2.1. Experiment 1a: lexical representation of Arabic digits, Tibetan numerals, and Mandarin numerals

2.1.1. Methods

Participants

Ninety Tibetan students (52 females, mean age: 16.1 years, range from 13 to 18) were recruited from a high school for students from ethnic minority regions.Footnote ¹ All the participants were high-school students who came to mainland China to prepare for the university entrance examination, and they lived in mainland China for an average of 0.75 years. As their native language, Tibetan was learned earlier than Mandarin which was exposed in the family from an early age. The systematic learning of Mandarin started as participants entered primary schools. As their school language, they used Mandarin most of the time in middle and high school. The teachers taught in Mandarin, including mathematics teaching. While they spoke Tibetan with their parents when they were at home. All participants were able to easily switch between Mandarin and Tibetan. Participant abilities for listening, reading, speaking, and writing Mandarin were evaluated by a five-point scale, in which ‘5’ stands for very proficient. The average Mandarin proficiency for listening, reading, speaking, and writing was 4.35, 4.43, 4.43, and 4.26, respectively. The average Mandarin proficiencies were 4.37, indicating a very proficient Mandarin level. All participants were physically and mentally healthy and none had participated in similar psychological experiments before. Participants who completed the experiment received compensation for participating.

Materials and design

Thirty Tibetan students (15 male, 15 female) were randomly selected from the high school for ethnic minorities. They were asked to evaluate the familiarity of the different number systems (i.e., Arabic digits, Tibetan numerals, and Mandarin numerals) by a five-point scale, in which ‘5’ stands for very familiar and ‘1’ stands for very unfamiliar. They had average scores of 4.90 out of 5 for familiarity with Arabic digits (1 through 100), 4.93 for familiarity with Tibetan numerals, and 4.90 for familiarity with Mandarin numerals. A t-test analysis found no significant difference in familiarity depending on the number format (p > 0.05).

Sixty pairs of corresponding two-digit Tibetan–Arabic and Mandarin–Arabic numerals (total 120) were randomly chosen (half even and half odd) and then divided into two groups for each pair (half even and half odd). One group of pairs for each language condition (e.g., Tibetan–Arabic) was randomly selected to be used in the learning phase and both groups appeared during the testing phase.

An equal number of pseudo-numerals for each of the three number formats were used as fillers for the lexical decision task. To match the Mandarin numerals, 10 Mandarin pseudo-numerals were chosen from simple characters that do not represent any quantities (甲, 乙, 丙, 丁, 天, 上, 人, 刀, 口, 云). Similarly, to match the Tibetan numerals and Arabic digits, 10 Tibetan pseudo-numerals were chosen from the Tibetan alphabet (ཆ, ས, བ, མ, ཤ, ཁ, ཉ, ཇ, ཕ, ཡ) and 10 symbols (#, *, ↓, ↑, ¥, △, ○, @, ♂, ♀) were chosen from a symbol font, respectively. Within each pseudo-numeral set, the pseudo-numerals were randomly paired to form nonnumerals two characters in length (matching the 2-digit pairs of real numerals).

The learning phase included 30 true-numerals and 30 pseudo-numerals. The testing phase included 60 true-numerals (30 studied-numerals or translation equivalents of the studied-numerals and 30 unstudied-numerals) and 60 pseudo-numerals. All numerals were randomly presented once, and the pseudo-numerals that appeared in the learning phase did not appear again in the testing phase.

The experiment adopted a 2 (testing numeral type: unstudied-numerals or studied-numerals) × 3 (language in learning phase-test phase set: Arabic–Arabic [A–A], Tibetan–Arabic [T–A], and Mandarin–Arabic [M–A]) factor mixed experimental design. The testing numeral type was the within-subjects variable, the phase set was the between-subjects variable, and the dependent variables were reaction time and accuracy of the decision-making task for Arabic digits during the testing phase.

Procedure

Before the formal experiment, participants were required to read and understand the instructions. Then they familiarized themselves with the task by completing a practice session. Throughout the experiment, they sat 50 cm from a computer monitor. The procedure for a trial is shown in Fig. 1. First, a red fixation cross appeared for 500 ms in the middle of the screen. Then, the stimuli appeared, and participants were asked to perform a decision task quickly and accurately. For each word, they pressed the ‘A’ key on the keyboard with their left hand if the word was a true-numeral and the ‘L’ key with their right hand if it was a pseudo-numeral. During the experiment, the left- and right-hand buttons were balanced (i.e., true-numeral with an ‘L’ key and pseudo-numeral with an ‘A’ key). If there they did not respond within 1,500 ms, the word disappeared automatically. After the response or the 1,500-ms limit, a blank screen was presented for 500 ms, and then the next trial began. After completing the practice task, the formal experiment began. The formal experiment had two stages: the learning phase and the testing phase. Instructions were given in Mandarin before each phase. A visual word (correct or wrong) feedback was provided after responses in the learning phase, but not in the test stage. The reaction time in ms and performance accuracy were recorded throughout the experiment.

