We explored preschool’s children’s understanding of the correspondence of 3-D objects and 2-D faces in a noveltask. In the “footprints” task children were shown a geometric solid, such as a pyramid or a prism, and asked to select whichshape the solid would make if it were dipped in ink and stamped on a piece of paper. Through a latent class analysis of children’serrors we found children differed significantly in their misconceptions about object structure. Three distinct classes of childrenemerged: children who could only match visible faces, children who believed solids have an ‘essential’ face irrespective ofrotation, and children who differentiated faces based on a solid’s rotation. We examined the characteristics of children in eachof these classes using a battery of spatial tasks and numeric tasks. Our results suggest errors found in older children’s andadults’ reasoning about geometric concepts develop prior to formal schooling.

Shape puzzles can elicit parent-child math talk, which is critical for early math learning. However, little is known abouthow the features of the puzzles impact parent-child interactions through parents math talk. Two- to four-year-old chil-dren and their parents (current N=30; target N=128) completed two shape puzzles. The control puzzle was typical ofcommercial puzzles, including nine distinct shapes. The experimental puzzle included multiple exemplars of shapes (e.g.,three different triangles, three different quadrilaterals). We hypothesized that parents would use richer math talk with theexperimental puzzle. We coded quantity and quality of parent math talk during the interactions. Preliminary results indi-cate that parents mostly used low-level math talk (naming shapes) for both puzzles, but they used more high-level mathtalk (comparing shapes, providing shape definitions) for the experimental than the control puzzle (p=0.054). We discussparticular puzzle features that can stimulate high-quality math talk during parent-child interactions.