In the United States, education policy calls for every student to graduate from high school prepared for college and a career. National legislation has mandated programs of study (POS), which offer aligned course sequences spanning secondary and postsecondary education, blending standards-based academic and career and technical education (CTE)…

This paper describes an investigation looking at the underlying mathematics of poker machines. The aim of the investigation is for students to get an appreciation of how poker machines are designed to ensure that in the long-term players will inevitably lose when playing. The first part of this paper describes how students can model a simple poker…

This study shows that residual variation can cause problems related to scaling in exponential random graph models (ERGM). Residual variation is likely to exist when there are unmeasured variables in a model--even those uncorrelated with other predictors--or when the logistic form of the model is inappropriate. As a consequence, coefficients cannot…

To be literate in a society where the information shared online is often exploited, learners should be exposed to multiple aspects of contemporary predictive modeling. This article explores an activity in which grade 10 students learned how a famous AI algorithm (the Apriori algorithm) uses conditional probability to automate the process of…

The 3-year graduation rate is a rarely measured metric in higher education compared to its 4- or 6- year graduation rate counterparts. For the first time in college (FTIC) students to graduate in three years, they must come with certain skills, abilities, plans, supports, or motivations. This project considers two distinct but interrelated ways of…

With the rapid emergence of K-12 online learning platforms, a new era of education has been opened up. It is crucial to have a dropout warning framework to preemptively identify K-12 students who are at risk of dropping out of the online courses. Prior researchers have focused on predicting dropout in Massive Open Online Courses (MOOCs), which…

We examine the long-run impacts of having a same-race teacher. First, we leverage data from the Tennessee STAR class-size experiment to show that black students randomly assigned to a black teacher in grades K-3 are 5 percentage points (7%) more likely to graduate from high school and 4 percentage points (13%) more likely to enroll in college than…

There has been a wealth of research conducted on the high school dropouts spanning several decades. It is estimated that compared with those who complete high school, the average high school dropout costs the economy approximately $250,000 more over his or her lifetime in terms of lower tax contributions, higher reliance on Medicaid and Medicare,…

According to our approach to mathematics education, the optimal aim of the teaching of mathematics is to assist students in achieving efficient mathematical work. But, what does efficient exactly mean in that case? And how can teachers reach this objective? The model of Mathematical Working Spaces with its three dimensions--semiotic, instrumental,…

The present study examined the ability of content domain (algebra, geometry, rational number, probability) to classify mathematics misconceptions. The study was conducted with 1,133 students in 53 algebra and geometry classes taught by 17 teachers from three high schools and one middle school across three school districts in a Midwestern state.…

Objective. To examine temporal changes in the correlates of experimental and current e-cigarette use and associations with tobacco quit attempts. Method. Repeated cross-sectional analyses of data from the 2011 (n = 17,741), 2012 (n = 23,194), and 2013 (n = 16,858) National Youth Tobacco Surveys--a nationally representative sample of U.S. middle…

Energy plays a central role in our society, so it is essential that all citizens understand what energy is and how it moves and changes form. However, research has shown that students of all ages have difficulty understanding these abstract concepts. This paper presents a summary of elementary, middle, and high school students' understanding of…

Modeling using mathematics and making inferences about mathematical situations are becoming more prevalent in most fields of study. Descriptive statistics cannot be used to generalize about a population or make predictions of what can occur. Instead, inference must be used. Simulation and sampling are essential in building a foundation for…

Differential item functioning (DIF) analysis is important in terms of test fairness. While DIF analyses have mainly been conducted with manifest grouping variables, such as gender or race/ethnicity, it has been recently claimed that not only the grouping variables but also contextual variables pertaining to examinees should be considered in DIF…

College graduation rates in the United States are low in both real and relative terms. This has left all stakeholders looking for novel solutions while perhaps ignoring extant but underused programs. This article examines the effect of "summer bridge" programs, which have students enroll in coursework prior to beginning their first full…