Early development of spatial‐numeric associations: evidence from spatial and quantitative performance of preschoolers

Numeric magnitudes often bias adults’ spatial performance. Partly because the direction of this bias (left‐to‐right versus right‐to‐left) is culture‐specific, it has been assumed that the orientation of spatial‐numeric associations is a late development, tied to reading practice or schooling. Challenging this assumption, we found that preschoolers expected numbers to be ordered from left‐to‐right when they searched for objects in numbered containers, when they counted, and (to a lesser extent) when they added and subtracted. Further, preschoolers who lacked these biases demonstrated more immature, logarithmic representations of numeric value than preschoolers who exhibited the directional bias, suggesting that spatial‐numeric associations aid magnitude representations for symbols denoting increasingly large numbers.     

Tactual and visual alphanumeric suffix effects

Two experiments tested the effects of suffixes on the recall of tactual and visual sequences of alphabetic characters presented at 19 letters per min. Scoring techniques allowed for the differentiation of losses of item and order information. In Experiment I performance decrements were found for both modalities, which were mainly caused by item loss at the more recent part of the serial position curve in the suffix conditions. In Experiment II, these effects were replicated and a non-alphabetic suffix led to greater decrements for both modalities than an alphabetical suffix. While a suffix effect based on the loss of item information is consistent with a sensory trace interpretation of the suffix effect, the presence of a visual suffix effect with slow stimulus presentation is not. Additionally, the greater effect of the non-alphanumeric suffix challenges attentional interpretations. Some possible explanations are proposed.     

The effects of articulatory suppression on reading ideographic and alphabetic numbers

The present experiments investigated the effects of articulatory suppression on reading numbers written alphabetically (one, two, etc.) or as Arabic numerals (1, 2, etc.). For alphabetic numbers, but not for numerals, a phonological representation can be generated and used for lexical access. If such phonological encoding occurs, and if it is harmed by irrelevant articulatory activity, then articulatory suppression should have a greater effect on the reading of alphabetic than on numeral representations of numbers. In contrast to a finding reported by Baron (1977), involving alphabetic and Roman numerals, in two experiments suppression was found to have essentially equivalent effects on the reading of both types of numbers. A third experiment explored a possible explanation for these discrepant findings. It is concluded that although alphabetic and numeral representations of numbers may be processed differently there is no evidence to support the idea that reading alphabetic numbers involves phonological encoding prior to lexical access.     

The spatial representation of numerical and non-numerical ordered sequences: Insights from a random generation task

It is widely believed that numbers are spatially represented from left to right on the mental number line. Whether this spatial format of representation is specific to numbers or is shared by non-numerical ordered sequences remains controversial. When healthy participants are asked to randomly generate digits they show a systematic small-number bias that has been interpreted in terms of “pseudoneglect in number space”. Here we used a random generation task to compare numerical and non-numerical order. Participants performed the task at three different pacing rates and with three types of stimuli (numbers, letters, and months). In addition to a small-number bias for numbers, we observed a bias towards “early” items for letters and no bias for months. The spatial biases for numbers and letters were rate independent and similar in size, but they did not correlate across participants. Moreover, letter generation was qualified by a systematic forward direction along the sequence, suggesting that the ordinal dimension was more salient for letters than for numbers in a task that did not require its explicit processing. The dissociation between numerical and non-numerical orders is consistent with electrophysiological and neuroimaging studies and suggests that they rely on at least partially different mechanisms.     

From algorithmic computing to direct retrieval: Evidence from number and alphabetic arithmetic in children and adults

A number of theories of mental arithmetic suggest that the ability to solve simple addition and subtraction problems develops from an algorithmic strategy toward a strategy based on the direct retrieval of the result from memory. In the experiment presented here, 2nd and 12th graders were asked to solve two tasks of number and alphabet arithmetic. The subjects transformed series of 1 to 4 numbers or letters (item span) by adding or subtracting an operand varying from 1 to 4 (operation span). Although both the item and operation span were associated with major and identical effects in the case of both numbers and letters at 2nd grade, such effects were clearly observable only in the case of letters for the adult subjects. This suggests the use of an algorithmic strategy for both types of material in the case of the children and for the letters only in the case of the adults, who retrieved numerical results directly from memory.     

