The SNARC Effect and the REVERSE SNARC Effect

Linkages between Number Concepts, Spatial Thinking, and Directionality of Writing: The SNARC Effect and the REVERSE SNARC Effect in English and Arabic Monoliterates, Biliterates, and Illiterate Arabic Speakers S AMAR Z EBIAN∗ ABSTRACT The current investigations coordinate math cognition and cultural approaches to numeric thinking to examine the linkages between numeric and spatial processes, and how these linkages are modified by the cultural artifact of writing. Previous research in the adult numeric cognition literature has shown that English monoliterates have a spatialised mental number line which is oriented from left-to-right with smaller magnitudes associated with the left side of space and larger magnitudes are associated with the right side of space. These associations between number and space have been termed the Spatial Numeric Association Response Code Effect (SNARC effect, Dehaene, 1992). The current study investigates the spatial orientation of the mental number line in the following groups: English monoliterates, Arabic monoliterates who use only the right-left writing system, Arabic-English biliterates, and illiterate Arabic speakers who only read numerals. Current results indicate, for the first time, a Reverse SNARC effect for Arabic monoliterates, such that the mental number line had a right-to-left directionality. Furthermore, a weakened Reverse SNARC was observed for Arabic-English biliterates, and no effect was observed among Illiterate Arabic speakers. These findings are especially notable since left-right biases are neurologically supported and are observed in pre-literate children regardless of which writing system is used by adults. The broader implications of how cultural artifacts affect basic numeric cognition will be discussed.

∗ American

University of Beirut, Lebanon

c Koninklijke Brill NV, Leiden, 2005

Journal of Cognition and Culture 5.1-2

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A predominating view among those who offer an alternative to the amodal model of adult numeric cognition (McCloskey, 1992) claims that the magnitude code is a spatialised mental number line which is oriented from left to right with smaller magnitudes associated with the left side of space and larger magnitudes associated with the right side of space. These associations between number and space have been termed the Spatial Numeric Association Response Code Effect (SNARC effect, see Bachtold, Baumuller & Brugger, 1998; Brysbaert, 1995; Dehaene, 1989; Dehaene & Akhavein, 1995; Dehaene, Bossini & Giraux, 1993; Dehaene & Cohen, 1991; Dehaene, Dupoux & Mehler, 1990; Fias, 2001; Reynvoet & Brysbaert, 1999; Zorzi, Priftis & Umilta, 2002; although see McCloskey, Macaruso & Whetstone, 1992; McClosky, Sokol & Goodman, 1986). I will proceed with the empirically supported view that the magnitude code involves linkages and associations to spatial processes. The current investigations build on a smaller sub-set of SNARC studies with French, English, and Dutch speaking monoliterates and with French-Persian biliterates who use both the left-right and right-left writing systems. These studies reveal that the directionality of the mental number line may be related to the directionality of ones’ reading and writing system (Dehaene, Bossini & Giraux, 1993; Fias, Lauwereyns & Lammertyn, 2001). Evidence for the Connection Between Number and Space? The view that number concepts are organized along a mental number line has a long history (Banks, Fujii & Kayra-Stuart, 1976; Galton, 1880; Dehaene, 1992, 1997; Dehaene & Akhavein, 1995; Dehaene & Cohen, 1991; Dehaene et al., 1993; Krueger, 1989; Meck & Church, 1983; Moyer & Landauer, 1967; Restle, 1970; Resnick, 1983; Seron, Pesenti, Noel, Deloche & Cornet, 1992). These findings, however, offer indirect and off-line evidence for an internalised mental number line. More recently, work has revealed that the spatialised mental number line is activated automatically, even in numeric tasks that do not require magnitude comparisons such as parity judgments tasks and in phoneme monitoring tasks with Arabic numerals (Dehaene & Cohen, 1991; Dehaene et al., 1993; Fias et al., 1996; Fias et al., 2001). These findings, together with an even larger body of work which finds the SNARC effect in the same-different judgment task, the line bisection task, and various versions of the numeric

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comparison task, offer strong evidence that numbers automatically invoke a sense of space, and that the mental number line may be an essential feature of a number’s magnitude code (Dehaene & Akhavein, 1995; Dehaene, Bosini & Giraux, 1993; Fias, Brysbaert, Geypens & d’Ydewalle, 1996, study 1; Fias, 2001, study 1). In addition to the SNARC effect, other less direct but compatible, evidence is found for the spatial properties of number concepts in the distance effect and in various imagery studies (Seron, Pesenti, Noël, Deloche & Cornet, 1992; Galton, 1880). Additionally, the spatial number line view is accepted and is consistent with assumptions made by Gallistel and Gelman, and Campbell, although the view is not an inherent part of both models of number processing (Campbell, 1994; Campbell & Clark, 1988; Gallistel, personal communication, Oct 21, 2002; for an alternative view see McCloskey, 1992; McCloskey, Macaruso & Whetstone, 1992; McCloskey, Sokol & Goodman, 1986). SNARC Studies and the Influence of Directionality of Writing Although a considerable number of studies have replicated the SNARC effect in an impressive diversity of tasks, the only known research which studies the origin of the SNARC effect was conducted by Dehaene, Bossini, and Giraux (1993). In study 7 from this report, a parity judgment task was used to investigate number conceptualisation in French Monoliterates and in Persian-French Biliterates from Iran whose native language was Persian and whose second language was French. Persian, like Arabic, is written from right-to-left. The Biliterate participants, twenty in total, had varying levels of bilingual fluency which was indirectly assessed by their date of immigration to France and age of second language acquisition. The task required participants to press one of two buttons depending on the parity of a visually presented Arabic numeral. In this task the SNARC effect is revealed if smaller numbers are responded to faster with the left hand and larger numbers are responded to faster with the right hand, regardless of the parity value. The parity judgment was merely a means of activating the magnitude code. Results suggested that the SNARC effect was weaker for the French-Persian Biliterates than the French Monoliterates; however, it was not reversed as predicted. Since it was difficult to draw strong conclusions from a weakened effect, Dehaene et al. conducted further

