DOMINIC W. MASSARO, editor
University of California, Santa Cruz

Discourse and Research on an Overlooked Aspect of Mathematical Reasoning

Reasoning by Mathematical Induction in Children's Arithmetic
By Leslie Smith. Advances in Learning and Instruction series. Boston: Pergamon, 2002. xviii + 170 pp. Cloth, $90.95..

Some time ago, I asked Nikki, a kindergartner, what she thought the largest number was. The girl responded, "A million." I then asked what number she thought came after a million. After a moment's thought, Nikki responded, "A million and one." I next asked what she thought came after a million and one. Again the girl thought for a moment and answered, "A million and two." I pressed Nikki further by asking what she thought came after a million and two. After a few moments of thoughtful reflection, she concluded, "There is no largest number." Nikki's sudden insight (rediscovery of the concept of infinity) illustrates informal mathematical induction.