In this paper, we consider some combinatorial and statistical aspects of the popular "Powerball" lottery game. It is not difficult for students in an introductory statistics course to compute the probabilities of winning various prizes, including the "jackpot" in the Powerball game. Assuming a unique jackpot winner, it is not difficult to find the…

Students in statistics service courses are frequently exposed to dogmatic approaches for evaluating the role of randomization in statistical designs, and inferential data analysis in experimental, observational and survey studies. In order to provide an overview for understanding the inference process, in this work some key statistical concepts in…

Item families, which are groups of related items, are becoming increasingly popular in complex educational assessments. For example, in automatic item generation (AIG) systems, a test may consist of multiple items generated from each of a number of item models. Item calibration or scoring for such an assessment requires fitting models that can…

A generally-educated individual should have some insight into how decisions are made in the very wide range of fields that employ statistical and probabilistic reasoning. Also, students of introductory probability and statistics are often best motivated by specific applications rather than by theory and mathematical development, because most…

This article describes the variety of strategies that can be used to determine the probability that a player wins a tennis game, given a probability of 60 percent that he or she wins each point. The article suggests strategies for using the problem in 9-12 classrooms.

Under the suppositional account of conditionals, when people think about a conditional assertion, "if p then q," they engage in a mental simulation in which they imagine p holds and evaluate the probability that q holds under this supposition. One implication of this account is that belief in a conditional equates to conditional probability…

This note introduces an interesting random walk on a straight path with cards of random numbers. The method of recurrent relations is used to obtain the convergent probability of the random walk with different initial positions.

In the discourse surrounding the Israeli-Palestinian conflict, extreme criticisms of Israel (e.g., Israel is an apartheid state, the Israel Defense Forces deliberately target Palestinian civilians), coupled with extreme policy proposals (e.g., boycott of Israeli academics and institutions, divest from companies doing business with Israel), have…

Gilbert Gottlieb's theory of probabilistic epigenesis replaced the nature-nurture dichotomy, and similar oppositions, with an integrated account of the development of the entire behavioral phenotype. In that theory, invariant developmental outcomes cannot be identified with an organism's 'nature,' if by that term is meant a set of predetermined…

When behavior suggests that the value of a reinforcer depends inversely on the value of the events that precede or follow it, the behavior has been described as a "contrast" effect. Three major forms of contrast have been studied: "incentive contrast," in which a downward (or upward) shift in the magnitude of reinforcement produces a relatively…

Most traditional models, frameworks, and findings that apply to the majority of students and faculty do not adequately apply to important subpopulations. The recommendations here will help researchers become more sensitive to the nuances among various educational subgroups, and to pay more attention to outliers.

A truancy intervention pilot project was implemented in an urban high school and incorporated two innovative approaches: (a) student enrollment in a school-based health center for comprehensive health services, and (b) recruitment of teachers from within the students' school to engage in mentored relationships. Students with 15 or more days of…

The No Child Left Behind Act has brought great attention to the effectiveness of math and literacy program in U.S. Schools. Literacy instruction was the hot topic of the 1990s, but numeracy has taken center stage in current education debates. Although the importance of literacy skills in other subject areas is quite obvious, the connection between…

Objective: The problems children have upon entering foster care can potentially explain prior research findings that frequent placement changes are associated with poor outcomes. This study sought to disentangle this cascading relationship in order to identify the independent impact of placement stability on behavioral outcomes downstream.…

In many mathematics classes, students are asked to learn via the discovery method, in the hope that the intrinsic beauty of mathematics becomes more accessible and that making conjectures, forming hypotheses, and analyzing patterns will help them compute fluently and solve problems creatively and resourcefully (NCTM 2000). The activity discussed…