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analyses to determine whether age of second language acquisition, years lapsed since arrival in France from Iran, and self ratings of Persian language skill predicted the strength of the SNARC effect. The results showed that participants with fewer years in a French literate environment had a weaker left-to-right bias (weaker SNARC). For International Arabic numerals only (not the East-Arabic numerals used in Persian and Arabic writing), French-Persian participants who learned French earlier had a stronger SNARC effect. These findings demonstrate that individuals who use both a left-right and a right-left writing system, will show a weaker but not completely reversed left-right SNARC effect and the strength of SNARC effect is predicted by various measures of second language skill and acculturation. Dehaene et al.’s (1993) findings suggest that directionality of writing and literacy skill in left-to-right writing systems has an influence on how numbers are mapped onto a horizontal number line, however, data from monoliterate groups who write and read only from right-left and data from illiterate individuals is required before we can make stronger claims about the influence of writing on the SNARC effect. In the current study the SNARC effect was investigated for the first time in Arabic Monoliterates who read and write only from right-toleft. If the SNARC effect is caused by directionality of writing, then we would expect a Reverse SNARC in the Arabic Monoliterate groups such that smaller numbers will be associated with the right side of a number line and large numbers will be associated with the left side. To ensure the comparability of the current findings to those of Dehaene et al. an Arabic-English Biliterate group, similar to Dehaene et al.’s PersianFrench Biliterates, will also be assessed. The control group will be an English Monoliterate group. In addition to investigating the SNARC in these three literate groups, it will be investigated for the first time in an Arabic speaking illiterate group. The illiterate participants were able to read numerals only, but could not read and write text. Their results allowed us to examine whether reading and writing practices per se, as opposed to simply living in a literate culture without having literacy skills, lead to the development of spatialised number concepts. Finally, to further investigate how level of language skill influences the spatialisation of number concepts, the SNARC effect was investigated in a small sample of Arabic-English


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biliterate children, herein referred to as the Child Biliterate group. The Child Biliterates read and write Arabic fluently, however their English language skills are somewhat weaker. Method for Oral Numeral Only SNARC Study Studies 1a, 1b, and 1c Introduction to Oral Numeral Only SNARC Studies. In the current study the SNARC effect will be investigated using a modified version of Dehaene and Akhavein’s (1995) same-different judgment task and not the task used by Dehaene et al. (1993) in the original bilingual study discussed above. There are several reasons for this change of task. First, the requirement to make parity judgments would be a difficult if not impossible task for Illiterate Arabic speakers who recognise numerals but have little or no knowledge of parity. Second, the original stimuli included number word stimuli which the Illiterate group could not read. Third, the requirement to make a bimanual response would have required speeded fine motor control. This is yet another novel task demand that requires more effort than speeded oral responses. All of these factors, which make the task increasingly novel and may create task demands that may make it difficult to interpret the findings, lead to the decision to use a modified version of the same-difference judgment task. In the original task, Dehaene and Akhavein had English speaking monoliterate university students judge whether two single digit numerals had the same or different numerical values, where one numeral was presented on the left side of the screen and the other numeral was presented on the right side (e.g., 1 8; 1 9; 2 8; and 2 9). The important manipulation was to reverse the order of the stimuli such that the larger number appeared on the left (i.e., 9 2; 8 1). In addition to the Arabic digit pairs, number word-numeral pairs were presented (i.e., one 9, nine 1; one nine; nine one). Number word stimuli were not used in the current version of the same-different judgment task. The task used in the current investigation was an oral version of Dehaene and Akhavein’s (1995) same-different judgment task, herein referred to as the Oral Numeral Only SNARC task. The current task had the added advantage of assessing, for the first time, whether

