How Can I Find a Pattern in this Random Data? The Convergence of Multiplicative and Probabilistic Reasoning

This classroom-based research study examines the thinking of pre-calculus students about multiplicative growth and decay within a probabilistic context, thus bringing together two research strands in mathematics education: students' understanding of exponential functions and students' reasoning about random events. Using a multi-stage approach to model development, a curriculum unit was designed to elicit students' creation of a model or system that could be used to describe and explain the behavior of an experienced, probabilistic system. The evidence suggests that while the students made sense of the underlying multiplicative structure of the problem situation, many students experienced a conflict between the concept of a pattern and the concept of randomness. Students encountered difficulty in reconciling the deterministic nature of a closed-form analytic solution with the non-deterministic nature of a sequence of random events. These results suggest that there is a need for students to gain experience with non-deterministic models using contexts that provide meaningful empirical data.