The ability to process the numerical magnitude of sets of items has been characterized in many animal species. Neuroimaging data have associated this ability to represent nonsymbolic numerical magnitudes (e.g., arrays of dots) with activity in the bilateral parietal lobes. Yet the quantitative abilities of humans are not limited to processing the numerical magnitude of nonsymbolic sets. Humans have used this quantitative sense as the foundation for symbolic systems for the representation of numerical magnitude. Although numerical symbol use is widespread in human cultures, the brain regions involved in processing of numerical symbols are just beginning to be understood. Here, we investigated the brain regions underlying the semantic and perceptual processing of numerical symbols. Specifically, we used an fMRI adaptation paradigm to examine the neural response to Hindu-Arabic numerals and Chinese numerical ideographs in a group of Chinese readers who could read both symbol types and a control group who could read only the numerals. Across groups, the Hindu-Arabic numerals exhibited ratio-dependent modulation in the left IPS. In contrast, numerical ideographs were associated with activation in the right IPS, exclusively in the Chinese readers. Furthermore, processing of the visual similarity of both digits and ideographs was associated with activation of the left fusiform gyrus. Using culture as an independent variable, we provide clear evidence for differences in the brain regions associated with the semantic and perceptual processing of numerical symbols. Additionally, we reveal a striking difference in the laterality of parietal activation between the semantic processing of the two symbols types.
The ability to understand and use numerical symbols is a culturally transmitted skill. Like literacy, symbolic numeracy only exists in cultures where it is explicitly instructed. The theoretical foundation (Dehaene, 1997) guiding the study of numerical cognition posits that symbolic numerical processing is scaffolded by a system of nonsymbolic numerical representation—one that is phylogenetically continuous (Brannon, 2006), ontogenetically foundational (Libertus & Brannon, 2009), and culturally universal (Zebian & Ansari, 2012; Gordon, 2004; Pica, Lemer, Izard, & Dehaene, 2004). This nonsymbolic system of numerical magnitude, dubbed the Approximate Magnitude System (ANS), is populated by neural representations of numerical magnitude that are imprecise in nature (Nieder & Dehaene, 2009). The representational imprecision can also be seen in symbolic representations of number, which suggests that numerical symbols are associated with the approximate magnitude representations of the ANS (Dehaene, Dupoux, & Mehler, 1990; Dehaene, 1989; Hinrichs, Yurko, & Hu, 1981; Duncan & McFarland, 1980; Sekuler & Mierkiewicz, 1977; Restle, 1970; Moyer & Landauer, 1967). In recent years, there has been a growing interest in the neural correlates specifically underlying the semantic processing of numerical symbols, as opposed to processes related to the visual processing of number symbols or other nonsemantic processes. Existing research has utilized three strategies to examine this question: (1) comparison of symbolic with nonsymbolic numerical processing, (2) examination of ontogenetic changes in symbolic number processing, and (3) training individuals to associate numerical magnitudes with novel symbols. Below, we briefly outline each of these approaches and their associated findings before introducing a novel approach to understanding the neural representations of numerical symbols, which is the focus of this report.
Following the first approach, a growing body of research comparing symbolic with nonsymbolic processing (Holloway, Price, & Ansari, 2010; Piazza, Pinel, Le Bihan, & Dehaene, 2007; Chochon, Cohen, van de Moortele, & Dehaene, 1999) has suggested that processing numerical symbols is associated with activation of the parietal cortex. When comparing symbolic and nonsymbolic numerical magnitude processing, hemispheric differences in the parietal cortex have been observed. Although the nonsymbolic representation of number has been associated with activity in the bilateral intraparietal sulcus (Dehaene, Piazza, Pinel, & Cohen, 2003), data from investigations using symbolic stimuli have converged to suggest that the left IPS may become specialized for the processing of numerical symbols (Ansari, 2008). Although these results are promising, it must also be acknowledged that symbolic and nonsymbolic numerical stimulus formats are, perceptually, quite different. Indeed, previous research has suggested that the processes involved in encoding numerical magnitude from symbolic and nonsymbolic formats are underpinned by distinct neural circuits (Holloway et al., 2010). In view of this, any differences between symbolic and nonsymbolic processing may represent encoding, representation, or both. Therefore, although comparisons of symbolic and nonsymbolic processing can provide a broad understanding of the neural representation of numerical symbols, they cannot be used to identify the brain regions specifically recruited to process the semantic meaning of numerical symbols.
The second approach investigates the effects of learning symbolic number representations by comparing age-related differences in the neural representation of numerical symbols. This approach has been taken by several studies. These studies have shown that the processing of numerical symbols undergoes an age-related shift in locus of activity from prefrontal regions earlier in development to inferior parietal regions later in development. Together, they suggest that the parietal lobe becomes tuned to numerical symbols over time (Holloway & Ansari, 2010; Houdé, Rossi, Lubin, & Joliot, 2010; Cantlon et al., 2009; Kaufmann et al., 2006; Ansari, Garcia, Lucas, Hamon, & Dhital, 2005). Using developmental time as an independent variable affords a more direct way of investigating what brain regions come on-line to process the semantic meaning of symbolic number. However, as with all developmental research, it remains unclear whether the age-related differences in brain activation represent maturational changes in the brain or changes as a function of learning. Specific to the present context, it is unresolved whether the shift from frontal to parietal regions reflects the age-related maturation of the parietal lobe, age-related differences in numerical understanding, or both.