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the SNARC effect is observable in tasks that do not require bimanual responses. Lebanese participants. Dehaene’s findings clearly suggest that level of second language skill is correlated with the strength of the SNARC effect. For this reason, I have included some details about the language skills of the five groups involved in this study. The first four groups are Arabic speaking, with varying levels of first and second language skill. The Arabic Monoliterate group consisted of 10 literate female and 9 literate male native Arabic speakers, residing in Lebanon with normal or corrected to normal vision. Most Arabic monoliterates had high-school or some university-level education which did not involve acquiring fluency in the two other official languages of Lebanon; French or English. Their ages ranged from 27-45. Some of the participants recognized letters in the French-English alphabet, and could read labels and signs with some effort. However, they could not read text, nor write in French or English. Work related and leisure literacy practices were performed in Arabic. The Arabic-English/Arabic-French Biliterate group, herein referred to as the Arabic Biliterate group, consisted of 17 high-school and university educated individuals. There were 13 females and 4 males, each of whom had received at least high-school levels of Arabic-French or Arabic-English language instruction in Lebanese state-run schools. Their ages ranged from 15-59. Their French or English language skills were strongly linked to school-based literacy practices. Second language reading and writing was not required in their work settings, and leisure reading and writing was performed in their native Arabic language. In the third group, there were eleven functionally illiterate Lebanese women, ranging in ages from 25-62. They could recognise East-Arabic numerals but could not read written Arabic text. None of these women received formal education. There were no men participants in this group. Illiterate men are generally harder to find because of the strong emphasis on acquiring at least minimal levels of quaranic literacy for men of their generation. The fourth group was the Arabic-English Biliterate Children, herein referred to as the Child Biliterate group. The eight children that participated in this study ranged in ages from eight to 12 years. These children spoke Arabic as their native language and learned Arabic literacy


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as their primary language in school. They attended private Western-style schools which provided daily formal English as a second language instruction as well as English instruction in maths and science. In the mathematics classroom, International Arabic rather than East Arabic numerals were used. The parents of these children were members of Arabic Monoliterate group. Euro-Canadian Participants. There were three separate English Monoliterate groups, all of whom were recruited from a Canadian university subject pool. The first group of 19 subjects, 12 females and 7 males ranging in ages from 18-43, participated in the Oral Numeral Only SNARC study. Two additional English speaking university student groups were tested on one of two other tasks which will be discussed later. The second English Monoliterate group, consisted of five right-handed females and 15 right handed males ranging in ages from 18-23. They were administered the Dehaene & Akhavein Bimanual Replication task. The third group, which consisted of 9 right handed females and 11 right handed males ranging in age from 19-23, was administered the Oral Version of the Dehaene and Akhavein Replication task. Apparatus. A MacIntosh Powerbook G3 laptop with a 14 Colour Liquid Crystal Display Monitor was used to present the stimuli. An external microphone which picked up the onset of speech was connected directly into the computer and mounted on the right side of the screen. The application program Superlab (version 1.74; Cedrus Corporation) was used to display stimuli and to record responses to the nearest millisecond. Stimulus presentation could not be synchronised with the screen refresh rate due to the properties of liquid computer displays on all laptop computers. The asynchrony between stimulus presentation and refresh rates is an unavoidable source of error variability in the reaction times resulting in a more conservative assessment of the SNARC effect. An estimate of the size of this variability could not be obtained for LCD monitors, however for standard monitors the variability is 15 milliseconds. Procedure. Participants were instructed to judge the numerical similarity of numerals flashed on the screen by saying “yes” into a microphone if

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the stimuli had the same numerical value and by saying “no” if they had different values. Participants in the Oral Numeral Only SNARC task were presented with two black numerals in 72 point font simultaneously on a white screen. One numeral appeared 35 mm to the left of the centre and the other numeral appeared 35 mm to the right of the centre of the screen. The numerals disappeared at response onset and were followed by a 1000 msec ISI. The importance of speed and accuracy was stressed, and practice trials were given until the participants felt comfortable with the task. Adapting procedures for the Arabic speaking group. The participants in the four Lebanese groups were administered the tasks in their homes, work places, or other convenient non-laboratory settings. These “field” conditions necessarily differed in some notable ways from the laboratory conditions under which the English Monoliterate groups were tested. I used several strategies to meet the demands of cross-cultural fieldwork while maintaining procedures that would allow meaningful and valid comparisons between the Arabic and the English Monoliterate groups. During the training phase of the experiment, participants were given warm up exercises and number of practice trials to get them accustomed to the many peculiar aspects of reaction time studies that make them very much unlike everyday numerical tasks such as: 1) the repetitious nature of the trials, 2) the requirement for highly speeded responses, 3) the requirement for sustained and highly focused attention, 4) the requirement to interface with computer equipment which involves: a) knowledge about the sensitivity of the microphone, b) the requirement to respond clearly with the words “yes” and “no” and no other words or sounds, c) experience with the time intervals between the onset of a stimulus, their verbal responses, and the presentation of a new stimulus. I also gave the participants enough trials to observe them making errors. Many of the participants became quite flustered after making errors and took more time to refocus compared to the English Monoliterates. Many of these difficulties were corrected during the training phase and when they occasionally arose during the testing phase, the interruption was noted and the corresponding trials were removed from the subject’s data set, and recorded as a non-trials. Appendix A provides a breakdown of


