Student teachers’ use of Monte Carlo simulation to solve probability problems: An analysis of 16 group answers

Abstract

Programming is included in the new curriculum for mathematics in Norwegian primary school. This means that student teachers need to gain experience in solving mathe­matical problems through programming. As a part of the subject of mathematics in the general teacher education program (grades 1–7), training in probability and Monte Carlo simulation with programming in Excel with Visual Basic for Applications (VBA) was included. A mandatory assignment involved the use of Monte Carlo simulation to solve the Chevalier de Méré problem and the Monty Hall problem. Following the students’ work, an NSD-approved study was designed. The sample in this study is 16 student teacher groups’ answers to the assignment related to programming and probability in the subject of mathematics. One finding from the study is that small errors may create major problems as some student teachers are not able to assess how sensible the answers that the program provides are. In addition, the lack of systematics gives incorrect answers. But in those cases where student teachers are able to program correctly, they are helped to solve the Chevalier de Méré problem. We also find that student teachers may get help from manual Monte Carlo simulation to solve the Monty Hall problem, given that it gives numerical values that are close to the expected value (p = 2/3), while in those cases where the numerical values are far from the expected value it may seem confusing. There are pros and cons to both manual and digital Monte Carlo simulation, and it seems that student teachers can benefit from solving problems using both methods. In order to get the best learning outcome, it is crucial that the teacher chooses good and relevant tasks, which means that the students both see the benefit of the simulation, and also have a certain opportunity to check the answer, so that randomness in the simulation and programming errors do not confuse.