Fig. 1.

Procedure of Experiment 1a.

2.1.2. Results and discussion

The data was excluded from the results if participants were not serious during the experiment and had accuracy rates higher than 70%. A three-sigma rule (Chen et al., Reference Chen, Wang and Peng2006, Reference Chen, Zhou, Gao and Dunlap2014; Pukelsheim, Reference Pukelsheim1994) was performed to delete the outliers, that is, the data beyond 3 standard deviations of the mean reaction times were excluded. No data was excluded in experiment 1a. The results are shown in Table 1 and Fig. 2. We performed ANOVA by participants (F ₁) and items (F ₂) separately.

Table 1.

Average reaction time (ms) and average accuracy rate (%) for Arabic digits in the test phase

Fig. 2.

Reaction times for the three learning-phase sets in the unstudied and studied conditions (ms).

The ANOVA for reaction time showed a significant main effect of testing numeral type for the participant analysis, F _{1(1, 87)} = 7.23, p < 0.05, η ² = 0.08. The mean reaction time in the studied condition (528.12 ms) was significantly shorter than in the unstudied condition (535.01 ms), p < 0.05. However, we did not find a significant effect of testing numeral type in the item analysis (p > 0.05). The main effect of the learning-phase set was not significant (p > 0.05) for the participant analysis, but it was significant for the item analysis, F _{2(2, 57)} = 44.84, p < 0.05, η ² = 0.61. The reaction time in the A–A condition (503.93 ms) was the fastest, followed by the T–A condition (541.58 ms), and the M–A condition (542.05 ms). Pairwise comparisons revealed a significant difference between A–A and T–A conditions (p < 0.05) and between A–A and M–A conditions (p < 0.05), but not between T–A and M–A conditions (p > 0.05). The interaction between testing numeral type and the learning-phase set was marginally significant, F _{1(2, 87)} = 2.77, p = 0.07, η ² = 0.06. Further simple effect analysis showed that when the stimuli in the learning phase were Arabic digits, the reaction time in the test phase for the studied numerals (506.40 ms) was significantly faster than for the unstudied numerals (521.81 ms), F _{1(1, 87)} = 12.06, p < 0.05, η ² = 0.12. However, when the stimuli in the learning phase were Tibetan and Mandarin numerals, there were no significant differences between the studied and unstudied conditions in the test phase (p > 0.05).

Therefore, although experiment 1a showed a long-term repetition-priming effect of Arabic numerals on Arabic numerals, the effect disappeared if the numerals in the learning phase were Tibetan or Mandarin (i.e., the cross-language conditions). This indicates that neither Tibetan numerals nor Mandarin numerals can activate Arabic digits at the lexical level. Thus, the results suggest that Arabic digits, Tibetan numerals, and Mandarin numerals are represented independently at the lexical level.

2.2. Experiment 1b: lexical representation of Tibetan and Mandarin numerals

2.2.2. Results and discussion

Data were analyzed in the same manner as in experiment 1a. No data were excluded. The results are shown in Table 2 and Fig. 3.

Table 2.

Average reaction time (ms) and average accuracy rate (%) for Tibetan numerals in the test phase

Fig. 3.

Reaction times for the two learning-test phase sets in the studied and unstudied conditions (ms).

The ANOVA revealed a significant main effect of testing numeral type in the participant analysis, F _{1(1, 58)} = 5.52,p < 0.05, η ² = 0.09, but not in the item analysis (p > 0.05). We also found a significant main effect of the learning-phase set, F _{1(1, 58)} = 6.02, p < 0.05, η ² = 0.09; F _{2(1, 58)} = 18.51, p < 0.05, η ² = 0.24. The interaction between the two factors was marginally significant, F _{1(1, 58)} = 3.33, p = 0.07, η ² = 0.05. Further simple effect analysis showed that when the stimuli in the learning phase were Tibetan numerals, the mean reaction time in the studied condition (576.33 ms) was significantly faster than in the unstudied condition (593.23 ms), with a 16.90-ms difference, F _{1(1, 58)} = 8.71, p < 0.05, η ² = 0.13. No significant differences between studied and unstudied conditions were found in the participant analysis or the item analysis when the stimuli in the learning phase were Mandarin numerals (p > 0.05).

