Micro and macro pattern analyses of FMRI data support both early and late interaction of numerical and spatial information

Perceived Motion and Operational Momentum: How Speed, Distance, and Time Influence Two-Digit Arithmetic

Operational momentum was originally defined as a bias toward underestimating outcomes of subtraction and overestimating outcomes of addition. It was suggested that these estimation biases are due to leftward attentional shift along the mental number-line (spatially organized internal representation of number) in subtraction and rightward shift in addition. This assumes the use of “recycled” mechanisms of spatial attention, including “representational momentum” – a tendency to overestimate future position of a moving object, which compensates for the moving object’s shift during preparation of a reaction. We tested a strong version of this assumption directly, priming two-digit addition and subtraction problems with leftward and rightward motion of varied velocity, as velocity of the tracked object was found to be a factor in determining representational momentum effect size. Operands were subsequently moving across the computer screen, and the participants’ task was to validate an outcome proposed at the end of the event, which was either too low, correct, or too high. We found improved accuracy in detecting too-high outcomes of addition, as well as complex patterns of interactions involving arithmetic operation, outcome option, speed, and direction of motion, in the analysis of reaction times. These results significantly extend previous evidence for the involvement of spatial attention in mental arithmetic, showing movement of the external attention focus as a factor directing internal attention in processing numerical information. As a whole, however, the results are incompatible with expectations derived from the strong analogy between operational and representational momenta. We suggest that the full model may be more complex than simply “moving attention along the mental number-line” as a direct counterpart of attention directed at a moving object.

Functionally distinct contributions of parietal cortex to a numerical landmark task: An fMRI study

This study aimed at establishing the neural basis of magnitude processing of multiple numbers from working memory. We designed a numerical landmark task and embedded it in a fragmented trial event-related fMRI design, allowing to separate encoding from decision processing. An attentional localiser task not involving numbers allowed further functional specification. The results show that in a numerical landmark task the right anterior intraparietal sulcus is involved in number encoding while more posterior parietal regions, bilateral superior parietal lobule and right inferior parietal lobule, provide domain-general support in the form of constructing a working memory representation or orienting spatial attention within that mental representation during number comparison. The results are in line with earlier studies reporting a functional distinction between anterior and posterior parietal contributions to number processing and further specify their role at a functional level.

On the genesis of spatial-numerical associations: Evolutionary and cultural factors co-construct the mental number line

Mapping numbers onto space is a common cognitive representation that has been explored in both behavioral and neuroimaging contexts. Empirical work probing the diverse nature of these spatial-numerical associations (SNAs) has led researchers to question 1) how the human brain links numbers with space, and 2) whether this link is biologically vs. culturally determined. We review the existing literature on the development of SNAs and situate that empirical work within cognitive and neuroscientific theoretical frameworks. We propose that an evolutionarily-ancient frontal-parietal circuit broadly tuned to multiple magnitude dimensions provides the phylogenetic substrate for SNAs, while enculturation and sensorimotor experience shape their specific profiles. We then use this perspective to discuss educational implications and highlight promising avenues for future research.

Probing the Neural Correlates of Number Processing

The cognitive and neural mechanisms that enable humans to encode and manipulate numerical information have been subject to an increasing number of experimental studies over the past 25 years or so. Here, I highlight recent findings about how numerical information is neurally coded, focusing on the theoretical implications derived from the most influential theoretical framework in numerical cognition—the Triple Code Model. At the core of this model is the assumption that bilateral parietal cortex hosts an approximate number system that codes for the cardinal value of perceived numerals. I will review studies that ask whether or not the numerical coding within this system is invariant to varying input notation, format, or modality, and whether or not the observed parietal activity is number-specific over and above the parietal involvement in response-related processes. Extant computational models of numerosity (the number of objects in a set) perception are summarized and related to empirical data from human neuroimaging and monkey neurophysiology.

