How do individual differences in children's domain specific and domain general abilities relate to brain activity within the intraparietal sulcus during arithmetic? An fMRI study

Previous research has demonstrated that children recruit the intraparietal sulcus (IPS) during arithmetic, which has largely been attributed to domain‐specific processes such as quantity manipulations. However, the IPS has also been found to be important for domain‐general abilities, such as visuo‐spatial working memory (VSWM). Based on the current literature it is unclear whether individual differences in domain‐specific skills, domain‐general skills, or a combination of the two, are related to the recruitment of the IPS during arithmetic. This study examines how individual differences in both domain general and domain specific competencies relate to brain activity in the IPS during arithmetic, and whether the relationships are related to how brain activity is measured. In a sample of 44 school‐aged children, we found that VSWM was only weakly related to a neural index of arithmetic complexity (neural problem size effect), whereas symbolic number processing skills (symbolic comparison and ordering) were related to overall arithmetic activity (both small and large problems). By simultaneously examining multiple domain‐general and domain specific measures, we were also able to determine that symbolic skills were a stronger predictor of brain activity within the IPS than domain general skills such as VSWM and domain specific skills such as non‐symbolic number processing. Together, these findings highlight that neural problem size effect may reflect different cognitive processes than brain activity across both small and large arithmetic problems, and that symbolic number processing skills are a critical predictor of variability in IPS activity during arithmetic. Hum Brain Mapp 38:3941–3956, 2017. © 2017 Wiley Periodicals, Inc.     

Neural correlates of symbolic and non-symbolic arithmetic

Recent evidence suggests that areas in and around the intraparietal sulcus (IPS) represent magnitude in a stimulus-independent format. However, it has not been established whether the same is true for mental arithmetic or whether activation for higher level numerical processing diverges as a function of stimulus format. We addressed this question in a functional imaging study by presenting participants with simple addition problems using both symbolic (Arabic numerals) and non-symbolic (arrays of dots) stimuli. Conjunction analysis revealed common neural substrates for symbolic and non-symbolic addition in the anterior IPS bilaterally, left posterior IPS, medial frontal gyrus and left precentral gyrus. Right parietal and frontal cortex showed greater activation for non-symbolic addition. Our results demonstrate that mental arithmetic, studied using addition problems, is processed within the IPS independent of stimulus form. Additionally we examined whether exact and approximate addition conditions activated different neural substrates as a function of stimulus format. We did not find any differences between exact and approximate addition using symbolic and non-symbolic stimuli. This could be due to the inability of the participants to suppress exact calculation for single-digit addition problems. In contrast to recent findings, we found no significant activation for exact addition condition in left, language-related areas.     

A comes before B,like 1 comes before 2. Is the parietal cortex sensitive to ordinal relationships in both numbers and letters? An fMRI‐adaptation study

How are number symbols (e.g., Arabic digits) represented in the brain? Functional resonance imaging adaptation (fMRI‐A) research has indicated that the intraparietal sulcus (IPS) exhibits a decrease in activation with the repeated presentation of the same number, that is followed by a rebound effect with the presentation of a new number. This rebound effect is modulated by the numerical ratio or difference between presented numbers. It has been suggested that this ratio‐dependent rebound effect is reflective of a link between the symbolic numerical representation system and an approximate magnitude system. Experiment 1 used fMRI‐A to investigate an alternative hypothesis: that the rebound effect observed in the IPS is related to the ordinal relationships between symbols (e.g., 3 comes before 4; C after B). In Experiment 1, adult participants exhibited the predicted distance‐dependent parametric rebound effect bilaterally in the IPS for number symbols during a number adaptation task, however, the same effect was not found anywhere in the brain in response to letters. When numbers were contrasted with letters (numbers > letters), the left intraparietal lobule remained significant. Experiment 2 demonstrated that letter stimuli used in Experiment 1 generated a behavioral distance effect during an active ordinality task, despite the lack of a neural distance effect using fMRI‐A. The current study does not support the hypothesis that general ordinal mechanisms underpin the neural parametric recovery effect in the IPS in response to number symbols. Additional research is needed to further our understanding of mechanisms underlying symbolic numerical representation in the brain.     