In summary, experiment 1b also showed a repetition-priming effect, provided that the numerals in the learning and test phases were presented in the same language (Tibetan). However, we did not observe a cross-language priming effect, indicating that Mandarin numerals failed to activate Tibetan numerals at the lexical level, again suggesting that Tibetan and Mandarin numerals are stored independently at the lexical level.

3.1. Experiment 2a: conceptual representation of Arabic digits, Tibetan numerals, and Mandarin numerals

3.1.1. Methods

Participants

Ninety Tibetan students (36 males and 54 females, mean age: 16.0 years, range from 13 to 18) were recruited. They were in the same high school as the participants in experiment 1 and had also lived in mainland China for an average of 0.75 years. The average Mandarin proficiency for listening, reading, speaking, and writing was 4.42, 4.23, 4.31, and 4.03, respectively. The average Mandarin proficiencies were 4.12.

Materials and design

Forty pairs of corresponding two-digit Tibetan–Arabic and Mandarin–Arabic numerals were randomly selected from those used in experiment 1 (half odd and half even), and 60 numerals (1–100, not including the 40 selected numerals) were used as fillers. The 40 pairs were randomly divided into two groups (half even and half odd in each group). One group of pairs was selected as the stimuli for the learning phase, while both groups were included in the testing phase. Thus, the learning phase contained 20 numerals and 20 fillers, and the testing phase included 40 numerals (20 previously seen numerals or their translated equivalents and 20 new numerals) and 40 fillers. Data analysis was the same as in Experiment 1a.

Procedure

The experimental procedure was almost the same as in experiment 1, except that participant made parity judgments instead of lexical decisions (see Fig. 4).

Fig. 4.

Procedure for Experiment 2a.

3.1.2. Results and discussion

We excluded three participants’ data because their accuracy rates were lower than 70%. We also excluded data beyond 3 standard deviations from the mean. Overall, 3.33% of the data were excluded from the analyses. The results are shown in Table 3 and Fig. 5.

Table 3.

Average reaction time (ms) and average accuracy rate (%) for Arabic digits in the test phase

Fig. 5.

Reaction times for the three learning-test phase sets in the studied and unstudied conditions (ms).

The ANOVA analysis for reaction time showed a significant main effect of testing numeral type in the participant analysis, F _{1(1, 84)} = 16.63, p < 0.001, η ² = 0.17, but not for the item analysis (p > 0.05). We also found a significant main effect of the learning-phase set, F _{1((2, 84)} = 5.72, p < 0.01, η ² = 0.12; F _{2(2, 37)} = 57.90, p < 0.05, η ² = 0.76. Participants responded fastest in the A–A condition, followed by the M–A and T–A conditions. Pairwise comparisons showed significant differences between A–A and T–A conditions (p < 0.05) and between A–A and M–A conditions (p < 0.05), but not between T–A and M–A conditions (p > 0.05). The interaction between the two factors was not significant (p > 0.05). In all three learning-test phase sets (A–A, T–A, M–A), reaction times for the studied numerals were significantly faster than those for the unstudied numerals (A–A: studied vs. unstudied = 615.04 vs. 630.85 ms, F _{1(1, 84)} = 4.78, p < 0.05, η ² = 0.05; T–A: 676.70 vs. 692.88 ms, F _{1(1, 84)} = 5.19, p < 0.05, η ² = 0.06; M–A: 662.01 vs. 681.08 ms, F _{1(1, 84)} = 6.72, p < 0.05, η ² = 0.07).

In summary, experiment 2a showed a priming effect for Arabic digits regardless of the number format in the learning phase. Specifically, we observed a cross-language long-term repetition-priming effect, indicating that the conceptual representation of Arabic digits was activated in the learning phase by the Mandarin and Tibetan numerals, suggesting that the semantic representation of Arabic digits and the semantic representation of Tibetan and Mandarin numerals are not stored separately.

3.2. Experiment 2b: conceptual representation of Tibetan and Mandarin numerals

3.2.2. Results and discussion

Data were analyzed as in experiment 2a and data from the same individuals were removed, as were data beyond 3 standard deviations from the reaction time mean. The experimental results are shown in Table 4 and Fig. 6.

Table 4.

Average reaction time (ms) and average accuracy rate (%) for Tibetan numerals in the test phase

Fig. 6.

