Impact of high mathematics education on the number sense

In adult number processing two mechanisms are commonly used: approximate estimation of quantity and exact calculation. While the former relies on the approximate number sense (ANS) which we share with animals and preverbal infants, the latter has been proposed to rely on an exact number system (ENS) which develops later in life following the acquisition of symbolic number knowledge. The current study investigated the influence of high level math education on the ANS and the ENS. Our results showed that the precision of non-symbolic quantity representation was not significantly altered by high level math education. However, performance in a symbolic number comparison task as well as the ability to map accurately between symbolic and non-symbolic quantities was significantly better the higher mathematics achievement. Our findings suggest that high level math education in adults shows little influence on their ANS, but it seems to be associated with a better anchored ENS and better mapping abilities between ENS and ANS.     

The Impact of Symbolic and Non-Symbolic Quantity on Spatial Learning

An implicit mapping of number to space via a “mental number line” occurs automatically in adulthood. Here, we systematically explore the influence of differing representations of quantity (no quantity, non-symbolic magnitudes, and symbolic numbers) and directional flow of stimuli (random flow, left-to-right, or right-to-left) on learning and attention via a match-to-sample working memory task. When recalling a cognitively demanding string of spatial locations, subjects performed best when information was presented right-to-left. When non-symbolic or symbolic numerical arrays were embedded in these spatial locations, and mental number line congruency prompted, this effect was attenuated and in some cases reversed. In particular, low-performing female participants who viewed increasing non-symbolic number arrays paired with the spatial locations exhibited better recall for left-to-right directional flow information relative to right-to-left, and better processing for the left side of space relative to the right side of space. The presence of symbolic number during spatial learning enhanced recall to a greater degree than non-symbolic number—especially for female participants, and especially when cognitive load is high—and this difference was independent of directional flow of information. We conclude that quantity representations have the potential to scaffold spatial memory, but this potential is subtle, and mediated by the nature of the quantity and the gender and performance level of the learner.     

When Numbers Get Heavy: Is the Mental Number Line Exclusively Numerical?

The mental number line, with its left-to-right orientation of increasing numerical values, is often regarded as evidence for a unique connection between space and number. Yet left-to-right orientation has been shown to extend to other dimensions, consistent with a general magnitude system wherein different magnitudes share neural and conceptual resources. Such observations raise a fundamental, yet relatively unexplored, question about spatial-numerical associations: What is the nature of the information represented along the mental number line? Here we show that this information is not exclusive to number, simultaneously accommodating numerical and non-numerical magnitudes. Participants completed the classic SNARC (Spatial-Numerical Association of Response Codes) task while sometimes wearing wrist weights. Weighting the left wrist–thereby linking less and more weight to right and left, respectively–worked against left-to-right orientation of number, leaving no behavioral trace of the mental number line. Our findings point to the dynamic integration of magnitude dimensions, with spatial organization instantiating representational currency (i.e., more/less relations) shared across magnitudes.     

Functional imaging of numerical processing in adults and 4-y-old children

Adult humans, infants, pre-school children, and non-human animals appear to share a system of approximate numerical processing for non-symbolic stimuli such as arrays of dots or sequences of tones. Behavioral studies of adult humans implicate a link between these non-symbolic numerical abilities and symbolic numerical processing (e.g., similar distance effects in accuracy and reaction-time for arrays of dots and Arabic numerals). However, neuroimaging studies have remained inconclusive on the neural basis of this link. The intraparietal sulcus (IPS) is known to respond selectively to symbolic numerical stimuli such as Arabic numerals. Recent studies, however, have arrived at conflicting conclusions regarding the role of the IPS in processing non-symbolic, numerosity arrays in adulthood, and very little is known about the brain basis of numerical processing early in development. Addressing the question of whether there is an early-developing neural basis for abstract numerical processing is essential for understanding the cognitive origins of our uniquely human capacity for math and science. Using functional magnetic resonance imaging (fMRI) at 4-Tesla and an event-related fMRI adaptation paradigm, we found that adults showed a greater IPS response to visual arrays that deviated from standard stimuli in their number of elements, than to stimuli that deviated in local element shape. These results support previous claims that there is a neurophysiological link between non-symbolic and symbolic numerical processing in adulthood. In parallel, we tested 4-y-old children with the same fMRI adaptation paradigm as adults to determine whether the neural locus of non-symbolic numerical activity in adults shows continuity in function over development. We found that the IPS responded to numerical deviants similarly in 4-y-old children and adults. To our knowledge, this is the first evidence that the neural locus of adult numerical cognition takes form early in development, prior to sophisticated symbolic numerical experience. More broadly, this is also, to our knowledge, the first cognitive fMRI study to test healthy children as young as 4 y, providing new insights into the neurophysiology of human cognitive development.     