One neuroimaging study has used the third approach to investigate the neural consequences of training individuals to associate numerical magnitude with novel symbols (Lyons & Ansari, 2009). These authors trained a group of adults to associate novel symbols with nonsymbolically presented numerical magnitudes (dot arrays) while fMRI data were recorded. Activity in the left inferior parietal cortex was systematically related to individual differences in how well novel symbols were connected to their semantic referents, giving further credence to the notion that left parietal regions can become tuned to the semantic information (numerical magnitude) associated with numerical symbols. Because this study was conducted with adult participants, the findings can be linked to learning-related processes independent of brain maturation. However, it is unclear exactly how the association of novel symbols with nonsymbolic numerical magnitudes is related to the learning of numerical symbols that occurs through enculturation, which involves a highly complex and developmentally protracted interplay of representations (verbal, semantic, and visual) and skills (subitizing, counting, and ordering). Indeed, a moment of introspection reveals that the visual form “31” does not only elicit an imprecise image of approximately 31 dots but rather calls forth a variety of mental representations including a distinct verbal tag, the knowledge of where 31 falls on a number line, and a quantitative understanding of “31-ness.” Thus, while providing important clues to the neural processes underlying the semantic processing of numerical symbols, the neural correlates elicited by such a training study should be considered as suggestive of, rather than equivalent to, the neural correlates of numerical symbol processing that results from enculturation.
In this study, we propose an alternative to the three approaches described above. An ecologically valid way to examine the semantic processing of symbolic number is to study differences in the neural responses to known and unknown symbolic representations of numerical magnitude. For example, individuals who are raised reading Chinese learn two different symbolic number systems: the Hindu-Arabic numerals and the logographic system of Chinese numerical ideographs. In contrast, individuals who learn to read languages such as English or Polish become fluent in using the Hindu-Arabic numeral system but have no knowledge of Chinese ideographs. It is possible, therefore, to utilize these naturally occurring groups to create an experimental scenario in which one group of participants has a semantic representation of a symbol while the other group does not. In addition to providing an ecologically valid way of identifying brain regions involved in the semantic processing of numerical symbols, this approach can also identify the brain regions involved in the asemantic, perceptual processing of number symbols. In other words, comparing the brain activation associated with processing numerical ideographs in the Chinese readers to those found in the control group, we should reveal regions involved in the semantic processing of numerical symbols. Inversely, when comparing the brain activations in the control group with those of the Chinese readers, we should isolate regions involved in the asemantic, or perceptual, processing of the symbols, because the control group can only process these symbols perceptually.
Against the background of the evidence reviewed above, we used this cross-linguistic approach to investigate the neural correlates involved in the semantic processing of numerical symbols that overcomes some of the limitations of the three methods discussed above. Specifically, we analyzed similarities and differences in brain activation associated with Hindu-Arabic numerals and Chinese numerical ideographs in participants who knew the semantic referents (numerical magnitude) of both types of symbols or only the Hindu-Arabic numerals. We reasoned that a comparison of the two symbol types would reveal the neural differences between semantic and nonsemantic processing of numerical symbols. In response to numerals, which can be semantically processed by both groups of participants, the IPS should show an activation pattern reflective of this common cultural knowledge. In contrast to numerals, numerical ideographs can be semantically processed by the Chinese readers, whereas in controls ideographs can only be processed as arbitrary shapes. Thus, a comparison between Chinese readers and controls should isolate regions recruited for the semantic processing of numerical symbols in a more direct fashion than was possible using the previous, above-discussed approaches.
To collect our data, we employed an fMRI adaptation paradigm, which takes advantage of a particular feature of the hemodynamic response measured by fMRI (Grill-Spector, Henson, & Martin, 2006). Specifically, if a particular aspect of a stimulus is presented repeatedly, the region or regions that respond to that feature will show a reduction in their hemodynamic response with repeated exposure (adaptation). A region that exhibits adaptation effects will also show a rebound response when the feature it encodes is changed. To put this in the present context: if a region encodes the semantic meaning of a specific numeral (hereafter referred to as the adaptation number), this region will adapt (decrease in response) to repeated exposure to the numeral. In addition, this region will rebound (increase in activation) when a novel numeral is presented (hereafter referred to as a deviant number). Most importantly, the extent of the rebound is a function of the numerical difference between the adapted number and the deviant in such a way that deviants that are further away on the “number line” from the adaptation number will lead to a relatively larger rebound response. This occurs because the internal representation of numerical magnitude is ratio dependent. Numbers that are close together on the “number line” (e.g., 6 and 8, ratio of 0.66) have a higher ratio and therefore share more representational overlap than numbers that are further apart (e.g., 6 and 12, ratio of 0.5). Ratio-dependent representation implies that if a region were responding to the numerical magnitude of a numerical symbol, the rebound in activation to a deviant should increase as the ratio between the adaptation and deviant numbers decreases (Piazza, Izard, Pinel, Le Bihan, & Dehaene, 2004).
Our use of fMRI adaptation affords us the confidence to compare the neural response to ideographs between the groups. If one uses an active task to compare the neuroanatomical correlates of different groups, one risks conflating group differences in competence with group differences in performance. In the present context, the aim is to isolate group differences in the semantic representation of numerical ideographs. By using an adaptation paradigm, we will be able to probe the neural representation of ideographs while avoiding confounding group differences in task performance.
However, our use of an adaptation design also faces a significant challenge. The question of semantic versus asemantic processing of numerical symbols was recently cast into sharp relief by Cohen (2009). This investigator reported data that decidedly showed that behavioral correlates previously assumed to reflect the semantic processing of Hindu-Arabic numerals in a particular cognitive task actually reflected the processing of the visual similarity (i.e., shape) of the numerals. Specifically, when visual similarity was pitted against numerical distance, it was found to account for unique variance in RT data. Although it could be argued that Cohen's findings were specific to the task he used, his data hinge upon a broader point: The visual similarity of the single digit Hindu-Arabic numerals is highly correlated with the semantic similarity of the single digit Hindu-Arabic numerals. Thus, data collected in an experimental design such as fMRI adaptation, which does not specifically direct attention to the semantics of numerals, faces the possibility that neural correlates evoked by semantic features of the numerals will be conflated with those that are evoked by visual features. We addressed this issue in two ways. Using similarity values adapted from Cohen's physical similarity function, we created a predictor to test for brain regions that respond to visual features of the numerals. In addition, our cross-linguistic design affords us another source of methodological traction on this issue. A comparison of the Chinese readers and the control group during ideograph processing could yield some important insights into the differences between the neuroanatomical correlates of ratio-dependent (semantic) and shape-dependent (visual) processing, because, whereas Chinese readers can process both the semantic and visual dimensions of the ideographs, the control group can only be sensitive to visual aspects of the ideographs.
