Stephan E. Vogel

Semantic and perceptual processing of number symbols: Evidence from a cross-linguistic fmri adaptation study

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.

Developmental specialization of the left parietal cortex for the semantic representation of Arabic numerals: an fMR-adaptation study.

Highlights • Age-related changes in the brain regions processing number symbols were investigated.• Brain activity of a group of 6- to 14-year-olds was measured with fMR-adaptation.• Ratio-dependent activation in the left IPS correlated with age.• Age-invariant ratio-dependent activation in the right IPS was found.• The construction of symbolic number depends on left IPS engagement.

Overlapping and distinct brain regions involved in estimating the spatial position of numerical and non-numerical magnitudes: An fMRI study

How are numerical and non-numerical magnitudes processed in the brain? Brain imaging research, primarily using comparison paradigms (i.e. judging which of two magnitudes is larger), has provided strong evidence demonstrating that the intraparietal sulcus (IPS) is a key region for processing both numerical (e.g. Arabic numerals, arrays of dots) and non-numerical magnitudes (e.g. height, brightness). These studies have suggested that there is both activation overlap and segregation in the brain regions involved in processing different dimensions of magnitude. In the present functional Magnetic Resonance Imaging (fMRI) study, we extended this line of investigation by probing the brain mechanisms underlying the mapping of numerical (Arabic numerals) and non-numerical magnitudes (brightness levels) onto a number line. Consistent with previous studies the present results revealed that number and brightness estimation was associated with overlapping activation within right lateralized areas of the posterior IPS. In addition, the contrast between number and brightness estimation revealed that bilateral anterior regions of the IPS are specifically involved in the process of estimating the position of symbolic numbers onto a number line. Furthermore, we found a significant influence of landmark reference points (0, 50 and 100) on brain activation in the right IPS for number estimation only. No regions were found to be specifically associated with brightness estimation. The results of this study reveal that the estimation of both numerical and non-numerical magnitude are associated with the engagement of a right lateralized magnitude system, but that symbolic number estimation is associated with additional engagement of bilateral regions of the anterior IPS.

Differential processing of symbolic numerical magnitude and order in first-grade children

A growing body of evidence has indicated a link between individual differences in childrens symbolic numerical magnitude discrimination (e.g., judging which of two numbers is numerically larger) and their arithmetic achievement. In contrast, relatively little is known about the processing of numerical order (e.g., deciding whether two numbers are in ascending or descending numerical order) and whether individual differences in judging numerical order are related to the processing of numerical magnitude and arithmetic achievement. In view of this, we investigated the relationships among symbolic numerical magnitude comparison, symbolic order judgments, and mathematical achievement. Data were collected from a group of 61 first-grade children who completed a magnitude comparison task, an order judgment task, and two standardized tests of arithmetic achievement. Results indicated a numerical distance effect (NDE) in both the symbolic numerical magnitude discrimination and the numerical order judgment condition. However, correlation analyses demonstrated that although individual differences in magnitude comparison correlated significantly with arithmetic achievement, performance on the order judgment task did not. Moreover, the NDE of the magnitude and order comparison performance was also found to be uncorrelated. These findings suggest that order and numerical magnitude processing may be underpinned by different processes and relate differentially to arithmetic achievement in young children.

On the ordinality of numbers: A review of neural and behavioral studies

The last several years have seen steady growth in research on the cognitive and neuronal mechanisms underlying how numbers are represented as part of ordered sequences. In the present review, we synthesize what is currently known about numerical ordinality from behavioral and neuroimaging research, point out major gaps in our current knowledge, and propose several hypotheses that may bear further investigation. Evidence suggests that how we process ordinality differs from how we process cardinality, but that this difference depends strongly on context-in particular, whether numbers are presented symbolically or nonsymbolically. Results also reveal many commonalities between numerical and nonnumerical ordinal processing; however, the degree to which numerical ordinality can be reduced to domain-general mechanisms remains unclear. One proposal is that numerical ordinality relies upon more general short-term memory mechanisms as well as more numerically specific long-term memory representations. It is also evident that numerical ordinality is highly multifaceted, with symbolic representations in particular allowing for a wide range of different types of ordinal relations, the complexity of which appears to increase over development. We examine the proposal that these relations may form the basis of a richer set of associations that may prove crucial to the emergence of more complex math abilities and concepts. In sum, ordinality appears to be an important and relatively understudied facet of numerical cognition that presents substantial opportunities for new and ground-breaking research.

Asymmetric processing of numerical and nonnumerical magnitudes in the brain: An fmri study

It is well established that, when comparing nonsymbolic magnitudes (e.g., dot arrays), adults can use both numerical (i.e., the number of items) and nonnumerical (density, total surface areas, etc.) magnitudes. It is less clear which of these magnitudes is more salient or processed more automatically. In this fMRI study, we used a nonsymbolic comparison task to ask if different brain areas are responsible for the automatic processing of numerical and nonnumerical magnitudes, when participants were instructed to attend to either the numerical or the nonnumerical magnitudes of the same stimuli. An interaction of task (numerical vs. nonnumerical) and congruity (congruent vs. incongruent) was found in the right TPJ. Specifically, this brain region was more strongly activated during numerical processing when the nonnumerical magnitudes were negatively correlated with numerosity (incongruent trials). In contrast, such an interference effect was not evident during nonnumerical processing when the task-irrelevant numerical magnitude was incongruent. In view of the role of the right TPJ in the control of stimulus-driven attention, we argue that these data demonstrate that the processing of nonnumerical magnitudes is more automatic than that of numerical magnitudes and that, therefore, the influence of numerical and nonnumerical variables on each other is asymmetrical.