Distinct representations of subtraction and multiplication in the neural systems for numerosity and language

It has been proposed that recent cultural inventions such as symbolic arithmetic recycle evolutionary older neural mechanisms. A central assumption of this hypothesis is that the degree to which a preexisting mechanism is recycled depends on the degree of similarity between its initial function and the novel task. To test this assumption, we investigated whether the brain region involved in magnitude comparison in the intraparietal sulcus (IPS), localized by a numerosity comparison task, is recruited to a greater degree by arithmetic problems that involve number comparison (single-digit subtractions) than by problems that involve retrieving number facts from memory (single-digit multiplications). Our results confirmed that subtractions are associated with greater activity in the IPS than multiplications, whereas multiplications elicit greater activity than subtractions in regions involved in verbal processing including the middle temporal gyrus (MTG) and inferior frontal gyrus (IFG) that were localized by a phonological processing task. Pattern analyses further indicated that the neural mechanisms more active for subtraction than multiplication in the IPS overlap with those involved in numerosity comparison and that the strength of this overlap predicts interindividual performance in the subtraction task. These findings provide novel evidence that elementary arithmetic relies on the cooption of evolutionary older neural circuits.     

The neural association between arithmetic and basic numerical processing depends on arithmetic problem size and not chronological age

The intraparietal sulcus (IPS) is thought to be an important region for basic number processing (e.g. symbol-quantity associations) and arithmetic (e.g. addition). Evidence for shared circuitry within the IPS is largely based on comparisons across studies, and little research has investigated number processing and arithmetic in the same individuals. It is also unclear how the neural overlap between number processing and arithmetic is influenced by age and arithmetic problem difficulty. This study investigated these unresolved questions by examining basic number processing (symbol-quantity matching) and arithmetic (addition) networks in 26 adults and 42 children. Number processing and arithmetic elicited overlapping activity in the IPS in children and adults, however, the overlap was influenced by arithmetic problem size (i.e. which modulated the need to use procedural strategies). The IPS was recruited for number processing, and for arithmetic problems more likely to be solved using procedural strategies. We also found that the overlap between number processing and small-problem addition in children was comparable to the overlap between number processing and large-problem addition in adults. This finding suggests that the association between number processing and arithmetic in the IPS is related to the cognitive operation being performed rather than age.     

Arithmetic strategy development and its domain-specific and domain-general cognitive correlates: A longitudinal study in children with persistent mathematical learning difficulties

Deficits in arithmetic fact retrieval constitute the hallmark of children with mathematical learning difficulties (MLD). It remains, however, unclear which cognitive deficits underpin these difficulties in arithmetic fact retrieval. Many prior studies defined MLD by considering low achievement criteria and not by additionally taking the persistence of the MLD into account. Therefore, the present longitudinal study contrasted children with persistent MLD (MLD-p; mean age: 9 years 2 months) and typically developing (TD) children (mean age: 9 years 6 months) at three time points, to explore whether differences in arithmetic strategy development were associated with differences in numerical magnitude processing, working memory and phonological processing. Our longitudinal data revealed that children with MLD-p had persistent arithmetic fact retrieval deficits at each time point. Children with MLD-p showed persistent impairments in symbolic, but not in nonsymbolic, magnitude processing at each time point. The two groups differed in phonological processing, but not in working memory. Our data indicate that both domain-specific and domain-general cognitive abilities contribute to individual differences in children's arithmetic strategy development, and that the symbolic processing of numerical magnitudes might be a particular risk factor for children with MLD-p.     

Functional dissociations between four basic arithmetic operations in the human posterior parietal cortex: a cytoarchitectonic mapping study

Although lesion studies over the past several decades have focused on functional dissociations in posterior parietal cortex (PPC) during arithmetic, no consistent view has emerged of its differential involvement in addition, subtraction, multiplication, and division. To circumvent problems with poor anatomical localization, we examined functional overlap and dissociations in cytoarchitectonically defined subdivisions of the intraparietal sulcus (IPS), superior parietal lobule (SPL) and angular gyrus (AG), across these four operations. Compared to a number identification control task, all operations except addition, showed a consistent profile of left posterior IPS activation and deactivation in the right posterior AG. Multiplication and subtraction differed significantly in right, but not left, IPS and AG activity, challenging the view that the left AG differentially subserves retrieval during multiplication. Although addition and multiplication both rely on retrieval, multiplication evoked significantly greater activation in right posterior IPS, as well as the prefrontal cortex, lingual and fusiform gyri, demonstrating that addition and multiplication engage different brain processes. Comparison of PPC responses to the two pairs of inverse operations: division versus multiplication and subtraction versus addition revealed greater activation of left lateral SPL during division, suggesting that processing inverse relations is operation specific. Our findings demonstrate that individual IPS, SPL and AG subdivisions are differentially modulated by the four arithmetic operations and they point to significant functional heterogeneity and individual differences in activation and deactivation within the PPC. Critically, these effects are related to retrieval, calculation and inversion, the three key cognitive processes that are differentially engaged by arithmetic operations. Our findings point to distribute representation of these processes in the human PPC and also help explain why lesion and previous imaging studies have yielded inconsistent findings.     

