical value or physical size of stimuli varying along both dimensions. The numerical distance effect appeared in all groups. In contrast, the size congruity effect started to appear only at the end of first grade. Based on our results, a model of internal representation of magnitude claiming that there are two different representations was propose. At the beginning of first grade children can automatically access only one of these representations and only from the end of first grade can they access both of these representations.     

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.     

Syntactical knowledge in a case of agrammatism: Evidence from transcoding Roman and Arabic numerals

The ability of an aphasic subject with agrammatism in both comprehension and production to transcribe quantities from Roman numerals to Arabic and the reverse was investigated. Systematic errors in the transcoding processes were observed that could not be accounted for by the peculiarities of the two ideographic coding systems or by difficulties with direct transcoding rules. The results are discussed in the framework of the current debate on preserved/impaired hierarchical syntactical knowledge of agrammatic subjects. The findings paralleled the results of previous studies on the transcoding skills of agrammatics from/to alphabetic numerals to/from digital forms. In the case of this particular patient, it is therefore tentatively concluded in favor of preserved syntactical knowledge.     

Operator and operand preview effects in simple addition and multiplication: A comparison of Canadian and Chinese adults

Using an arithmetic-based retrieval-induced forgetting (RIF) paradigm, researchers have found evidence that participants with very high arithmetic proficiency (Chinese adults), but not less-skilled participants (Canadian adults), solved some simple additions (e.g. 3 + 2) using fast procedural skills. Here we sought converging evidence for this using the operator-priming paradigm. Previous research testing simple addition and multiplication found that a 150-ms preview of the operator (+ or ×) facilitated only addition performance. This was taken as evidence that addition, but not multiplication, was solved by procedural algorithms that could be primed by presentation of the plus sign. In the present study, Chinese and Canadian adults (N = 144) were tested in the operator-priming paradigm but, in contrast to the RIF results, there was little evidence that operator-priming effects differed between the groups and robust operator priming was observed in both addition and multiplication. Thus, the operator preview results did not reinforce the results of previous research but the experiment revealed robust group differences in operand preview effects: For the Chinese, but not the Canadians, a preview of the numerical operands produced much greater facilitation for multiplication than addition. The fact that CN obtained a mean 103-ms gain for multiplication from the 150-ms preview of the operands strongly suggests that multiplication was their default operation in this paradigm. This result adds a potentially important new phenomenon to the behavioural distinctions between Chinese and North American adults' arithmetic skills.     

Children's and adults' reading of nonwords: effects of regularity and consistency.

The procedures used by novice readers to assemble pronunciations for nonwords were investigated. Children in Grades 1-3 read aloud consonant-vowel-consonant and longer monosyllabic nonwords. By the end of Grade 1, children displayed a good grasp of grapheme-phoneme (G-P) correspondences (e.g., ai, ow). Grade 2 and 3 readers increasingly used larger orthographic correspondences termed rimes (e.g., -ook, -ild). However, G-P correspondences determined most responses. Adults likewise used G-P rules when reading aloud nonwords and were more accurate at applying the rules. The strong reliance of Grade 1 and 2 readers on G-P rules was also demonstrated by their superior oral reading of regular words along with a tendency to regularize exception words (e.g., reading bull to rhyme with dull).     

Cognitive addition and multiplication: Evidence for a single memory network

In an experiment using verification task procedures, 100 subjects responded to simple and complex problems of addition and multiplication. Identical structural parameters were found to model reaction time accurately to both addition and multiplication problems. Slope estimates for a memory network parameter did not differ significantly between simple and complex problems within an operation or between addition and multiplication problems. Both complex addition and complex multiplication problems were processed columnwise, with column sums or products being retrieved from an interrated memory network. The two types of complex problems included similar processes for carrying and for encoding of single digits, and both were self-terminated when an error in the units column was encountered. Addition and multiplication facts appear to be retrieved from a single interrelated memory network. A conceptual model for this interrelated network is discussed.     

Ambivalence and defense: effects of a repressive style on normal adolescents' and young adults' mixed feelings.

