Evidence against continuous variables driving numerical discrimination in infancy

Over the past decades, abundant evidence has amassed that demonstrates infants’ sensitivity to changes in number. Nonetheless, a prevalent view is that infants are more sensitive to continuous properties of stimulus arrays such as surface area and contour length than they are to numerosity. Very little research, however, has directly addressed infants’ sensitivity to contour. Here we used a change detection paradigm to assess infants’ acuity for the cumulative contour length of an array when the array’s surface area and number were held constant. Seven-month-old infants detected a threefold change in contour length but failed to detect a twofold change. These results, in conjunction with previously published data on numerosity discrimination using the same experimental paradigm, suggest that infants are not more sensitive to changes in contour length compared to changes in numerosity. Consequently, these findings undermine the claim that attention towards contour length is the primary driver of numerical discrimination in infancy

Attending to One of Many: When Infants are Surprisingly Poor at Discriminating an Item's Size

Despite a prevailing assumption in the developmental literature that changes in continuous quantities (i.e., surface area, duration) are easier to detect than changes in number, very little research has focused on the verity of this assumption. The few studies that have directly examined infants’ discriminations of continuous extent have revealed that infants discriminate the duration of a single event and the area of a single item with similar levels of precision (Brannon et al., 2006; vanMarle and Wynn, 2006). But what about when items are presented in arrays? Infants appear to be much worse at representing the cumulative surface area compared to the numerosity of an array (Cordes and Brannon, 2008a), however this may be due to a noisy accumulation process and not a general finding pertaining to representations of the extent within an array. The current study investigates how well infants detect changes in the size of individual elements when they are presented within an array. Our results indicate that infants are less sensitive to continuous properties of items when they are presented within a set than when presented in isolation. Specifically we demonstrate that infants required a fourfold change in item size to detect a change when items were presented within a set of homogeneous elements. Rather than providing redundant cues that aided discrimination, presenting a set of identical elements appeared to hamper an infant's ability to detect changes in a single element's size. In addition to providing some of the first evidence to suggest that the presence of multiple items may hinder extent representations, these results provide converging lines of evidence to support the claim that, contrary to popular belief, infants are better at tracking number than continuous properties of a set

Significant Inter-Test Reliability across Approximate Number System Assessments

The approximate number system (ANS) is the hypothesized cognitive mechanism that allows adults, infants, and animals to enumerate large sets of items approximately. Researchers usually assess the ANS by having subjects compare two sets and indicate which is larger. Accuracy or Weber fraction is taken as an index of the acuity of the system. However, as Clayton et al., (2015) have highlighted, the stimulus parameters used when assessing the ANS vary widely. In particular, the numerical ratio between the pairs, and the way in which non-numerical features are varied often differ radically between studies. Recently, Clayton et al. (2015) found that accuracy measures derived from two commonly used stimulus sets are not significantly correlated. They argue that a lack of inter-test reliability threatens the validity of the ANS construct. Here we apply a recently developed modeling technique to the same data set. The model, by explicitly accounting for the effect of numerical ratio and non-numerical features, produces dependent measures that are less perturbed by stimulus protocol. Contrary to their conclusion we find a significant correlation in Weber fraction across the two stimulus sets. Nevertheless, in agreement with Clayton et al., we find that different protocols do indeed induce differences in numerical acuity and the degree of influence of non-numerical stimulus features. These findings highlight the need for a systematic investigation of how protocol idiosyncrasies affect ANS assessments

Electrophysiological evidence for notation independence in numerical processing

BACKGROUND: A dominant view in numerical cognition is that numerical comparisons operate on a notation independent representation (Dehaene, 1992). Although previous human neurophysiological studies using scalp-recorded event-related potentials (ERPs) on the numerical distance effect have been interpreted as supporting this idea, differences in the electrophysiological correlates of the numerical distance effect in symbolic notations (e.g. Arabic numerals) and non-symbolic notations (e.g. a set of visually presented dots of a certain number) are not entirely consistent with this view. METHODS AND RESULTS: Two experiments were conducted to resolve these discrepancies. In Experiment 1, participants performed a symbolic and a non-symbolic numerical comparison task ("smaller or larger than 5?") with numerical values 1–4 and 6–9 while ERPs were recorded. Consistent with a previous report (Temple & Posner, 1998), in the symbolic condition the amplitude of the P2p ERP component (210–250 ms post-stimulus) was larger for values near to the standard than for values far from the standard whereas this pattern was reversed in the non-symbolic condition. However, closer analysis indicated that the reversal in polarity was likely due to the presence of a confounding stimulus effect on the early sensory ERP components for small versus larger numerical values in the non-symbolic condition. In Experiment 2 exclusively large numerosities (8–30) were used, thereby rendering sensory differences negligible, and with this control in place the numerical distance effect in the non-symbolic condition mirrored the symbolic condition of Experiment 1. CONCLUSION: Collectively, the results support the claim of an abstract semantic processing stage for numerical comparisons that is independent of input notation