Attention to number: The convergence of numerical magnitude processing,attention, and mathematics in the inferior frontal gyrus

Research indicates that the neurocognitive system representing nonsymbolic numerical magnitudes is foundational for the development of mathematical competence. However, recent studies found that the most common task used to measure numerical acuity, the nonsymbolic number comparison task, is heavily influenced by non‐numerical visual parameters of stimuli that increase executive function demands. Further, this influence may be a confound invalidating theoretical accounts of the relation between number comparison performance and mathematical competence. Instead of acuity, the relation may depend on one's ability to attend to numerical information in the face of competing, non‐numerical cues. The current study investigated this issue by measuring neural activity associated with numerical magnitude processing acuity, domain‐general attention, and selective attention to number via functional magnetic resonance imaging while children 8–11 years old completed a nonsymbolic number comparison task and a flanker task. Results showed that activation in the right inferior frontal gyrus during incongruent versus congruent trials of the comparison task, our construct for attention to number, predicted mathematics achievement after controlling for verbal IQ, flanker accuracy rate, and the neural congruency effect from the flanker task. In contrast, activity in frontal and parietal regions responding to differences in difficulty of numerical comparisons, our construct for numerical magnitude processing acuity, did not correlate with achievement. Together, these findings suggest a need to reframe existing models of the relation between number processing and math competence to include the interaction between attention and use of numerical information, or in other words “attention to number.”     

Examining pitch and numerical magnitude processing in congenital amusia: A quasi-experimental pilot study

Introduction: Congenital amusia is a developmental disorder associated with deficits in pitch height discrimination or in integrating pitch sequences into melodies. This quasi-experimental pilot study investigated whether there is an association between pitch and numerical processing deficits in congenital amusia. Since pitch height discrimination is considered a form of magnitude processing, we investigated whether individuals with amusia present an impairment in numerical magnitude processing, which would reflect damage to a generalized magnitude system. Alternatively, we investigated whether the numerical processing deficit would reflect a disconnection between nonsymbolic and symbolic number representations. Method: This study was conducted with 11 adult individuals with congenital amusia and a control comparison group of 6 typically developing individuals. Participants performed nonsymbolic and symbolic magnitude comparisons and number line tasks. Results were available from previous testing using the Montreal Battery of Evaluation of Amusia (MBEA) and a pitch change detection task (PCD). Results: Compared to the controls, individuals with amusia exhibited no significant differences in their performance on both the number line and the nonsymbolic magnitude tasks. Nevertheless, they showed significantly worse performance on the symbolic magnitude task. Moreover, individuals with congenital amusia, who presented worse performance in the Meter subtest, also presented less precise nonsymbolic numerical representation. Conclusions: The relationship between meter and nonsymbolic numerical discrimination could indicate a general ratio processing deficit. The finding of preserved nonsymbolic numerical magnitude discrimination and mental number line representations, with impaired symbolic number processing, in individuals with congenital amusia indicates that (a) pitch height and numerical magnitude processing may not share common neural representations, and (b) in addition to pitch processing, individuals with amusia may present a deficit in accessing nonsymbolic numerical representations from symbolic representations. The symbolic access deficit could reflect a widespread impairment in the establishment of cortico-cortical connections between association areas.     

Neural correlates of symbolic number processing in children and adults

Using functional magnetic resonance imaging, we examined developmental differences in the functional neuroanatomy underlying symbolic number processing. Twelve adults and 12 children had to judge the relative magnitude of two single-digit Arabic numerals. We investigated which brain areas were significantly (P<0.005, uncorrected) more activated during processing of number pairs with small relative to large numerical distances. In the adult group, symbolic distance modulated bilateral parietal regions. In contrast, the group of children primarily engaged frontal regions. We conclude that the functional neuroanatomy underlying symbolic numerical magnitude processing undergoes an ontogenetic shift towards greater parietal engagement. This change may reflect maturation of underlying representations and increasing automaticity in mapping between numerical symbols and the magnitudes they represent.     

