The purpose of this study was twofold. First, to explore middle and high school students' intuitively-based (mis)conceptions in probability, particularly availability and representativeness heuristics. Second, to investigate teachers' awareness of these intuitively-based (mis)conceptions and the effectiveness of their instructional practices to…

A more motivating way of introducing students to probability theory is through real-world problems. Since heuristics play an important role in our probabilistic judgement, knowing how to avoid incorrect probabilistic reasoning, which leads to several biases, could help students to develop more critical thinking skills. In this paper, we present a…

The aim of this study is to explore the judgments and reasoning in probabilistic tasks that require comparing two probabilities either with or without introducing an additional degree of uncertainty. The reasoning associated with the task having an additional condition of uncertainty has not been discussed in previous studies. The 66 undergraduate…

The Monty Hall dilemma (MHD) is a counterintuitive probability problem in which participants often use misleading heuristics, such as the equiprobability bias. Finding the optimal solution to the MHD requires inhibition of these heuristics. In the current study, we investigated the relation between participants' equiprobability bias and their MHD…

Purpose: The purpose of this paper is to develop a quantitative model of problem solving performance of students in the computer-based mathematics learning environment. Design/methodology/approach: Regularized logistic regression was used to create a quantitative model of problem solving performance of students that predicts whether students can…

If the prospective students of probability lack a background in mathematical proofs, hands-on classroom activities may work well to help them to learn to analyze problems correctly. For example, students may physically roll a die twice to count and compare the frequency of the sequences. Tools such as graphing calculators or Microsoft Excel®…

The purpose of this article is to address the lack of research on teachers' knowledge of probability. As has been the case in prior research, we asked prospective mathematics teachers to determine which of the presented sequences of coin flips was least likely to occur. However, instead of using the traditional perspectives of heuristic and…