Children’s schemes for anticipating the validity of nets for solids

摘要

There is growing acknowledgement of the importance of spatial abilities to student achievement across a broad range of domains and disciplines. Nets are one way to connect three-dimensional shapes and their two-dimensional representations and are a common focus of geometry curricula. Thirty-four students at year 6 (upper primary school) were interviewed on two occasions about their anticipation of whether or not given nets for the cube- and square-based pyramid would fold to form the target solid. Vergnaud’s (Journal of Mathematical Behavior, 17(2), 167–181, 1998, Human Development, 52, 83–94, 2009) four characteristics of schemes were used as a theoretical lens to analyse the data. Successful schemes depended on the interaction of operational invariants, such as strategic choice of the base, rules for action, particularly rotation of shapes, and anticipations of composites of polygons in the net forming arrangements of faces in the solid. Inferences were rare. These data suggest that students need teacher support to make inferences, in order to create transferable schemes.