Because the central question of this study focuses on group similarities and differences in the semantic processing of symbolic numerical magnitudes, it is crucial to verify that any potential group differences we report are specific to having acquired a symbolic representation and not because of group differences in the more basic nonsymbolic representations of the ANS. Therefore, we collected neuroimaging data while participants performed a nonsymbolic comparison task on three different numerical ratios. We then tested whether the effect of numerical ratio on nonsymbolic comparison differed between the groups.
In summary, we presented two types of numerical symbols: (1) the standard Hindu-Arabic numerals and (2) simplified Chinese ideographs to two groups of participants: (1) Chinese/English bilinguals who could read the ideographs and (2) English/Other bilinguals who could not read the ideographs nor any related ideographs from other east Asian writing systems. We hypothesized that if the neural signal in the IPS is tuned to cultural symbols of numerical magnitude, then we should demonstrate a ratio-dependent rebound response to the numerals, in both groups, but only see a rebound response to ideographs in the Chinese readers.
Twenty-six adults from undergraduate and graduate faculties at The University of Western Ontario were recruited into two groups of thirteen participants. The first group comprised individuals who reported the ability to read both Chinese and English fluently (age = 20–29 years, mean = 25 years; 4 men). The other group consisted of individuals who reported fluent reading in English and another non-East-Asian language (18–34 years, mean = 25 years; 4 men). After viewing the ideographs, participants were asked whether they recognized the symbols. All Chinese readers were able to indicate the correct numerical value for each ideograph. In contrast, none of the control group participants were able to indicate the meaning of the ideographs. All participants gave informed consent consistent with the policies of the Human Subjects Research Ethics Board at the University of Western Ontario.
The English language abilities of the participants in each group were measured in two ways. All individuals were students enrolled in the University of Western Ontario and, as such, were either native English speakers or demonstrated English proficiency in accordance with admissions policies at the university. Both groups completed the Reading Fluency, Word Attack, Math Fluency, and Calculation subtests of the Woodcock Johnson III Tests of Achievement. The control group showed significantly higher reading scores than the Chinese readers on both the Reading Fluency (M = 99.7, SE = 4.16, M = 89.42, SE = 2.70, t(20) = 2.14, p = .045) and the Word Attack subtests (M = 102.20, SE = 3.28, M = 90.75, SE = 2.74, t(20) = 2.70, p = .014). Relative to the control group, the Chinese Readers exhibited significantly higher scores on both the Math Fluency (M = 129.17, SE = 1.46, M = 98.60, SE = 6.23, t(20) = 5.20, p < .001) and Calculation tests relative to the control group (M = 126.17, SE = 3.68, M = 96.40, SE = 4.53, t(20) = 5.78, p < .001). Note that, although the groups differed in reading, both groups showed scores well within the normal range (85–115). This was not the case in mathematics; the control group scored within the normal range, whereas the Chinese readers scored above the normal range. Because of attrition, four individuals (three from the control group and one from the Chinese readers) did not complete the standardized tests, which resulted in a final sample of 22 participants who completed the standardized tests. Nonetheless, these individuals were included in the fMRI analysis (n = 26) described below. In other words, the results of the standardized tests come from a sample of 22 participants (10 from the control group and 12 from the group of Chinese readers), whereas the neuroimaging data include all 26 participants.
Parameters for stimuli were based on a recently published study investigating the neural correlates of numeral processing using fMRI adaptation (Notebaert, Nelis, & Reynvoet, 2011). The adaptation number (6) as well as the deviants (3, 4, 5, 8, 9, and 12) were presented in black on a gray background (color values: 211, 211, 211) using E-Prime 1.2 software. These numerical magnitudes were presented as Hindu-Arabic numerals and simplified ideographs. To control for low-level perceptual effects that could confound the adaptation/rebound signal, both the font and the location of the stimuli were varied across trials. In the numeral condition, stimuli were presented in either Times New Roman (40 pt) or Courier New (40 pt). In the ideograph condition, stimuli were presented in either SimSun (40 pt) or STHeiti (40 pt). Font was randomized across trials such that each font appeared an equal number of times for both the adaptation and deviant numerical magnitudes over the course of an experimental run. In addition to variations in font, the stimuli were presented in one of six locations 2° from the center of the display. The variation in location was pseudorandomized such that stimuli did not appear in the same location twice in a row.
Numerals and ideographs were presented in four separate runs, each of which consisted of a stream of symbols punctuated by blank screens. Each stream of symbols appeared for 200 msec. Each of the blank screens appeared for 1200 msec. The background color of the screen was the same when the screen was blank and when it contained a symbol. The stream of symbols consisted of a series of adaptation trials followed by either a deviant trial (36 total), a catch trial (12 total), or a null trial (12 total).
Adaptation trials consisted of repeated presentations of the numeral 6 between 5 and 9 times (average of 7 repeats). During a deviant trial, a numerical magnitude that deviated from the adaptation number was presented. Deviants included 3, 4, 5, 8, 9, and 12. For analysis purposes, deviants were binned by ratio: large ratio, 2.0 (deviants 3 and 12); medium ratio, 1.5 (deviants 4 and 9); and small ratio, 1.25 (deviants 5 and 8). Each deviant numerical magnitude was randomly dispersed through the run, resulting in 12 trials for each ratio over the course of a run. For the 12 catch trials, the adaptation number (6) was presented in red font. Participants were asked to press a button any time they saw a red symbol. The catch trials were randomly dispersed through the run. The 12 null trials consisted of the presentation of a numeral 6 in the same font as the adaptation trials. Thus, to the participant, a null trial looked identical to an adaptation trial. An illustration of the adaptation, deviant, null, and catch trials can be seen in Figure 1.