The Map in Our Head Is Not Oriented North: Evidence from a Real-World Environment

Like most physical maps, recent research has suggested that cognitive maps of familiar environments may have a north-up orientation. We demonstrate that north orientation is not a necessary feature of cognitive maps and instead may arise due to coincidental alignment between cardinal directions and the built and natural environment. Experiment 1 demonstrated that pedestrians have difficulty pointing north while navigating a familiar real-world environment with roads, buildings, and green spaces oriented oblique to cardinal axes. Instead, north estimates tended to be parallel or perpendicular to roads. In Experiment 2, participants did not demonstrate privileged memory access when oriented toward north while making relative direction judgments. Instead, retrieval was fastest and most accurate when orientations were aligned with roads. In sum, cognitive maps are not always oriented north. Rather, in some real-world environments they can be oriented with respect to environment-specific features, serving as convenient reference systems for organizing and using spatial memory.     

Spatial learning impairment in a murine model of AIDS.

Mice infected with an immunosuppressive murine leukemia virus (MuLV) mixture, LP-BM5, displayed profound and selective deficits in spatial learning in a modified Morris water maze. These deficits appeared before the appearance of gross neurological impairment or histopathological changes in the central nervous system. Thus, LP-BM5-infected mice displayed deficits in several aspects of trained performance compared to controls. Furthermore, a failure to exhibit any evidence of task acquisition in this maze was observed almost twice as frequently (P less than 0.0005) in infected mice as in uninfected controls. Moreover, in the absence of gross visual, motoric, or motivational impairment, LP-BM5 MuLV-infected animals exhibited neither the target directed search pattern nor the spatial preference characteristic of controls. The spatial learning and memory deficit described here is the first report of cognitive impairment accompanying viral-induced immunosuppression in a nonprimate species.     

Characterizing spatial extinction in an abbreviated version of the Barnes maze

Adult male Wistar rats were trained to find an escape box in the Barnes maze in order to characterize the extinction process of a learned spatial preference. To do so, once they had fully acquired the spatial task, they were repeatedly exposed to the maze without the escape box. Multiple behavioral measurements (grouped into motor skill and spatial preference indicators) were followed up throughout the complete training process. Animals gained efficiency in finding the escape box during acquisition, as indicated by the reduction in the time spent escaping from the maze, the number of errors, the length of the traveled path, and by the increase in exploration accuracy and execution speed. When their retention and preference were tested 24 h later, all the subjects retained their enhanced performance efficiency and accuracy and displayed a clear-cut preference for the escape hole and its adjacent holes. Almost all motor skill indicators followed an inverse, though not monotonic, pattern during the extinction training, returning to basal levels after three trials without escape box, displaying a transient relapse during the fifth extinction trial. Preference indicators also followed a reverse pattern; however, it took seven trials for them to return to basal levels, relapsing during the eighth extinction trial. The abbreviated Barnes maze acquisition, evaluation, and extinction procedures described herein are useful tools for evaluating the effects of behavioral and/or pharmacological treatment on different stages of spatial memory, and could also be used for studying the neurophysiological and neurobiological underpinnings of this kind of memory.     

Pigeons' memory for sequences of light flashes: reliance on temporal properties and evidence for delay interval/gap confusion

In Experiment 1, pigeons were trained to discriminate between sequences of two and four light flashes (illumination of the feeder). Retention functions obtained with dark delays exhibited a choose-many bias at a 1-s delay and a choose-few bias at delays of 4 and 8s. Retention functions obtained with illuminated delays only displayed a slight choose-few bias. In Experiment 2, additional birds were trained with the same sample sequences. However, the intertrial interval was illuminated by the houselight for Group Light, and it was dark for Group Dark. The acquisition data suggested that multiple temporal features of the light flash sequences controlled choice responding. For both groups, the retention functions were similar to those obtained in Experiment 1. In Experiment 3, baseline training with a 1-s dark delay eliminated the choose-many bias, but a significant choose-few bias at extended dark delays was still observed. Pigeons discriminate light flash sequences by relying on temporal properties of the sequence rather than using an event switch to count flashes. The biased-forgetting effects obtained in these studies appear to be primarily due to confusion between the delay interval and the gap between light flashes.     

