Effects of three interventions on children's spatial structuring and coordination of area units

We examine the effects of 3 interventions designed to support Grades 2-5 children's growth in measuring rectangular regions in different ways. We employed the microge-netic method to observe and describe conceptual transitions and investigate how they may have been prompted by the interventions. We compared the interventions with respect to children's learning and then examined patterns in observable behaviors before and after transitions to more sophisticated levels of thinking according to a learning trajectory for area measurement Our findings indicate that creating a complete record of the structure of the 2-dimensional array-by drawing organized rows and columns of equal-sized unit squares-best supported children in conceptualizing how units were built, organized, and coordinated, leading to improved performance.