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the number of non-trials for each group, as well as outlier trials and errors. The testing conditions unavoidably lead to a high level of random error variance which should not be correlated in any systematic way with the effects being observed. Consequently, if the directionality of writing influences number conceptualisation, the effect would have to be very robust to outweigh error variance caused by the testing conditions and the task demands. Stimuli. The English Monoliterate groups were presented with different combinations of International Arabic numeral pairs made up of the following set of numerals used in Dehaene and Akhavein’s (1995) original study: 1, 2, 8, 9. The Arabic Monoliterate, Adult Arabic-English/French Biliterate, Illiterate, and Biliterate Child groups, were presented with the identical set of East Arabic numerals (i.e., , , , ). There were five types of stimulus pairs which varied according to numerical disparity, and spatial orientation. There were three levels of numerical disparity: equal numeral pairs (i.e., 1 1), close pairs that differed by one value (i.e., 1 2), and far pairs that differed by six or more values (i.e., 1 9; 2 8). The trials were also varied by spatial orientation; for the left-right orientation the smaller numeral was on the left (1 2; 2 9), and for the right-left orientation the smaller numeral was on the right (2 1; 9 2). The numeral pairs of interest in our SNARC studies were the two “far” leftright and right-left far trials, since all previous studies have observed the SNARC effect on far trials only (Brysbaret, 1995; Dehaene and Akhavein, 1995; Dehaene, Bossini & Giraux, 1993; Dehaene, Dupoux & Mehler, 1990). The close trials were filler trials which reliably took longer to judge but were included to create some variability in the decision making process and to ensure that judgments were grounded in semantic processing as opposed to perceptually-based judgments. The close pair trials were not included in the statistical analyses. Participants made “same-different” numerical judgments for 96 randomised trials, 48 numerically equal trials and 48 numerically different trials. Within the different trials they received 16 left-right far trials, 16 right-left far trials, 8 left-right close trials, 8 right-left close trials. It is important to note that Dehaene and Akhavein (1995) did not include an equal number of same and different trials. This methodological difficulty,

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which arguably creates biases in the decision making processes and potentially changes how the stimulus is being processed, was corrected in the current investigation. Consequently, participants made the same number of “yes” and “no” judgments, in accordance with the accepted convention in reaction time studies. Results Study 1a Oral Numeral Only SNARC Study with Arabic Monoliterates, Arabic-French/Arabic English Biliterates, and English Monoliterates A 2 × 3 analysis of variance was conducted to investigate whether the speed of right-left and left-right judgments was affected by the directionality of writing practiced in the three groups: Arabic Monoliterates, English Monoliterates, and Arabic-English Biliterates. The two other groups, Illiterates and Child Biliterates were not included in this analysis because their RTs were much longer. Results, shown in Table 11 , reveal a significant interaction between group and the directionality of the numeral pairs, F (2, 50) = 3.17, p = .044. In this analysis only the interaction between the left-right/right-left pairs and group was of empirical significance, however see Appendix B for details of the other effects. To determine which groups showed a SNARC or a Reverse SNARC effect, simple main effect posthoc tests were conducted. The Arabic Monoliterate group showed a Reverse SNARC. They responded 27 msec faster to numerals oriented from right-left compared to left-right numeral pairs, Q (2, 50) = 3.55, p < .05. ArabicFrench/Arabic-English Biliterates showed a 15 msec non-significant trend toward a Reverse SNARC effect, Q (2, 50) = 1.953, n.s. Finally, the English Monoliterate group showed a non-significant trend towards the SNARC effect, Q (2, 50) = 1.487, n.s. The non-significant SNARC effect for the English Monoliterates is contrary to Dehaene’s findings which showed a significant SNARC in French and English monoliterates in a bimanual parity judgment task and in a same-different judgment task. The non-

1 Tables 1, 2, 3 used with permission from B. Setiadi, A. Supratiknya, W. Lonner, & Y. Poortinga (2004). On going themes in psychology and culture. Yogyakarta: Kanisius Press.


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Table 1 Oral Numeral Only SNARC Study: The mean length of time in milliseconds it took Arabic Monoliterates, Arabic-English Biliterates, English Monoliterates, Lebanese Illiterates, and Child Biliterates to make left-right and right-left numerical judgments Groups

Mean Raw Scores

Difference Score

left-right (i.e., 1 9)

right-left (i.e., 9 1)

Arabic Monoliterates (n = 19)

812 (106)

785 (112.)*

27

Arabic-French/ English Biliterates (n = 17)

755 (126)

740 (125)

15

English Monoliterate (n = 19)

764 (128)

775 (138)

−11

Illiterate (n = 11)

926 (72)

910 (75)

16

Biliterate Child (n = 8)

1080 (158)

1028 (194)*

52

* Significant

difference (p < .05) between left-right and right-left responses, as assessed by posthoc tests.

significant results of the English monoliterate group will be explored in two follow-up studies, which will be reported after the findings from the Illiterate and Child Biliterate group are reported. Results Study 1b Illiterate Oral Numeral Only SNARC study A paired t-test revealed no SNARC effect or Reverse SNARC, for the Illiterate group t (10) = 1.02, p > .05 (see Table 1). This result supports the theoretically motivated hypothesis that reading and writing practices and not simply being in a literate environment contributes to the directionality of the mental number line.

