UC Santa Barbara

Following Robbie Case’s branch of neo-Piagetian theory, this dissertation proposed a central geometric structure for the domain of geometry. In consultation with a professor of mathematics skilled in early childhood mathematics education, a series of geometry investigations was designed, and manipulatives of special triangles were 3D printed for use in the study. Forty-eight children from 2 California charter schools participated in the study. Sixteen students from each of second-, fourth-, and sixth grade participated. Children completed the Figural Intersections Test to assess M-capacity (mental attention), the WISC-V block design subtest to assess spatial visualization, and the WISC-V visual span test to assess visuospatial working memory. Children completed an identical series of pretest and posttest spatial items to assess learning over the course of the sessions. Geometry investigations were video recorded, transcribed and analyzed for a subset of students. Two students from each grade were selected for analysis. The maximal variation method of purposeful sampling was used as the selection framework (Emmel, 2014). For each grade level, the student who showed the lowest initial performance and no improvement from pretest to posttest was contrasted with the student who showed the most improvement. Children in the no-improvement group used fewer words to describe their activities when prompted, showed more constrained experimentation during the investigations, and exhibited fewer examples of hierarchical learning instances than their peers who did improve from pretest to posttest. Theoretical and educational implications are discussed below, as well as limitations and recommendations for future studies.