While all humans are capable of non-verbally representing numerical quantity using so-called the approximate number system (ANS), there exist considerable individual differences in its acuity. For example, in a non-symbolic number comparison task, some people find it easy to discriminate brief presentations of 14 dots from 16 dots while others do not. Quantifying individual ANS acuity from such a task has become an essential practice in the field, as individual differences in such a primitive number sense is thought to provide insights into individual differences in learned symbolic math abilities. However, the dominant method of characterizing ANS acuity—computing the Weber fraction (w)—only utilizes the accuracy data while ignoring response times (RT). Here, we offer a novel approach of quantifying ANS acuity by using the diffusion model, which accounts both accuracy and RT distributions. Specifically, the drift rate in the diffusion model, which indexes the quality of the stimulus information, is used to capture the precision of the internal quantity representation. Analysis of behavioral data shows that w is contaminated by speed-accuracy tradeoff, making it problematic as a measure of ANS acuity, while drift rate provides a measure more independent from speed-accuracy criterion settings. Furthermore, drift rate is a better predictor of symbolic math ability than w, suggesting a practical utility of the measure. These findings demonstrate critical limitations of the use of w and suggest clear advantages of using drift rate as a measure of primitive numerical competence.
approximate number system; diffusion model; math ability; speed-accuracy tradeoff; Weber fraction
A nonverbal primitive number sense allows approximate estimation and mental manipulations on numerical quantities without the use of numerical symbols. In a recent randomized controlled intervention study in adults, we demonstrated that repeated training on a non-symbolic approximate arithmetic task resulted in improved exact symbolic arithmetic performance, suggesting a causal relationship between the primitive number sense and arithmetic competence. Here, we investigate the potential mechanisms underlying this causal relationship. We constructed multiple training conditions designed to isolate distinct cognitive components of the approximate arithmetic task. We then assessed the effectiveness of these training conditions in improving exact symbolic arithmetic in adults. We found that training on approximate arithmetic, but not on numerical comparison, numerical matching, or visuo-spatial short-term memory, improves symbolic arithmetic performance. In addition, a second experiment revealed that our approximate arithmetic task does not require verbal encoding of number, ruling out an alternative explanation that participants use exact symbolic strategies during approximate arithmetic training. Based on these results, we propose that nonverbal numerical quantity manipulation is one key factor that drives the link between the primitive number sense and symbolic arithmetic competence. Future work should explore implications from this finding that training young children on approximate arithmetic tasks even before they solidify the symbolic number understanding may be fruitful for improving readiness for math education.
Numerical cognition; approximate number system; cognitive training; math; approximate arithmetic; arithmetic
Recent functional magnetic resonance imaging research has demonstrated that letters and numbers are preferentially processed in distinct regions and hemispheres in the visual cortex. In particular, the left visual cortex preferentially processes letters compared to numbers, while the right visual cortex preferentially processes numbers compared to letters. Because letters and numbers are cultural inventions and are otherwise physically arbitrary, such a double dissociation is strong evidence for experiential effects on neural architecture. Here, we use the high temporal resolution of event-related potentials (ERPs) to investigate the temporal dynamics of the neural dissociation between letters and numbers. We show that the divergence between ERP traces to letters and numbers emerges very early in processing. Letters evoked greater N1 waves (latencies 140–170 ms) than did numbers over left occipital channels, while numbers evoked greater N1s than letters over the right, suggesting letters and numbers are preferentially processed in opposite hemispheres early in visual encoding. Moreover, strings of letters, but not single letters, elicited greater P2 ERP waves, (starting around 250 ms) than numbers did over the left hemisphere, suggesting that the visual cortex is tuned to selectively process combinations of letters, but not numbers, further along in the visual processing stream. Additionally, the processing of both of these culturally defined stimulus types differentiated from similar but unfamiliar visual stimulus forms (false fonts) even earlier in the processing stream (the P1 at 100 ms). These findings imply major cortical specialization processes within the visual system driven by experience with reading and mathematics.
