Paradoxical Simulations to Enhance Education in Mathematics

Abstract

The subject of probability and statistics is easily dismissed by students as assemblages of formulae to be rote-memorized. We propose here an integration of simulation-based activities with certain mathematical paradoxes using patchwork assessment to first-year undergraduates, such that they can better appreciate the real-world context of probability and statistics. The proposed examples alongside various facilitation skills for the instructor are discussed. We also provide an original spreadsheet simulation program in Excel and Visual Basic for Applications to reproduce the numerical experiments. This program is capable of running Monte Carlo simulations for all three seminal Parrondo's paradox variants, and can be easily used by students and instructors; moreover, the computed datasets and code are fully-transparent, thereby allowing interactive discussions, modifications and extensions, and further analyses. Our findings suggest that the proposed teaching strategy is useful, and we hope that this work will initiate the significant adoption of paradoxical simulations in teaching practice. The interactive program is freely available on open science framework.

Keywords

• Mathematics
• interdisciplinary
• education
• paradoxical simulations
• smart classroom
• Parrondo’s paradox