To Örebro University

The aim of the present study is to explore strategies in enumerating units of three dimensional (3D) arrays. We analyse enumeration strategies of students in grade 3 (ages 8 to 9) in situations of cubical and spherical representations of units of 3D arrays. By exploring students’ strategies in these two situations, we find that difficulties in enu- merating units in 3D arrays can be traced to difficulties in units-locating, with the con- sequence of applying double and triple counting. Our results also indicate that spherical units can serve as perceptual clues in units-locating and in assembling units into rel- evant composites. With input from our findings, we suggest research to investigate the following three hypotheses: (i) spherical units can turn students away from double and triple counting, (ii) spherical units can support students’ units-locating process and their ability to assemble units into relevant composites and (iii) teaching of enumerating 3D arrays should start with spherical units before cubical units.