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Results Study 1c Biliterate Child Oral Numeral Only SNARC study Results of a paired t-test showed a significant Reverse SNARC where right-left numeral pairs were judged 52 msec faster than left-right pairs, t (7) = -2.68, p < .05 (see Table 1). This was similar to the results of the Monoliterate Adults of Study 1a, however, the size of the effect was much larger; 52 msec compared to 27 msec. The effect in the Child Biliterate group was also larger than the non-significant trend of 15 msec observed in the Adult Biliterate group. Discussion Study 1a, 1b, and 1c Results of the Oral Numeral Only SNARC study show, for the first time, clear support for the hypothesis that the directionality of the right-left writing system has an effect on number conceptualisation. In the Arabic Monoliterate group, reading and writing from right-to-left gives rise to a Reverse SNARC, while this effect was not significant in either the Adult Arabic-English/French Biliterate group or in the English Monoliterate group. The non-significant trend towards the Reverse SNARC in the Adult Biliterate group suggests that the strength of the Reverse SNARC effect is weakened by the influences of a left-to-right writing system but not completely reversed. These results parallel those found in Dehaene et al.’s (1993) study in which highly skilled Persian-French biliterates did not show a significant SNARC effect compared to French monoliterates. The main difference, however, between the present Arabic Biliterate group and Dehaene’s Persian-French Biliterate group is the direction of the trend. For the Arabic Biliterate group, influences of the left-right writing system weaken the Reverse SNARC, while in the Persian-French biliterate group, the weakened trend was towards the SNARC effect. Thus it seems that one’s level of skill with the left-to-right writing system, as well as their skills in the right-left writing system has an effect on the size of the SNARC effect and the size of the Reverse SNARC. Further support is available in the results of the Child Biliterate group who showed the strongest Reverse SNARC. These findings suggest that second language skill, which is just beginning to develop in these children, is not sufficiently strong to weaken


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the Reverse SNARC effect caused by the influences of the more prominent Arabic right-to-left writing system. Results from the illiterate group, which do not show a significant Reverse SNARC, further support the view that the spatialisation of number concepts is influenced by the specific visio-motor process involved reading and writing and not simply being in a literate environment. Results from the illiterate group cannot be compared to the similar trend towards a Reverse SNARC in the Adult Biliterate group since the overall response times for Illiterates was 170.5 msec slower than the Adult Biliterate response times, and because the overall error rates were higher (see Appendix A). This difference in speed of responding and the fact there are no previous findings which compare the size of the Reverse SNARC effect in biliterates and illiterates limits our ability to make meaningful effect size comparisons between the Biliterate and Illiterate groups. Turning to the English Monoliterate group and their performance in the Oral Numeral Only task, the most surprising finding was the lack of a significant SNARC effect. The discrepant findings may have resulted from two methodological differences between the current task and the one used by Dehaene & Akhavein (1995). First, recall that the stimulus pairs in Dehaene and Akhavein’s study included different combinations of number words and numerals, whereas the stimuli in the current task included only numeral-numeral pairs. Second, Dehaene and Akhavein employed a bimanual task whereas the Oral Numeral Only task required an oral response. It is possible that the requirement to make bimanual responses influences performance or interacts in some way with the processing of the spatialised visual display. Due to these methodological differences, a task identical to the bimanual same-different judgment task used in Dehaene and Akhavein’s (1995) study was administered to a new group of 20 English Monoliterates. Method for the Replication of Dehaene and Akhavein’s (1995) Bimanual Study Study 1d Apparatus. A MacIntosh Powerbook G3 laptop was used to present the stimuli. The computer was interfaced with a model MK6 Psychscope

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Button box (MacWhinney, Laxman & Taylor, 1999). The application program PsyScope (version 1.02, Cohen, MacWhinney, Flatt & Provost, 1993) was used to present, time, and record the responses to the nearest millisecond. Materials and Procedure. The current task was conducted using the materials and procedures of Dehane & Akhavein’s same-different judgment task with English Monoliterates only. Combinations of numeral and number word pairs were presented on a laptop computer screen (e.g., Numeral word pairs: one nine; Number word-Numeral pairs, one 9; NumeralNumber Word, 9 one, and Numeral-Numeral pairs, 9 1). Moreover, close and far numeral pairs were included for all stimulus types: leftright far (one 9), right-left far (nine 1), left-right close (one 2), and right-left close (nine 8). Participants received 256 randomised trials in the first block and a newly randomised set of 256 randomised trials in the second block. It is important to note that one-third of the trials in this task were “yes” trials with identical numerals and two-thirds were “no” trials that had numerals of differing magnitudes. Although, the unequal proportion of yes/no trials allows for a higher level of guessing and potentially biases subjects to make more perceptually based judgments, we followed Dehaene and Akhavein’s original study to see if their results were replicable. Results and Discussion Study 1d Replication of Dehaene and Akhavein’s Bimanual SNARC study with English Monoliterates In the Bimanual Number Word and Numeral SNARC task, I studied whether the time it took to make a difference judgment was affected by left-right compared to right-left orientation of stimulus pair (left-right/rightleft factor), the presence of number word and numeral combinations (notation factor), and the hand in which the difference judgment was made (hand of response). A 2 × 4 × 2 repeated measures analysis of variance was conducted to assess these effects. Left and right handed responses and the SNARC effect. The only significant main effect observed was for the notation factor, F (3, 64) = 64.06, p < .001 (see Appendix C for a summary of the analysis of variance results for


