How do high school students solve probability problems? A mixed methods study on probabilistic reasoning

Abstract

ABSTRACTWhen studying a complex research phenomenon, a mixed methods design allows to answer a broader set of research questions and to tap into different aspects of this phenomenon, compared to a monomethod design. This paper reports on how a sequential equal status design (QUAN → QUAL) was used to examine students’ reasoning processes when solving probability problems. A select clustered sampling resulted in the inclusion of 168 high school students in a first, quantitative phase, in which a questionnaire was used to assess how they solved probability problems. This questionnaire included probability items that were based on the outcome orientation, the representativeness misconception, and the equiprobability bias. In a second, qualitative phase, 18 students who were purposefully sampled from the first research phase were interviewed in order to conduct an in-depth study of their probabilistic reasoning processes. In this paper, we illustrate and discuss how several mixed methods research purposes were realized throughout our study: development, expansion, and initiation.