Letter processing; number processing; ERP; hemispheric specialization
The parietal cortex is central to numerical cognition. The right parietal region is primarily involved in basic quantity processing, while the left parietal region is additionally involved in precise number processing and numerical operations. Little is known about how the 2 regions interact during numerical cognition. We hypothesized that functional connectivity between the right and left parietal cortex is critical for numerical processing that engages both basic number representation and learned numerical operations. To test this hypothesis, we estimated neural activity using functional magnetic resonance imaging in participants performing numerical and arithmetic processing on dot arrays. We first found task-based functional connectivity between a right parietal seed and the left sensorimotor cortex in all task conditions. As we hypothesized, we found enhanced functional connectivity between this right parietal seed and both the left parietal cortex and neighboring right parietal cortex, particularly during subtraction. The degree of functional connectivity also correlated with behavioral performance across individual participants, while activity within each region did not. These results highlight the role of parietal functional connectivity in numerical processing. They suggest that arithmetic processing depends on crosstalk between and within the parietal cortex and that this crosstalk contributes to one's numerical competence.
arithmetic processing; functional connectivity; intraparietal sulcus; numerical cognition
Humans share with nonhuman animals an approximate number system (ANS) that permits estimation and rough calculation of number without symbols. Recent studies show a correlation between the acuity of the ANS and symbolic math performance throughout development and into adulthood, suggesting that the ANS may serve as a cognitive foundation for the uniquely human capacity for symbolic mathematics. Such a proposition leads to the untested prediction that training aimed at improving ANS performance will transfer to improvement in symbolic mathematics. Here, in two experiments, we show that ANS training on approximate addition and subtraction of arrays of dots, selectively improves symbolic addition and subtraction. This finding strongly supports the hypothesis that complex math skills are fundamentally linked to rudimentary preverbal quantitative abilities, provides the first direct evidence that ANS and symbolic math may be causally related, and raises the possibility that interventions aimed at the ANS could benefit children and adults who struggle with math.
Number comprehension; mathematical ability
Advances in modern neuroimaging in combination with behavioral genetics have allowed neuroscientists to investigate how genetic and environmental factors shape human brain structure and function. Estimating the heritability of brain structure and function via twin studies has become one of the major approaches in studying the genetics of the brain. In a classical twin study, heritability is estimated by computing genetic and phenotypic variation based on the similarity of monozygotic and dizygotic twins. However, heritability has traditionally been measured for univariate, scalar traits, and it is challenging to assess the heritability of a spatial process, such as a pattern of neural activity. In this work, we develop a statistical method to estimate phenotypic variance and covariance at each location in a spatial process, which in turn can be used to estimate the heritability of a spatial dataset. The method is based on a dimensionally-reduced model of spatial variation in paired images, in which adjusted least squares estimates can be used to estimate the key model parameters. The advantage of the proposed method compared to conventional methods such as a voxelwise or mean-ROI approaches is demonstrated in both a simulation study and a real data study assessing genetic influence on patterns of brain activity in the visual and motor cortices in response to a simple visuomotor task.
Heritability; Intraclass Correlation; Twin Study; Spatial Analysis; Genetics
Previous studies have found that cortical responses to different stimuli become less distinctive as people get older. This age-related dedifferentiation may reflect the broadening of the tuning curves of category-selective neurons (broadening hypothesis) or it may be due to decreased activation of category-selective neurons (attenuation hypothesis). In this study, we evaluated these hypotheses in the context of the face-selective neural network. Over 300 participants, ranging in age from 20 to 89 years, viewed images of faces, houses, and control stimuli in a functional magnetic resonance imaging session. Regions within the core face network and extended face network were identified in individual subjects. Activation in many of these regions became significantly less face-selective with age, confirming previous reports of age-related dedifferentiation. Consistent with the broadening hypothesis, this dedifferentiation in the fusiform face area (FFA) was driven by increased activation to houses. In contrast, dedifferentiation in the extended face network was driven by decreased activation to faces, consistent with the attenuation hypothesis. These results suggest that age-related dedifferentiation reflects distinct processes in different brain areas. More specifically, dedifferentiation in FFA activity may be due to broadening of the tuning curves for face-selective neurons, while dedifferentiation in the extended face network reflects reduced face- or emotion-selective activity.
The visual recognition of letters dissociates from the recognition of numbers at both the behavioral and neural level. In this article, using fMRI, we investigate whether the visual recognition of numbers dissociates from letters, thereby establishing a double dissociation. In Experiment 1, participants viewed strings of consonants and Arabic numerals. We found that letters activated the left midfusiform and inferior temporal gyri more than numbers, replicating previous studies, whereas numbers activated a right lateral occipital area more than letters at the group level. Because the distinction between letters and numbers is culturally defined and relatively arbitrary, this double dissociation provides some of the strongest evidence to date that a neural dissociation can emerge as a result of experience. We then investigated a potential source of the observed neural dissociation. Specifically, we tested the hypothesis that lateralization of visual number recognition depends on lateralization of higher-order numerical processing. In Experiment 2, the same participants performed addition, subtraction, and counting on arrays of nonsymbolic stimuli varying in numerosity, which produced neural activity in and around the intraparietal sulcus, a region associated with higher-order numerical processing. We found that individual differences in the lateralization of number activity in visual cortex could be explained by individual differences in the lateralization of numerical processing in parietal cortex, suggesting a functional relationship between the two regions. Together, these results demonstrate a neural double dissociation between letter and number recognition and suggest that higher-level numerical processing in parietal cortex may influence the neural organization of number processing in visual cortex.