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all factors). Results of a Tukey HSD post hoc analysis show that the numeral-numeral pairs, collapsing across hand use and left-right/right-left factor, were judged faster (M = 363) than numeral word-numeral pairs (M = 432), Q (3, 57) = 7.41, p < .01, and faster than numeral-numeral word pairs, (M = 446), Q (3, 57) = 8.97, p < .01 and numeral wordnumeral word pairs, (M = 429), Q (3, 57) = 7.12, p < .01. It is likely that numeral-numeral pairs can be judged quickly by means of perceptual similarity, faster than the other three notation conditions that required word reading. This main effect is not theoretically meaningful and will not be discussed further. The primary main effect of interest, the leftright/right-left factor, showed a non-significant trend towards the SNARC effect, F (1, 19) = 2.893, p = .10. Thus the current results, while in the same direction, do not replicate those from Dehaene & Akhavein which showed a significant SNARC effect. Referring to Table 2, the trends in the means indicate that the strongest SNARC effect was observed in the number word-numeral condition when participants responded with their right hand only. Exploratory post hoc analyses showed a significant SNARC only when participants responded with their right hand to number word-numeral pairs, Q (3, 57) = 3.16, p < .01. The same analysis was conducted for left hand responses and results show no SNARC, F (1, 19) = 0.45, n.s., and no SNARC by notation interaction, F (3, 57) = 0.15, n.s. The failure to replicate Dehaene and Akhavein’s (1995) main findings which showed a SNARC effect and no SNARC by notation interaction, suggests that the SNARC effect (as it is revealed in the same-different bimanual judgment task) is unstable. The current findings suggest at least two factors that may have influenced the stability of the effect. First, handedness could be an influencing factor since the effect is observed for the right hand only. In an attempt to rule out this possibility, an oral Version of Dehaene and Akhavein’s original bimanual task was conducted to assess the SNARC effect in a new English Monoliterate group for a final time. The materials, and procedure were identical to the Bimanual replication study, expect that the participants responded “yes”, into a microphone, when the numeral pairs had the same value and “no” when they had different values. There was one further difference, the same number of “yes” and “no” trials were included to deemphasise perceptually based judgments.

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Table 2 Bimanual Replication SNARC study: Mean length of time in milliseconds it takes Right Handed English Monoliterates to make left-right and right-left numerical difference judgment with their right and left hands when presented with four types of number pairs: number word-numeral, number word-number word, numeral-numeral, and numeralnumber word Difference Judgment with Right Hand Left-right

Right-left

Difference Score

Number word-Number word Number word-Numeral Numeral-Number word Numeral-Numeral

441 418 424 350

(87) (68) (65) (59)

449 (82) 442 (89)* 427 (73) 360 (69)

−8 −24* −3 −10

Mean

408 (63)

419 (71)

−11

Difference Judgment with Left Hand Left-right

Right-left

Number word-Number word Number word-Numeral Numeral-Number word Numeral-Numeral

440 428 439 373

456 438 427 372

Mean

420 (72)

(67) (71) (81) (86)

Difference Score

(82) (82) (65) (78)

−16 −10 12 1

423 (71)

−3

* Significant

difference (p < .05) between left-right and right-left responses, as assessed with simple main effect tests.

Results and Discussion Study 1e Oral Version of Dehaene and Akhavein’s (1995) Original Bimanual Task The main purpose of this study was to check whether the SNARC found in Dehaene and Akhavein’s can be observed in an oral version of the task. Results of a repeated measures analysis of variance did not reveal a significant main effect for the left-right/right-left factor: left-right stimulus pairs were not judged significantly faster, (M = 582, SD = 112), than right-left pairs, (M = 585, SD = 114), F (1, 19) = .514, n.s. (see Table 3). Turning to the interaction between the left-right factor and notation, the SNARC effect interacted significantly with notation, F (3, 57) = 6.32,


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Table 3 Oral Version of Replication Study: Mean length of time in milliseconds it takes English Monoliterates to make left-right and right-left numerical difference judgment with four types of number pairs: number word-numeral, number word-number word, numeralnumeral, and numeral-number word Left-to-right Number word-Number word Number word-Numerical Numeral-Number word Numeral-Numeral

614 579 599 534

(127) (100) (118) (104)

Mean

581 (112)

Right-to-left

Difference Score

615 (126) 621 (119)* 596 (110) 510 (102)

−1 −42* 3 24

585 (114)

−4

* Significant difference (p < .05) between left-right and right-left responses, as assessed by posthoc tests.

p = .001 (see Table 3). Planned simple main effect tests showed that the left-right SNARC was significant only in the number word-numeral condition: left-right number word-numeral pairs (M = 579, SD = 99) were judged faster than right-left number word-numeral pairs, (M = 621, SD = 119) Q (1, 19) = 5.68, p < .05 (see Table 3 for the means for all notation conditions). The effect was not significant in the number wordnumber word, numeral-numeral, nor the numeral-number word notation conditions. This finding is completely consistent with the finding from the Bimanual replication study above. Conclusions from the attempted replication studies. Two conclusions can be drawn from the results of the two attempted replication studies. First, the requirement to respond bimanually does not seem to be the main factor driving the SNARC effect since the same results were observed in both the bimanual and the oral version of the study (see also Nuerk, Wood, Graf, Knops & Willmes, 2003). Second, the SNARC effect is strongest for the mixed notation format, when a number word appears on the left side of the screen in tasks that require participants to judge whether left-right compared to right-left stimulus pairs have the same or different numerical values. Speculating, these findings may arise from two interacting factors. First, it may be the case that the same-different judgment task can be performed based on perceptual similarity alone by