Memory representation of alphabetic position and interval information.

The authors conducted 3 sets of experiments. In the 1st set of experiments, participants made alphabetic position estimations. In the 2nd set, participants made interletter distance estimations. In the 3rd set, they made comparative judgments of the alphabetic order of a pair of letters. The results showed that participants had highly accurate ordinal level information about the alphabet in memory but that interval level information was systematically distorted. In addition, alphabetic serial information was found to be used in 2 distinct modes in memory, depending on whether the representation could be contained within the span of immediate memory.     

Cambridge University versus Hebrew University: The impact of letter transposition on reading English and Hebrew

Is reading similarly affected by letter transposition in all alphabetic orthographies? “The Cambridge University effect,” demonstrating that jumbled letters have little effect on reading, was examined using rapid serial visual presentation (RSVP) in English and in Hebrew. Hebrew-English bilinguals were presented sentences in both languages containing words with transposed letters. Sentences were presented rapidly on the screen word by word, and participants had to reproduce the sequence of words perceived. We found a marked difference in the effect of transpositions in the two languages. In English, transpositions had little effect on performance, whereas in Hebrew, performance deteriorated dramatically for words with transposed letters. The differential effects of transposition are accounted for by the difference in lexical organization in Hebrew and in English, suggesting that models of reading in alphabetic orthographies may be language specific.     

Contraction bias in memorial quantifying judgment: does it come from a stable compressed memory representation or a dynamic adaptation process?

A common response bias in psychophysical judgments is regression toward the mean (overestimation of small and underestimation of large values, or the response contraction bias). The same bias is observed in magnitude estimation from memorized quantities. Participants estimated alphabetic interval distances between 2 letters for different levels of interletter distances. The underestimated and overestimated values and the point of least error changed, depending on the level of alphabetic distances judged; furthermore, their estimation showed a progressively increasing tendency toward the mean, rendering the estimation progressively less accurate as the estimation task was repeated. We conclude that the regression toward the mean in memorial quantifying judgment derives from a cognitive adaptation process rather than from a permanent, compressed memory representation of the stimuli. Two opposing views on the adaptive meaning of this judgment bias are discussed.     

Developmental changes in free recall: The interaction of task structure and age

Free-recall learning and organization were measured for 3rd, 7th, and 11th graders under conditions which varied the type and amount of task structure. Task structure for the input or list-presentation phase was manipulated by using a random, constant, or alphabetic item sequence across trials. Task structure for the output or recall phase was manipulated by providing standard instructions or instructions which suggested the possible use of an alphabetic ordering scheme. Recall performance and organization showed an interaction between age and both manipulations of task structure. The 3rd graders required the maximal amount of task structure (alphabetic order with alphabetic instructions) to demonstrate recall facilitation relative to the completely unstructured control condition. The 7th graders showed recall facilitation for intermediate and high levels of task structure, and the 11th graders showed recall facilitation for low, intermediate, and high levels of task structure. The results are related to current hypotheses about developmental changes in recall performance and their relationship to changes in the systematic use of organizational strategies.     

Is “Σ” purple or green? Bistable grapheme-color synesthesia induced by ambiguous characters

People with grapheme-color synesthesia perceive specific colors when viewing different letters or numbers. Previous studies have suggested that synesthetic color experience can be bistable when induced by an ambiguous character. However, the exact relationship between processes underlying the identity of an alphanumeric character and the experience of the induced synesthetic color has not been examined. In the present study, we explored this by focusing on the temporal relation of inducer identification and color emergence using inducers whose identity could be rendered ambiguous upon rotation of the characters. Specifically, achromatic alphabetic letters (W/M) and digits (6/9) were presented at varying angles to 9 grapheme-color synesthetes. Results showed that grapheme identification and synesthetically perceived grapheme color covary with the orientation of the test stimulus and that synesthetes were slower naming the experienced color than identifying the character, particularly at intermediate angles where ambiguity was greatest.     

