Developing an Understanding of Children's Justifications for the Circle Area Formula.

In this study we investigated eighth grade students’ informal justification for the circle area formula to expand accounts of the measurement knowledge for middle-school age students. Data were collected during three paired interviews of a three-year teaching experiment. Here we describe schemes students exhibited as they operated on measurement tasks at a level we have described as “conceptual area measurer”; the tasks prompted the use of square units to quantify a figure that is not rectilinear. We found students could follow and rehearse a rationale for the validity of the circle area formula with substantive opportunities for movement and figural operations with units, or with decompositions from unit images that coordinated circle and rectangle images.