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highly skilled participants such as undergraduate psychology students. Since the task involves a categorical judgment which may not require access to the semantic magnitude code, perceptual comparison is emphasised and magnitude comparison is deemphasised. This explanation may suggest why the SNARC effect is observed in some studies but not others and why it is observed among the Arabic groups who are unlikely to have developed strategies for avoiding conceptual processing. In addition to this factor, the presence of a number word on the left side of the screen may invoke leftright visual scanning patterns for the mixed number word-numeral format which is the default scanning pattern for English speakers (Rayner, 1999). This left-right bias is not be observed for the numeral-numeral stimuli, nor for the number word-number word stimuli since decisions can be made based on surface notation and not conceptually-based processes. Moreover, one further question remains; why is the SNARC effect observed for number word-numeral notation (one 9 vs nine 1), but not for numeral-number word notation (1 nine; 9 one)? This question did not arise in Dehaene and Akhavein’s (1995) research because they found no notation effect. I will speculate that Arabic numerals invoke a spatialised number line more directly and more intensely than number words. This weaker association between number words and the magnitude code may give rise to weaker and unstable findings with respect to number word stimuli (Fias, 2001). General Discussion Reverse SNARC Effect Findings The main findings from the SNARC studies show that Arabic numerals are conceptualised as points along an analogical number line, which seems to exploit the same spatial dimension as one’s reading and writing system. In the Oral Numeral Only SNARC study, it was shown, for the first time, that Arabic Monoliterates who use a right-to-left writing system think about numbers as starting from the right and increasing in magnitude to the left. This newly discovered effect has been coined the Reverse SNARC effect. This view is further supported by the findings from the Illiterate Lebanese group who do not show a Reverse SNARC, revealing that it is the visio-motor skills involved in reading and writing in a right-left direction that is giving rise to the Reverse SNARC and not simply being


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immersed in a literate culture that displays numbers from right to left. Further extending our understanding of the influences of directionality of writing on numeral conceptualisation, the results from the Adult Biliterate group, which show only a trend towards the Reverse SNARC, suggest that the biliterates’ native Arabic right-to-left writing system still has a marked influence over number conceptualisation. Influences from Arabic writing are even stronger among Child Biliterates who show the strongest Reverse SNARC effect. This further suggests that high levels of English-assecond language skill is required before the Reverse SNARC is significantly weakened. It can be concluded from the current and past research, that the tendency to spatialised numbers from right-to-left, which is influenced by right-to-left literacy, is weakened more if the opposite left-to-right reading skills are strong, and weakened less if left-to-right language skill is weak (Dehaene et al., 1993). These converging lines of evidence which show a relationship between level of second language skill and strength of the directionality of the spatialisation effect, nevertheless need to be followed up with research which more directly assesses degree of second language skill. Additionally, the Reverse SNARC effect needs to be examined in other numeric tasks, such as parity judgment, number comparison, and number bisection, all of which show more stable, robust SNARC effects. If the Reverse SNARC effect is robust and directly linked to the magnitude code, it should be found in a diverse array of numeric tasks. The Implications of the SNARC and Reverse SNARC for Understanding Semantically Based Number Processes and Cultural Cognition The SNARC and the Reverse SNARC effect fit into a larger class of findings which reveal spatial biases that correspond with directionality of writing including the following off-line tasks: line bisection, arrangement of temporally successive pictorial events, circle drawing task, speeded dot-filling task, perceptual exploration and object naming, and various kinds of graphic reproduction tasks (Elkind & Weiss, 1967; Fischer, 2001; Goodnow, Friedman & Bernbaum, 1973; Kugelmass & Lieblich, 1979; for right-left biases see Fagard & Dahme, 2003; Gelmacher & Moussa, 1999; Lieblich, Ninio & Kugelmass, 1975; Nachshon, 1985; Tversky, Kugelmass & Winter, 1991). The depth of spatial biases are revealed by Maass & Russo (2003) who reported a right-left directional bias

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in a sentence comprehension task that involved pictorially representing spatial events (i.e., The girl pushes/pulls the boy). Arabic participants were more likely to position the subject of sentence to the right of the object (boy) rather than to the left which was the tendency among Italian monoliterates. These findings are additionally significant since developmental and neuropsychological studies of spatial bias find a leftright bias in preliterate children (Fagard & Dahem, 2003; Hausmann, Waldie & Corballis, 2003; Tversky, Kugelmass & Winter, 1991). In the context of the broader research on directionality biases, the SNARC and Reverse SNARC are particularly noteworthy because they show that spatial biases are deeply rooted automatic processes that modify a domain that we did not expect to show cross-cultural differences. These findings suggest the impact that even benign or seemingly non-productive aspect of cultural artifacts, such as directionality of the writing system, have the potential to modify neurologically supported cognitive function. The neuropsychological evidence further suggests that the Reverse SNARC, compared to the SNARC, is less stable and may be easily weakened by the acquisition of a left-right writing system. With respect to the current findings which further support the view among SNARC researchers that spatial processing is automatically activated during number conceptualization, the ensuing question with respect to the Reverse SNARC effect is whether the directionality of the number line itself has consequences for numeric processing. I am concerned here with the implications of a directional spatial bias on number processing in general. On the one hand, one may argue that number conceptualization in English is identical to number conceptualization in Arabic, regardless of the directionality of the number line. However, this view may be problematic when we consider research which shows how linguistic influences modify semantically based number processing (Campbell, Kanz & Xue, 1999). Alternatively, others argue that these linguistic influences arise from encoding and decoding processes and that the magnitude code itself is not affected by linguistic processes (Brysbaert, Fias & Noël, 1998). Further research is needed to discern which processes are being modified by the directionality of the number line. There may be other reasons to question the view that directionality biases are inconsequential, and are optional cultural artifacts that are