Magnitude processing of symbolic and non-symbolic proportions: an fMRI study

Background

Recent research indicates that processing proportion magnitude is associated with activation in the intraparietal sulcus. Thus, brain areas associated with the processing of numbers (i.e., absolute magnitude) were activated during processing symbolic fractions as well as non-symbolic proportions. Here, we investigated systematically the cognitive processing of symbolic (e.g., fractions and decimals) and non-symbolic proportions (e.g., dot patterns and pie charts) in a two-stage procedure. First, we investigated relative magnitude-related activations of proportion processing. Second, we evaluated whether symbolic and non-symbolic proportions share common neural substrates.

Methods

We conducted an fMRI study using magnitude comparison tasks with symbolic and non-symbolic proportions, respectively. As an indicator for magnitude-related processing of proportions, the distance effect was evaluated.

Results

A conjunction analysis indicated joint activation of specific occipito-parietal areas including right intraparietal sulcus (IPS) during proportion magnitude processing. More specifically, results indicate that the IPS, which is commonly associated with absolute magnitude processing, is involved in processing relative magnitude information as well, irrespective of symbolic or non-symbolic presentation format. However, we also found distinct activation patterns for the magnitude processing of the different presentation formats.

Conclusion

Our findings suggest that processing for the separate presentation formats is not only associated with magnitude manipulations in the IPS, but also increasing demands on executive functions and strategy use associated with frontal brain regions as well as visual attention and encoding in occipital regions. Thus, the magnitude processing of proportions may not exclusively reflect processing of number magnitude information but also rather domain-general processes.

     

Neural substrates for forward and backward recitation of numbers and the alphabet: a close examination of the role of intraparietal sulcus and perisylvian areas

Despite numerous studies on the neural basis of numerical processing, few studies have examined the neural substrates of one of the most basic numerical processing-number sequence recitation. The present study used fMRI to investigate neural substrates of number sequence recitation, focusing on the intraparietal sulcus (IPS) and perisylvian areas. This study used a 2 (number versus alphabet) x 2 (forward versus backward recitation) design. 12 Chinese undergraduates were asked to recite overtly but gently numerical and alphabetical sequences forward and backward. Results showed that, for both numerical and alphabetic sequences, the left IPS was activated when performing backward recitation, but not when performing forward recitation. In terms of perisylvian areas, all four tasks elicited activation in bilateral superior temporal gyrus and inferior frontal gyrus, but forward recitation elicited greater activation in the left posterior superior temporal gyrus than did backward recitation, whereas backward recitation elicited greater activation in the left inferior frontal gyrus than did forward recitation. These results suggest that forward recitation of numbers and the alphabet is typically based on verbal processing of numbers implemented in the perisylvian area, whereas backward recitation would likely require additional neural resources in the IPS.     

Are numbers special? The comparison systems of the human brain investigated by fMRI

Many studies have suggested that the intraparietal sulcus (IPS), particularly in the dominant hemisphere, is crucially involved in numerical comparisons. However, this parietal structure has been found to be involved in other tasks that require spatial processing or visuospatial attention as well. fMRI was used to investigate three different magnitude comparisons in an event-related-block design: (a) Which digit is larger in numerical value (e.g., 2 or 5)? (b) Which digit is brighter (e.g., 3 or 3)? (c) Which digit is physically larger (e.g., 3 or 3)? Results indicate a widespread cortical network including a bilateral activation of the intraparietal sulci for all different comparisons. However, by computing contrasts of brain activation between the respective comparison conditions and applying a cortical distance effect as an additional criterion, number-specific activation was revealed in left IPS and right temporal regions. These results indicate that there are both commonalities and differences in the spatial layout of the brain systems for numerical and physical comparisons and that especially the left IPS, while involved in magnitude comparison in general, plays a special role in number comparison.     

