Poster #25 - A Tale of Paths Between Two Points: Children’s Identification of Linearity on Different Geometric Surfaces

• In Event: 1-169 - Poster Session 04
  In Poster Session: PS 04 Section - Cognitive Processes

Integrative Statement

Formal geometry is one of the greatest feats of human cognition, yet some of its rules and axioms may nevertheless conflict with our basic intuitions about the spatial world. For example, our verbal reasoning about the sum of a planar triangle’s three angle sizes is scale-dependent, while the formal rule that dictates their sum is scale-independent (Hart et al., in press). Despite such conflicts, recent work has revealed that, when given a path connecting two points on a picture of a sphere, adults succeed in recognizing whether that path is the shortest path between the points, regardless of whether it looks like a straight line or a curve in the picture (see Fig. 1; Jordan et al., 2018). Because few adults encounter formal spherical geometry in school, their success might depend on everyday activities like navigating by efficient paths on a variety of terrains or recognizing objects by their shape skeletons and part structures. Might such successful and flexible judgments about linearity—i.e. the shortest distance between two points—emerge in childhood, long before we encounter such formal concepts in school?
Thirty-seven 6-8-year-old children (median = 7.81 years, range = 6.05 years – 8.99 years, 17 females) were presented with a computer task displaying 56 pictures of straight and curved paths on planes and spheres (Fig. 1). Prior to test trials, children were introduced to a snail, whose aim was to reach a mushroom by navigating various scenarios via inefficient or efficient paths (e.g. traversing a precariously skinny bridge versus a wide bridge; moving three heavy blocks out of the way versus two). After five practice scenarios with informative feedback, children were presented with test trials in which two different colored points represented the snail and mushroom and a single black trajectory represented a path (Fig. 1.). Children said “yes” or “no” to whether the depicted trajectory was the “easiest” path between the two points. Both practice and test trials varied in absolute path length.
Children succeeded in identifying the shortest distance between two points on all planar conditions (Fig. 2). Nevertheless, children had a strong tendency to say “yes” to paths that looked like lines on spheres, even when such lines were not the shortest distance between the two points (i.e., the Arc/Line condition). Likewise, they had a strong tendency to say “no” to curves on spheres. Both tendencies suggest a robust planar bias. Nevertheless, children were significantly more likely to correctly respond “no” to Arc/Curves than Geo/Curves (P = 0.008), demonstrating some successful differentiation between geodesic- and arc-curves on spheres. These striking results suggest that, since children are not drawing upon the complex formalisms of spherical geometry, our identification of the shortest distances between two points on different surfaces may be rooted in more basic intuitions about geometry gained through our everyday interactions with objects and spaces.

Authors

• Holly Huey, New York University
  Presenting Author

• Nicole Loncar, New York University
  Non-Presenting Author

• Matthew Jordan, New York University
  Non-Presenting Author

• Moira Rose Dillon, New York University
  Non-Presenting Author