A number of memorable tasks have been revealed through collegial exchanges with underlying philosophical, theoretical, and potentially nefarious motivations. Such was the origin of the probability problem, and the various differences of opinion, presented herein. This article recounts how, together, we explored and disputed the probabilities…

This research aims to determine the thinking activity types dominated by a mental process in producing answers characterized by automatic, unconscious, and subjective-empirical processes (system 1) in solving problems so that the default-interventionist interaction occurs. This research novelty is the formulation of the contents and thinking…

This paper reports on an exploratory study about probabilistic intuition in learning mathematics for decision-making. The analysis was carried out on a group of high school students in relation to their probabilistic intuition in problem-solving, after performing playful learning activities on a simulation platform specifically designed for this…

Many challenges are identified when students solve mathematic problems especially in solving probability word problems. This study was conducted to identify the major challenges faced by matriculation college students while solving the probability of an event word problem. Seven matriculation college students were the sample for this case study.…

This work reports the results of an investigation that aimed to know the informal reasoning of high school students with and about the frequency approach of probability and the law of large numbers when they were faced with a problem about random intervals. The research question was as follows: What features of students' reasoning about the…

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…

Everyone, including teachers, is prone to randomness misconceptions. In this article, we investigate the perceptions of randomness held by New Zealand secondary school teachers. The responses to a question asked in an online, anonymous questionnaire sent to New Zealand teachers will be explored. One question asked participants to create a sequence…

Findings on children's proportional reasoning abilities strongly vary across studies. This might be due to the different contexts that can be used in proportional problems: fair-sharing, mixtures, and probability. A review of the scientific literature suggests that the context of proportional problems may not only impact the difficulty of the…

This research presents the results of the implementation of a model-eliciting activity called Brickyards, designed to promote the learning of the binomial distribution. The theoretical framework used was the Models and Modeling Perspective, and the participants were undergraduate students enrolled in a probability and statistics course of the…

Problem-based learning (PBL) has been widely applied as an alternative to improve learning outcomes, but it is still little studied in the context of the probability theory course. This study described how implementing the PBL model improves students' problem-solving and critical thinking skills in probability theory course and evaluates its…

Many problems in real life are full of uncertainty. Probabilistic thinking is one way to solve this uncertainty problem. The personality abilities that are interesting to examine include how independent the students are in facing probabilistic solutions. For this reason, it is necessary to study the probabilistic thinking profile of prospective…

We present an exploratory study of Costa Rican and Spanish students' (11-16-year-olds) competence to compare probabilities in urns and compare ratios in mixture problems. A sample of 704 students in Grades 6 through to Grade 10, 292 from Costa Rica and 412 from Spain, were given one of two forms of a questionnaire with three probability comparison…

In this study, it was aimed to examine the probability problems which were posed based on continuous sample space and discrete sample space. Participants of the study consisted of 48 university students selected by using the convenience sampling method. Eight tasks related to continuous and discrete variables were designed by the researcher. Eight…

Challenging behavior can impact the learning environment and prevent educators and students from demonstrating behavioral and academic success. Schools and districts may implore a framework of tiered systems of support to respond to students struggling behaviorally or academically. These systems provide a decision-making process to aid educators'…

Thirty-three children treated for congenital hyperinsulinism (CHI) (13 boys; 13 with focal forms of CHI, median age 10 months) entered the study. The mothers were requested to fill-in the Ages and Stages Questionnaire to estimate communication, gross motor, fine motor, problem solving and personal-social skills. Children with focal forms had…