Ambivalence has been associated in theoretical works with psychopathology and with defenses against conflict. Ambivalence was operationalized as mixed feelings. Seventy-five 9th graders (27 boys and 48 girls), 50 12th graders (19 men and 31 women), and 80 Yale University undergraduates (38 men and 42 women) completed questionnaires assessing ambivalence, psychopathological symptoms, and repressive and nonrepressive styles. Compared with nonrepressive subjects, repressive subjects at all grade levels reported lower levels of mixed feelings and relatively less uncertainty about their feelings. Whereas the absence of felt anxiety was sufficient for lower self-reported psychopathological symptoms, a repressive style was necessary for lower self-reported ambivalence.     

Hearing loss and perceptual effort: Downstream effects on older adults' memory for speech

A group of older adults with good hearing and a group with mild-to-moderate hearing loss were tested for recall of the final three words heard in a running memory task. Near perfect recall of the final words of the three-word sets by both good- and poor-hearing participants allowed the inference that all three words had been correctly identified. Nevertheless, the poor-hearing group recalled significantly fewer of the nonfinal words than did the better hearing group. This was true even though both groups were matched for age, education, and verbal ability. Results were taken as support for an effortfulness hypothesis: the notion that the extra effort that a hearing-impaired listener must expend to achieve perceptual success comes at the cost of processing resources that might otherwise be available for encoding the speech content in memory.     

Children's and adults' parafoveal processes in German: Phonological and orthographic effects

Phonological and orthographic information has been shown to play an important role in parafoveal processing in skilled adult reading in English. In the present study, we investigated whether similar parafoveal effects can be found in children using the boundary eye tracking method. Children and adults read sentences in German with embedded target nouns which were presented in original, pseudohomophone (PsH), transposed-letter (TL), lower-case and control conditions to assess phonological and orthographic preview effects. We found evidence of PsH preview benefit effects for children. We also found TL preview benefit effects for adults, while children only showed these effects under specific conditions. Results are consistent with the developmental view that reading initially depends on phonological processes and that orthographic processes become increasingly important.     

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.     

Attention and the acquisition of new knowledge: their effects on older adults' associative memory deficit

Older adults experience a selective associative memory deficit by demonstrating intact item memory relative to impaired associative memory when compared with younger adults. Age-related deficits in associative memory have been suggested to arise from declines in attentional resources, and the role of attention during encoding and retrieval in associative memory for words and their spatial locations was investigated in the current experiment. Additionally, the tendency of younger and older adults to use knowledge acquired during encoding to improve their associative memory judgments through a strategic associative memory process was also investigated. Younger and older adults studied a list of words with each word belonging to one of four categories, which followed one of four mathematical probability structures for their presentation. Older adults exhibited intact item memory and impaired associative memory relative to full attention younger adults. In addition, both older and younger adults demonstrated an ability to engage in strategic associative memory, by learning and later using the probability structure introduced at study to guide their associative memory judgments. In contrast, dividing the attention of younger adults during encoding impaired item memory, associative memory and strategic associative memory, whereas dividing attention at retrieval did not result in similar deficits. These data add to a growing body of literature demonstrating older adults to exhibit a selective associative memory deficit that is not simulated by dividing the attention of younger adults at encoding or retrieval. Furthermore, younger and older adults maintain the ability to use new knowledge to guide their associative judgments.     

Older adults' decoding of emotions: role of dynamic versus static cues and age-related cognitive decline

Although age-related deficits in emotion recognition have been widely explored, the nature and scope of these deficits remain poorly understood. We conducted two experiments to examine whether these deficits are less pronounced when older adults evaluate dynamic compared with static images, and second, whether age-related cognitive decline exacerbates these deficits. Our results suggest that age-related cognitive decline exacerbates older adults' deficits in detecting anger, but only from static faces. Furthermore, older adults do not show emotion recognition deficits when evaluating global emotions from dynamic images of faces.     

