Many poor children are underprepared for demanding primary school curricula. Research in cognitive science suggests that school achievement could be improved by preschool pedagogy in which numerate adults engage children’s spontaneous, nonsymbolic mathematical concepts. To test this suggestion, we designed and evaluated a game-based preschool curriculum intended to exercise children’s emerging skills in number and geometry. In a randomized field experiment with 1540 children (average age 4.9 years) in 214 Indian preschools, 4 months of math game play yielded marked and enduring improvement on the exercised intuitive abilities, relative to no-treatment and active control conditions. Math-trained children also showed immediate gains on symbolic mathematical skills but displayed no advantage in subsequent learning of the language and concepts of school mathematics.
Diverse animal species primarily rely on sense (left–right) and egocentric distance (proximal–distal) when navigating the environment. Recent neuroimaging studies with human adults show that this information is represented in 2 scene-selective cortical regions—the occipital place area (OPA) and retrosplenial complex (RSC)—but not in a third scene-selective region—the parahippocampal place area (PPA). What geometric properties, then, does the PPA represent, and what is its role in scene processing? Here we hypothesize that the PPA represents relative length and angle, the geometric properties classically associated with object recognition, but only in the context of large extended surfaces that compose the layout of a scene. Using functional magnetic resonance imaging adaptation, we found that the PPA is indeed sensitive to relative length and angle changes in pictures of scenes, but not pictures of objects that reliably elicited responses to the same geometric changes in object-selective cortical regions. Moreover, we found that the OPA is also sensitive to such changes, while the RSC is tolerant to such changes. Thus, the geometric information typically associated with object recognition is also used during some aspects of scene processing. These findings provide evidence that scene-selective cortex differentially represents the geometric properties guiding navigation versus scene categorization.
Pictorial symbols such as photographs, drawings, and maps are ubiquitous in modern cultures. Nevertheless, it remains unclear how children relate these symbols to the scenes that they represent. The present work investigates 4-year-old children’s (N = 144) sensitivity to extended surface layouts and objects when using drawings of a room to find locations in that room. Children used either extended surfaces or objects when interpreting drawings, but they did not combine these two types of information to disambiguate target locations. Moreover, children’s evaluations of drawings depicting surfaces or objects did not align with their use of such information in those drawings. These findings suggest that pictures of all kinds serve as media in which children deploy symbolic spatial skills flexibly and automatically.
Humans possess a developmentally precocious and evolutionarily ancient Approximate Number System (ANS) whose sensitivity correlates with uniquely human symbolic arithmetic skills. Recent studies suggest that ANS training improves symbolic arithmetic, but such studies may engender performance expectations in their participants that in turn produce the improvement. Here we assessed 6- to 8-year-old children’s expectations about the effects of numerical and non-numerical magnitude training, as well as states of satiety and restfulness, in the context of a study linking children’s ANS practice to their improved symbolic arithmetic. We found that children did not expect gains in symbolic arithmetic after exercising the ANS, though they did expect gains in ANS acuity after training on any magnitude task. Moreover, children expected gains in symbolic arithmetic after a good night’s sleep and their favorite breakfast. Thus, children’s improved symbolic arithmetic after ANS training cannot be explained by their expectations about that training.
Research on animals, infants, children, and adults provides evidence that distinct cognitive systems underlie navigation and object recognition. Here we examine whether and how these systems interact when children interpret 2D edge-based perspectival line drawings of scenes and objects. Such drawings serve as symbols early in development, and they preserve scene and object geometry from canonical points of view. Young children show limits when using geometry both in non-symbolic tasks and in symbolic map tasks that present 3D contexts from unusual, unfamiliar points of view. When presented with the familiar viewpoints in perspectival line drawings, however, do children engage more integrated geometric representations? In three experiments, children successfully interpreted line drawings with respect to their depicted scene or object. Nevertheless, children recruited distinct processes when navigating based on the information in these drawings, and these processes depended on the context in which the drawings were presented. These results suggest that children are flexible but limited in using geometric information to form integrated representations of scenes and objects, even when interpreting spatial symbols that are highly familiar and faithful renditions of the visual world.
Human adults from diverse cultures share intuitions about the points, lines, and figures of Euclidean geometry. Do children develop these intuitions by drawing on phylogenetically ancient and developmentally precocious geometric representations that guide their navigation and their analysis of object shape? In what way might these early-arising representations support later-developing Euclidean intuitions? To approach these questions, we investigated the relations among young children’s use of geometry in tasks assessing: navigation; visual form analysis; and the interpretation of symbolic, purely geometric maps. Children’s navigation depended on the distance and directional relations of the surface layout and predicted their use of a symbolic map with targets designated by surface distances. In contrast, children’s analysis of visual forms depended on the size-invariant shape relations of objects and predicted their use of the same map but with targets designated by corner angles. Even though the two map tasks used identical instructions and map displays, children’s performance on these tasks showed no evidence of integrated representations of distance and angle. Instead, young children flexibly recruited geometric representations of either navigable layouts or objects to interpret the same spatial symbols. These findings reveal a link between the early-arising geometric representations that humans share with diverse animals and the flexible geometric intuitions that give rise to human knowledge at its highest reaches. Although young children do not appear to integrate core geometric representations, children’s use of the abstract geometry in spatial symbols such as maps may provide the earliest clues to the later construction of Euclidean geometry.
Localization of tactile stimuli to the hand and digits is fundamental to somatosensory perception. However, little is known about the development or genetic bases of this ability in humans. We examined tactile localization in normally developing children, adolescents, and adults and in people with Williams syndrome (WS), a genetic disorder resulting in a wide range of severe visual-spatial deficits. Normally developing 4-year-olds made large stimulus-localization errors, sometimes across digits, but nevertheless their errors revealed a structured internal representation of the hand. In normally developing individuals, errors became exponentially smaller over age, reaching the adult level by adolescence. In contrast, people with WS showed large localization errors regardless of age and a significant proportion of cross-digit errors, a profile similar to that of normally developing 4-year-olds. Thus, tactile localization reflects internal organization of the hand even early in normal development, undergoes substantial development in normal children, and is susceptible to developmental, but not organizational, impairment under genetic deficit.
Authorship attribution often suffers from charges of vicious circularity, of conflating authorship and style. We argue for a more virtuous circularity for attribution arguments made through the quantitative analyses of stylometry. Our study investigated temporal lexeme usage, which has been suggested as a mark of authorship style, in the corpus traditionally attributed to Chrétien de Troyes. Our analyses revealed different usage patterns for these lexemes after line 6150 of the Lancelot, possibly indicating the signature of another author in the text (traditionally presumed to be that of Godefroy de Lagny). By embracing probabilistic arguments instead of certainties, digital philology can employ stylometry to consider questions of authorship attribution for medieval texts.
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