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.     

Facilitating Effect of Multisensory Letter Encoding on Reading and Spelling in 5‐Year‐Old Children

This study aims at identifying the effect of training in the acquisition of the alphabetic principle in 5‐year‐old children. We compared the effect of multisensory training of letters in visual, haptic, graphomotor, visuo‐haptic, and visuo‐graphomotor groups. For each training type, we contrasted trained versus untrained letters in reading and spelling tasks. First, visuo‐haptic and visuo‐graphomotor training improved letter‐sound correspondence acquisition scores more than the other types of training, and this improvement persisted in the second post‐test. A cross‐modal transfer was revealed by the fact that scores increased after blindfold haptic and graphomotor experiences. Moreover, performance on untrained letters also improved, suggesting an indirect effect following the specific trained letters training. The results argue in favor of a facilitating effect of multisensory encoding on acquisition of the alphabetic principle. Practical implications for the prevention of future reading difficulties are discussed. Copyright © 2015 John Wiley & Sons, Ltd.     

An analysis of confusion errors in naming letters under speed stress

Three subjects named six visually presented letters under two levels of speed stress. The obtained confusion matrices for each stress condition were fit by Luce’s choice theory, which provided measures of stimulus similarity and response bias. Speed stress produced proportional increases in pairwise similarity measures but had no systematic effect on response biases. In Experiment 2, the same three subjects named the same letters under two levels of stimulus quality and a constant response-time deadline. As with speed stress, degrading the stimulus produced proportional increases in pairwise similarity measures but had no systematic effect on response biases. In Experiment 3, two of the subjects participating in Experiments 1 and 2 named the six letters under conditions where the probabilities of the letters were unequal. The letters toward which the subject had been most biased in Experiments 1 and 2 were assigned low probabilities, and the letters toward which he was least biased were assigned high probabilities. The result of this manipulation was to completely reverse the ordering of the response bias parameters of the Luce choice model. It is suggested that the present methodology provides a means of validating as psychological constructs the parameters of various mathematical models of stimulus recognition.     

Locus of selectivity in a visual memory task using a color value indicator

Selection of high vs low valued letters from a briefly presented visual array was investigated. An indicator specifying the value of letters occurred before or after the array. Selection could occur during input to memory or during output from memory in the before condition, but only at output in the after condition. Previous research using an alphabetic instruction, which required letter identification prior to selection, attributed selection to output. A color instruction in the -present experiment, not requiring letter identification, showed the locus of selection to be at input. Experiment 2 replicated these findings and used an interference technique to add further support. In addition, contrary to previous findings, these results indicated that the selection process caused no deficit in overall recall.     

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.     

Effect of consonant/vowel letter organisation on the syllable counting task: evidence from English

Recent studies in alphabetic writing systems have investigated whether the status of letters as consonants or vowels influences the perception and processing of written words. Here, we examined to what extent the organisation of consonants and vowels within words affects performance in a syllable counting task in English. Participants were asked to judge the number of syllables in written words that were matched for the number of spoken syllables but comprised either 1 orthographic vowel cluster less than the number of syllables (hiatus words, e.g., triumph) or as many vowel clusters as syllables (e.g., pudding). In 3 experiments, we found that readers were slower and less accurate on hiatus than control words, even when phonological complexity (Experiment 1), number of reduced vowels (Experiment 2), and number of letters (Experiment 3) were taken into account. Interestingly, for words with or without the same number of vowel clusters and syllables, participants’ errors were more likely to underestimate the number of syllables than to overestimate it. Results are discussed in a cross-linguistic perspective.