Reaction times for the two learning/test phase sets in the studied and unstudied conditions (ms).

ANOVA analysis for reaction time showed a significant main effect of testing numeral type in both participant and item analyses, F _{1(1, 55)} = 4.84, p < 0.05, η ² = 0.08; F _{2(1, 38)} = 4.47, p < 0.05, η ² = 0.11. The main effect of the learning-phase set was not significant for the participant analysis (p > 0.05), but it was significant for the item analysis, F _{1(1, 38)} = 4.99, p < 0.05, η ² = 0.12. The interaction between the two factors was not significant for the participant analysis (p > 0.05), but it was for the item analysis, F _{2(1, 38)} = 2.08, p < 0.05, η² = 0.05. Further simple effect analysis showed that in both the T–T and M–T conditions, the reaction time was faster for the studied numerals than for the unstudied numerals, with the difference being significant for the T–T condition and marginally significant for the M–T condition (T–T: 760.69 vs. 773.52 ms, F _{1(1, 55)} = 1.62, p > 0.05, η ² = 0.03; M–T: 770.78 vs. 789.56 ms, F _{1(1, 55)} = 3.36, p = 0.07, η ² = 0.06).

Therefore, experiment 2b again revealed a repetition-priming effect in the cross-language condition. Specifically, conceptual representations of Tibetan numerals were activated in the learning phase by the Mandarin numerals, again suggesting that the semantic representations of Tibetan and Mandarin numerals are stored together.

4.1. Lexical and conceptual representations of numbers in Tibetan–Mandarin bilinguals

In our two experiments, we treat the three kinds of number notations as three languages. They have different physical forms (e.g., the Arabic digit ‘9’, the mandarin word 九, and the Tibetan word དགུ་) but have the same meaning. We want to know how these number notations are represented in the brain at the lexical and conceptual levels. Thus, in experiment 1, to examine the characteristics of their lexical representations, bilingual participants completed the task in which they judged whether they were seeing true-numerals or pseudo-numerals, but did not have to access the meaning of the number. In experiment 2, to examine characteristics of the conceptual representation of these number formats, participants perform a parity judgment task in which semantic access to the number was required. Evidence of a priming effect at the lexical or conceptual level would indicate that the number notations share lexical or conceptual representations.

In the current study, neither the Tibetan nor Mandarin numerals presented in the learning phase activated the lexical information of their corresponding Arabic digits, nor did the Mandarin numerals presented in the learning phase activate the corresponding Tibetan numerals. This indicates that the lexical information for Arabic digits, Tibetan numerals, and Mandarin numerals are stored independently. The fact that the facilitation effect of Tibetan numerals and Mandarin numerals on Arabic digits, and the facilitation effect of Mandarin numerals on Tibetan numerals at the conceptual level illustrate that Arabic digits, Tibetan number words, and Mandarin number words share conceptual representations. Thus, our results are inconsistent with the Independent Representational Model (Kolers, Reference Kolers1963), which suggested that each language has a separate system of memory representation. Rather, our results were more in line with the Shared Representational Model (e.g., Kroll & Stewart, Reference Kroll and Stewart1994; Potter et al., Reference Potter, So, Eckardt and Feldman1984) or the Distributed Feature Model (Groot et al., Reference Groot, Dannenburg and Vanhell1994); bilinguals have a shared conceptual store and separate lexical stores for these three number notations.

Our results were consistent with previous studies of bilingualism. For example, Li et al. (Reference Li, Mo, Wang and Luo2006) and Mo et al. (Reference Mo, Li and Wang2005) both examined Chinese–English bilinguals in their studies on the lexical representation of words, finding that the two languages are represented independently at the lexical level. Cui and Zhang (Reference Cui and Zhang2009) and Gao et al. (Reference Gao, Wang, Guo, Zhang and Bai2015) also studied the representation of words in bilingual Chinese minorities. They also found that in Tibetan–Chinese bilinguals, lexical information was stored separately. Like results on conceptual representation, previous studies have also found that the semantic representations of equivalent words in bilinguals are costored (Cui & Zhang, Reference Cui and Zhang2009; Gao et al., Reference Gao, Wang, Guo, Zhang and Bai2015; Li et al., Reference Li, Mo, Wang and Luo2006a; Li & Li, Reference Li and Li2019; Mo et al., Reference Mo, Li and Wang2005; Wen & Rabigul, Reference Wen and Rabigul2006). Although there is a very strong argument that numerical concepts have an ontogenetic origin and a neural basis that are independent of language (see Gelman & Butterworth, Reference Gelman and Butterworth2005, for a review), we found that for skilled bilinguals, representation of numbers at the lexical and conceptual levels was similar to that for general words. Moreover, connections between number and language have been proposed on theoretical and empirical grounds (Dehaene & Cohen, Reference Dehaene and Cohen1991; McCloskey, Reference McCloskey1992; Spelke & Tsivkin, Reference Spelke and Tsivkin2001).