Neural substrates of numerosity estimation in autism

Visual skills, including numerosity estimation are reported to be superior in autism spectrum disorders (ASD). This phenomenon is attributed to individuals with ASD processing local features, rather than the Gestalt. We examined the neural correlates of numerosity estimation in adults with and without ASD, to disentangle perceptual atypicalities from numerosity processing. Fourteen adults with ASD and matched typically developed (TD) controls estimated the number of dots (80-150) arranged either randomly (local information) or in meaningful patterns (global information) while brain activity was recorded with magnetoencephalography (MEG). Behavioral results showed no significant group difference in the errors of estimation. However, numerical estimation in ASD was more variable across numerosities than TD and was not affected by the global arrangement of the dots. At 80-120 ms, MEG analyses revealed early significant differences (TD > ASD) in source amplitudes in visual areas, followed from 120 to 400 ms by group differences in temporal, and then parietal regions. After 400 ms, a source was found in the superior frontal gyrus in TD only. Activation in temporal areas was differently sensitive to the global arrangement of dots in TD and ASD. MEG data show that individuals with autism exhibit widespread functional abnormalities. Differences in temporal regions could be linked to atypical global perception. Occipital followed by parietal and frontal differences might be driven by abnormalities in the processing and conversion of visual input into a number-selective neural code and complex cognitive decisional stages. These results suggest overlapping atypicalities in sensory, perceptual and number-related processing during numerosity estimation in ASD.

Reduced beta band connectivity during number estimation in autism

Recent evidence suggests that disruption of integrative processes in sensation and perception may play a critical role in cognitive and behavioural atypicalities characteristic of ASD. In line with this, ASD is associated with altered structural and functional brain connectivity and atypical patterns of inter-regional communication which have been proposed to contribute to cognitive difficulties prevalent in this group. The present MEG study used atlas-guided source space analysis of inter-regional phase synchronization in ASD participants, as well as matched typically developing controls, during a dot number estimation task. This task included stimuli with globally integrated forms (animal shapes) as well as randomly-shaped stimuli which lacked a coherent global pattern. Early task-dependent increases in inter-regional phase synchrony in theta, alpha and beta frequency bands were observed. Reduced long-range beta-band phase synchronization was found in participants with ASD at 70-145 ms during presentation of globally coherent dot patterns. This early reduction in task-dependent inter-regional connectivity encompassed numerous areas including occipital, parietal, temporal, and frontal lobe regions. These results provide the first evidence for inter-regional phase synchronization during numerosity estimation, as well as its alteration in ASD, and suggest that problems with communication among brain areas may contribute to difficulties with integrative processes relevant to extraction of meaningful 'Gestalt' features in this population.

The impact of mathematical proficiency on the number-space association

A specific instance of the association between numerical and spatial representations is the SNARC (Spatial Numerical Association of Response Codes) effect. The SNARC effect describes the finding that during binary classification of numbers participants are faster to respond to small/large numbers with the left/right hand respectively. Even though it has been frequently replicated, important inter-individual variability has also been reported. Mathematical proficiency is an obvious candidate source for inter-individual variability in numerical judgments, but studies investigating its influence on the SNARC effect remain scarce. The present experiment included a total of 95 University students, divided into three groups differing significantly in their mathematical proficiency levels. Using group analyses, it appeared that the three groups differed significantly in the strength of their number-space associations in a parity judgment task. This result was further confirmed on an individual level, with higher levels in arithmetic leading to relatively weaker SNARC effects. To explain this negative relationship we propose accounts based on differences in access to qualitatively different numerical representations and also consider more domain general factors, with a focus on inhibition capacities.

