Students' spatial structuring of 2D arrays of squares

We define spatial structuring as the mental operation of constructing an organization or form for an object or set of objects. It is an essential mental process underlying students' quantitative dealings with spatial situations. In this article, we examine in detail students' structuring and enumeration of 2-dimensional (2D) rectangular arrays of squares. Our research indicates that many students do not "see" the row-by-column structure we assume in such arrays. We describe the various levels of sophistication in students' structuring of these arrays and elaborate the nature of the mental process of structuring.