Current theories of cognitive aging argue that neural representations become less distinctive in old age, a phenomenon known as dedifferentiation. The present study used multi-voxel pattern analysis (MVPA) to measure age differences in the distinctiveness of distributed patterns of neural activation evoked by different categories of visual images. We found that neural activation patterns within the ventral visual cortex were less distinctive among older adults. Further, we report that age differences in neural distinctiveness extend beyond the ventral visual cortex: older adults also showed decreased distinctiveness in early visual cortex, inferior parietal cortex, and medial and lateral prefrontal cortex. Neural distinctiveness scores in early and late visual areas were highly correlated, suggesting shared mechanisms of age-related decline. Finally, we investigated whether older adults can compensate for altered processing in visual cortex by encoding stimulus information across larger numbers of voxels within the visual cortex or in regions outside visual cortex. We found no evidence that older adults can increase the distinctiveness of distributed activation patterns, either within or beyond the visual cortex. Our results have important implications for theories of cognitive aging and highlight the value of MVPA to the study of neural coding in the aging brain.
aging; fMRI; MVPA; dedifferentiation; compensation; ventral visual cortex
The visual word form area (VWFA) is a region of left inferior occipitotemporal cortex that is critically involved in visual word recognition. Previous studies have investigated whether and how experience shapes the functional characteristics of VWFA by comparing neural response magnitude in response to words and nonwords. Conflicting results have been obtained, however, perhaps because response magnitude can be influenced by other factors such as attention. In this study, we measured neural activity in monozygotic twins, using functional magnetic resonance imaging. This allowed us to quantify differences in unique environmental contributions to neural activation evoked by words, pseudowords, consonant strings, and false fonts in the VWFA and striate cortex. The results demonstrate significantly greater effects of unique environment in the word and pseudoword conditions compared to the consonant string and false font conditions both in VWFA and in left striate cortex. These findings provide direct evidence for environmental contributions to the neural architecture for reading, and suggest that learning phonology and/or orthographic patterns plays the biggest role in shaping that architecture.
Recent neuroimaging studies using multi-voxel pattern analysis (MVPA) show that distributed patterns of brain activation elicited by different visual stimuli are less distinctive in older adults than in young adults. However, less is known about the effects of aging on the neural representation of movement. The present study used MVPA to compare the distinctiveness of motor representations in young and older adults. We also investigated the contributions of brain structure to age differences in the distinctiveness of motor representations. We found that neural distinctiveness was reduced in older adults throughout the motor control network. Although aging was also associated with decreased gray matter volume in these regions, age differences in motor distinctiveness remained significant after controlling for gray matter volume. Our results suggest that age-related neural dedifferentiation is not restricted to sensory perception and is instead a more general feature of the aging brain.
Functional localizers are routinely used in neuroimaging studies to test hypotheses about the function of specific brain areas. The specific tasks and stimuli used to localize particular regions vary widely from study to study even when the same cortical region is targeted. Thus, it is important to ask whether task and stimulus changes lead to differences in localization or whether localization procedures are largely immune to differences in tasks and contrasting stimuli. We present two experiments and a literature review that explore whether face localizer tasks yield differential localization in the fusiform gyrus as a function of task and contrasting stimuli. We tested standard localization tasks---passive viewing, 1-back, and 2-back memory tests---and did not find differences in localization based on task. We did, however, find differences in the extent, strength and patterns/reliabilities of the activation in the fusiform gyrus based on comparison stimuli (faces vs. houses compared to faces vs. scrambled stimuli).
We investigated whether individual differences in neural specificity—the distinctiveness of different neural representations—could explain individual differences in cognitive performance in older adults. Neural specificity was estimated based on how accurately multivariate pattern analysis identified neural activation patterns associated with specific experimental conditions. Neural specificity calculated from a same-different task on two categories of visual stimuli (faces and houses) significantly predicted performance on a range of fluid processing behavioral tasks (dot-comparison, digit-symbol, Trails-A, Trails-B, verbal-fluency) in older adults, whereas it did not correlate with a measure of crystallized knowledge (Shipley-vocabulary). In addition, the neural specificity measure accounted for thirty percent of the variance in a composite measure of fluid processing ability. These results are consistent with the hypothesis that loss of neural specificity, or dedifferentiation, contributes to reduced fluid processing ability in old age.