Rapid proportion comparison with spatial arrays of frequently used meaningful visual symbols

It has been shown that when two arrays of Arabic numerals were briefly presented, observers could accurately indicate which array contained the larger number of a target numeral. This study investigated whether this rapid proportion comparison can be extended to other meaningful symbols that share some of notable properties of Arabic numerals. We tested mainly several Japanese Kanji letters, each of which represents a meaning and can work as a word. Using physically identical stimulus sets that could be interpreted as different types of letters, Experiment 1 first confirmed the rapid proportion comparison with Arabic numerals for Japanese participants. Experiment 2 showed that the rapid proportion comparison can be extended to Kanji numerals. Experiment 3 successfully demonstrated that rapid proportion judgments can be found with non-quantitative Kanji letters that are used frequently. Experiment 4 further demonstrated the rapid proportion comparison with frequently used meaningful non-letter symbols (gender icons). The rapid processing cannot be attributed to fluent processing of familiar items, because it was not found with familiar phonograms (Japanese Kana letters). These findings suggest that the rapid proportion comparison can be commonly found with frequently used meaningful symbols, even though their meaning is not relevant to the task.     

Verbal interference with perceptual classification: The effect of semantic structure

In a task of the same form as the standard Stroop test, the relevant attribute was ellipse size and the required responses were the numbers 1 through 6 assigned to each of the ellipses in order of increasing size. The irrelevant attribute consisted of either alphabet letters or the numerical symbols 1 through 6 displayed in the center of each ellipse. The numerals produced more interference with the classification of the relevant attribute than the alphabet letters, supporting Klein’s (1964) results. In addition, the interference due to the irrelevant numerical symbols increased as the distance between the values of the relevant and irrelevant attributes was decreased. Since “distance” is a structural property of the number system, this indicated that the competing response tendencies aroused by the irrelevant numericals involved the semantic structure for numbers. The same results were obtained when numerical quantity, rather than ellipse size, was the relevant attribute.     

Letter position dyslexia in Arabic: from form to position

This study reports the reading of 11 Arabic-speaking individuals with letter position dyslexia (LPD), and the effect of letter form on their reading errors. LPD is a peripheral dyslexia caused by a selective deficit to letter position encoding in the orthographic-visual analyzer, which results in migration of letters within words, primarily of middle letters. The Arabic orthography is especially interesting for the study of LPD because Arabic letters have different forms in different positions in the word. As a result, some letter position errors require letter form change. We compared the rate of letter migrations that change letter form with migrations that do not change letter form in 10 Arabic-speaking individuals with developmental LPD, and one bilingual Arabic and Hebrew-speaking individual with acquired LPD. The results indicated that the participants made 40% letter position errors in migratable words when the resulting word included the letters in the same form, whereas migrations that changed letter form almost never occurred. The error rate of the Arabic-Hebrew bilingual reader was smaller in Arabic than in Hebrew. However, when only words in which migrations do not change letter form were counted, the rate was similar in Arabic and Hebrew. Hence, whereas orthographies with multiple letter forms for each letter might seem more difficult in some respects, these orthographies are in fact easier to read in some forms of dyslexia. Thus, the diagnosis of LPD in Arabic should consider the effect of letter forms on migration errors, and use only migratable words that do not require letter-form change. The theoretical implications for the reading model are that letter form (of the position-dependent type found in Arabic) is part of the information encoded in the abstract letter identity, and thus affects further word recognition processes, and that there might be a pre-lexical graphemic buffer in which the checking of orthographic well-formedness takes place.     

