One critical objective of high-quality education is to provide citizens literate in science, technology, engineering, and math (STEM) to ensure economic success (as reported by Newcombe (Harnessing spatial thinking to support STEM learning (OECD Education Working Papers, No. 161), OECD Publishing, Paris, 2017). Many studies have found a correlation between STEM skills and spatial ability. A meta-analysis of studies (as reported by Hawes et al. (in Davis (ed), Spatial reasoning in the early years: Principles, assertions, and speculations, Routledge, New York, 2015) reported that interventions to teach spatial skills resulted in significant improvement, approximately doubling the number of people with spatial skills associated with being an engineer. Most educational programs lack a focus on spatial skills, especially in early years when children are developing their spatial sense of the world and building a foundation for later, more complex, spatial skills. Little research exists showing what young children do when allowed to explore materials with little or no adult direction. This qualitative study was designed to address that gap and provide evidence of spatial skills in young children, specifically toddlers (12–36 months old). A variety of common household materials were set out during free play time, and educators provided minimal guidance while children played. Trained videographers recorded for 10 h (twice a week for 1 h over a 5-week period). Video was open coded for spatial actions children displayed with the materials. The initial codes were then reviewed for common themes and compared to those found in previous studies. Results show that toddlers demonstrated a wide range of spatial skills without educator direction and stayed engaged for long periods of time. Based on these results, implications are presented for educators to support spatial development.

This thesis examines the role of function in representations of space by robots - that is, dealing directly and explicitly with those aspects of space and objects in space that serve some purpose for the robot. It is suggested that taking function into account helps increase the generality and robustness of solutions in an unpredictable and complex world, and the suggestion is affirmed by several instantiations of functionally conceived spatial models. These include perceptual models for the "on" and "in" relations based on support and containment; context-sensitive segmentation of 2-D maps into regions distinguished by functional criteria; and, learned predictive models of the causal relationships between objects in physics simulation. Practical application of these models is also demonstrated in the context of object search on a mobile robotic platform. / QC 20111125