Incorporating Vygotsky's concept formation theory and Berger's appropriation theory, an assessment which highlights authentic operations with the concept of area was designed and administered to 44 sixth grade students to determine what types of understanding they maintained. The results indicated the more novel the situation, the more diverse stages of understanding were exhibited by children. Inconsistent levels of reasoning across different items were revealed for most individuals. We suggest that novel assessments grounded in concept formation theories may provide greater insights on children's understanding of mathematics. [For the complete proceedings, see ED584443.]