The role of Hebrew letter names in early literacy: the case of multiphonemic acrophonic names

English-speaking children spell letters correctly more often when the letters' names are heard in the word (e.g., B in beach vs. bone). Hebrew letter names have been claimed to be less useful in this regard. In Study 1, kindergartners were asked to report and spell initial and final letters in Hebrew words that included full (CVC), partial (CV), and phonemic (C) cues derived from these letter names (e.g., kaftor, kartis, kibepsilonl, spelled with /kaf/). Correct and biased responses increased with length of congruent and incongruent cues, respectively. In Study 2, preschoolers and kindergartners were asked to report initial letters with monosyllabic or disyllabic names (e.g., /kaf/ or /samepsilonx/, respectively) that included the cues described above. Correct responses increased with cue length; the effect was stronger with monosyllabic letter names than with disyllabic letter names, probably because the cue covered a larger ratio of the letter name. Phonological awareness was linked to use of letter names.     

Response-retrieval and negative priming

The existence of across-notation automatic numerical processing of two-digit (2D) numbers was explored using size comparisons tasks. Participants were Arabic speakers, who use two sets of numerical symbols—Arabic and Indian. They were presented with pairs of 2D numbers in the same or in mixed notations. Responses for a numerical comparison task were affected by decade difference and unit-decade compatibility and global distance in both conditions, extending previous findings with Arabic digits (Nuerk, Weger, & Willmes, 2001). Responses for a physical comparison task were affected by congruency with the numerical size, as indicated by the size congruency effect (SiCE). The SiCE was affected by unit-decade compatibility but not by global distance, thus suggesting that the units and decades digits of the 2D numbers, but not the whole number value were automatically translated into a common representation of magnitude. The presence of similar results for same- and mixed-notation pairs supports the idea of an abstract representation of magnitude.     

Number processing of Arabic and Hebrew bilinguals: Evidence supporting the distance effect

In the current study, a direct assessment of the effect of language lexical‐syntactic structure and magnitude semantic access on numerical processing was made by contrasting the performance of Arabic/Hebrew bilinguals in a digital (Hindi‐digits/Arabic‐digits) and verbal numerical comparison task (Arabic, an inverted language: Units‐Decades, Hebrew, a non‐inverted language: Decades‐Units). Our data revealed in the digital presentation format (Experiment 1) a regular distance effect in Arabic language‐Hindi digits and Hebrew language‐Arabic digits, characterized by an inverse relation between reaction times and numerical distance with no difference in the mean reaction times of participants in Arabic‐L1 and Hebrew‐L2. This indicates that both lexical digits of two‐digit numbers in L1 and L2 are similarly processed and semantically accessed. However in the verbal presentation format (Experiment 2) a similar pattern of distance effect was found, but the mean reaction times in Arabic were lower than in Hebrew in each numerical distance. This indicates that the processing of two‐digit number words in L1 and L2 is semantically accessed and determined by the syntactic structure of each language.     

The involvement of letter names in the silent processing of isolated letters: A developmental perspective

This study was designed to clarify the nature of the mental representations underlying the processing of letters. A total of 96 Hebrew readers randomly recruited from three levels of education were asked to make rapid same/different judgments for Hebrew letter dyads with monosyllabic and bisyllabic names. The results obtained from the performance of participants under perceptual and conceptual processing conditions suggest that Hebrew readers access nominal letter representations in order to mediate letter processing in tasks that cannot be resolved on the basis of a sheer perceptual analysis of the letters?? visual properties. The finding that the retrieval of nominal letter representations was evident for participants who differed rather markedly in their letter-processing speeds highlights the central role of letter names in the processing of isolated letters.     

Learning of letter names follows similar principles across languages: Evidence from Hebrew

Letter names play an important role in early literacy. Previous studies of letter name learning have examined the Latin alphabet. The current study tested learners of Hebrew, comparing their patterns of performance and types of errors with those of English learners. We analyzed letter-naming data from 645 Israeli children who had not begun formal reading instruction: a younger group (mean age 5 years 2 months) and an older group (mean age 6 years 2 months). Children's errors often involved letters with similar shapes or letters adjacent to one another in the alphabet. Most Hebrew letter names are not very similar to one another phonologically, and there were fewer phonologically based confusions than in English. We found both general frequency effects and frequency effects that reflected the letters in individual children's names. On average, girls knew more letter names than did boys. The results suggest that letter name learning follows similar principles across languages.     

