Spatial reasoning and spatial structures are relatively new areas of research in mathematics education. In this study of children exploring spatial conceptions of grid structures, twenty-one children (ages 4-9) were given a series of tasks involving square grids during virtual interviews. As a result of an ideal-type analysis of the qualitative data, a typology of conceptions of grids emerged showing five distinct categories sequenced from very early conceptions of square grids (as a series of isolated cells) to more coordinated structuring (as related and intersecting rows and columns). The five categories - Single Cell Structuring, Partial Unit Building, Whole Figure and Parts-of-Figure Noticing, Composite Unit Structuring and Coordinated Structuring - are described through illustrative examples. Students' gestures, language and diagrams were considered together when constructing the types. Interestingly, the spatial structure of grids was not readily apparent to many students and in fact was found to be complex for students to conceptualize. With minimal research on grids as a spatial structure in the mathematics education research field, there is strong potential for further investigation in this area.
Author Keywords: Grids, Mathematics, Spatial reasoning, Young Children