Geocadabra Construction Box: A dynamic geometry interface within a 3D visualization teaching-learning trajectory for elementary learners (Invited Article)

Abstract

This study focuses on the integration of a 3-D dynamic geometry interface to enhance the 3-D visualization capacity of 8-9-year-old children who attend an after-school program. Each year, all third grade children, who attend a dual-language urban elementary school, are invited to participate, typically beginning with 20-25 participants. The program runs for one hour per week for the duration of the academic year. The research team (a university researcher and one or more classroom teachers) uses design research principles (Cobb, et al., 2003) to develop and refine teaching-learning trajectories for the program. They use socially mediated instructional strategies, constantly challenging learners to find multiple solutions and explanations to a wide variety of spatial problems. Learners work with figures made from wooden cubes, 2-D pictures that resemble these figures, and with iconic representations (such as top-view numeric or top, side and front plane views) that do not directly resemble the figures. Through the integration of Geocadabra (Lecluse, 2005), the 3-D dynamic digital interface, learners move easily among the different representations and then can mentally abstract properties of these figures. They were able to visualize and accurately enumerate cubes of a complex 2-D conventional picture, but were also able to determine multiple solutions for given sets of front, side and top view diagrams, which do not always correlate with only one 3-D solution. With the current curricular focus on predominantly symbolic numeration, systematic integration of visualization, even as a representation tool for number work, into the elementary curriculum is problematic.