Each participant first completed the two ideograph runs followed by the two numeral runs. This fixed order was used to ensure that the control participants did not use the numerical information from the numeral task to guess what the ideographs meant. Because the trial duration (1400 msec) is not a multiple of the scan repetition time (TR = 2000 msec), a natural jitter (oversampling) was created in the time course of data acquisition.
Nonsymbolic Comparison Task
After the adaptation runs were completed, participants performed an active nonsymbolic numerical comparison task in which two dot arrays were presented. In this task, participants were instructed to select the side of the screen with the dot array that contained the larger magnitude of dots with a button press as quickly and accurately as possible. The dot arrays were paired such that they represented one of three numerical ratios: 0.5, 0.66, or 0.75. Contour length, density, and individual dot size were controlled such that the larger number of dots could not be reliably predicted from any of the nonnumerical variables continuous with it. Specifically, in half of the trials, the total area of each array in a given pair was equal, whereas the perimeters of each area were set such that the ratio between them was the inverse of the ratio of the number of dots. In the other half of the trials, the areas of each array in a given pair were defined such that the ratio between them was the inverse of the ratio between the number of dots, whereas the overall perimeter of each array in a pair was the same for both arrays. Sixteen trials for each ratio were presented in an event-related fashion with a jittered intertrial interval of 5–9 sec (average = 7500 msec).
fMRI Data Acquisition
Functional and structural images were acquired in a 3-T Siemens Tim Trio whole-body MRI scanner, using a Siemens 32-channel head coil. A gradient EPI T2* sequence sensitive to the BOLD contrast was used to acquire 38 functional images per volume, which were collected in an interleaved order (3 mm thickness, 80 × 80 matrix, TR = 2000 msec, echo time = 52 msec, flip angle = 78°) and covered the whole brain. Three hundred fifty-five volumes were acquired for each functional run. High-resolution anatomical images were acquired with a T1-weighted MPRAGE sequence (1 × 1 × 1 mm, T1 = 2300 msec, echo time = 4.25 msec, TR = 2300 msec, flip angle = 9°).
fMRI Data Preprocessing
All functional images were preprocessed using BrainVoyager QX 2.4.1. The steps included slice scan time correction (cubic spline interpolation), correction for 3-D head motion (trilinear motion detection and sinc motion correction), and temporal high-pass filtering (GLM-Fourier 2 cycles). All runs had less than 3 mm overall head motion and were thus included in the analysis. Each functional image was then coregistered to the subject's anatomical image, transformed into Talairach space, and smoothed with a 6-mm FWHM Gaussian smoothing kernel.
Each of the statistical maps reported in our study was first thresholded with an uncorrected p value of .001. Subsequently, the maps were corrected for multiple comparisons to a statistical level of p < .05 using the cluster level correction plugin built into BrainVoyager. A review of this approach to multiple comparison corrections can be found here (Forman et al., 1995).
The analysis of these data was adapted from one recently published by Notebaert and colleagues (2011). For each participant, a design matrix was created with three predictors: a parametrically weighted predictor for all ratio trials (parametric effect of ratio), a predictor in which all ratio trials were weighted equally (main effect of deviance), and a predictor for catch trials. The adaptation and null trials were modeled as baseline. In the ratio predictor, all of the deviant trials were included and each was given a weight value equal to that of its ratio to the adaptation number (see Table 1). Deviants 5 and 8 were given a weight of 1.25; deviants 4 and 9 were given a weight of 1.5; deviants 3 and 12 were given a weight of 2.0. To allow the general linear model (GLM) to mathematically distinguish the ratio effect from the main effect, the BrainVoyager analysis package automatically centered the weights on zero by subtracting the mean of the weights from each weight before convolving the predictors with the hemodynamic response function. A whole-brain multisubject GLM was calculated to test for regions exhibiting a significant ratio-dependent parametric increase of activation with increasing ratio. The resulting GLM consisted of three predictors, including one for catch trials (when the number turned red and participants had to press a button), one for the main effect of deviance, and a final one for the parametric effect of ratio. To maximize the sensitivity of the parametric test of ratio, we used a conjunction analysis to isolate regions whose activation profile exhibited both a significant main effect of deviance and a significant parametric effect of ratio. This approach was used because a region could theoretically show a significant effect of ratio but not show any evidence of numerical processing (main effect of deviance) greater than baseline. We avoided this problem by testing for regions that were sensitive to a conjunction of the main effect of deviance (all deviants > baseline) and the parametric effect of ratio (increased activation with decreasing ratio). To plot the ratio effect in each region, we extracted and plotted a parameter estimate of the mean activation across runs for the null trials and each deviant number (see Figures 2,3–4).
We designed our analyses to test the two a priori hypotheses outlined above. To review: commensurate with previous literature evincing its role in the semantic processing of numerals, we hypothesized that the IPS would show ratio-dependent processing in response to the Hindu-Arabic numerals. We expected that this activity would be highly similar across both groups. We tested this with Analysis 1, which canvassed the brain for regions showing ratio-dependent modulation (Main ∩ Parametric) in the Hindu-Arabic Numeral condition. We first tested for regions showing ratio-dependent modulation across both groups (Analysis 1a). We followed this by examining whether any regions showed significant group differences in ratio-dependent modulation by Hindu-Arabic numerals (MainChinese ∩ ParametricChinese) > (MainControl ∩ ParametricControl) (Analysis 1b). Following the same line of reasoning, we also hypothesized that the IPS would show ratio-dependent modulation in response to ideographs, but only in the Chinese readers. Mirroring our first analysis, Analysis 2 identified the ratio-dependent neural correlates of ideograph processing (Main ∩ Parametric). Initially, we looked within the Chinese and control groups separately to test for regions showing ratio-dependent modulation in response to the ideographs (Analyses 2a and 2b, respectively). We then tested whether any regions reflected significant group differences in the semantic processing of ideographs (MainChinese ∩ ParametricChinese) > (MainControl ∩ ParametricControl) (Analysis 2c).
