This research project will investigate the effects social organization, learning technologies, and their interrelationships, have on the geometric reasoning of PreK-3 students. Social organization is operationalized here as the strategic grouping of students into triads to engage in collaborative problem solving. Learning technologies are operationalized here as physical and virtual manipulative types (tangrams, pentominoes, geoboards) together with supporting software designed to facilitate students in accessing their mathematical knowledge. Based on findings from preliminary work in this area, it is proposed that learning technologies allow for fluid exchanges between peers, and transitions between physical and virtual manipulatives, significantly enhancing geometric reasoning. The current project presents a robust research and design framework that combines iterative cycles of field studies in the classroom with development and experimentation in the lab. The goal is to design, develop and prototype a tabletop computer interface that allows for unprecedented exchanges among student peers and transitions between manipulative types. The tabletop interface will serve first as the apparatus that facilitates experimental manipulations, later being used, through iterative refinement, as the learning technology platform by which students gain access to mathematical knowledge. The advancement proposed by the current work is that it places all interaction on the horizontal tabletop. This is critical in that it removes confounding effects of different seating and screen orientations from pilot study findings. Manipulations of geometric artifacts reside along two dimensions of research questions: the effects of social interaction and of learning technology on geometric reasoning. Hence, the proposed studies will allow investigation of different transitions between fully functional and fully operational thinking, functional and qualitative operational thinking, and qualitative and quantitative parametric thinking with the same interaction morphologies.
The proposed research has the potential to make significant contributions to the following intellectual domains: 1) child development -understanding children's development of mathematical reasoning in terms of learning trajectories 2) mathematics education - understanding teachers' use of advanced learning technologies and role in classroom instruction, and children's learning of mathematics using advanced learning technologies; 3) learning sciences - refining techniques for the analysis, design, and development of advanced learning technologies in use; 4) human-computer interaction -design of interfaces that aid learning to include gestural interaction, tangible manipulation, and horizontal displays; and 5) psycholinguistics - grounding of concepts developed in other domains in the classroom environment. Results from the research will also have much to say about the participation of girls in the mathematics classroom, a goal being to encourage rich discourse of all students. In addition, developed technologies may have implications for the education of special needs children as instructional interfaces can be modified and reconfigured to meet the diverse needs of this underrepresented group. A significant outcome of collaboration among these disciplines will be cutting-edge research opportunities for doctoral students and groundwork for the establishment of new curricula and, possibly, degree programs.