Orthographic structure versus morphological structure: principles of lexical organization in a given language

Most models of visual word recognition in alphabetic orthographies assume that words are lexically organized according to orthographic similarity. Support for this is provided by form-priming experiments that demonstrate robust facilitation when primes and targets share similar sequences of letters. The authors examined form-orthographic priming effects in Hebrew, Arabic, and English. Hebrew and Arabic have an alphabetic writing system but a Semitic morphological structure. Hebrew morphemic units are composed of noncontiguous phonemic (and letter) sequences in a given word. Results demonstrate that form-priming effects in Hebrew or Arabic are unreliable, whereas morphological priming effects with minimal letter overlap are robust. Hebrew bilingual subjects, by contrast, showed robust form-priming effects with English material, suggesting that Semitic words are lexically organized by morphological rather than orthographic principles. The authors conclude that morphology can constrain lexical organization even in alphabetic orthographies and that visual processing of words is first determined by morphological characteristics.     

The development of automaticity in accessing number magnitude

This study traces developmental changes in automatic and intentional processing of Arabic numerals using a numerical-Stroop paradigm. In Study 1, university students compared the numerical or physical size of Arabic numerals varying along both dimensions. In Study 2, first graders (mean age = 6 years 6 months), third graders (mean age = 8 years 4 months), and fifth graders (mean age = 10 years 3 months) were tested to examine developmental changes in numerical and physical comparisons. In the numerical comparison task, a size congruity effect was found at all ages (i.e., relative to a neutral control, congruent physical sizes facilitated, and incongruent sizes interfered with, the numerical comparison). The pattern of facilitation and interference, however, was modulated by age. In the physical comparison task, the incongruity between physical and numerical size affected only older children and adults. These findings strongly suggest that the automatization in number processing is achieved gradually as numerical skills progress.     

Mapping Among Number Words,Numerals, and Nonsymbolic Quantities in Preschoolers

In mathematically literate societies, numerical information is represented in 3 distinct codes: a verbal code (i.e., number words); a digital, symbolic code (e.g., Arabic numerals); and an analogical code (i.e., quantities; Dehaene, 1992). To communicate effectively using these numerical codes, our understanding of number must involve an understanding of each representation as well as how they map to other representations. In the current study, we looked at 3- and 4-year-old children’s understanding of Arabic numerals in relation to both quantities and number words. The results suggest that the mapping between quantities and numerals is more difficult than the mapping between numerals and number words and between number words and quantities. Thus, we compared 2 competing models designed to investigate how children represent the meanings of Arabic numbers—whether numerals are mapped directly to the quantities they represent or instead if numerals are mapped to quantities indirectly via a direct mapping to number words. We found support for the latter suggesting that children may first map numerals to number words (another symbolic representation) and only through this mapping are numerals subsequently tied to the quantities they represent. In addition, unlike both mappings involving quantity, the mapping between the 2 symbolic representations of number (numerals and number words) was not set-size-dependent, therefore providing further evidence that children may map symbols to other symbols in the absence of a quantity referent. Together, the results provide new insight into the important processes involved in how children acquire an understanding of symbolic representations of number.     

Knowing letter names and learning letter sounds: a causal connection

Two experiments tested the common assumption that knowing the letter names helps children learn basic letter-sound (grapheme-phoneme) relation because most names contain the relevant sounds. In Experiment 1 (n=45), children in an experimental group learned English letter names for letter-like symbols. Some of these names contained the corresponding letter sounds, whereas others did not. Following training, children were taught the sounds of these same "letters." Control children learned the same six letters, but with meaningful real-word labels unrelated to the sounds learned in the criterion letter-sound phase. Differences between children in the experimental and control groups indicated that letter-name knowledge had a significant impact on letter-sound learning. Furthermore, letters with names containing the relevant sound facilitated letter-sound learning, but not letters with unrelated names. The benefit of letter-name knowledge was found to depend, in part, on skill at isolating phonemes in spoken syllables. A second experiment (n=20) replicated the name-to-sound facilitation effect with a new sample of kindergarteners who participated in a fully within-subject design in which all children learned meaningless pseudoword names for letters and with phoneme class equated across related and unrelated conditions.     

