Supporting engineering students learning mathematical induction with an online tutorial

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.