Orientation responses to biological odours in the human newborn. Initial pattern and postnatal plasticity

The initiai pattern and development of odour preference was studied in infants simultaneously exposed to amniotic fluid (AF) and maternal lacteal secretion (L). Five groups of varying age (range: 1–5 days) and breast-feeding experience (range: 0–32 feeds) were studied. Before postnatal day 3, no evidence of differentiation of AF and L was apparent. After 3 days and 7–12 breast-feeding episodes, a significant preference for L arised. The initial stage (days 1–3) may reflect fetal acquisition of AF odour and sensory/motivational equivalence of AF and L odours. The second stage (days 4–5) may reflect the infants' perception of change in milk quality and increasing experience with milk. This sequential development attests to a high plasticity in the initial stage of human olfactory development.     

Processing ordinality and quantity: the case of developmental dyscalculia

In contrast to quantity processing, up to date, the nature of ordinality has received little attention from researchers despite the fact that both quantity and ordinality are embodied in numerical information. Here we ask if there are two separate core systems that lie at the foundations of numerical cognition: (1) the traditionally and well accepted numerical magnitude system but also (2) core system for representing ordinal information. We report two novel experiments of ordinal processing that explored the relation between ordinal and numerical information processing in typically developing adults and adults with developmental dyscalculia (DD). Participants made "ordered" or "non-ordered" judgments about 3 groups of dots (non-symbolic numerical stimuli; in Experiment 1) and 3 numbers (symbolic task: Experiment 2). In contrast to previous findings and arguments about quantity deficit in DD participants, when quantity and ordinality are dissociated (as in the current tasks), DD participants exhibited a normal ratio effect in the non-symbolic ordinal task. They did not show, however, the ordinality effect. Ordinality effect in DD appeared only when area and density were randomized, but only in the descending direction. In the symbolic task, the ordinality effect was modulated by ratio and direction in both groups. These findings suggest that there might be two separate cognitive representations of ordinal and quantity information and that linguistic knowledge may facilitate estimation of ordinal information.     

Acquisition of the Cardinal Principle Coincides with Improvement in Approximate Number System Acuity in Preschoolers

Human mathematical abilities comprise both learned, symbolic representations of number and unlearned, non-symbolic evolutionarily primitive cognitive systems for representing quantities. However, the mechanisms by which our symbolic (verbal) number system becomes integrated with the non-symbolic (non-verbal) representations of approximate magnitude (supported by the Approximate Number System, or ANS) are not well understood. To explore this connection, forty-six children participated in a 6-month longitudinal study assessing verbal number knowledge and non-verbal numerical acuity. Cross-sectional analyses revealed a strong relationship between verbal number knowledge and ANS acuity. Longitudinal analyses suggested that increases in ANS acuity were most strongly related to the acquisition of the cardinal principle, but not to other milestones of verbal number acquisition. These findings suggest that experience with culture and language is intimately linked to changes in the properties of a core cognitive system.     

Effect of bilingualism on lexical stress pattern discrimination in French-learning infants

Monolingual infants start learning the prosodic properties of their native language around 6 to 9 months of age, a fact marked by the development of preferences for predominant prosodic patterns and a decrease in sensitivity to non-native prosodic properties. The present study evaluates the effects of bilingual acquisition on speech perception by exploring how stress pattern perception may differ in French-learning 10-month-olds raised in bilingual as opposed to monolingual environments. Experiment 1 shows that monolinguals can discriminate stress patterns following a long familiarization to one of two patterns, but not after a short familiarization. In Experiment 2, two subgroups of bilingual infants growing up learning both French and another language (varying across infants) in which stress is used lexically were tested under the more difficult short familiarization condition: one with balanced input, and one receiving more input in the language other than French. Discrimination was clearly found for the other-language-dominant subgroup, establishing heightened sensitivity to stress pattern contrasts in these bilinguals as compared to monolinguals. However, the balanced bilinguals' performance was not better than that of monolinguals, establishing an effect of the relative balance of the language input. This pattern of results is compatible with the proposal that sensitivity to prosodic contrasts is maintained or enhanced in a bilingual population compared to a monolingual population in which these contrasts are non-native, provided that this dimension is used in one of the two languages in acquisition, and that infants receive enough input from that language.     

Do infants associate spiders and snakes with fearful facial expressions?

