Probability theory has extensive applications across various domains, such as statistics, computer science, and finance. In probability education, students are introduced to fundamental principles which may include mathematical topics such as combinatorics and symmetric sample spaces. Students pursuing degrees in computer science possess a robust…

The ability to relate physical concepts and phenomena to multiple mathematical representations--and to move fluidly between these representations--is a critical outcome expected of physics instruction. In upper-division quantum mechanics, students must work with multiple symbolic notations, including some that they have not previously encountered.…

Using software to teach statistical inference in introductory courses opens the door for methods and practices that are more conceptually appealing to students. With an increasing number of fields requiring competency in statistics including data science, natural and social sciences, public health and more, it is crucial that we as instructors…

This research investigates the abilities of undergraduate students to apply scientific reasoning in Indonesia, with a particular focus on the concept of force and motion. Forty-three first-year undergraduate students from an Indonesian private institution, comprising 20 males and 23 females, performed the Scientific Reasoning Test of Motion (SRTM)…

Concerns about the influence of misconceptions, culture and social setting on probabilistic reasoning of teacher trainees led to a study in this area to explore the reasoning of preservice teachers from a college of education in Ghana. This study investigates preservice teachers' misconceptions and difficulties in probabilistic problems solving…

We developed and tested strategies for using spatial representations to help students understand core probability concepts, including the multiplication rule for computing a joint probability from a marginal and conditional probability, interpreting an odds value as the ratio of two probabilities, and Bayesian inference. The general goal of these…

Research on teaching and learning quantum physics (QP) frequently explores students' conceptual difficulties to identify common patterns in their reasoning. The abstractness of QP is often found to be at the origin of students' conceptual difficulties. Due to this abstract nature students resort to common sense reasoning or classical thinking when…

There is a growing interest in conducting research in educational mathematics in the area of the didactics of probability, where the main difficulties that students have in understanding the concepts related to statistical inference have been revealed. For this research, the concept of the empirical rule and a practical application created by…

We investigate the level of understanding of probability as related to games and gambling, and the concept of independence of events using a convenience sample of college undergraduates taking an introductory course in applied business statistics. We examined the students' perception of the role of skill in winning at four different games through…

A strong foundation in early number concepts is crucial for students' future success in statistics. Despite its importance in statistics, many first-year students struggle to comprehend the normal distribution due to a lack of basic number sense. Students get confused about the order and magnitude of negative z-scores on a standard normal curve or…

Probability signifies a mainstream strand in mathematics curricula. Nonetheless, many curricular documents prepared for teachers might not offer enough support. In such a situation, a further reflection on teachers' professional knowledge for teaching probability is demanded; especially, from the perspective of probabilistic reasoning (PoPR) that…

The author of this article describes a game-theory-based economics class on how people should, and do, form beliefs, communicate, and make decisions under uncertainty. Topics include Bayesian and non-Bayesian belief updating, the value of information, communication games, advertising, political media, and social learning. The only prerequisite is…

Playing board games is known to improve pre-school student numeracy and many board games are used to motivate and explore concepts in probability. This study investigates whether college students in liberal arts mathematics courses assigned to play the board game "Settlers of Catan" develop a stronger grasp of basic probability concepts…

Conceptual appropriation is central to the teaching-learning and development processes. The intellectual stage is expressed by writing, verbalization and the use of the object under construction, among other means of expression. This paper discusses the conceptual appropriation by means of the creation of collaborative situations in which the…

We consider the ability to complete an investigative cycle as an indicator of the robustness of students' statistical knowledge. From this standpoint, we analyzed the written reports of primary education student teachers when they developed an investigative cycle in a Chilean and a Spanish university. In their development of the stages of the…