@article {3589, title = {From Map Reading to Geometric Intuitions}, journal = {Developmental Psychology}, year = {2018}, month = {03/2018}, abstract = {

The origins and development of our geometric intuitions have been debated for millennia. The present study links children{\textquoteright}s developing intuitions about the properties of planar triangles to their developing abilities to read purely geometric maps. Six-year-old children are limited when navigating by maps that depict only the sides of a triangle in an environment composed of only the triangle{\textquoteright}s corners and vice versa. Six-year-old children also incorrectly judge how the angle size of the third corner of a triangle varies with changes to the other two corners. These limitations in map reading and in judgments about triangles are attenuated, respectively, by 10 and 12 years of age. Moreover, as children get older, their map reading predicts their geometric judgments on the triangle task. Map reading thus undergoes developmental changes that parallel an emerging capacity to reason explicitly about the distance and angle relations essential to euclidean geometry. (PsycINFO Database Record (c) 2018 APA, all rights reserved)

Supplemental materials: http://dx.doi.org/10.1037/dev0000509.supp
}, keywords = {euclidean geometry, mathematical cognition, spatial cognition, spatial symbols}, issn = {0012-1649}, doi = {http://dx.doi.org/10.1037/dev0000509}, url = {http://psycnet.apa.org/record/2018-12810-001}, author = {Moira R Dillon and Elizabeth S Spelke} } @article {4192, title = {The statistical shape of geometric reasoning}, journal = {Scientific Reports}, volume = {8}, year = {2018}, month = {08/2018}, abstract = {

Geometric reasoning has an inherent dissonance: its abstract axioms and propositions refer to perfect, idealized entities, whereas its use in the physical world relies on dynamic perception of objects. How do abstract Euclidean concepts, dynamics, and statistics come together to support our intuitive geometric reasoning? Here, we address this question using a simple geometric task {\textendash} planar triangle completion. An analysis of the distribution of participants{\textquoteright} errors in localizing a fragmented triangle{\textquoteright}s missing corner reveals scale-dependent deviations from a deterministic Euclidean representation of planar triangles. By considering the statistical physics of the process characterized via a correlated random walk with a natural length scale, we explain these results and further predict participants{\textquoteright} estimates of the missing angle, measured in a second task. Our model also predicts the results of a categorical reasoning task about changes in the triangle size and shape even when such completion strategies need not be invoked. Taken together, our findings suggest a critical role for noisy physical processes in our reasoning about elementary Euclidean geometry.

}, doi = {10.1038/s41598-018-30314-y}, url = {http://www.nature.com/articles/s41598-018-30314-y}, author = {Hart, Yuval and Moira R Dillon and Andrew Marantan and Cardenas, Anna L. and Elizabeth S Spelke and Mahadevan, L.} } @conference {2603, title = {Spatial cognition across development}, booktitle = {SRCD}, year = {2017}, address = {Austin, TX}, author = {Moira R Dillon and Elizabeth S Spelke} } @article {2606, title = {Young children{\textquoteright}s use of distance and angle information during map reading}, year = {2017}, address = {Austin, TX}, author = {Moira R Dillon and Elizabeth S Spelke} } @article {2596, title = {Young Children{\textquoteright}s Use of Surface and Object Information in Drawings of Everyday Scenes}, journal = {Child Development}, year = {2016}, doi = {10.1111/cdev.12658}, author = {Moira R Dillon and Elizabeth S Spelke} } @article {1668, title = {Children{\textquoteright}s expectations about training the approximate number system.}, journal = {British Journal of Developmental Psychology}, volume = {33}, year = {2015}, chapter = {411}, abstract = {

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{\textquoteright}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{\textquoteright}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{\textquoteright}s sleep and their favorite breakfast. Thus, children{\textquoteright}s improved symbolic arithmetic after ANS training cannot be explained by their expectations about that training.

}, author = {Moira R Dillon and Pires, A. C. and Hyde, D. C. and Elizabeth S Spelke} } @conference {1669, title = {Connecting core cognition, spatial symbols, and the abstract concepts of formal geometry.}, booktitle = {Cognitive Development Society Post-Conference, More on Development}, year = {2015}, author = {Moira R Dillon and Elizabeth S Spelke} } @article {1955, title = {From spatial symbols to Euclidean intuitions}, number = {ID: 316 / PS - I: 50}, year = {2015}, month = {10/2015}, address = {Columbus, OH}, abstract = {