Do infants preferentially learn to fear stimuli that represent an ancestral danger? This question was addressed using event-related brain potentials in 9-month-old infants (N = 38). In Experiment 1, infants saw fearful and neutral faces gazing towards spiders and flowers. Then spiders and flowers were presented again without faces. Infants responded with increased attention (signaled by the Negative central, Nc component) to stimuli associated with fear. In particular, spiders that were gaze-cued with a fearful as compared to a neutral expression elicited an increased Nc response. In Experiment 2, targets were snakes and fish. Snakes elicited increased Nc amplitude compared to fish irrespective of emotion condition. Results speak to the evolution-based fear-relevance of spiders and snakes. Our findings provide partial support for social fear learning and preparedness theory (Experiment 1) and non-associative accounts of fear acquisition (Experiment 2). We conclude that both kinds of fear acquisition seem to play a role in early human development.     

Preschoolers' precision of the approximate number system predicts later school mathematics performance

The Approximate Number System (ANS) is a primitive mental system of nonverbal representations that supports an intuitive sense of number in human adults, children, infants, and other animal species. The numerical approximations produced by the ANS are characteristically imprecise and, in humans, this precision gradually improves from infancy to adulthood. Throughout development, wide ranging individual differences in ANS precision are evident within age groups. These individual differences have been linked to formal mathematics outcomes, based on concurrent, retrospective, or short-term longitudinal correlations observed during the school age years. However, it remains unknown whether this approximate number sense actually serves as a foundation for these school mathematics abilities. Here we show that ANS precision measured at preschool, prior to formal instruction in mathematics, selectively predicts performance on school mathematics at 6 years of age. In contrast, ANS precision does not predict non-numerical cognitive abilities. To our knowledge, these results provide the first evidence for early ANS precision, measured before the onset of formal education, predicting later mathematical abilities.     

Kin recognition by larval wood frogs (Rana sylvatica): effects of diet and prior exposure to conspecifics

Summary We investigated kin recognition by larval wood frogs (Rana sylvatica) in blind laboratory experiments using spatial affinity as a recognition assay. Tadpoles reared with full-sibs displayed a significant preference for familiar full-sibs over unfamiliar non-kin, but failed to discriminate between unfamiliar full-sibs and unfamiliar paternal half-sibs. Tadpoles reared in social isolation (with or without maternal egg jelly) from the two-celled embryonic stage displayed a significant preference for unfamiliar full-sibs over unfamiliar non-kin. Tadpoles reared on a meat diet with their full-sibs: 1) exhibited a significant preference for unfamiliar full-sibs fed meat over unfamiliar non-kin fed meat, 2) failed to discriminate between unfamiliar full-sibs fed lettuce and unfamiliar non-kin fed meat, 3) exhibited a significant preference for unfamiliar non-kin fed meat over unfamiliar non-lin fed lettuce, 4) failed to discriminate between unfamiliar full-sibs fed meat and unfamiliar full-sibs fed lettuce, and 5) displayed a significant spatial preference for odors associated with meat (a familiar food) over odors associated with lettuce (an unfamiliar food). Our results, together with those of Cornell et al. (1989), indicate that the recognition cue of larval R. sylvatica has both genetic and environmental (dietary) components. Our findings establish that previous exposure to maternal egg jelly, kin, or conspecifics is not necessary for the development of kin recognition ability in larval R. sylvatica. Our results are more consistent with the self-learning of recognition cues (a form of phenotype matching) than with a recognition mechanism that involves a genetically fixed recognition template. Finally, our results indicate that increasing similarity between the recognition template and perceived cue does not necessarily result in increasing spatial affinity for kin.     

Hierarchical complexity of combinatorial manipulation in capuchin monkeys (Cebus apella)

The purpose of this study was to examine the hierarchical complexity of combinatorial manipulation in capuchin monkeys (Cebus apella). Two experiments were conducted. In Experiment 1 capuchins were presented with an apparatus designed to accommodate the use of probing tools. In Experiment 2 the same capuchins were presented with sets of nesting containers. Five of the ten subjects used probing tools and seven subjects placed objects in the containers. The capuchins' behavior reflected three hierarchically organized combinatorial patterns displayed by chimpanzees and human infants. Although the capuchins sometimes displayed the two more complex patterns (“pot” and “subassembly”), their combinatorial behavior was dominated by the simplest pattern (“pairing”). In this regard capuchins may not attain the same grammar of manipulative action that has been reported for chimpanzees and young human children. © 1994 Wiley-Liss, Inc.     