Because of the relative nature of fMRI analysis, any voxelwise group difference we detect could reflect three different patterns that would have distinct functional implications. On the one hand, it is possible that both groups could show a significant effect but that this effect is significantly greater in one group relative to the other. Alternately, it is possible that neither group exhibits an effect that is significantly different than baseline but that the groups differ enough that we detect a significant difference. Finally, it is possible that one group shows an effect that is significantly greater than baseline, but the other group does not. To test between these hypotheses, any significant group difference will be further analyzed using simple contrasts of the means with baseline (one-way t test) to further determine the nature of the group difference.
Distinguishing Shape from Semantic Processing
As noted in the Introduction, a recent behavioral study demonstrated that, in some contexts, the shape of Hindu-Arabic numerals can be processed independently of the semantic meaning of the numerals (Cohen, 2009). To address whether any of the ratio-dependent effects we observe could be accounted for by differences in the visual features of the numerals, we performed an analysis looking for an effect of numeral shape similarity on the hemodynamic response function. We created a physical similarity predictor using an adapted version of the physical similarity function outlined by Cohen (2009). Using this approach, each numeral is first converted into the type of numeral that is used in old-fashioned digital alarm clocks or other appliances. In this way, each numeral can be created out of a pattern of seven lines, some of which are shared between two numerals and some which are not shared. We then calculated the ratio of shared features to the number of shared features plus the number of nonshared features (Shared/[Shared + Not Shared]). As the number of not shared features increases (i.e., as the numerals become visually dissimilar), the denominator of the equation increases and the calculated similarity value decreases. Using this Physical Similarity Function, we calculated the following similarity values and used them as weights in a parametric predictor: Numeral 3 = 1.75, Numeral 4 = 2.33, Numeral 5 = 1.2, Numeral 8 = 1.17, Numeral 9 = 1.75, Numeral 12 = 2.25. These weights correlated with the ratio weights (r = .63). In harmony with the ratio-dependent analysis, we examined which brain regions exhibited a significant conjunction of the Main and Parametric effects of the shape predictor.
In addition to our analysis using a physical similarity predictor, the cross-linguistic nature of our study afforded us an additional and unique way to investigate differences between shape and semantic response to numerical symbols. Because the control group did not know the meaning of the Chinese symbols, any response to numerical ideographs could therefore only be caused by differences in the visual features of the symbols rather than their meaning. Therefore, Analysis 2b, described above, provided data to examine the asemantic (shape-dependent) response to numerical ideographs (MainControl ∩ ParametricControl).
To analyze the nonsymbolic comparison task, we modeled the numerical ratio of each trial resulting in a parametric predictor with three ratios (.25, .50, and .75). This predictor was then regressed across the whole brain and resulted in a GLM that tested for a main effect of comparison (all trials equally weighted) and a parametric effect of ratio (each trial weighted by ratio). To isolate regions of the cortex that are sensitive to the numerical ratio of the nonsymbolic arrays that participants compared, we looked for regions that exhibited a conjunction of the main and parametric effects of nonsymbolic numerical comparison. In other words, we looked for regions that responded both to all numerical magnitudes positively and which also showed a parametric increase in activation in response to increasing ratio. We then directly compared the neural correlates of the nonsymbolic ratio effect between groups across the whole brain. This analysis was included to verify that the two groups showed comparable numerical representation in response to nonsymbolic numerical stimuli.
Although it was only indirectly relevant to our central question, our data provided a unique opportunity to examine the relationship between individual differences in nonsymbolic representations of magnitude and mathematical achievement scores in adults. As reported above, the Chinese group demonstrated better mathematical achievement relative to the control group. We were therefore curious whether behavioral performance on the nonsymbolic comparison task administered in the scanner was systematically related to mathematical achievement scores. This question is driven by the mixture of results reported by previous studies testing the association between nonsymbolic magnitude representation and arithmetic performance. Evidence from some studies has supported a link between these two variables (Halberda, Mazzocco, & Feigenson, 2008), whereas other studies have found that math skills are correlated with symbolic but not nonsymbolic representations of numerical magnitude (Holloway & Ansari, 2009). We examined whether the group difference in mathematical achievement was related to better behavioral performance on the nonsymbolic comparison task. In accordance with previous literature (Bugden, Price, McLean, & Ansari, 2012; Bugden & Ansari, 2011), we used a regression analysis to create standardized regression coefficients reflecting the parametric effect of ratio (.25, .50, .75) on RT for each individual. We then examined group differences in these values to establish whether the nonsymbolic ratio effect is related to mathematical achievement. In addition to RT, we also examined whether individual differences in overall accuracy accounted for differences in math achievement.
Analysis 1: Adaptation to Hindu-Arabic Numerals
Analysis 1a revealed that both the left IPS and the left fusiform gyrus (FG) showed a significant response to the conjunction of main and parametric effects for Hindu-Arabic numerals across both groups (Figure 2). These were the only regions revealed in this analysis. No other regions were significantly activated when the threshold was lowered to p < .05, uncorrected. The parietal activation spanned the left IPS from anterior to posterior portions of the sulcus. To determine whether both groups activated the left IPS equally, we conducted a whole-brain between groups t test (MainChinese ∩ ParametricChinese) > (MainControl ∩ ParametricControl) (Analysis 1b, not pictured). The results of this analysis statistically demonstrated that the activation in the left IPS and left FG was comparable across groups, as no region showed greater activation for one group relative to the other even at p < .05, uncorrected.
Analysis 2: Adaptation to Ideographs
Analysis 2a demonstrated that activation in a posterior portion of the right IPS showed ratio-dependent modulation in response to numerical ideographs in the Chinese readers (Figure 3). No other regions were found to show significant ratio-dependent modulation in Chinese readers at our predetermined threshold. However, if a more liberal threshold (p < .005, cluster corrected to p < .05) is used, Analysis 2a reveals bilateral posterior IPS and left fusiform gyrus activation. The control group also showed a neural response to numerical ideographs. Analysis 2b, which examined the control group separately from the Chinese readers, revealed that the left fusiform gyrus, but no regions in the IPS, showed a significant conjunction of main and parametric effects (see Figure 5) in the control group. No other regions showed such an effect at the lower threshold of p < .05, uncorrected.
