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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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.
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.
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.
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.
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.
Chi, M. T., & Wylie, R. (2014). The ICAP framework: Linking cognitive engagement to active learning outcomes. Educational Psychologist,49(4), 219–243.
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.
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.
Csíkszentmihályi, M. (1990). Flow: The psychology of optimal experience. New York: Harper Perennial.
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.
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.
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.
Fendos, J. (2018). US experiences with STEM education reform and implications for Asia. International Journal of Comparative Education and Development,20(1), 51–66.
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.
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.
Hare, A. C. (1997). Active learning and assessment in mathematics. College Teaching,45(2), 76–77.
Hestenes, D., Wells, M., & Swackhamer, G. (1992). Force concept inventory. The Physics Teacher,30(3), 141–158.
Hong Kong Curriculum Development Council (HKCDC). (2015). Promotion of STEM education. Unleashing potential in innovation. Central: Education Bureau.
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.
Kaur, B. (2010). Towards excellence in mathematics education—Singapore’s experience. Procedia-Social and Behavioral Sciences,8, 28–34.
King, A. (1993). From sage on the stage to guide on the side. College Teaching,41(1), 30–35.
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.
Lampert, M. (2001). Teaching problems and the problems of teaching. Yale: Yale University Press.
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.
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.
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.
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.
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.
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.
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.
Nguyen, P. M. (2008). Culture and cooperation: Cooperative learning in Asian Confucian heritage cultures. The case of Viet Nam. Utrecht: Utrecht University.
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.
Rosenthal, J. S. (1995). Active learning strategies in advanced mathematics classes. Studies in Higher Education,20(2), 223–228.
Silberman, M. (1996). Active learning: 101 strategies to teach any subject. Des Moines: Prentice-Hall.
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.
VanGundy, A. B. (2008). 101 Activities for teaching creativity and problem solving. New Jersey: Wiley.
Watkins, R. (2005). 75 E-learning activities: Making online learning interactive. San Francisco: Pfeiffer.
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.
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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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
- Active learning
- Problem-based learning
- Peer assessment
- Interactive online whiteboards