4.2. Relationship between the central findings and current models of number processing

How can we relate the current critical findings to current models of number processing? We mentioned three number processing models in the introduction: the abstract-modular model proposed by McCloskey (Reference McCloskey1992), McCloskey and Macaruso (Reference McCloskey and Macaruso1995), and McCloskey et al. (Reference McCloskey, Sokol and Goodman1986), the triple-code model proposed by Cohen and Dehaene (Reference Cohen and Dehaene1995) and Dehaene (Reference Dehaene1992), and the encoding-complex model proposed by Campbell (Reference Campbell1994) and Campbell and Epp (Reference Campbell and Epp2004). These models agree that Arabic digits and number words are processed by separate input modules. For example, the abstract-modular model proposed two different input systems for Arabic digits and number words onto a common abstract representation of magnitude (McCloskey, Reference McCloskey1992). The triple-code model specifies three different modules, including a visual Arabic system for mediating Arabic digital input, an auditory-verbal system for mediating the written and spoken number-word input, and a system for estimation (Dehaene, Reference Dehaene1992). Dehaene et al. (Reference Dehaene, Dehaene-Lambertz and Cohen1998) proposed that verbal numerals and Arabic digits have independent visual recognition systems. The encoding-complex model also involves format-specific activation in one or more representational codes (e.g., visual and verbal). Our results from experiment 1 were consistent with the proposition hypothesized by these models of number processing; different number notations are stored separately at the lexical level (i.e., physical forms) in the brain. This is consistent with the idea of different input systems found in the three number-processing models.

At the conceptual level, it seems that our results are consistent with the abstract-modular model (McCloskey, Reference McCloskey1992). The numeral comprehension module in this model converts different number forms (e.g., Arabic digits, Tibetan numerals, Mandarin numerals) into a common abstract code, which is much the same as a common conceptual representation shared by number notations. Similarly, the triple-code model also assumes that tasks that activate semantics are not affected by the numeral form.

Interestingly, we analyzed the data from the learning phase to examine the response difference between the three notations. In detail, a significant difference was found between number words and Arabic numerals (M = 511 ms, SD = 69.8 ms) when they performed a lexical decision task (Tibetan: M = 607 ms, SD = 89.5 ms, t ₍₂₉₎ = 4.32, p < 0.001; Mandarin: M = 602 ms, SD = 75.1 ms, t ₍₂₉₎ = 4.85, p < 0.001). And the significant difference was also found in the parity judgment task (Arabic: M = 666 ms, SD = 78.0 ms; Tibetan: M = 776 ms, SD = 133.5 ms, t ₍₂₉₎ = 3.51, p < 0.01; Mandarin: M = 757 ms, SD = 97.1 ms, t ₍₂₉₎ = 3.87, p < 0.001). Obviously, the current results are inconsistent with the abstract-modular model. According to this model, the responses to the three number notations should be the same. However, responses to both Tibetan and Mandarin numerals were found to be slower than those to Arabic digits, which supported the triple-code model or the encoding-complex model. Moreover, our results were consistent with previous studies of number processing in which Arabic digits were processed faster than number words in numerical and magnitude-judgment tasks or in simple addition and multiplication tasks (Campbell et al., Reference Campbell, Kanz and Xue1999; Damian, Reference Damian2004).