Semantic access in number processing investigated with Japanese Kanji and Kana numerals

In number processing, semantic representations are efficiently activated. These representations frequently affect task performance, as demonstrated by semantic effects such as the distance effect (longer reaction times to closer numerical pairs in comparison tasks). The objective of this study was to investigate whether efficient semantic access is a distinctive feature of number processing using the Japanese language. Japanese was chosen to investigate possible effects of ideographic processing and word frequency: Kanji numerals in Japanese are ideograms and are used frequently, while Kana numerals are phonograms and are used infrequently. The results confirmed a distance effect in the numerical and physical matching tasks with both Arabic and Kanji numerals regardless of notation or task (Experiment 1). However, the effect was not observed with the Kana pairs (Experiment 2), thereby suggesting that semantic access is not always efficient in number processing. The results can be explained coherently within a general framework of word recognition by assuming that both the type of character and the word frequency play a critical role in determining the efficiency of semantic access.     

Differences between literates and illiterates on symbolic but not nonsymbolic numerical magnitude processing

The study of numerical magnitude processing provides a unique opportunity to examine interactions between phylogenetically ancient systems of semantic representations and those that are the product of enculturation. While nonsymbolic representations of numerical magnitude are processed similarly by humans and nonhuman animals, symbolic representations of numerical magnitude (e.g., Hindu–Arabic numerals) are culturally invented symbols that are uniquely human. Here, we report a comparison of symbolic and nonsymbolic numerical magnitude processing in two groups of participants who differ substantially in their level of literacy. In this study, level of literacy is used as an index of level of school-based numeracy skill. The data from these groups demonstrate that while the processing of nonsymbolic numerical magnitude (numerical distance effect) is unaffected by an individual’s level of literacy, the processing of Hindu–Arabic numerals differs between literate and illiterate individuals who live in a literature culture and have limited symbolic recognition skills. These findings reveal that nonsymbolic numerical magnitude processing is unaffected by enculturation, while the processing of numerical symbols is modulated by literacy.     

Learning of letter names and sounds and their contribution to word recognition

This study investigated knowledge of letter names and letter sounds, their learning, and their contributions to word recognition. Of 123 preschoolers examined on letter knowledge, 65 underwent training on both letter names and letter sounds in a counterbalanced order. Prior to training, children were more advanced in associating letters with their names than with their sounds and could provide the sound of a letter only if they could name it. However, children learned more easily to associate letters with sounds than with names. Training just on names improved performance on sounds, but the sounds produced were extended (CV) rather than phonemic. Learning sounds facilitated later learning of the same letters' names, but not vice versa. Training either on names or on sounds improved word recognition and explanation of printed words. Results are discussed with reference to cognitive and societal factors affecting letter knowledge acquisition, features of the Hebrew alphabet and orthography, and educational implications.     

Letter form as a constraint for errors in neglect dyslexia and letter position dyslexia

Does letter-form constrain errors in peripheral dyslexia? In Hebrew, 5 of the 22 letters have two different letter forms, one is used only when the letter occurs in word-final position, the other form is used in initial and middle positions. Is the information on final-forms encoded in the letter identity information and used for word identification, or is it discarded? The current research explored this question through the effect of final vs. non final letter form on the error pattern in neglect dyslexia (neglexia) and letter position dyslexia (LPD). Left word-based neglexia results in errors of omission, substitution and addition of letters in the left side of words, which in Hebrew is the end of the word. We examined whether final letter form blocks the addition of letters to the end of the word and whether omissions of letters after letters in non-final form are avoided. The predominant error type in LPD is migration of letters within words. We tested whether migrations also occur when they cause form change of either final-form letters that move to middle position or middle-form letters that move to final position. These questions were assessed in both acquired and developmental neglexia and LPD. The results indicated a strong effect of final letter-form on acquired neglexia and on acquired and developmental LPD, which almost completely prevented form-changing errors. This effect was not found in developmental neglexia, where words that end in final-form letters were actually more impaired than other words, probably because final-form letters appear only on the neglected side of the word for Hebrew-reading children with left developmental neglexia. These data show that early visuo-orthographic analysis is sensitive to final letter form and that final letter form constrains errors in peripheral dyslexia.     