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used strategically and do not modify semantically based numeric processing. Although the current findings do not directly rule out this possibility, cultural cognition work on spatial schemas clearly shows that differential spatial schemas have profound consequences on diverse domains of abstract thought (Kita, Danziger & Stolz, 2001; Levinson & Brown, 1994; Levinson, 1997). Research shows that Mopan Mayans, compared to the Yucatec Mayans, have a habitual tendency to use non-lateral and projected pointing to refer to spatial location of objects. In comparison, the Yucatec’s habitually use the projected lateral axis of to-the-right-of and to-the-left-of. These findings have been shown to extend to non-spatial concepts such as time and plot development and paradigmatic contrasts (when two things are being compared). This body of work shows that cultural specificity in the habitual conceptualization of space productively organizes abstract thought and suggests that spatial frameworks are complexly related to the internal organization of the cognitive domain from which it borrows its structure. It remains to be seen whether the left-to-right compared to the right-to-left spatial schemes are equally productive in modifying number conceptualization in different basic processes but also in higher-order numeric tasks. However, at this time one may question the view that there are no consequences to the directionality of the number line and that Arabic speakers habitually think from right to left about numbers and English speakers think from left-to-right because of processes completely unrelated to magnitude processing. In closing, I wish to emphasis that that although I have offered a preliminary attempt to explain why directionality of writing influences number conceptualisation, other puzzling issues remain with respect to how East Arabic numerals are written and named. The written form of East Arabic numerals have a left-to-right order with the largest digit value placed to the left of the smaller digit value and so on, as is the case for International Arabic numerals written in English. For example the East Arabic numeral, OI (51) appears in a left-to-right order with the decade digit 5 appearing to the left of the units digit 1, as it is in International Arabic numeral notation. Despite this similarity in the written form, the order in which the numerals 5 and 1 are written down on a page, and the way “51” is named follows a right-to-left ordering, such that the East Arabic digit 1 is written first and the decade digit 5

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is written second. Similarly, when the number “51” is spoken in Arabic, it is spoken as one plus fifty, thus the way it is spoken parallels the rightto-left order in which the digits are written. It is not clear whether the motor processes and the corresponding conceptual processes involved in this specific number notation system strengthens or weakens the right-left spatialisation of number concepts. Speculating on these influences it may be the case that the left-right orientation of East Arabic Numerals may partly limit the independent influences of a right-to-left writing system on number conceptualisation. Admitting these complexities, future research is needed to establish the robustness of the Reverse SNARC effect before we confidently argue that the directionality of the number line arises from the directionality of an individual’s reading and writing system. This research is currently underway in our labs. If it turns out that the directionality of writing fundamentally affects the number line and number conceptualisation, then we need to reconsider the nature of the relationship between artifacts and number conceptualisation.

Appendix A Number of Errors, Non-trials, and Outliers for Oral Numeral Only Task for Arabic Monoliterates, Arabic-English Biliterates, English Monoliterates, Arabic Illiterates, and the Child sample Number of Errors

Number of Non-trials

Number of Outliers

Arabic Monoliterates (n = 19)

50 2.6%

65 2.8%

29 1.5%

Arabic-English/French Biliterates (n = 17)

41 2.5%

55 3.3%

34 2.0%

English Monoliterates (n = 19)

19 1%

15 .8%

26 1.4%

Lebanese Illiterates (n = 11)

23 2.1%

30 2.8%

26 2.4%

Child Biliterates (n = 8)

29 3.6%

14 1.8%

19 2.5%


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Appendix B Analysis of Variance Table for Oral Numeral Only Study Main Effects Left-Right/Right-Left Group Interaction Effect Left-Right/Right-Left × Group

F (1, 50) = 2.494, p > .05 F (1, 50) = .867, n.s. F (1, 50) = 3.168, p = .05

Appendix C Analysis of Variance Table for Replication of Dehaene and Akhavein’s Bimanual SNARC Study Main Effects Left-Right/Right-Left Hand of Response Notation 2-way Interactions Hand of Response × Left-Right/ Right-Left Notation × Left-Right/Right-Left Hand of Response × Notation 3-way Interactions Hand of Response × Notation × Left-Right/Right-Left

F (1, 19) = 2.89, n.s. F (1, 19) = .703, n.s. F (3, 57) = 64.06, p < .001 F (1, 19) = 1.72, n.s. F (3, 57) = 1.20, n.s. F (3, 57) = .889, n.s. F (3, 57) = .886, n.s.

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