Orientation variance as a quantifier of structure in texture

I consider how structure is derived from texture containing changes in orientation over space, and propose that multi-local orientation variance (the average orientation variance across a series of discrete images locales) is an estimate of the degree of organization that is useful both for spatial scale selection and for discriminating structure from noise. The oriented textures used in this paper are Glass patterns, which contain structure at a narrow range of scales. The effect of adding noise to Glass patterns, on a structure versus noise task (Maloney et al., 1987), is compared to discrimination based on orientation variance and template matching (i.e. having prior knowledge of the target's orientation structure). At all but very low densities, the variance model accounts well for human data. Next, both models' estimates of tolerable orientation variance are shown to be broadly consistent with human discrimination of texture from noise. However, neither model can account for subjects' lower tolerance to noise for translational patterns than other (e.g. rotational) patterns. Finally, to investigate how well these structural measures preserve local orientation discontinuities, I show that the presence of a patch of unstructured dots embedded in a Glass pattern produces a change in multi-local orientation variance that is sufficient to account for human detection (Hel Or and Zucker, 1989). Together, these data suggest that simple orientation statistics could drive a range of 'texture tasks', although the dependency of noise resistance on the pattern type (rotation, translation, etc.) remains to be accounted for.     

Spontaneous symmetry breaking in self–organizing neural fields

We extend the theory of self-organizing neural fields in order to analyze the joint emergence of topography and feature selectivity in primary visual cortex through spontaneous symmetry breaking. We first show how a binocular one-dimensional topographic map can undergo a pattern forming instability that breaks the underlying symmetry between left and right eyes. This leads to the spatial segregation of eye specific activity bumps consistent with the emergence of ocular dominance columns. We then show how a 2-dimensional isotropic topographic map can undergo a pattern forming instability that breaks the underlying rotation symmetry. This leads to the formation of elongated activity bumps consistent with the emergence of orientation preference columns. A particularly interesting property of the latter symmetry breaking mechanism is that the linear equations describing the growth of the orientation columns exhibits a rotational shift-twist symmetry, in which there is a coupling between orientation and topography. Such coupling has been found in experimentally generated orientation preference maps     

Can Infants Tell the Difference between Gold and Yellow?

There is a large literature focused on the color perception of matte surface. However, recent research showed that the component of surface specular reflection, such as glossiness, also affects categorical color perception. For instance, the color term “gold” was used to name high specular stimuli within a specific range of chromaticity, which overlaps with those of yellow and orange for low specular stimuli. In the present study, we investigated whether the component of surface specular reflectance affects the color perception of 5- to 8-month-old infants by using the preferential looking technique. In the first experiment, we conducted a simple test to determine whether infants perceive yellow and gold as the same color by comparing their preference for these colors over green. If the infants perceive yellow and gold as the same color, they would show similar preference scores over green. On the other hand, if infants show different preference scores over green, it indicates that infants do not perceive yellow and gold as the same color. Only the 7–8 month-old infants showed different preference scores for gold and yellow over green. This result indicates that the 7–8 month-old infants perceive gold and yellow as different colors. In Experiment 2, we eliminated the component of specular reflectance on the gold surface and presented it against green to infants. A similar preference score of yellow over green was obtained. This result suggests that the difference between the preference scores for gold and yellow over green in Experiment 1 was based on representations of glossiness.     

Circadian chronotypes among wild-captured west Andean octodontids

Rest activity pattern was studied in wild-captured males of Octodon degus (n=9), Octodon bridgesi (n=3), and Spalacopus cyanus (n=6) (Rodentia: Octodontidae). Ten-minute resolution actograms were constructed from data obtained by an automated acquisition system. After two months of habituation to a stable light-dark schedule, recordings were performed in isolation chambers under a 12: 12 Light Dark schedule. A free-running period (constant darkness) was recorded for O. bridgesi and S. cyanus. O. degus displayed a crepuscular pattern of rest activity rhythm. Entrained O. bridgesi and S. cyanus displayed nocturnal preference, with rest anticipating light phase and without crepuscular activity bouts. Under constant darkness, active phase occurred at subjective night in O. bridgesi and S. cyanus. Wild-captured O. bridgesi and S. cyanus possess a circadian driven nocturnal preference, while wild O. degus displays a crepuscular profile. Diurnal active phase preference of wild S. cyanus colonies observed in the field could not be explained solely by photic entrainment, since social and/or masking processes appear to be operative. The genus Octodon includes species with diverse chronotypes. We propose that crepuscular diurnal pattern observed in O. degus is a recent acquisition among the octodontid lineage.