Analysis 2c revealed only one region whose activation pattern reflected group differences in ratio-dependent modulation in response to numerical ideographs: the posterior right IPS (Figure 4). In this region, which overlapped with the right posterior IPS region from Analysis 2a, the effect of numerical ratio (parametric effect) was greater in the Chinese readers compared with the control group participants. Tested against zero, the Chinese group showed significant ratio-dependent activity in the IPS (mean = 0.406, SE = 0.101, t(12) = 4.0, p = .001). This was not the case for the control group who did not exhibit ratio-dependent activation in response to Chinese ideographs that was statistically different than zero (mean = 0.153, SE = 0.089, t(12) = 1.7, p = .11) (Figure 4, bar chart). No group difference was found in the left FG even when the statistical threshold was reduced to p < .05.
Physical Similarity Analysis
We examined the effect of physical similarity in two ways. Our first approach tested the parametric effect of physical similarity using parametric values calculated using the adapted verions of Cohen's formula, described above (Cohen, 2009). This analysis revealed that the left fusiform gyrus, but not the IPS, demonstrated an activation pattern that was parametrically modulated by the shape predictor. Our second approach to investigating shape-dependent processing of numerical symbols was to examine the ratio-dependent response to numerical ideographs in the control group (Analysis 2b). This analysis also revealed a significant activation in the left fusiform gyrus (see Figure 5).
Nonsymbolic Comparison Analysis
The behavioral data from the nonsymbolic comparison task across the groups showed higher RT for increasing ratio, but no group by ratio interaction Fratio (2, 44) = 133, p < .001; Fratio ×group (2, 44) = 1.4, p = .25. Similarly, error rate increased with increasing ratio across the groups, but this pattern did not differ between groups Fratio (2, 44) = 29, p < .001; Fratio ×group (2, 44) = 1.4, p = .27.
On the neural level, across the groups, a network of frontal and parietal regions showed a significant conjunction between the main and parametric effect. These included the right anterior IPS (35, −41, 36), the right posterior IPS (20, −62, 39), the left IPS (−22, −50, 39), the anterior cingulate gyrus (5, 10, 45), the right anterior insula (32, 19, 9), and the right inferior frontal gyrus (41, 4, 27). However, none of these regions, nor any others, showed significant group differences, even at the reduced threshold of p < .05, uncorrected.
Of the two regions in the right IPS revealed by this analysis, the more posterior site overlapped partially with the right IPS regions identified by Analyses 2a and 2c. The left IPS region that was elicited through the nonsymbolic comparison task was dorso-medial to and did not overlap with the region found in Analysis 1a (Hindu-Arabic numerals across groups).
Investigations characterizing the neural circuitry underlying the processing of numerical symbols in the brain typically fall into one of three categories: developmental studies, training studies, and those that contrast symbolic and nonsymbolic processing. All three of these have yielded important clues about the symbolic representation of numerical magnitude in the brain. However, as discussed above, all three also suffer their particular limitations. Although developmental studies reveal the effect of chronological age on functional brain organization, such studies cannot be used to establish whether brain changes are caused by maturation of brain circuits, experience and learning, or a complex interaction between these factors (Poldrack, 2010). Training studies, although free of brain maturation confounds, conflate a relatively brief period of training with the breadth and depth of learning that results from prolonged processes of enculturation. Comparisons of symbolic and nonsymbolic processing can provide broad insights into the neural correlates of number symbol processing but are limited in their specificity. Indeed, none of these approaches has yielded insight into the differences in neural substrates of the semantic relative to the asemantic/perceptual processing of numerical symbols.
The present experiment was designed to further constrain our understanding of the brain regions that underlie semantic and asemantic processing of number symbols. We hypothesized that parietal regions would be implicated in the semantic processing of symbolic numerical magnitudes and, furthermore, that the left parietal lobe, in particular, would respond to numerical symbols. Although previous adaptation experiments have characterized the neural correlates of symbolic number processing using similar adaptation designs (Notebaert et al., 2011; Cohen Kadosh, Cohen Kadosh, Kaas, Henik, & Goebel, 2007; Piazza et al., 2007), our study diverged from this previous research in its ability to distinguish semantic from asemantic processing of numerical symbols. Moreover, our investigation of the semantic processing of numerical ideographs is the first of its kind.
To test our hypotheses, we investigated the neural correlates specific to the semantic processing of numerical symbols by comparing the neural correlates underlying Chinese ideographs, which were known only to one group, and Hindu-Arabic numerals, which were known to both groups. Using an fMRI adaptation paradigm, we isolated brain regions whose activation patterns reflected sensitivity to the numerical magnitudes embedded in numerical symbols-both numerals (Analysis 1) and ideographs (Analysis 2). We then tested whether these results could be accounted for by differences in numerical shape or by group differences in how basic nonsymbolic numerical magnitudes are represented. We found partial support for our hypotheses. Commensurate with previous studies, we discovered that the left IPS shows sensitivity to the numerical ratio of Hindu-Arabic numerals. In contrast, the right IPS was implicated in the semantic representation of numerical ideographs only in those participants who knew their numerical meaning. The left fusiform gyrus, on the other hand, exhibited activation related to the physical similarity of the numerical symbols rather than ratio-dependent processing. Below, we discuss the results we obtained against the background of our hypotheses and put forth a theoretical explanation for the symbol-dependent laterality differences observed across our analyses.