Representation of numerosity in posterior parietal cortex

Humans and animals appear to share a similar representation of number as an analog magnitude on an internal, subjective scale. Neurological and neurophysiological data suggest that posterior parietal cortex (PPC) is a critical component of the circuits that form the basis of numerical abilities in humans. Patients with parietal lesions are impaired in their ability to access the deep meaning of numbers. Acalculiac patients with inferior parietal damage often have difficulty performing arithmetic (2 + 4?) or number bisection (what is between 3 and 5?) tasks, but are able to recite multiplication tables and read or write numerals. Functional imaging studies of neurologically intact humans performing subtraction, number comparison, and non-verbal magnitude comparison tasks show activity in areas within the intraparietal sulcus (IPS). Taken together, clinical cases and imaging studies support a critical role for parietal cortex in the mental manipulation of numerical quantities. Further, responses of single PPC neurons in non-human primates are sensitive to the numerosity of visual stimuli independent of low-level stimulus qualities. When monkeys are trained to make explicit judgments about the numerical value of such stimuli, PPC neurons encode their cardinal numerical value; without such training PPC neurons appear to encode numerical magnitude in an analog fashion. Here we suggest that the spatial and integrative properties of PPC neurons contribute to their critical role in numerical cognition

Neurocognitive Development of Risk Aversion from Early Childhood to Adulthood

Human adults tend to avoid risk. In behavioral economic studies, risk aversion is manifest as a preference for sure gains over uncertain gains. However, children tend to be less averse to risk than adults. Given that many of the brain regions supporting decision-making under risk do not reach maturity until late adolescence or beyond it is possible that mature risk-averse behavior may emerge from the development of decision-making circuitry. To explore this hypothesis, we tested 5- to 8-year-old children, 14- to 16-year-old adolescents, and young adults in a risky-decision task during functional magnetic resonance imaging (fMRI) data acquisition. To our knowledge, this is the youngest sample of children in an fMRI decision-making task. We found a number of decision-related brain regions to increase in activation with age during decision-making, including areas associated with contextual memory retrieval and the incorporation of prior outcomes into the current decision-making strategy, e.g., insula, hippocampus, and amygdala. Further, children who were more risk-averse showed increased activation during decision-making in ventromedial prefrontal cortex and ventral striatum. Our findings indicate that the emergence of adult levels of risk aversion co-occurs with the recruitment of regions supporting decision-making under risk, including the integration of prior outcomes into current decision-making behavior. This pattern of results suggests that individual differences in the development of risk aversion may reflect differences in the maturation of these neural processes

Monotonic Coding of Numerosity in Macaque Lateral Intraparietal Area

As any child knows, the first step in counting is summing up individual elements, yet the brain mechanisms responsible for this process remain obscure. Here we show, for the first time, that a population of neurons in the lateral intraparietal area of monkeys encodes the total number of elements within their classical receptive fields in a graded fashion, across a wide range of numerical values (2–32). Moreover, modulation of neuronal activity by visual quantity developed rapidly, within 100 ms of stimulus onset, and was independent of attention, reward expectations, or stimulus attributes such as size, density, or color. The responses of these neurons resemble the outputs of “accumulator neurons” postulated in computational models of number processing. Numerical accumulator neurons may provide inputs to neurons encoding specific cardinal values, such as “4,” that have been described in previous work. Our findings may explain the frequent association of visuospatial and numerical deficits following damage to parietal cortex in humans

Decision-Making Under Risk in Children, Adolescents, and Young Adults

Adolescents often make risky and impulsive decisions. Such behavior has led to the common assumption that a dysfunction in risk-related decision-making peaks during this age. Differences in how risk has been defined across studies, however, make it difficult to draw conclusions about developmental changes in risky decision-making. Here, we developed a non-symbolic economic decision-making task that can be used across a wide age span and that uses coefficient of variation (CV) in reward as an index of risk. We found that young children showed the strongest preference for risky compared to sure bet options of equal expected value, adolescents were intermediate in their risk preference, and young adults showed the strongest risk aversion. Furthermore, children's preference for the risky option increased for larger CVs, while adolescents and young adults showed the opposite pattern, favoring the sure bet more often as CV increased. Finally, when faced with two gambles in a risk–return tradeoff, all three age groups exhibited a greater preference for the option with the lower risk and return as the disparity in risk between the two options increased. These findings demonstrate clear age-related differences in economic risk preferences that vary with choice set and risk. Importantly, adolescence appears to represent an intermediate decision-making phenotype along the transition from childhood to adulthood, rather than an age of heightened preference for economic risk

Numerical Rule-Learning in Ring-Tailed Lemurs (Lemur Catta)

We investigated numerical discrimination and numerical rule-learning in ring-tailed lemurs (Lemur catta). Two ring-tailed lemurs were trained to respond to two visual arrays, each of which contained between one and four elements, in numerically ascending order. In Experiment 1, lemurs were trained with 36 exemplars of each of the numerosities 1–4 and then showed positive transfer to trial-unique novel exemplars of the values 1–4. In Experiments 2A and 2B, lemurs were tested on their ability to transfer an ascending numerical rule from the values 1–4 to novel values 5–9. Both lemurs successfully ordered the novel values with above chance accuracy. Accuracy was modulated by the ratio between the two numerical values suggesting that lemurs accessed the approximate number system when performing the task