Inversion Errors in Arabic Number Reading: Is There a Nonsemantic Route?

This article reports on a mildly aphasic patient with major disorders in reading, writing, and number processing. His predominant error type in reading aloud Arabic numbers and in matching heard numerals with Arabic numbers was the violation of the inversion rule of the German Arabic number reading system. According to this rule most of the two-digit numbers or numbers in the final and prefinal position of longer digit strings have to be read beginning with the final digit (e.g., 26 → sechsundzwanzig (literally translated: six-and-twenty)). It is argued that AT's inversion errors (e.g., 26 → zweiundsechzig (literally translated: two-and-sixty)) are not consistent with the predictions of single route models of Arabic number reading but are in agreement with proposals of a visually based asemantic reading routine in addition to a semantically mediated reading routine.     

Writing and rewriting numerals: a dissociation within the transcoding processes

In the present study we report the case of A.B., a patient with a specific, though not isolated, deficit in transcoding verbal to Arabic numerals. Despite perfect production of Arabic numerals in a writing to dictation task, she frequently produced syntactic errors when the input was in written verbal form (e.g., duecentotrenta [two hundred and thirty] --> 20030). In absence of problems in the verbal comprehension system, A.B.'s performance is difficult to accommodate within current models of number processing. In the attempt to interpret the present findings, we suggest that different numerical codes, i.e, spoken and written verbal numerals, activate with different efficiency the transcoding algorithm.     

阿拉伯数字与汉字大写数字认知的大脑功能一侧化实验研究

用半视野速示术检查阿拉伯数字和汉字大写数字在三种任务加工条件（认读、简单相加、奇偶概念异同判断）下进行认知的大脑两半球机能活动一侧化效应。结果表明：以被试正确反应的百分数为指标,两类数字的三种任务加工均没有表现出明显的视野（大脑半球）优势。以被试正确反应的反应时为指标,两类数字的认读和简单相加也未出现视野（大脑半球）的明显差别,而两类数字的奇偶概念异同判断却出现了差异显著的右视野（左半球）优势。     

Pure left neglect for Arabic numerals

Arabic numerals are diffused and language-free representations of number magnitude. To be effectively processed, the digits composing Arabic numerals must be spatially arranged along a left-to-right axis. We studied one patient (AK) to show that left neglect, after right hemisphere damage, can selectively impair the computation of the spatial frames underpinning recognition and understanding of Arabic numerals, without impairing the spatial frames for coding alphabetic strings or for coding environmental spatial information. The presence in our brain of these specific and precise spatial frames must be rooted in the paramount importance of Arabic numerals processing in our everyday activities.     

Grey parrot number acquisition: The inference of cardinal value from ordinal position on the numeral list

A Grey parrot (Psittacus erithacus) had previously been taught to use English count words ("one" through "sih" [six]) to label sets of one to six individual items (Pepperberg, 1994). He had also been taught to use the same count words to label the Arabic numerals 1 through 6. Without training, he inferred the relationship between the Arabic numerals and the sets of objects (Pepperberg, 2006b). In the present study, he was then trained to label vocally the Arabic numerals 7 and 8 ("sih-none", "eight", respectively) and to order these Arabic numerals with respect to the numeral 6. He subsequently inferred the ordinality of 7 and 8 with respect to the smaller numerals and he inferred use of the appropriate label for the cardinal values of seven and eight items. These data suggest that he constructed the cardinal meanings of "seven" ("sih-none") and "eight" from his knowledge of the cardinal meanings of one through six, together with the place of "seven" ("sih-none") and "eight" in the ordered count list.     

