This study’s research question was to investigate whether the interventions affected students’ performances on the stochastic games part in the academic year 2024-2025. The main results are that students’ performances have improved, and there is no evidence of a causal relationship between the interventions and students’ performances in this study.

This study was conducted during my SUTQ trajectory and began with my observation that students’ performances on the stochastic games part of the course had been consistently low for many years. The main lines of this study were as follows. Initially, I identified the underlying problem using baseline data. A literature study identified possible solutions and educational methods. Thereafter, the interventions were designed. After implementing the interventions, I collected data on students’ performances and their participation in the interventions. That data allowed me to draw conclusions.

To identify the underlying problem, I conducted interviews with three students and my co-teacher, reviewed past test scores, and examined past course evaluations. Supported by the literature study, the most likely cause of the low-level performance was the lack of knowledge of discrete-time Markov chains, which is a prerequisite for the stochastic games part.

The interventions were designed and implemented to refresh the master’s students’ prior knowledge of discrete-time Markov chains in two weekly online lessons. Each lesson consisted of four components and was presented one week before the course covered its material (as in [1]). The first component indicated important pre-knowledge skills and pointed the students to materials covering these skills. The second component was a pencast [2] that showed a worked example illustrating the weekly skills. Thirdly, the students had access to practice questions to train their skills. The fourth component was a weekly quiz, which allowed students to test their mastery of the weekly skills (as formative e-assessment [3]).

This study has several limitations. First, it was very hard to measure the students’ participation in the interventions. That could have been a reason why it was hard to quantify the effect of the interventions on the students’ performances. Second, in the 2024-2025 edition of the course, a relatively higher number of Applied Mathematics (AM) students participated compared to previous years. The MSc Game Theory course attracts participants from the MSc programmes AM and Industrial Engineering and Management. Students from other programmes, such as Computer Science or Applied Physics, may also join.

Despite the lack of a causal relationship and the limitations of this study, several experiences suggest that the interventions may help prepare students for the stochastic games part. The interviewed students responded favorably to the refresher on discrete-time Markov chains, describing it as helpful for completing the tutorial exercises on stochastic games and for developing a deeper conceptual understanding of the material. Additionally, a student’s question in class regarding the comparatively lower prerequisite requirements—relative to previous years—suggests that the refresher may also help bridge gaps in prior knowledge. In light of these experiences, I intend to continue offering the refresher to Game Theory students.

If you would like to learn more about the full study, I would be happy to share it with you. Please feel free to get in touch.

References:

[1] E. Bertrand, D.T. McArdle, L. Thoma, and L. Wu. Implementing online programs in gateway mathematics courses for students with prerequisite deficiencies. PRIMUS, 31(2):119–132, 2021.
[2] B. Loch, C.R. Jordan, T.W. Lowe, and B.D. Mestel. Do screencasts help to revise prerequisite mathematics? An investigation of student performance and perception. International Journal of Mathematical Education in Science and Technology, 45(2):256–268, 2014.
[3] S. McCallum and M.M. Milner. The effectiveness of formative assessment: student views and staff reflections. Assessment & Evaluation in Higher Education, 46(1):1–16, 2021.