Active Learning in Undergraduate Mathematics Tutorials Via Cooperative Problem-Based Learning and Peer Assessment with Interactive Online Whiteboards

Abstract

It has been well documented that active learning (AL) improves student learning outcomes in education. This quasi-experimental study explores the effect of active learning on students’ knowledge of calculus concepts, in the form of the Calculus Concept Inventory (CCI), regular assignment scores, and test scores, during an 8-week calculus tutorial program. The active pedagogies used were cooperative problem-based learning and peer assessment, implemented using an interactive online whiteboard (IOWB) called RealtimeBoard. This study reveals statistically significant evidence that active learning increases students’ conceptual understanding and graded assignment performance in a first-year calculus class in Hong Kong. Furthermore, this study contributes towards a better understanding of how active learning can be implemented effectively in Asian tertiary mathematics education.

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References

  1. Baltes, S., & Diehl, S. (2014). Sketches and diagrams in practice. Proceedings of the 22nd ACM SIGSOFT International Symposium on Foundations of Software Engineering (pp. 530–541). ACM.

  2. Bonwell, C. C., & Eison, J. A. (1991). Active Learning: Creating Excitement in the Classroom. 1991 ASHE-ERIC Higher Education Reports. Washington, DC: ERIC Clearinghouse on Higher Education.

  3. Bradforth, S. E., Miller, E. R., Dichtel, W. R., Leibovich, A. K., Feig, A. L., Martin, J. D., et al. (2015). University learning: Improve undergraduate science education. Nature News,523(7560), 282.

    Article  Google Scholar 

  4. Braun, B., White, D., Bremser, P., Duval, A. M., & Lockwood, E. (2017). What does active learning mean for mathematicians? Notices of the American Mathematical Society,64(2), 124–129.

    Article  Google Scholar 

  5. Cheng, X., Lee, K. K. H., Chang, E. Y., & Yang, X. (2016). The “flipped classroom” approach: Stimulating positive learning attitudes and improving mastery of histology among medical students. Anatomical Sciences Education,10(4), 317–327.

    Article  Google Scholar 

  6. Chi, M. T., & Wylie, R. (2014). The ICAP framework: Linking cognitive engagement to active learning outcomes. Educational Psychologist,49(4), 219–243.

    Article  Google Scholar 

  7. Chien, Y. T., Lee, Y. H., Li, T. Y., & Chang, C. Y. (2015). Examining the effects of displaying clicker voting results on high school students’ voting behaviors, discussion processes, and learning outcomes. Eurasia Journal of Mathematics, Science and Technology Education,11(5), 1089–1104.

    Google Scholar 

  8. Conference Board of the Mathematical Sciences (CBMS). (2016). Active learning in post-secondary mathematics education. Retrieved from January 1, 2018, from http://www.cbmsweb.org/Statements/Active_Learning_Statement.pdf.

  9. Csíkszentmihályi, M. (1990). Flow: The psychology of optimal experience. New York: Harper Perennial.

    Google Scholar 

  10. Epstein, J. (2013). The calculus concept inventory-measurement of the effect of teaching methodology in mathematics. Notices of the American Mathematical Society,60(8), 1018–1027.

    Article  Google Scholar 

  11. Fairweather, J. (2009). Work allocation and rewards in shaping academic work. In J. Enders & E. Weert (Eds.), The changing face of academic life (pp. 171–192). London: Palgrave Macmillan.

    Google Scholar 

  12. Faye, P. M. D., Gueye, A. D., & Lishou, C. (2017). Virtual Classroom Solution with WebRTC in a Collaborative Context in Mathematics Learning Situation. In C. M. F. Kebe, et al. (Eds.), Innovation and interdisciplinary solutions for underserved areas (pp. 66–77). Cham: Springer.

    Google Scholar 

  13. Fendos, J. (2018). US experiences with STEM education reform and implications for Asia. International Journal of Comparative Education and Development,20(1), 51–66.

    Article  Google Scholar 

  14. Freeman, S., Eddy, S. L., McDonough, M., Smith, M. K., Okoroafor, N., Jordt, H., et al. (2014). Active learning increases student performance in science, engineering, and mathematics. Proceedings of the National Academy of Sciences,111(23), 8410–8415.

    Article  Google Scholar 

  15. Hake, R. R. (1998). Interactive-engagement versus traditional methods: A six-thousand-student survey of mechanics test data for introductory physics courses. American Journal of Physics,66(1), 64–74.

    Article  Google Scholar 

  16. Hare, A. C. (1997). Active learning and assessment in mathematics. College Teaching,45(2), 76–77.

    Article  Google Scholar 

  17. Hestenes, D., Wells, M., & Swackhamer, G. (1992). Force concept inventory. The Physics Teacher,30(3), 141–158.

    Article  Google Scholar 

  18. Hong Kong Curriculum Development Council (HKCDC). (2015). Promotion of STEM education. Unleashing potential in innovation. Central: Education Bureau.