The role of numerical magnitude and order in the illusory perception of size and brightness

Processing magnitudes constitutes a common experience across multiple dimensions, for example when one has to compare sizes, duration, numbers, sound height or loudness. From a cognitive point of view, however, it is still unclear whether all these experiences rely on a common system, or on distinct systems, with more or less strong associations. One particularly striking way of observing such interference between the spatial and numerical dimensions consists in eliciting a bias in size judgment through the mere perception of irrelevant numerical stimuli. In such experimental context though, two questions remain open. First, it is still unknown whether the direction of the bias is related to the magnitude of the number presented, or to their position in an ordinal sequence, and thus could be elicited by other non-numerical ordinal sequences such as letters of the alphabet. Second, it is still unclear whether the observed interactions generalize to other continuous dimension of magnitude such as brightness. In the study reported here, both letters and numbers were used in a size- and a brightness-reproduction task. We observed a dissociation between the two types of stimuli when reproducing size, the illusion being elicited solely by numbers. When reproducing brightness, however, neither the letters nor the numbers elicited a bias. These findings suggest that, while only numerical magnitude, and not letters, elicits a bias in size perception, the concurrent processing of magnitude and brightness does not bring about the same illusion, supporting the idea of a relative independence in the processing of these two dimensions.

Individual differences in solving arithmetic word problems

BACKGROUND

With the present functional magnetic resonance imaging (fMRI) study at 3 T, we investigated the neural correlates of visualization and verbalization during arithmetic word problem solving. In the domain of arithmetic, visualization might mean to visualize numbers and (intermediate) results while calculating, and verbalization might mean that numbers and (intermediate) results are verbally repeated during calculation. If the brain areas involved in number processing are domain-specific as assumed, that is, that the left angular gyrus (AG) shows an affinity to the verbal domain, and that the left and right intraparietal sulcus (IPS) shows an affinity to the visual domain, the activation of these areas should show a dependency on an individual's cognitive style.

METHODS

36 healthy young adults participated in the fMRI study. The participants habitual use of visualization and verbalization during solving arithmetic word problems was assessed with a short self-report assessment. During the fMRI measurement, arithmetic word problems that had to be solved by the participants were presented in an event-related design.

RESULTS

We found that visualizers showed greater brain activation in brain areas involved in visual processing, and that verbalizers showed greater brain activation within the left angular gyrus.

CONCLUSIONS

Our results indicate that cognitive styles or preferences play an important role in understanding brain activation. Our results confirm, that strong visualizers use mental imagery more strongly than weak visualizers during calculation. Moreover, our results suggest that the left AG shows a specific affinity to the verbal domain and subserves number processing in a modality-specific way.

The Body of Evidence: What Can Neuroscience Tell Us about Embodied Semantics?

Semantic knowledge is based on the way we perceive and interact with the world. However, the jury is still out on the question: to what degree are neuronal systems that subserve acquisition of semantic knowledge, such as sensory-motor networks, involved in its representation and processing? We will begin with a critical evaluation of the main behavioral and neuroimaging methods with respect to their capability to define the functional roles of specific brain areas. Any behavioral or neuroscientific measure is a conflation of representations and processes. Hence, a combination of behavioral and neurophysiological interactions as well as time-course information is required to define the functional roles of brain areas. This will guide our review of the empirical literature. Most research in this area has been done on semantics of concrete words, where clear theoretical frameworks for an involvement of sensory-motor systems in semantics exist. Most of this evidence still stems from correlational studies that are ambiguous with respect to the behavioral relevance of effects. Evidence for causal effects of sensory-motor systems on semantic processes is still scarce but evolving. Relatively few neuroscientific studies so far have investigated the embodiment of abstract semantics for words, numbers, and arithmetic facts. Here, some correlational evidence exists, but data on causality are mostly absent. We conclude that neuroimaging data, just as behavioral data, have so far not disentangled the fundamental link between process and representation. Future studies should therefore put more emphasis on the effects of task and context on semantic processing. Strong conclusions can only be drawn from a combination of methods that provide time-course information, determine the connectivity among poly- or amodal and sensory-motor areas, link behavioral with neuroimaging measures, and allow causal inferences. We will conclude with suggestions on how this could be accomplished in future research.