Our first hypothesis stated that across both groups the meanings of Hindu-Arabic numerals should be represented in the parietal lobe in and around the intraparietal sulcus. Consistent with this hypothesis, the results from Analysis 1a showed that activity in the left IPS was found to be correlated with numerical ratio. The activation in this region was not found to differ between groups (Analysis 1b), suggesting that the role of this brain area in Hindu-Arabic numeral processing was equivalent in both groups. We also showed parietal activation in response to the Chinese numerical ideographs, but commensurate with our hypothesis, only in the Chinese readers who were the only participants who knew what the symbols meant. This group difference was statistically confirmed with Analysis 2c, which revealed that the effect of numerical ratio was found to be significantly stronger in the right IPS in the group of Chinese readers relative to the control group. A series of planned t tests demonstrated that the group difference in the right IPS was characterized by significant parametric modulation to the semantics of the ideographs in the Chinese readers that was absent in the control group.
In addition to demonstrating the role of the IPS in the semantic processing of numerical ideographs, our data also demonstrate a high degree of similarity in the neural correlates underlying the representation of Hindu-Arabic numerals across both groups. The null result of Analysis 1b, even at a low threshold, suggests that the cultural and linguistic differences between the groups do not influence the basic representation of symbolic numerical magnitude. This fact stands in direct contrast to other research suggesting that cultural differences influence the neural correlates of basic arithmetic (Tang et al., 2006). Taken together, our data and those of Tang et al. (2006) suggest that the role of culture and language on the neuroanatomical substrates of numerical processing depends on the nature of the process being observed. Although the basic representation of symbolic numerical magnitude may be highly comparable across culture, arithmetic processing with its deeper reliance on linguistic processing and the mental manipulation of numerical magnitudes appears to be more susceptible to cultural influences. Future research is necessary to truly clarify the role of culture in numerical neurocognition.
Taken together, the findings from Analyses 1 (adaptation to Hindu-Arabic numerals across groups), 2a (adaptation to Chinese ideographs in Chinese readers), and 2c (adaptation to Chinese ideographs between groups) provide strong evidence for the role of the parietal lobe in the semantic representation of numerical symbols. Our results validate previous data linking the IPS to the semantic representation and processing of symbolic numerical magnitude by providing an exact replication of the data reported by Notebaert et al. (2011). We provide an important extension to these previous findings with our demonstration that the parietal response to numerical symbols is general across cultures.
In addition to the high similarity in the processing of Arabic numerals in the two groups, they also exhibited absolutely no difference in the neural response to numerical ratio when the numerical magnitudes were presented as nonsymbolic arrays in the context of an active, numerical magnitude comparison task. Of the three perceptual formats (Hindu-Arabic numerals, numerical ideographs, and nonsymbolic arrays) that were tested in this study, the only one that showed significant differences between the groups was the culture-specific Chinese ideographs.
In accordance with previous research, which has hinted at left hemisphere dominance for numerical symbol processing, we anticipated finding left hemisphere dominance for both numerals and ideographs. We found partial support for this hypothesis. The analyses reported suggest a strong left lateralization in the parietal activation underlying the processing of Hindu-Arabic numerals, which is consistent with data reported by Notebaert et al. (2011). The left-lateralization of numerals, however, stands in contrast to the right parietal response to numerical ideographs. However, the neural response to numerical ideographs shows much weaker evidence of lateralization as a slightly reduced statistical threshold revealed bilateral IPS response to ideographs. What can account for these notation dependent differences in laterality? We propose that the neural differences could reflect differences in how numerals and ideographs are used in Chinese culture. For this proposal to be considered plausible, two conditions must be met. It must be the case that, in Chinese culture, ideographs and numerals are used in divergent ways. Second, it must be demonstrated that specialization of the left hemisphere is possible, such as through changes in laterality over developmental time.
Speaking to the first condition, numerical ideographs, while clearly recognized and understood by readers of the Chinese languages, are used less frequently than the Hindu-Arabic numerals, which officially replaced them in 1955 (for more information see the chapter entitled “Spoken Numbers and Number Symbols in China and Japan” in Menninger, 1992). Ifrah sums up this point nicely: “The [Hindu-Arabic numerals] are a kind of visual Esperanto: Europeans, Asiatics, Africans, Americans or Oceanics, incapable of communicating by the spoken word, understand each other perfectly when they write numbers using the figures 0, 1, 2, 3, 4…, and this is one of the most notable features of our present number-system. In short, numbers are today the one true universal language” (Ifrah, 2000, p. 594) Both cultures use Hindu-Arabic numerals, rather than ideographs or number words, to teach and perform formal mathematical operations. Indeed, as Menninger states, “There is another difference between the [Hindu-Arabic] and the Chinese numerals: with the former it is possible to make written computations, but not with the latter…. Thus the Chinese have always made their computations on the abacus…” (Menninger, 1992, p. 458). The use of numerals for mathematical training implies that educated individuals from both cultures have had a great deal more practice (and therefore have more fluency in) accessing the quantitative meaning of Hindu-Arabic numerals relative to number words or ideographs.
Does the left hemisphere show developmental and functional specialization in other domains? Evidence for this second condition can be found in neuroimaging studies of the development of reading. Such research has demonstrated a right-to-left shift in the neural correlates related to syntactic processing (Nuñez et al., 2011) as well as phonological, semantic, and orthographic tasks (Spironelli & Angrilli, 2009). In similar fashion, our data suggest that activity in the IPS shifts from bilateral recruitment for nonsymbolic and relatively unrefined symbolic representation of numerical magnitude (such as can be found in contemporary use of Chinese numerical ideographs) to a left-lateralized recruitment as symbolic representations become highly refined (such as can be found in contemporary use of Hindu-Arabic numerals). This assertion presupposes that the representation of numerical magnitude is present in the parietal lobe before formal schooling and is focused in the right intraparietal sulcus, as has been shown in recent studies (Hyde & Spelke, 2010; Izard, Dehaene-Lambertz, Dehaene, 2008; Cantlon, Brannon, Carter, & Pelphrey, 2006). We suggest that, as is the case in reading, it is possible that the left IPS becomes increasingly active in the representation of numerical magnitude over developmental time through an interaction of brain maturation and training in the use of numerical symbols. Our data, we argue, rather than suggesting that the left IPS is specialized for the representation of numerical symbols in general, instead show that the left IPS is specialized for the highly fluent semantic processing that underlies the use of Hindu-Arabic numerals in Chinese and Western culture and which differentiates the use of numerals from numerical ideographs in Chinese culture. Although this explanation is commensurate with ours and other data, it must be acknowledged that until it is directly tested it remains a speculative possibility as to the nature of the hemispheric differences observed in our study.