Euclidean\  geometry\  is\  highly\  intuitive\  to\  adults\  from\  diverse\  cultures,\  but\  the\  sources\  of\  these\  intuitions\  remain\  unknown.\  The\  present study investigates whether children{\textquoteright}s understanding of Euclidean geometry is linked to their use of spatial symbols.\  Six - ,\  10,\  and\  12 - year - old\  children\  were\  given\  tests\  of\  navigation\  by\  purely\  geometric\  maps, which\  required\  them\  to\  place\  objects\  in\  fragmented\  3D\  environments\  using\  2D\  maps\  highlighting\  the\  same\  or\  different\  geometric\  information\  as\  the\  3D\  environments.\  Children\  also\  completed\  a\  test\  of\  abstract\  geometric\  reasoning\  focused\  on\  triangle\  completion .\  Performance\  on\  the\  geometric\  reasoning\  test\  improved\  markedly\  with\  age,\  and\  this\  improvement\  was\  associated\  with\  more\  integrated\  interpretations\  of\  the\  geometric\  maps\  and\  environments.\  These\  findings\  connect\  the\  achievement\  of\  Euclidean\  intuitions\  to\  the mastery\  of\  spatial\  symbols.

}, url = {http://cogdevsoc.org/sites/default/files/Official\%20Full\%20Conference\%20Proceedings_10.10.pdf}, author = {Moira R Dillon and Elizabeth S Spelke} } @article {1670, title = {From spatial symbols to Euclidean intuitions.}, year = {2015}, author = {Moira R Dillon and Elizabeth S Spelke} } @article {1671, title = {Infants{\textquoteright} sensitivity to shape changes.}, year = {2015}, author = {Moira R Dillon and Izard, V. and Elizabeth S Spelke} } @article {867, title = {Isolating angle in infants{\textquoteright} detection of shape}, year = {2015}, author = {Moira R Dillon and V{\'e}ronique Izard and Elizabeth S Spelke} } @conference {869, title = {Reorientation ability predicts early spatial symbol reading}, booktitle = {2015 Society for Research in Child Development Biennial Meeting}, year = {2015}, author = {Moira R Dillon and Elizabeth S Spelke} } @conference {868, title = {Young children{\textquoteright}s automatic and alternating use of scene and object information in spatial symbols.}, booktitle = {Budapest CEU Conference on Cognitive Development}, year = {2015}, abstract = {

Although symbolic understanding has long been studied, little is known about the 2D shape information children use to relate symbols to their 3D referents. Our previous research suggests that young children rely on length and angle to find locations on objects, but on distance and direction to find locations in scenes. These studies, however, either presented drawings from non-canonical perspectives or probed children{\textquoteright}s use of symbols in unusual environments. Moreover, these studies explored the factors that limit children{\textquoteright}s understanding of spatial symbols, not the sources of their flexibility in this domain.

For the present study, we showed 144 4-year-old children three types of drawings of a typical room, depicting the room{\textquoteright}s objects, its extended surfaces, or both. In one task, children used the drawings to find targets located either at the junction of two extended surfaces in a room or next to objects in the room. In another task, children judged whether drawings that include just scene or just object information are better depictions of targets at these two types of locations.

\ \ \ \ \ \ \ \ \ \ \  We found that the limitations previously observed in children{\textquoteright}s use of spatial symbols extend to highly realistic perspectival drawings: children perform better with scene drawings when targets are located at the junctions of extended surfaces in the room and better with object targets when targets are located near objects, but gain no additional benefit when presented with both types of information. In addition, children show no awareness of this pattern in their performance: they judge drawings of objects to be more informative of all target locations. Common drawings evidently present geometric information in a format automatically accessible to cognitive systems for navigation and object recognition. Young children nevertheless fail to integrate the information that these systems represent, even when shown drawings of the most familiar and natural kinds.

}, author = {Moira R Dillon and Elizabeth S Spelke} } @article {866, title = {Core geometry in perspective}, journal = {Developmental Science}, year = {2014}, month = {11/2014}, abstract = {

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.

}, doi = {10.1111/desc.12266}, author = {Moira R Dillon and Elizabeth S Spelke} } @article {1349, title = {Core foundations of abstract geometry}, journal = {Proceedings of National Academy of Sciences of the United States of America}, volume = {110}, year = {2013}, chapter = {14191}, abstract = {

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{\textquoteright}s use of geometry in tasks assessing: navigation; visual form analysis; and the interpretation of symbolic, purely geometric maps. Children{\textquoteright}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{\textquoteright}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{\textquoteright}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{\textquoteright}s use of the abstract geometry in spatial symbols such as maps may provide the earliest clues to the later construction of Euclidean geometry.

}, author = {Moira R Dillon and Yi Huang and Elizabeth S Spelke} }