In pursuing goals, people seek favorable odds. We investigated whether young children use this fact to infer goals from people's actions across two experiments on Canadian 3- to 7-year-old children (N = 316; 167 girls, 149 boys). Participants' demographic information was not formally collected, but the region is predominantly middle-class and…

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…

This paper examines coin-toss comparison questions from two recent studies involving undergraduate students and high school teachers and connects to findings from two prior studies in the literature. Considering possible sample spaces employed by participants, this is a reflection on whether one sequence could be more likely depending on the…

The Premack principle states that any Response A can reinforce any other Response B if the independent rate of A is greater than the independent rate of B (Premack, 1959). Applying the Premack principle involves arranging the environment to restrict access to certain responses based on relative probabilities of a set of given responses (Timberlake…

The recent commentary by Beaujean and Farmer (2020) on the original paper by Dixon et al. (2019) serves a cautionary tale of selective p-values, the law of small N sizes, and the type-II error. We believe these authors have crafted a somewhat questionable argument in which only 57% of the original Dixon et al. data were re-analyzed, based on a…

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.…

Effective undergraduate statistical education requires training using real-world data. Textbook datasets seldom match the complexities and messiness of real-world data and finding these datasets can be challenging for educators. Consulting and industrial datasets often have nondisclosure agreements. Academic datasets often require subject area…

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…

Subjects with initially extreme observations upon remeasurement are found closer to the population mean. This tendency of observations toward the mean is called regression to the mean (RTM) and can make natural variation in repeated data look like real change. Studies, where subjects are selected on a baseline criterion, should be guarded against…

Educating students to apply probability literacy and reasoning in out-of-school contexts requires the previous preparation of teachers, which should include the assessment of their mathematical and didactic knowledge. Consequently, we investigated three research questions concerning the probabilistic reasoning and literacy of 66 prospective…

When we monitor our learning, often measured via judgments of learning (JOLs), this metacognitive process can change what is remembered. For example, prior work has demonstrated that making JOLs enhances memory for related, but not unrelated, word pairs in younger adults. In the current study, we examined potential age-related differences in…

Not knowing the population size is a common problem in data-limited contexts. Drawing on work in Sierra Leone, this short take outlines a four-step solution to this problem: (1) estimate the population size using expert interviews; (2) verify estimates using interviews with participants sampled; (3) triangulate using secondary data; and (4)…

In statistics classes, the central limit theorem has been demonstrated using simulation-based illustrations. Known population distributions such as a uniform or exponential distribution are often used to consider the behavior of the sample mean in simulated samples. Unlike such simulations, a number of real-data-based simulations are here…

A computer science camp for pre-collegiate students was operated during the summers of 2022 and 2023. The effect the camp had on attitudes was quantitatively assessed using a survey instrument. However, enrollment at the summer camp was small, which meant the well-known Pearson's Chi-Squared to measure the significance of results was not applied.…