PROCEEDINGS OF THE 15TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 2)
2012
Portland, Oregon
Promoting students’ object-based reasoning with infinite sets
Page: 2-618
Recent research about the thorny Tennis Ball Problem has revealed that students respond in different ways depending on the type of properties they generalize from the finite steps to the envisioned final state of the infinite process. These generalizations, in turn, depend on the features of the finite steps their attention is directed toward. Undergraduate students who attend to the labeling of objects, rather than simply counting the objects, are using object-based reasoning, which is crucial to their ability to understand Cantorian set theory. We propose a sequence of tasks centered around the Tennis Ball Problem that our research has shown to help students build object-based reasoning.