Probabilistic thinking in prospective teachers from the use of TinkerPlots for simulation: Hat problem

Abstract

Solving real-life problems through mathematical modeling is one of the aims of modern mathematics curricula. For this reason, prospective mathematics teachers need to acquire modeling skills and use these skills in learning environments in terms of creating rich learning environments. With this study, it is aimed to examine the reflections of using a simulation on a problem involving uncertainty on the probabilistic thinking of prospective teachers. The activity includes an experimental review of the famous Hat problem. It was observed that the hat problem, which started as a puzzle, was linked to coding theory and reached the limit of mathematics, statistics, and computer science research. Research findings revealed that the simulation-supported learning environment not only contributes to prospective teachers' probabilistic thinking skills, but also offers the opportunity to experience different methods (such as working with real data, technology assisted learning, modeling) in teaching and learning mathematics. It has been concluded that simulations have a unique potential that other methods do not have in terms of gaining statistical thinking as well as problem solving and modeling skills.