A Close Encounter with INFINITY: Inventing New Mathematics

As a college mathematics teacher for six years, the author has learned his share of pedagogical techniques through research, practice, and reflection. He adopts new theories into classroom practice, differentiates instruction when necessary, and remains open to the diversity his students bring with respect to academic readiness, cultural norms, and learning styles. Through these experiences, the author has learned what typically works and what needs attention. But he learned his biggest lesson just recently with his calculus 2 class. While approaching the end of a unit on infinite series, he did his usual brainstorming for an optional assignment--something to pique student interest in this unit. In this article, the author first discusses two student responses to share the fruits of their efforts. Second, he includes some anecdotes about what his students gained from this experience. The author closes with some of his realizations from having done this activity. (Contains 2 figures.)