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: | , , , , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2019
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/105962 http://hdl.handle.net/10220/48860 http://dx.doi.org/10.1109/ACCESS.2019.2892742 |
| _version_ | 1826110985872605184 |
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| author | Cheong, Kang Hao Koh, Jin Ming Tan, Zong Xuan Boo, Brenda Oon Eng Lee, Guan Ying Yeo, Darren Jiansheng |
| author2 | School of Social Sciences |
| author_facet | School of Social Sciences Cheong, Kang Hao Koh, Jin Ming Tan, Zong Xuan Boo, Brenda Oon Eng Lee, Guan Ying Yeo, Darren Jiansheng |
| author_sort | Cheong, Kang Hao |
| collection | NTU |
| 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 | 2024-10-01T02:43:12Z |
| format | Journal Article |
| id | ntu-10356/105962 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T02:43:12Z |
| publishDate | 2019 |
| record_format | dspace |
| spelling | ntu-10356/1059622019-12-10T13:12:28Z Paradoxical simulations to enhance education in Mathematics Cheong, Kang Hao Koh, Jin Ming Tan, Zong Xuan Boo, Brenda Oon Eng Lee, Guan Ying Yeo, Darren Jiansheng School of Social Sciences Mathematics DRNTU::Social sciences::Psychology Interdisciplinary 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. Published version 2019-06-20T03:32:16Z 2019-12-06T22:01:40Z 2019-06-20T03:32:16Z 2019-12-06T22:01:40Z 2019 Journal Article Cheong, K. H., Koh, J. M., Yeo, D. J., Tan, Z. X., Boo, B. O. E., & Lee, G. Y. (2019). Paradoxical simulations to enhance education in Mathematics. IEEE Access, 7, 17941-17950. doi:10.1109/ACCESS.2019.2892742 https://hdl.handle.net/10356/105962 http://hdl.handle.net/10220/48860 http://dx.doi.org/10.1109/ACCESS.2019.2892742 en IEEE Access © 2019 IEEE. This work is licensed under a Creative Commons Attribution 3.0 License. For more information, see http://creativecommons.org/licenses/by/3.0/ 10 p. application/pdf |
| spellingShingle | Mathematics DRNTU::Social sciences::Psychology Interdisciplinary Cheong, Kang Hao Koh, Jin Ming Tan, Zong Xuan Boo, Brenda Oon Eng Lee, Guan Ying Yeo, Darren Jiansheng Paradoxical simulations to enhance education in Mathematics |
| 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 DRNTU::Social sciences::Psychology Interdisciplinary |
| url | https://hdl.handle.net/10356/105962 http://hdl.handle.net/10220/48860 http://dx.doi.org/10.1109/ACCESS.2019.2892742 |
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