As students progress from working with whole numbers to working with integers, they must wrestle with the big ideas of number values and order. Using objects to show positive quantities is easy, but no physical negative quantities exist. Therefore, when talking about integers, the author refers to number values instead of number quantities. The…

Formulas, problem types, keywords, and tricky techniques can certainly be valuable tools for successful counters. However, they can easily become substitutes for critical thinking about counting problems and for deep consideration of the set of outcomes. Formulas and techniques should serve as tools for students as they think critically about…

There has been much research and discussion on the principles of standards-based grading, and there is a growing consensus of best practice. Even so, the actual process of implementing standards-based grading at a school or district level can be a significant challenge. There are very practical questions that remain unclear, such as how the grades…

The temperature dependence of the Gibbs energy and important quantities such as Henry's law constants, activity coefficients, and chemical equilibrium constants is usually calculated by using the Gibbs-Helmholtz equation. Although, this is a well-known approach and traditionally covered as part of any physical chemistry course, the required…

Cluster randomized trials (CRTs), or studies in which intact groups of individuals are randomly assigned to a condition, are becoming more common in the evaluation of educational programs, policies, and practices. The website for the National Center for Education Evaluation and Regional Assistance (NCEE) reveals they have launched over 30…

"Belief state" refers to the set of possible world states satisfying the agent's (usually imperfect) knowledge. The use of belief state allows the agent to reason about the world with incomplete information, by considering each possible state in the belief state individually, in the same way as if it had perfect knowledge. However, the…

In a traditional regression-discontinuity design (RDD), units are assigned to treatment and comparison conditions solely on the basis of a single cutoff score on a continuous assignment variable. The discontinuity in the functional form of the outcome at the cutoff represents the treatment effect, or the average treatment effect at the cutoff.…

With the rise of the internet, mobile communications, electronic transactions, and personal broadcasting, the scale of connectedness has grown immensely. Not only can an individual interact with thousands and millions of others, but details about those interactions are being stored in databases, for later retrieval and analysis. Two key concepts…

Neuropsychological investigations of FMR1 premutation carriers without FXTAS present one domain resulting in contradictory findings, namely that of mathematical skills. One reason for this might be that standard clinical batteries used so far may be inadequate to uncover precise deficits within specific mathematical skills. In fact, these…

Outcome studies in biomedical research usually focus on testing mean changes across samples of subjects and, in so doing, often obscure changes in individuals. These changes, however, may be very informative in studies in which large or homogeneous samples are unavailable and mechanisms of action are still under scrutiny, as is often the case for…

As a new physics teacher, I was explaining how to find the weight of an object sitting on a table near the surface of the Earth. It bothered me when a student asked, "The object is not accelerating so why do you multiply the mass of the object by the acceleration due to gravity?" I answered something like, "That's true, but if the table were not…

From a formal point of view, a composite indicator is an aggregate of all dimensions, objectives, individual indicators and variables used for its construction. This implies that what defines a composite indicator is the set of properties underlying its mathematical aggregation convention. In this article, I try to revise the theoretical debate on…

Because electric fields are both invisible and three dimensional, they can be quite difficult to introduce to students. Simple diagrams are unable to convey the complexity or depth of the field, and computer simulations in isolation do not provide a familiar spatial context for students to understand what they see. Through "immersing"…

Computer simulations continue to prove to be a valuable tool in physics education. Based on the needs of an Aviation Physics course, we developed the PHYSics of FLIght Simulator (PhysFliS), which numerically solves Newton's second law for an airplane in flight based on standard aerodynamics relationships. The simulation can be used to pique…

In the current study, we evaluated various robust statistical methods for comparing two independent groups. Two scenarios for simulation were generated: one of equality and another of population mean differences. In each of the scenarios, 33 experimental conditions were used as a function of sample size, standard deviation and asymmetry. For each…