Abstract
This article describes a classroom teaching experience that transforms a routine middle school textbook problem about a bouncing ball into an extended mathematical inquiry. Through systematic variation of the problem's parameters—initial height, rebound ratio, and number of bounces—students are guided to notice patterns, formulate conjectures, and pose new questions. The progression leads naturally from finite distance calculations to infinite geometric series and repeating decimals. A concrete bread-sharing metaphor is introduced to make infinite sums tangible, enabling students to grasp \(\sum_{n=1}^{\infty} (1/3)^n = 1/2\) and the equality \(0.999\ldots = 1\) without formal algebra. Student responses reveal moments of surprise and genuine conceptual insight. The approach illustrates how careful sequencing of examples, meaningful metaphors, and an emphasis on student-generated questions can transform a single textbook exercise into a rich learning experience. The teacher's role as a designer of mathematical inquiries is highlighted throughout.
Keywords
Problem posing, infinite processes, geometric series, middle school mathematics, conceptual understanding, mathematical metaphor, teacher as designer
How to Cite
Imaninezhad, M., (2026) “The Art of Problem Posing: From Bouncing Balls to Infinite Series”, Ohio Journal of School Mathematics 103(1): 6, 74-85. doi: https://doi.org/10.18061/ojsm.7188