The effects of pure pair repetition on younger and older adults' associative memory

Although aging causes relatively minor impairment in recognition memory for components, older adults' ability to remember associations between components is typically significantly compromised, relative to that of younger adults. This pattern could be associated with older adults' relatively intact familiarity, which helps preserve component memory, coupled with a marked decline in recollection, which leads to a decline in associative memory. The purpose of the current study is to explore possible methods that allow older adults to rely on pair familiarity in order to improve their associative memory performance. Participants in 2 experiments were repeatedly presented with either single items or pairings of items prior to a study list so that the items and the pairs were already familiar during the study phase. Pure pair repetition (the effects of pair repetition after the effects of item repetition are taken into account) increased associative memory for older and younger adults. Findings based on remember and know judgments suggest that familiarity but not recollection is involved in mediating the repetition effect.     

Sign- versus goal-tracking: effects of conditioned-stimulus-to-unconditioned-stimulus distance.

Three pigeons were exposed sequentially across experimental phases to five different distances between the conditioned stimulus and the site of the unconditioned stimulus in a sign-/goal-tracking procedure. A computer-controlled tracking system provided a continuous record of the bird's position by continuously monitoring the location of the bird's head in three-dimensional space. It was found that birds sign-tracked (i.e., approached the conditioned stimulus) when the conditioned stimulus was closest to the site of the unconditioned stimulus, goal-tracked (i.e., approached the site of the unconditioned stimulus in the presence of the conditioned stimulus) when the conditioned stimulus was farthest from the site of the unconditioned stimulus, and engaged in both sign- and goal-tracking (or something intermediate) at intermediate conditioned-stimulus-to-unconditioned-stimulus distances. When both sign- and goal-tracking occurred, the former tended to occur in the first half and the latter in the second half of the interval in which the conditioned stimulus was present. The results suggest (a) whether sign- or goal-tracking (or both) occurs is a function of the distance of the conditioned stimulus from the site of the unconditioned stimulus, (b) the fact that pigeons but not rats have been found to sign-track consistently throughout the duration of the conditioned stimulus may be due to quantitatively rather than qualitatively different effects of conditioned-stimulus-to-unconditioned-stimulus distance across species (i.e., a "short" conditioned-stimulus-to-unconditioned-stimulus distance for a pigeon may be a "long" one for a rat), and (c) sign- and goal-tracking may be competing behavioral tendencies that can (e.g., at intermediate conditioned-stimulus-to-unconditioned-stimulus distances) cancel each other out. The findings lend support to theories that specify an interaction between phylogenetic and reinforcement variables in determining whether sign- or goal-tracking will occur in any given experimental preparation.     

Semantic processing of Arabic,Kanji, and Kana numbers: Evidence from interference in physical and numerical size judgments

Two experiments were conducted with the following objectives (1) to replicate the finding of similar semantic representation of Arabic and written-word (Kanji and Kana) numbers with a direct numerical task, (2) to investigate the automatic semantic processing of Arabic and written-word numbers, and (3) to verify whether the assumption of a common semantic representation is valid in an indirect numerical task. Subjects were asked to judge which of two numbers (e.g, 6-8) was larger either in its numerical size (Experiment 1) or in its physical size (Experiment 2) using the three notations. Effects of two factors were analyzed: the congruity between numerical and physical size and the numerical distance. The effects of these factors were very similar across the three notations in Experiment 1, but were drastically different in Experiment 2. The results of Experiment 2 demonstrated the nonsemantic processing of Kana numbers, and suggest that there may be separate semantic representations for Arabic and Kanji numbers.     

Children and adults' distance estimations in a large-scale environment: effects of time and clutter

In two experiments adults (mean age = 19-5), sixth graders (mean age = 11-8), fourth graders (mean age = 9-8), and second graders (mean age = 7-8) walked a straight line distance through a large-scale environment. Subjects were then asked to estimate the time taken to traverse each half of the walk and to estimate the distance between objects seen along the walk. In Experiment 1 each half of the walk was traversed in the same amount of time but contained a different number of objects (clutter). Time and distance estimates were related, but were not affected by the number of intervening objects encountered between locations. In Experiment 2 subjects again encountered a different number of objects along each half of the walk but each half was traversed in varying amounts of time. Again, time and distance estimates were related, and there was no clutter effect. There were no consistent developmental differences across the two experiments. It was concluded that (1) Thorndyke's clutter effect does not occur across all types of spatial cognition tasks, and (2) children and adults tend to relate time and distance across a variety of distance estimation tasks.