Here, we would like to adopt the encoding-complex model proposed by Campbell and Epp (Reference Campbell and Epp2004) and the work by Bernardo (Reference Bernardo2001) to explain the characteristics of number processing in Tibetan–Mandarin bilinguals. The encoding-complex model contains five representational systems: L1 visual codes and Arabic visual codes for numeral input and output processes; L1 and L2 verbal number codes for processing the language-based components, including the lexical processes; and a magnitude code that provides the conceptual foundation of quantity and serves as the central nexus of the model. The efficiency of interactions between these codes is expected to correspond to how our participants’ history of experience of tasks, numeral formats, and languages affect the encoding pathways. This model explains our research results very well: a shared conceptual representation (i.e., the magnitude code) and a separately stored lexical representation. Specifically, it assumes that one more code, the Tibetan visual code, is included in addition to the five codes proposed by Campbell and Epp (Reference Campbell and Epp2004). Fig. 7 depicts an encoding-complex model of Tibetan–Mandarin bilinguals’ number representation. The result that Arabic digits, Tibetan number words, and Mandarin number words are stored separately corresponds to three independent visual codes for Arabic, Tibetan, and Mandarin in the model. The magnitude code corresponds to the fact that all the numerals share a common conceptual representation. In the model, darker arrows represent stronger links between the codes. The result that the responses were faster for Arabic digits was shown in the model by darker-arrow links than the links between visual code and magnitude code. In addition, a faster response for the Mandarin numerals than the Tibetan numerals was shown in the model by darker-arrow links between Mandarin visual code and magnitude (see more discussion below). However, the current study did not explore all the links in the model, such as the pathways between the verbal number code and the magnitude code, which were shown by bidirectional arrows with a dotted outline. The model will be improved by future research.

Fig. 7.

Encoding-complex model of number processing in Tibetan–Mandarin bilinguals.

Two problems regarding the participants whom we recruited should also be clarified. On one hand, we would like to explain the relationship between the Tibetan and Chinese languages. Although the Sino-Tibetan language family includes early literary languages such as Chinese and Tibetan, there are great differences between the language types within the Sino-Tibetan language family. The Sino-Tibetan language family is traditionally presented as divided into Sinitic (i.e., Chinese) and Tibeto-Burman branches, which show many differences in typological contrasts such as written form, word order, and morphology. For the word order, Chinese word order is subject-verb-object while Tibetan word order is subject-object-verb. For the written form, Chinese is ideographic while Tibetan is recorded in alphabetic scripts. In the number domain, just like the languages, Tibetan number words are in alphabetic written form while Chinese number words are in ideographic written form. Hence, we consider those who master both Tibetan and Chinese to be bilinguals and these two languages can cause differences in information processing.

On the other hand, the participants’ language proficiency should also be illustrated. The Tibetan–Mandarin bilinguals in the current study have been studying and speaking Mandarin for a long time, and they have been living in mainland China for a period of time as we described in the method. Moreover, we asked participants about their daily use of Mandarin in mainland China after the experiment. The participants and the people around them speak Mandarin in their daily lives. Most of the participants recruited in the current study passed the national Chinese language test or the practice test for the college entrance examination. The examination is proved to be more scientific, and more comprehensive than the Chinese proficiency test for minorities (Level 3) (Hua, Reference Hua2020). Thus, we consider them to be balanced bilinguals, and they have no impact on the findings of numeral representations, which is also consistent with the finding of no effect of language experience on brain activity underlying arithmetic by Brignoni-Pérez (Reference Brignoni‐Pérez, Matejko, Jamal and Eden2021).

Another finding of the current experiment further supports this problem. In the present study, we found a faster response for the Mandarin numerals than the Tibetan numerals, even though Tibetan was the native language (L1). It should be noted that Arabic digits were assumed to be processed much the way objects are; the semantic information was accessed directly just like in picture naming (Damian, Reference Damian2004; Fias, Reference Fias2001; Fias et al., Reference Fias, Reynvoet and Brysbaert2001; McCloskey, Reference McCloskey1992). Studies in Chinese word recognition found that the word meaning is mainly achieved directly through orthography (Zhou et al., Reference Zhou, Bai, Shu and Qu1999; Zhou & Marslen-Wilson, Reference Zhou and Marslen-Wilson2000). Thus, the reason why Chinese number words were processed faster than Tibetan numerals could be that the semantic information for both Mandarin numerals and Arabic digits could be accessed directly through the written form. Interestingly, this result was also consistent with the more specific propositions of the BECM (Bernardo, Reference Bernardo2001). In Bernardo’s study, they suggested that the stronger verbal code is not always in the native language, but in the language used for learning and practicing arithmetic tasks. The Tibetan–Mandarin bilinguals recruited here not only learned and used Arabic digits at an early age in school but also have been studying and living in mainland China for a period of time. Using Mandarin verbal numbers more frequently might strengthen the link between the Mandarin visual code and the magnitude code.

In summary, by conducting two experiments, we investigated the representation of Arabic digits, Tibetan numerals, and Mandarin numerals at the lexical and conceptual levels. Results showed that these number notations shared a conceptual representation but had independent lexical representations. Among three number-processing models, our results are best explained by the encoding-complex model.