Domain-specific and domain-general changes in children's development of number comparison

The numerical distance effect (inverse relationship between numerical distance and reaction time in relative number comparison tasks) has frequently been used to characterize the mental representation of number. The size of the distance effect decreases over developmental time. However, it is unclear whether this reduction simply reflects developmental changes in domain-general speed of processing and whether it is specific to numerical compared with non-numerical magnitude. To examine these open questions, we conducted a cross-sectional study with 6-, 7-, and 8-year-old children as well as adult college students. Participants performed comparisons on Arabic numerals, arrays of squares, squares of varying luminance and bars of varying height. To control for general age-related changes in reaction time, a measure of speed of processing was used as a covariate in the analysis. A significant developmental decrease in the distance effect was found across numerical and non-numerical comparison tasks over and above general changes in processing speed. However, this change was not found to differ as a function of format. These data suggest that developmental changes in the distance effect are reflective of changes in a domain-general comparison process, rather than domain-specific developmental changes in number representations. However, analysis of overall reaction times revealed significantly greater developmental changes for numerical relative to non-numerical comparison tasks. These findings highlight the importance of taking multiple measures into account when characterizing developmental changes in numerical magnitude processing. Implications for theories of numerical cognition and its development are discussed.     

Use of numerical symbols by the chimpanzee (Pan troglodytes): Cardinals, ordinals, and the introduction of zero

An adult female chimpanzee with previous training in the use of Arabic numerals 1–9 was introduced to the meaning of "zero" in the context of three different numerical tasks. The first two were cardinal tasks where the subject was required either to select numerals corresponding to the number of items presented on a computer screen (productive use of numerals) or to match sets of the appropriate size to numerals presented as samples (receptive use). The third task addressed the ordinal meaning of the same symbols where the subject was required to respond to numerals sequentially, arranging them into an ascending series. The subject mastered the recognition of the meaning of zero in all three tasks. However, details of her usage of the symbol revealed that transfer of the meaning between different kinds of tasks was incomplete, suggesting that the level of abstraction characteristic of human numerical ability was not attained in the chimpanzee. Over the course of acquisition leading to the high levels of accuracy eventually observed, the newly introduced zero appeared to shift along the length of a continuous numerical scale toward the lower end, while confusions with 1 remained the most frequently encountered mistakes. Such patterns of error thus suggest that Ai's understanding of the meaning of zero in relation to the rest of the number symbols was not consistent with an "absence of items versus presence of items" scheme. Electronic Publication     

Doomed to Read in a Second Language: Implications for Learning

The aim of the study was to elucidate whether and how reliance on a second language impacts the learning of new information under very basic learning conditions. The paradigm used to investigate this issue required individuals to learn a series of associations between numerals and particular letter strings. Participants were two groups of university students: (1) individuals for whom spoken Hebrew was the mother tongue and written Hebrew a primary orthography (L1 group), and (2) individuals for whom Hebrew, both spoken and written, was a second language (L2 group). Data were collected under two conditions. In the language-dependent condition (LDC), the paradigm required learning associations between eight numerals and the letter strings of eight familiar Hebrew words. In the language-independent condition (LIC), it required learning associations between eight numerals and eight random letter strings in Hebrew. Results suggest that learners may be significantly disadvantaged when compelled to learn new information mediated in a second language. This disadvantage appears to manifest itself at a very basic learning level and in instances where new information is mediated by language that is fairly overlearned by the L2 learner.