Interactive problem solving environments, such as intelligent tutoring systems and educational video games, produce large amounts of transactional data which make it a challenge for both researchers and educators to understand how students work within the environment. Researchers have modeled the student-tutor interactions using complex network…

Online adaptive tutoring systems are increasingly being used in classrooms as a way to provide guided learning for students. Such tutors have the potential to provide tailored feedback based on specific student needs and misunderstandings. Bayesian knowledge tracing (BKT) is used to model student knowledge when knowledge is assumed to be changing…

This article concerns the effect of context on people's judgments about sequences of chance outcomes. In Experiment 1, participants judged whether sequences were produced by random, mechanical processes (such as a roulette wheel) or skilled human action (such as basketball shots). Sequences with lower alternation rates were judged more likely to…

The quantal hypothesis is central to the modern understanding of how a neurotransmitter is released from synapses. This hypothesis expresses that a neurotransmitter is packaged together in quanta that are released probabilistically. The experiments that led to the quantal hypothesis are often related in introductory neuroscience textbooks, but…

The authors generated exact probability distributions for sample sizes up to 35 in each of three groups ("n" less than or equal to 105) and up to 10 in each of four groups ("n" less than or equal to 40). They compared the exact distributions to the chi-square, gamma, and beta approximations. The beta approximation was best in…

This article presents "The Two Children Problem," published by Martin Gardner, who wrote a famous and widely-read math puzzle column in the magazine "Scientific American," and a problem presented by puzzler Gary Foshee. This paper explains the paradox of Problems 2 and 3 and many other variations of the theme. Then the authors…

People consider alternative causes when deciding whether a cause is responsible for an effect (diagnostic inference) but appear to neglect them when deciding whether an effect will occur (predictive inference). Five experiments were conducted to test a 2-part explanation of this phenomenon: namely, (a) that people interpret standard predictive…

The sequential probability ratio test (SPRT) is a common method for terminating item response theory (IRT)-based adaptive classification tests. To decide whether a classification test should stop, the SPRT compares a simple log-likelihood ratio, based on the classification bound separating two categories, to prespecified critical values. As has…

The publishers of the Major Field Test in Business (MFT-B), an assessment of learning instrument, provide a list of institutions utilizing the instrument and a table that allows for comparison of local MFT-B mean scores to those of other institutions. The absence of information regarding the comparison group's characteristics limits the validity…

Real-world phenomena simulation models, which can be used to engage middle-school students with probability, are described. Links to R instructional material and easy-to-use code are provided to facilitate implementation in the classroom.

This is an activity for younger learners in which the concepts of relative frequency and probability are explored, illustrating how a creative, non-transmission teaching approach using bottle tops can enable students to develop their understanding in an engaging fashion and at almost no cost.

Problems teaching probability in Tonga (in the South Pacific) led to the question how language and culture affect the understanding of probability and uncertainty. The research uses a discursive approach to find the endorsed narratives which underlie Tongans' reasoning in situations of uncertainty. I aim to justify the claim that the Tongan…

In 1963, the Nobel Prize-winning ethologist Niko Tinbergen proposed a framework for the scientific study of animal behaviour by outlining four questions that should be answered to have a complete understanding: causation, ontogeny, function and evolution. At present, Tinbergen's framework is still considered the best way to guide animal…

Foetus developmental vulnerability in pre-school children of traumatized antenatal mothers in Cheptais and Mount Elgon Sub-Counties, Bungoma County, Kenya is a study meant to establish the effects of trauma of the mother on the unborn child who was born and now is in pre-school level of education. Through observation by the mother through neonate,…

Instead of reserving the study of probability and statistics for special fourth-year high school courses, the Common Core State Standards for Mathematics (CCSSM) takes a "statistics for all" approach. The standards recommend that students in grades 6-8 learn to summarize and describe data distributions, understand probability, draw…