EMPIRICAL APPROACHES TO PROBABILITY PROBLEMS: AN ACTION RESEARCH

The purpose of this study is to explain the modelling and modelling process problems which require probability thinking ability by using simulations in an instructional way. For that purpose, action research was performed with 46 prospective mathematics teachers who were university students in Turkey. The simulation based activities executed in this study are based on Look, Think and Act cycle in Stringer’s action research. Two open ended popular probability problems (Cereal Box and Birthday Problems) were asked to the prospective mathematics teachers. The responses about each problem are analyzed and presented in tables with percentage and frequency. When the data were investigated, it was seen that the prospective teachers gave the wrong answers or did not answer the questions. Since the aim of the study is to adopt experimental rather than theoretical approaches in the solutions of the problems, the focus was on creating simulation models for problems, doing experiments, visualisation of the results and calculation processes. Then, experimental and theoretical solutions were compared. Thus, the relations and models which help to understand the theoretical solutions of probability problems by using experimental data were proposed. Moreover, the study also sheds light on the questions of how to use the TinkerPlots in order to increase the comprehension of students and how to integrate the technology into probability teaching. In this case, it is thought that the study will be beneficial to researchers, teachers and students alike