Fronto‐insular‐parietal network engagement underlying arithmetic word problem solving

Mathematical word problems are ubiquitous and standard for teaching and evaluating generalization of mathematical knowledge for real‐world contexts. It is therefore concerning that the neural mechanisms of word problem solving are not well understood, as these insights represent strong potential for improving education and remediating deficits in this domain. Here, we investigate neural response to word problems via functional magnetic resonance imaging (fMRI). Healthy adults performed sentence judgment tasks on word problems that either contained one‐step mathematical operations, or nonarithmetic judgments on parallel narratives without any numerical information. Behavioral results suggested that the composite efficiency measurement of combining accuracy and RT did not differ between the two problem types. Arithmetic sentence judgments elicited greater activation in the fronto‐insular‐parietal network including intraparietal sulcus (IPS), dorsolateral prefrontal cortex (PFC), and anterior insula (AI) than narrative sentence judgment. Narrative sentence judgments, conversely, resulted in greater activation predominantly in the left ventral PFC, angular gyrus and perisylvian cortex compared with reading arithmetic sentences. Moreover, task‐dependent functional connectivity analyses showed the AI circuits were more strongly coupled with IPS during arithmetic sentence judgments than nonarithmetic sentences. Finally, activations in the IPS during arithmetic were highly correlated with out‐of‐scanner performance on a distinct set of problems with the same characteristics. These results show arithmetic word problem performance differences may rely more heavily on fronto‐insular‐parietal circuits for mathematical model building than narrative text comprehension of similar difficulty. More broadly, our study suggests that quantitative measurements of brain mechanisms can provide pivotal role for uncovering crucial arithmetic skills.     

Parietal representation of symbolic and nonsymbolic magnitude

The close behavioral parallels between the processing of quantitative information conveyed by symbolic and nonsymbolic stimuli led to the hypothesis that there exists a common cerebral representation of quantity (Dehaene, Dehaene-Lambertz, & Cohen, 1998). The neural basis underlying the encoding of number magnitude has been localized to regions in and around the intraparietal sulcus (IPS) by brain-imaging studies. However, it has never been demonstrated that these same regions are also involved in the quantitative processing of nonsymbolic stimuli. Using functional brain imaging, we explicitly tested the hypothesis of a common substrate. Angles, lines, and two-digit numbers were presented pairwise, one to the left and one to the right of the fixation point. In the three comparison tasks, participants (n = 18) pressed the key on the side of the largest quantity. In the three control tasks, they indicated the side on which dimming occurred. A conjunction analysis between the three subtractions (comparison task-control task) revealed a site in left IPS that is specifically responsive when two stimuli have to be compared quantitatively, irrespective of stimulus format. The results confirm the hypothesis that quantity is represented by a common mechanism for both symbolic and nonsymbolic stimuli in IPS. In addition, the interaction between task and type of stimulus identified a region anterior to the conjunction site, not specific for quantitative processing, but reflecting general processes loaded by number processing.     

Neurodevelopmental differences in child and adult number processing: An fMRI-based validation of the triple code model

The triple code model of numerical cognition (TCM) details the neurocognitive mechanisms associated with perceiving and manipulating numerical information in exact symbolic (Arabic digits and number words) and approximate nonsymbolic numerical magnitude (e.g., dot arrays) representation codes. The current study provides a first empirical fMRI-based investigation into neurodevelopmental differences in 30 healthy children’s and 44 healthy adults’ recruitment of neural correlates associated with the Arabic digit, number word, and nonsymbolic magnitude codes. Differences between the two groups were found in cingulate regions commonly associated with domain-general aspects of cognitive control, as opposed to neural correlates of number processing per se. A primary developmental difference was identified in verbal number discrimination, where only adults recruited left-lateralized perisylvian language areas in accordance with the TCM. We therefore call for a revision of the verbal code and a formulation of separate child and adult-specific neurocognitive mechanisms associated with the discrimination of number words. Although further research is necessary, results indicate that numerical discrimination abilities in middle-school-aged children operate close to adult-level maturity. Neurodevelopmental differences may be more apparent in younger children, or on the level of functional network dynamics as opposed to a shift in recruited neural substrates.     

