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

There is growing acknowledgement of the importance of spatial abilities tostudent achievement across a broad range of domains and disciplines. Nets are one wayto connect three-dimensional shapes and their two-dimensional representations and area common focus of geometry curricula. Thirty-four students at year 6 (upper primaryschool) were interviewed on two occasions about their anticipation of whether or notgiven 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 Devel-opment, 52,83–94, 2009 ) four characteristics of schemes were used as a theoreticallens to analyse the data. Successful schemes depended on the interaction of operationalinvariants, such as strategic choice of the base, rules for action, particularly rotation ofshapes, and anticipations of composites of polygons in the net forming arrangements offaces in the solid. Inferences were rare. These data suggest that students need teachersupport to make inferences, in order to create transferable schemes.