书写习惯对数字空间表征SNARC效应的影响

本文设计两个实验,采用大小判断任务,选取读写习惯相反的维、汉大学生为研究对象,探讨两类被试对阿拉伯数字和母语数字空间表征的一致性与差异性。结果发现：（1）维、汉被试均表现出对阿拉伯小数反应左手快于右手,对大数反应右手快于左手,即出现正向SNARC效应;（2）维吾尔族被试表现出对母语小数反应右手快于左手,对大数反应左手快于右手,即对母语数字出现反向SNARC效应;汉族被试表现出对母语小数反应左手快于右手,对大数反应右手快于左手,即对母语数字出现正向SNARC效应。结论：（1）维、汉被试对于阿拉伯数字的SNARC效应存在一致性;（2）维、汉被试母语数字的SNARC效应存在差异性;（3）数字空间对应性与书写习惯是导致结果的重要因素。     

Language function and dysfunction among Chinese- and English-speaking polyglots: Cortical stimulation, Wada Testing, and clinical studies

Language functions in a group of Chinese- and English-speaking polyglots living in a multiracial society have been investigated by several methods: the effects of cortical stimulation on object-naming and reading tasks in patients who required awake craniotomy, lateralization of cerebral dominance for speech by the Wada Test, and the pattern of language loss and recovery following stroke. The data indicate that these polyglots were all left hemisphere dominant for the languages tested: no consistent evidence for increased participation by the right hemisphere for language functions was found. The cortical stimulation experiments provided data most compatible with the "differential localization" model of cerebral localization in bilingualism. The variable which most influenced performance in all of these investigations was which language was used primarily for speaking as well as reading and writing at the time of the study.     

Further evidence for addition and numerical competence by a Grey parrot (Psittacus erithacus)

A Grey parrot (Psittacus erithacus), able to quantify sets of eight or fewer items (including heterogeneous subsets), to sum two sequentially presented sets of 0–6 items (up to 6), and to identify and serially order Arabic numerals (1–8), all by using English labels (Pepperberg in J Comp Psychol 108:36–44, 1994; J Comp Psychol 120:1–11, 2006a; J Comp Psychol 120:205–216, 2006b; Pepperberg and Carey submitted), was tested on addition of two Arabic numerals or three sequentially presented collections (e.g., of variously sized jelly beans or nuts). He was, without explicit training and in the absence of the previously viewed addends, asked, “How many total?” and required to answer with a vocal English number label. In a few trials on the Arabic numeral addition, he was also shown variously colored Arabic numerals while the addends were hidden and asked “What color number (is the) total?” Although his death precluded testing on all possible arrays, his accuracy was statistically significant and suggested addition abilities comparable with those of nonhuman primates.     

Macaques’ (Macaca mulatta) use of numerical cues in maze trials

We tested the ability of number-trained rhesus monkeys to use Arabic numeral cues to discriminate between different series of maze trials and anticipate the final trial in each series. The monkeys prior experience with numerals also allowed us to investigate spontaneous transfer between series. A total of four monkeys were tested in two experiments. In both experiments, the monkeys were trained on a computerized task consisting of three reinforced maze trials followed by one nonreinforced trial. The goal of the maze was an Arabic numeral 3, which corresponded to the number of reinforced maze trials in the series. In experiment 1 (n=2), the monkeys were given probe trials of the numerals 2 and 4 and in experiment 2 (n=2), they were given probe trials of the numerals 2–8. The monkeys receiving the probe trials 2 and 4 showed some generalization to the new numerals and developed a pattern of performing more slowly on the nonreinforced trial than the reinforced trial before it for most series, indicating the use of the changing numeral cues to anticipate the nonreinforced trial. The monkeys receiving probe trials of the numerals 2–8 did not predict precisely when the nonreinforced trial would occur in each series, but they did incorporate the changing numerals into their strategy for performing the task. This study provides the first evidence that number-trained monkeys can use Arabic numerals to perform a task involving sequential presentations.     

汉字数字与阿拉伯数字的阈下启动研究

该研究采用了反应窗技术和回归分析范式,通过两个实验对汉字数字和阿拉伯数字的启动效应进行了实验探索。结果表明(1)在客观阔限以下,汉字数字和阿拉伯数字都可以被加工到语义水平,而数字的表征形式对启动效应无影响;(2)在本研究中,在启动数字为汉字数字的条件下,当觉察水平高于客观阈限时,不存在启动效应。     

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.     

