Making sense of shape: An analysis of children's written responses

In this study, we examine a large set of student responses to a constructed-response geometry item on the National Assessment of Educational Progress (NAEP) administered in 1992 and 1996. The item asks students to name the similarities and differences between a parallelogram and a rectangle of equal area presented side by side on a grid. Through categorization of student work utilizing the constant comparison method [Lincoln, Y. S., & Guba, E. G. (1985). Naturalistic Inquiry, Beverly Hills, CA: Sage Publications], we identified two distinct categories of responses. The first group of responses indicates that students view the two figures as the same based on flexible prototypes while the second group indicates students view the two figures as distinct shapes based on inflexible prototypes. The research uncovers responses that show evidence of students’ development of a dynamic figural concept in which student understanding is based on sense-making that involves mentally manipulating the shapes. In addition, the research highlights the richness of the evidence obtained from constructed-response items administered as part of standardized assessments.