Paradoxical Simulations to Enhance Education in Mathematics
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 bet...
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IEEE
2019-01-01
|
| Series: | IEEE Access |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/8611076/ |
| _version_ | 1818416003668770816 |
|---|---|
| author | Kang Hao Cheong Jin Ming Koh Darren J. Yeo Zong Xuan Tan Brenda Oon Eng Boo Guan Ying Lee |
| author_facet | Kang Hao Cheong Jin Ming Koh Darren J. Yeo Zong Xuan Tan Brenda Oon Eng Boo Guan Ying Lee |
| author_sort | Kang Hao Cheong |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-14T11:43:59Z |
| format | Article |
| id | doaj.art-adf577a5280d4393870a54a042751e75 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-14T11:43:59Z |
| publishDate | 2019-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-adf577a5280d4393870a54a042751e752022-12-21T23:02:42ZengIEEEIEEE Access2169-35362019-01-017179411795010.1109/ACCESS.2019.28927428611076Paradoxical Simulations to Enhance Education in MathematicsKang Hao Cheong0https://orcid.org/0000-0002-4475-5451Jin Ming Koh1Darren J. Yeo2Zong Xuan Tan3Brenda Oon Eng Boo4Guan Ying Lee5Engineering Cluster, Singapore Institute of Technology, SingaporeScience and Math Cluster, Singapore University of Technology and Design, SingaporeDepartment of Psychology and Human Development, Peabody College, Vanderbilt University, Nashville, TN, USADepartment of Computer Science, Yale University, New Haven, CT, USASchool of Computing Science, University of Glasgow Singapore, SingaporeSchool of Computing Science, University of Glasgow Singapore, SingaporeThe 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.https://ieeexplore.ieee.org/document/8611076/Mathematicsinterdisciplinaryeducationparadoxical simulationssmart classroomParrondo’s paradox |
| spellingShingle | Kang Hao Cheong Jin Ming Koh Darren J. Yeo Zong Xuan Tan Brenda Oon Eng Boo Guan Ying Lee Paradoxical Simulations to Enhance Education in Mathematics IEEE Access Mathematics interdisciplinary education paradoxical simulations smart classroom Parrondo’s paradox |
| title | Paradoxical Simulations to Enhance Education in Mathematics |
| title_full | Paradoxical Simulations to Enhance Education in Mathematics |
| title_fullStr | Paradoxical Simulations to Enhance Education in Mathematics |
| title_full_unstemmed | Paradoxical Simulations to Enhance Education in Mathematics |
| title_short | Paradoxical Simulations to Enhance Education in Mathematics |
| title_sort | paradoxical simulations to enhance education in mathematics |
| topic | Mathematics interdisciplinary education paradoxical simulations smart classroom Parrondo’s paradox |
| url | https://ieeexplore.ieee.org/document/8611076/ |
| work_keys_str_mv | AT kanghaocheong paradoxicalsimulationstoenhanceeducationinmathematics AT jinmingkoh paradoxicalsimulationstoenhanceeducationinmathematics AT darrenjyeo paradoxicalsimulationstoenhanceeducationinmathematics AT zongxuantan paradoxicalsimulationstoenhanceeducationinmathematics AT brendaoonengboo paradoxicalsimulationstoenhanceeducationinmathematics AT guanyinglee paradoxicalsimulationstoenhanceeducationinmathematics |