Neurodevelopmental differences in task-evoked number network connectivity: Comparing symbolic and nonsymbolic number discrimination in children and adults

Numerical cognition can take place in multiple representational formats, such as Arabic digits (e.g., 1), verbal number words (e.g., “two”), and nonsymbolic (e.g., •••) numerical magnitude. Basic numerical discrimination abilities are key factors underlying the development of arithmetic abilities, acting as an important developmental precursor of adult-level numeracy. While prior research has begun to detail the neural correlates associated with basic numerical discrimination skills in different representational formats, the interactions between functional neural circuits are less understood. A growing body of evidence suggests that the functional networks recruited by number discrimination tasks differ between children and adults, which may provide valuable insights into the development of numerical cognition. To this end, we posed two questions: how do the interactions between functional circuits associated with number processing differ in children and adults? Are differences in functional network connectivity modulated by numerical representational codes? A theoretically motivated 22 ROI analysis indicated significant functional connectivity differences between children and adults across all three codes. Adults demonstrated sparser and more consistent connectivity patterns across codes, indicative of developmental domain-specialization for number processing. Although neural activity in children and adults is similar, the functional connectivity supporting number processing appears subject to substantial developmental maturation effects.     

Shared and distinct neural circuitry for nonsymbolic and symbolic double‐digit addition

Symbolic arithmetic is a complex, uniquely human ability that is acquired through direct instruction. In contrast, the capacity to mentally add and subtract nonsymbolic quantities such as dot arrays emerges without instruction and can be seen in human infants and nonhuman animals. One possibility is that the mental manipulation of nonsymbolic arrays provides a critical scaffold for developing symbolic arithmetic abilities. To explore this hypothesis, we examined whether there is a shared neural basis for nonsymbolic and symbolic double‐digit addition. In parallel, we asked whether there are brain regions that are associated with nonsymbolic and symbolic addition independently. First, relative to visually matched control tasks, we found that both nonsymbolic and symbolic addition elicited greater neural signal in the bilateral intraparietal sulcus (IPS), bilateral inferior temporal gyrus, and the right superior parietal lobule. Subsequent representational similarity analyses revealed that the neural similarity between nonsymbolic and symbolic addition was stronger relative to the similarity between each addition condition and its visually matched control task, but only in the bilateral IPS. These findings suggest that the IPS is involved in arithmetic calculation independent of stimulus format.     

Neuroscience of learning arithmetic—Evidence from brain imaging studies

It is widely accepted that the human brain is remarkably adaptive not only in child development, but also during adulthood. Aim of this work is to offer an overview and a systematic analysis of neuroimaging studies on the acquisition of arithmetic expertise. In normally developing children and adults, the gain of arithmetic competence is reflected by a shift of activation from frontal brain areas to parietal areas relevant for arithmetic processing. A shift of activation is also observed within the parietal lobe from the intraparietal sulci to the left angular gyrus. Increases in angular gyrus activation with gaining of expertise have also been documented in other cognitive domains. It appears that the left angular gyrus activation is modulated by inter-individual differences in arithmetic performance. The comparison of normal individuals with exceptionally performing individuals (e.g., calculating prodigies) suggests that the experts’ arithmetic proficiency relies on a more extended activation network than the network found in non-experts. In expert individuals with long-lasting, extensive mathematical training, specific structural brain modifications are also evident.     

Response-selection-related parietal activation during number comparison

Neuroimaging studies of number comparison have consistently found activation in the intraparietal sulcus (IPS). Recently, it has been suggested that activations in the IPS vary with the distance between the numbers being compared. In number comparison, the smaller the distance between a number and the reference the longer the reaction time (RT ). Activations in the right or left IPS, however, have also been related to attentional and intentional selection. It is possible, therefore, that activity in this region is a reflection of the more basic stimulus and response-selection processes associated with changes in RT. This fMRI experiment investigated the effect of numerical distance independently from RT. In addition, activations during number comparison of single-digit and double-digit stimuli were compared. During number comparison blocks, subjects had to indicate whether digits were greater or smaller than a reference (5 or 65). In control blocks, they were asked to perform a perceptual task (vertical line present/absent) on either numerical or nonnumerical stimuli. Number comparison versus rest yielded a large bilateral parietal-posterior frontal network. However, no areas showed more activation during number comparison than during the control tasks. Furthermore, no areas were more active during comparison of numbers separated by a small distance than comparisons of those separated by a large distance or vice versa. A left-lateralized parietal-posterior frontal network varied significantly with RT. Our findings suggest that magnitude and numerical-distance-related IPS activations might be difficult to separate from fundamental stimulus and response-selection processes associated with RT changes. As is the case with other parameters, such as space, magnitude may be represented in the context of response selection in the parietal cortex. In this respect, the representation of magnitude in the human IPS may be similar to the representation of magnitude in other nonhuman primates.