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.     

Hemispheric specialization for reading

Behavioral laterality tasks with linguistic stimuli were used to assess the differential processing efficiencies of the cerebral hemispheres in right- and left-handed adults. Findings from a lateralized lexical decision task with concrete nouns supported Zaidel's (1983) "direct access" model of hemispheric functioning. A dual task consisting of oral and silent reading indicated that the right hand was significantly more disrupted than the left during unimanual finger tapping; however, some bilateral interference was observed. Taken together the findings suggest that although the left hemisphere was relatively more efficient, the right hemisphere was dynamically involved in the reading process.     

Dissociation of mechanisms of reading in Alzheimer's disease.

The role of spelling-to-sound correspondence rules in oral word reading was investigated by asking patients with Alzheimer's Disease (AD) and normal controls to read aloud pronounceable letter strings that do not happen to be real words. These pseudowords were of two types: those that have orthographically similar "neighbors," and those that have no neighbors. The patients with AD were mildly impaired relative to the normal controls in reading pseudowords with neighbors, but were markedly impaired in reading pseudowords with no neighbors. The results are interpreted as favoring a model of reading in which words and pseudowords are normally read via the same lexical mechanism. An ancillary route involving the conscious application of spelling-to-sound rules is available only to cognitively intact readers.     

Semantic processing in the production of numerals across notations

In the present work, we conducted a series of experiments to explore the processing stages required to name numerals presented in different notations. To this end, we used the semantic blocking paradigm previously used in psycholinguist studies. We found a facilitative effect of the semantic blocked context relative to the mixed context for Arabic digits and number words. However, the blocked context produced an interference effect for physical numerosity and Roman numbers. Our results provided further evidence to models suggesting that Arabic digits may be named through an asemantic route similar to that of number words, whereas a semantic route is mandatory to name physical numerosity and Roman numerals.     

Ordinality and inferential abilities of a grey parrot (Psittacus erithacus)

A grey parrot (Psittacus erithacus), able to label the color of the bigger or smaller object in a pair (I. M. Pepperberg & M. V. Brezinsky, 1991), to vocally quantify < or =6 item sets (including heterogeneous subsets; I. M. Pepperberg, 1994), and separately trained to identify Arabic numerals 1-6 with the same vocal English labels but not to associate Arabic numbers with their relevant physical quantities, was shown pairs of Arabic numbers or an Arabic numeral and a set of objects and was asked for the color of the bigger or smaller one. The parrot's success showed he (a) understood number symbols as abstract representations of real-world collections, (b) inferred the relationship between the Arabic number and the quantity via stimulus equivalence, and (c) understood the ordinal relationship of his numbers.     

Long-term retention of the differential values of Arabic numerals by chimpanzees (<Emphasis Type="Italic">Pan troglodytes</Emphasis>)

As previously reported (Beran and Rumbaugh, 2001), two chimpanzees used a joystick to collect dots, one-at-a-time, on a computer monitor, and then ended a trial when the number of dots collected was equal to the Arabic numeral presented for the trial. Here, the chimpanzees were presented with the task again after an interval of 6 months and then again after an additional interval of 3.25 years. During each interval, the chimpanzees were not presented with the task, and this allowed an assessment of the extent to which both animals retained the values of each Arabic numeral. Despite lower performance at each retention interval compared to the original study, both chimpanzees performed above chance levels in collecting a quantity of dots equal to the target numeral, one chimpanzee for the numerals 1-7, and the second chimpanzee for the numerals 1-6. For the 3.25-year retention, errors were more dispersed around each target numeral than in the original study, but the chimpanzees' performances again appeared to be based on a continuous representation of magnitude rather than a discrete representation of number. These data provide an experimental demonstration of long-term retention of the differential values of Arabic numerals by chimpanzees.