Supporting engineering students learning mathematical induction with an online tutorial

Supporting engineering students learning mathematical induction with an online tutorial

M. Gabel, V. Bar Lukianov, T. Margalit (2022).  Supporting engineering students learning mathematical induction with an online tutorial. 896-906.

We describe an online tutorial that was developed in order to support first year engineering students' learning about mathematical induction (MI). The tutorial integrates theoretical explanations, examples and interactive reflective questions, and was designed to increase students’ engagement by creating frequent interactions and using a varied collection of reflective questions. The tutorial was developed according to research-based knowledge concerning students’ difficulties with MI and considering global vs. local proof comprehension. We examined the effects of the MI tutorial on the following students’ achievements: (i) students’ grade in the final quiz of the tutorial (FTG); (ii) students’ grade in the MI question in the final exam of the course. We collected students’ initial/final quiz-grades (ITG, FTG), the time students worked on the tutorial, the number of final quiz trials and students’ grades in the MI question in the final exam in five semesters (before/after incorporating the tutorial). Our findings indicate that the mean FTG is significantly higher than the mean ITG (e.g., in the first semester, N=152, mean ITG=34.5; mean FTG=73.2). Apparently, the instructional part of the tutorial had a positive short-term effect on students’ FTG. However, we did not find a major effect of the MI tutorial on students’ grade in the MI exam question (regardless of the type of claims to be proved and other circumstantial exam settings). We also found that most students answer the MI question in the exam, which may suggest that students believe that they understand the use of MI; yet, their mean grade in this question is not very high (51.7-68.8). In addition, a change in course policy (including the FTG in the course’s final grade), motivated students to achieve a high FTG but the time that students worked on the tutorial decreased, which may explain the lack of long-term effect.

Authors (New): 
Mika Gabel
Vladimir Bar Lukianov
Tamar Margalit
Pages: 
896-906
Affiliations: 
Tel Aviv Academic College of Engineering, Israel
Keywords: 
Proof teaching
Mathematical induction
Online tutorial
Tertiary Mathematics
CDIO Standard 2
CDIO Standard 8
CDIO Standard 11
Year: 
2022
Reference: 
Alcock, L. (2009). E-Proofs: Student experience of online resources to aid understanding of mathematical proofs. In Proceedings of the Twelfth Special Interest Group of the Mathematical Association of America Conference on Research on Undergraduate Mathematics Education, Raleigh, NC. From Aug. 29, 2021, http://sigmaa.maa.org/rume/crume2009/Alcock1_LONG.pdf: 
Alcock, L., Hodds, M., Roy, S., & Inglis, M. (2015). Investigating and improving undergraduate proof comprehension. Notices of the American Mathematical Society, 62(7), 741-752.: 
Bennedsen, J. (2021). Assessing students’ professional criticism skills – a mathematics course case. In Proceedings of the 17th International CDIO Conference (pp.294-303), hosted online by Chulalongkorn University & Rajamangala University of Technology. Bangkok, Thailand, June 21-23, 2021.: 
Biza, I., Giraldo, V., Hochmuth, R., Khakbaz, A., & Rasmussen, C. (2016). Research on teaching and learning mathematics at the tertiary level: State-of-the-art and looking ahead. ICME-13 Topical Surveys, Springer International Publishing AG Switzerland.: 
Ernest, P. (1984). Mathematical induction: A pedagogical discussion. Educational Studies in Mathematics, 15(2), 173-189.: 
González, A., León, M., & Sarmiento, M. (2020). Strategies for the mathematics learning in engineering CDIO curricula. In Proceedings of the 16th International CDIO Conference, Vol. 2 (pp.206-215) hosted online by Chalmers University of Technology. Gothenburg, Sweden, June 8-10, 2021.: 
Gunderson, D. S. (2010). Handbook of mathematical induction: Theory and applications. CRC Press.: 
Mejia-Ramos, J. P., Fuller, E., Weber, K., Rhoads, K., & Samkoff, A. (2012). An assessment model for proof comprehension in undergraduate mathematics. Educational Studies in Mathematics, 79(1), 3-18.: 
Movshovitz-Hadar, N. (1993). The false coin problem, mathematical induction and knowledge fragility. Journal of Mathematical Behavior, 12, 253-268.: 
Pick, L., & Cole, J. (2021). Building student agency through online formative quizzes. In Proceedings of the 17th International CDIO Conference, hosted online by Chulalongkorn University & Rajamangala University of Technology (pp.646-655). Bangkok, Thailand, June 21-23, 2021.: 
Ron G., & Dreyfus T. (2004). The use of models in teaching proof by mathematical induction. In M. J. Høines & A. B. Fuglestad (Eds.), Proceedings of the 28th International Conference for the Psychology of Mathematics Education, Vol. 4 (pp. 113-120). Bergen, Norway: Bergen University College.: 
Selden, A., & Selden, J. (2008). Overcoming students’ difficulties in learning to understand and construct proofs. In M. P. Carlson & C. Rasmussen (Eds.), Making the Connection: Research and practice in undergraduate mathematics (pp. 95-110). Washington, DC: MAA Notes vol. 73.: 
Selden, A., & Selden, J. (2013). Proof and problem solving at university level. Montana Mathematics Enthusiast, 10(1-2), 303–334.: 
Stylianides, G.J., Sandefur, J., & Watson, A. (2016). Conditions for proving by mathematical induction to be explanatory. Journal of Mathematical Behavior, 43, 20–34.: 
Stylianides, G. J., & Stylianides, A. J. (2017). Research-based interventions in the area of proof: past, the present, and the future. Educational Studies in Mathematics, 96(2), 119–127.: 
Young. J. W. A. (1908). On mathematical induction. The American Mathematical Monthly, 15(8-9), 145- 153.: 
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