    Google Scholar 

  19. Kao, L. S., & Green, C. E. (2008). Analysis of variance: Is there a difference in means and what does it mean? Journal of Surgical Research,144(1), 158–170.

    Article  Google Scholar 

  20. Kaur, B. (2010). Towards excellence in mathematics education—Singapore’s experience. Procedia-Social and Behavioral Sciences,8, 28–34.

    Article  Google Scholar 

  21. King, A. (1993). From sage on the stage to guide on the side. College Teaching,41(1), 30–35.

    Article  Google Scholar 

  22. Kogan, M., & Laursen, S. L. (2014). Assessing long-term effects of inquiry-based learning: A case study from college mathematics. Innovative Higher Education,39(3), 183–199.

    Article  Google Scholar 

  23. Lampert, M. (2001). Teaching problems and the problems of teaching. Yale: Yale University Press.

    Google Scholar 

  24. Leung, F. K. S. (2013). Technology in the Mathematics Curriculum. In M. A. Clements, A. J. Bishop, C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.), Third international handbook of mathematics education (pp. 517–524). New York: Springer.

    Google Scholar 

  25. Liljedahl, P. (2016). Building thinking classrooms: Conditions for problem-solving. In P. Felmer, E. Pehkonen, & J. Kilpatrick (Eds.), Posing and solving mathematical problems (pp. 361–386). Cham: Springer.

    Google Scholar 

  26. Liljedahl, P. (2018). On the edges of flow: Student problem solving behavior. In N. Amado, et al. (Eds.), Broadening the scope of research on mathematical problem solving: A focus on technology, creativity and affect (pp. 505–524). New York, NY: Springer.

    Google Scholar 

  27. Liljedahl, P., & Allan, D. (2013). Studenting: The case of “now you try one”. In A. M. Lindmeier & A. Heinze (Eds.), Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 257–264). Kiel, Germany: PME.

  28. Liu, J., & Zhang, Y. (2017). Implementation of information-based teaching system for young college teachers based on iOS platform. International Journal of Emerging Technologies in Learning (iJET),12(08), 14–26.

    Article  Google Scholar 

  29. Metz, S. M. V., Marin, P., & Vayre, E. (2015). The shared online whiteboard: An assistance tool to synchronous collaborative design. Revue Européenne de Psychologie Appliquée/European Review of Applied Psychology,65(5), 253–265.

    Article  Google Scholar 

  30. National Research Council. (2001). Adding it up: Helping children learn mathematics. In J. Kilpatrick, J. Swafford, & B. Findell (Eds.), Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.

    Google Scholar 

  31. Nguyen, P. M. (2008). Culture and cooperation: Cooperative learning in Asian Confucian heritage cultures. The case of Viet Nam. Utrecht: Utrecht University.

    Google Scholar 

  32. Pham, T. T. H., & Renshaw, P. (2013). How to enable Asian teachers to empower students to adopt student-centred learning. Australian Journal of Teacher Education,38(11), 5.

    Article  Google Scholar 

  33. Rosenthal, J. S. (1995). Active learning strategies in advanced mathematics classes. Studies in Higher Education,20(2), 223–228.

    Article  Google Scholar 

  34. Silberman, M. (1996). Active learning: 101 strategies to teach any subject. Des Moines: Prentice-Hall.

    Google Scholar 

  35. Šumak, B., Pušnik, M., Heričko, M., & Šorgo, A. (2017). Differences between prospective, existing, and former users of interactive whiteboards on external factors affecting their adoption, usage and abandonment. Computers in Human Behavior,72, 733–756.

    Article  Google Scholar 

  36. VanGundy, A. B. (2008). 101 Activities for teaching creativity and problem solving. New Jersey: Wiley.

    Google Scholar 

  37. Watkins, R. (2005). 75 E-learning activities: Making online learning interactive. San Francisco: Pfeiffer.

    Google Scholar 

  38. Wu, W. H., Yan, W. C., Kao, H. Y., Wang, W. Y., & Wu, Y. C. J. (2016). Integration of RPG use and ELC foundation to examine students’ learning for practice. Computers in Human Behavior,55, 1179–1184.

    Article  Google Scholar 

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Acknowledgements

This project is funded by the University Grants Council of Hong Kong. Grant tittle: “Developing Active Learning Pedagogies and Mobile Applications in University STEM Education” (PolyU2/T&L/16-19).

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Correspondence to Oi-Lam Ng.

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Ng, O., Ting, F., Lam, W.H. et al. Active Learning in Undergraduate Mathematics Tutorials Via Cooperative Problem-Based Learning and Peer Assessment with Interactive Online Whiteboards. Asia-Pacific Edu Res 29, 285–294 (2020). https://doi.org/10.1007/s40299-019-00481-1

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Keywords

  • Active learning
  • Mathematics
  • Problem-based learning
  • Peer assessment
  • Interactive online whiteboards