On the ordinality of numbers

The last several years have seen steady growth in research on the cognitive and neuronal mechanisms underlying how numbers are represented as part of ordered sequences. In the present review, we synthesize what is currently known about numerical ordinality from behavioral and neuroimaging research, point out major gaps in our current knowledge, and propose several hypotheses that may bear further investigation. Evidence suggests that how we process ordinality differs from how we process cardinality, but that this difference depends strongly on context-in particular, whether numbers are presented symbolically or nonsymbolically. Results also reveal many commonalities between numerical and nonnumerical ordinal processing; however, the degree to which numerical ordinality can be reduced to domain-general mechanisms remains unclear. One proposal is that numerical ordinality relies upon more general short-term memory mechanisms as well as more numerically specific long-term memory representations. It is also evident that numerical ordinality is highly multifaceted, with symbolic representations in particular allowing for a wide range of different types of ordinal relations, the complexity of which appears to increase over development. We examine the proposal that these relations may form the basis of a richer set of associations that may prove crucial to the emergence of more complex math abilities and concepts. In sum, ordinality appears to be an important and relatively understudied facet of numerical cognition that presents substantial opportunities for new and ground-breaking research.

The left intraparietal sulcus adapts to symbolic number in both the visual and auditory modalities: Evidence from fMRI

Abstract A growing body of evidence from functional Magnetic Resonance Imaging adaptation (fMRIa) has implicated the left intraparietal sulcus (IPS) as a crucial brain region representing the semantic of number symbols. However, it is currently unknown to what extent the left IPS brain activity can be generalized across modalities (e.g., Arabic digits and spoken number words) and how robust and reproducible numerical adaptation effects are. In two separate fMRIa experiments we habituated the brain response of 20 native English‐speaking (Experiment 1) and 34 native German‐speaking (Experiment 2) adults to Arabic digits or spoken number words. Consistent with previous findings, experiment 1 revealed numerical ratio dependent adaptation to Arabic numerals in the left IPS using both conventional and cortex‐based alignment techniques. Experiment 2 revealed numerical ratio dependent signal recovery in the left IPS following adaptation to both Arabic numerals and spoken number words using both conventional and cortex‐based alignment techniques. Together, these findings suggest that the left IPS is involved in symbolic number processing across modalities. HighlightsHabituating the brain to numbers yields a numerical ratio dependent signal recovery.Both visual and auditory symbolic number processing is associated with the left IPS.The neural signal recovery response to numbers is highly specific and reproducible.

Processing the Order of Symbolic Numbers: A Reliable and Unique Predictor of Arithmetic Fluency

A small but growing body of evidence suggests a link between individual differences in processing the order of numerical symbols (e.g., deciding whether a set of digits is arranged in ascending/descending order or not) and arithmetic achievement. However, the reliability of behavioral correlates measuring symbolic and non-symbolic numerical order processing and their relationship to arithmetic abilities remain poorly understood. The present study aims to fill this knowledge gap by examining the behavioral correlates of numerical and non-numerical order processing and their unique associations with arithmetic fluency at two different time points within the same sample of individuals. Thirty-two right-handed adults performed three order judgment tasks consisting of symbolic numbers (i.e., digits), non-symbolic numbers (i.e., dots), and letters of the alphabet. Specifically, participants had to judge as accurately and as quickly as possible whether stimuli were ordered correctly (in ascending/descending order, e.g., 2-3-4; ●●●●-●●●-●●; B-C-D) or not (e.g., 4-5-3; ●●●●-●●●●●-●●●; D-E-C). Results of this study demonstrate that numerical order judgments are reliable measurements (i.e., high test-retest reliability), and that the observed relationship between symbolic number processing and arithmetic fluency accounts for a unique and reliable portion of variance over and above the non-symbolic number and the letter conditions. The differential association of symbolic and non-symbolic numbers with arithmetic support the view that processing the order of symbolic and non-symbolic numbers engages different cognitive mechanisms, and that the ability to process ordinal relationships of symbolic numbers is a reliable and unique predictor of arithmetic fluency.

Corrigendum to “Overlapping and distinct brain regions involved in estimating the spatial position of numerical and non-numerical magnitudes: An fMRI study” [Neuropsychologia 51 (2013) 979–989]

How are numerical and non-numerical magnitudes processed in the brain? Brain imaging research, primarily using comparison paradigms (i.e. judging which of two magnitudes is larger), has provided strong evidence demonstrating that the intraparietal sulcus (IPS) is a key region for processing both numerical (e.g. Arabic numerals, arrays of dots) and non-numerical magnitudes (e.g. height, brightness). These studies have suggested that there is both activation overlap and segregation in the brain regions involved in processing different dimensions of magnitude. In the present functional Magnetic Resonance Imaging (fMRI) study, we extended this line of investigation by probing the brain mechanisms underlying the mapping of numerical (Arabic numerals) and non-numerical magnitudes (brightness levels) onto a number line. Consistent with previous studies the present results revealed that number and brightness estimation was associated with overlapping activation within right lateralized areas of the posterior IPS. In addition, the contrast between number and brightness estimation revealed that bilateral anterior regions of the IPS are specifically involved in the process of estimating the position of symbolic numbers onto a number line. Furthermore, we found a significant influence of landmark reference points (0, 50 and 100) on brain activation in the right IPS for number estimation only. No regions were found to be specifically associated with brightness estimation. The results of this study reveal that the estimation of both numerical and non-numerical magnitude are associated with the engagement of a right lateralized magnitude system, but that symbolic number estimation is associated with additional engagement of bilateral regions of the anterior IPS. & 2013 Elsevier Ltd. All rights reserved.