Dice are considered one of the oldest gambling devices and thus many mathematicians have been interested in various dice gambling games in the past. Dice have been used to teach probability, and dice rolls can be effectively simulated using technology. The National Council of Teachers of Mathematics (NCTM) recommends that teachers use simulations…

This paper investigates the effect of family size and birth order on educational attainment. An instrumental variables approach is used to identify the effect of family size. Instruments for the number of children are twins at last birth and the sex mix of the first two children. The effect of birth order is identified, by examining the relation…

Comparing the predicted and actual rolls of combinations of both two and three dice can help to introduce many of the basic concepts of statistical thermodynamics, including multiplicity, probability, microstates, and macrostates, and demonstrate that entropy is indeed a measure of randomness, that disordered states (those of higher entropy) are…

This article presents a problem set which includes a selection of probability problems. Probability theory started essentially as an empirical science and developed on the mathematical side later. The problems featured in this article demonstrate diversity of ideas and different concepts of probability, in particular, they refer to Laplace and…

Preference for working on variable schedules and temporal discrimination were simultaneously examined in two experiments using a discrete-trial, concurrent-chains arrangement with fixed interval (FI) and random interval (RI) terminal links. The random schedule was generated by first sampling a probability distribution after the programmed delay to…

Among 180 Turkish university students, the probability of suicide was strongly predicted by both hopelessness and deficiencies in problem solving. In addition, for women, unhealthy attachment styles (preoccupied and dismissing) also predicted suicidality. The clinical implications of these findings are that psychotherapists should focus on helping…

If questioned about their beliefs, psychometricians in one camp would argue the firm conviction that the Rasch model is mathematically elegant and intuitive as well as plausible for practitioners, pointing out the advantages of a simple model that "counts" every item in the same way. Psychometricians of another camp would argue that the three…

Using the College Board SAT registration and questionnaire data of 2010 high school graduating seniors, we found clear patterns by race/ethnicity and parental education on two outcomes: out-of-state score-sending and out-of-state college attendance. White students had the highest rates and Hispanic students had the lowest rates, and there was a…

The purpose of this study was to evaluate the impact of Achieve3000, a differentiated online literacy curriculum, on students' scores on the California State Test (CST). In the 2011-12 school year, 1,957 students in Chula Vista began using Achieve3000's solutions in 3rd through 8th grade. Using a form of propensity score matching called Inverse…

In the present research, we evaluated the effectiveness of a multi-year professional development program in mathematics for elementary teachers. Each year the program focused on a different domain of mathematics. We found the program increased teachers' knowledge of (a) number and operations, (b) measurement and geometry, and (c) probability and…

For students who major in meteorology, engaging in weather forecasting can motivate learning, develop critical-thinking skills, improve their written communication, and yield better forecasts. Whether such advances apply to students who are not meteorology majors has been less demonstrated. To test this idea, a weather discussion and an eLearning…

This paper estimates risk reductions for each layer of security designed to prevent commercial passenger airliners from being commandeered by terrorists, kept under control for some time, and then crashed into specific targets. Probabilistic methods are used to characterize the uncertainty of rates of deterrence, detection, and disruption, as well…

Using data from a 40-year longitudinal study, the authors examined 3 related hypotheses about the effects of grade skipping on future educational and occupational outcomes in science, technology, engineering, and mathematics (STEM). From a combined sample of 3,467 mathematically precocious students (top 1%), a combination of exact and propensity…

The ability to increase the number of engineering graduates depends on many factors including our country's P-16+ educational system, the job market and the engineering professions. Students need to be prepared for the rigorous math and science components of engineering programs, but they also must have interest in engineering as a profession,…

Introduction: Breast cancer affects the lives of millions of women each year in the United States. Early detection by mammography screening can reduce the risk for advanced stages of breast cancer and improve the probability of long-term survival in women. Electronic medical records (EMRs) have been identified as a successful approach for…