In addition to constraining our understanding of the semantic processing of number symbols in the brain, the present results also shed light on a recent issue that has been raised in the study of numerical cognition. Cohen (2009) demonstrated that a parametric response to numerical ratio is correlated with physical similarity between numerals when participants have to decide whether a target number is the same or different compared a reference number (in his study participants had to decide whether a target Arabic numeral was a 5 or not). More specifically, Cohen's results showed that the physical similarity between the target and reference was a better predictor of RT variability than the numerical ratio, suggesting that subjects were relying on perceptual similarity between the symbols to a greater extent than their semantic referents. Against the background of these findings, Cohen pointed out that we should be cautious how we interpret some behavioral effects that have often been linked to the semantic processing of numerical symbols, as the data may be equally well accounted for by metrics of the physical similarity between numerical symbols. This observation also has implications for brain imaging studies, such as the one reported here. In view of these issues, we investigated whether any brain regions were modulated by the physical similarity between the adaptation number and the deviants in the Hindu-Arabic numeral condition. The only region to show an effect of physical similarity was the left fusiform gyrus. Thus, the present findings suggest that physical similarity and the numerical magnitude of number symbols are being processed in parallel in the brain, with the IPS sensitive to the numerical magnitude and the fusiform to the physical similarity between the adaptation stimulus (6) and the deviants.
Another way in which our experiment allows us to look at the difference between semantic and perceptual processing of numerical symbols is through the comparison of the activation in response to the ideographs between the two groups. Specifically, in Analysis 2b, Chinese numerical ideographs elicited ratio-dependent responses in the left fusiform gyrus in the control group in a region overlapping with the area that exhibited response to the physical similarity of the Hindu-Arabic numerals. Because this group of participants had no knowledge of the meaning of the ideographs, it is impossible that the response in this group was related to the semantic processing of the ideographs. Instead, the response must have been related to the visual processing of the shape of the ideographs. The fusiform gyrus (see Figure 5) has been implicated in shape processing in other studies (e.g., Starrfelt & Gerlach, 2007), making this interpretation likely. Moreover, the fusiform gyrus has long been postulated as a likely candidate for the visual processing of numerals. In his seminal “Triple Code Model,” Dehaene demonstrated through a review of behavioral and neuropsychological findings that the processing of numerical symbols is built on three subprocesses that each handle a different level of information or “code” provided by the symbol: (1) the semantic code, which processes the numerical magnitude represented by the symbol; (2) the verbal code, which processes auditory number names of the symbols; and the (3) visual code, which processes the visual form of the symbols (Dehaene, 1992). In addition, the neuroanatomical substrate of these three codes were hypothesized as follows: (1) the semantic processing of numerical symbols is underpinned by the bilateral parietal lobe; (2) the verbal processing of numerals is housed in the inferior frontal gyrus as well as the middle and superior temporal gyri; and (3) the bilateral occipito-temporal regions support the processing of the visual forms of the symbols (Dehaene & Cohen, 1995). In this context it should be acknowledged that in a recent study comparing the brain responses to letters, Arabic numerals, and scrambled symbols, Price and Ansari (2011) found no evidence for a category-specific processing of Arabic numerals in the fusiform gyrus, implicating instead the left angular gyrus in such processing. The present findings did not contrast the processing of visual similarity between number symbols and other symbol categories, and thus, although the data suggest that the fusiform plays a role in the visual processing of number symbols, it is unclear whether such processing is category specific. Taken together, our findings support this dissociation between the perceptual and semantic processing of numerical symbols in the brain and lend further support that activation of the parietal cortex during symbolic number tasks is reflective of the processing of the semantic referents of numerical symbols.
As a final note, the two groups exhibited substantially different mathematical achievement abilities. Despite these differences, the two groups showed remarkably similar neural and behavioral correlates of nonsymbolic number processing. We demonstrated that, although the Chinese group showed higher mathematical skills, their mean nonsymbolic ratio effect was no different from the control group. The current body of literature on the potential relationship between nonsymbolic processing and math is characterized currently by a very mixed pattern of findings. Some studies report a significant relationship (Halberda & Feigenson, 2008; Halberda et al., 2008), whereas other researchers have failed to find similar results (Holloway & Ansari, 2009; Mundy & Gilmore, 2009). The data from this study provide another piece of the puzzle, which can help future researchers clarify the relationship between basic, nonsymbolic numerical representation and mathematical performance.
In summary, the findings reported in the present article make two principal contributions. First, we showed that the left parietal cortex is specialized for the representation of Hindu-Arabic numerals. Against the background of previous demonstrations that the left IPS houses a neural representation that is more finely tuned than that of the right IPS (Piazza et al., 2007), this brain region may represent an optimal site for the precise numerical representations communicated by the Hindu-Arabic numerals in cultures that use these numerals for mathematical computations. Second, the cross-linguistic nature of our study showed clear evidence that the IPS activity is related to semantic rather than asemantic processing—only participants who have a semantic representation of numerical symbols show responses to these in the IPS. Furthermore, this study reveals that the fusiform gyrus is likely involved in asemantic visual processing of numerical symbols. Future studies should address the development of connectivity between these regions to clarify further how their interplay constructs the symbolic representation of number.
Reprint requests should be sent to Daniel Ansari, Department of Psychology, Westminster Hall, The University of Western Ontario, London, ON N6A 3K7, Canada, or via e-mail: firstname.lastname@example.org.