This fourth book in the Mathematics Recovery series equips teachers with detailed pedagogical knowledge and resources for teaching number to 7 to 11-year olds. Drawing on extensive programs of research, curriculum development, and teacher development, the book offers a coherent, up-to-date approach emphasizing computational fluency and the…

Solving new problems can be made easier if one can build on experiences with other problems one has already successfully solved. The ability to exploit earlier problem-solving experiences in solving new problems seems to require several cognitive sub-abilities. Minimally, one needs to be able to retrieve relevant knowledge of earlier solved…

The SEED schools, which combine a "No Excuses'' charter model with a five-day-a-week boarding program, are America's only urban public boarding schools for the poor. We provide the first causal estimate of the impact of attending SEED schools on academic achievement, with the goal of understanding whether changing a student's environment through…

The purpose of this study was to examine how nursing efficacy for drug-dosage calculation instruction is determined. Medication administration is a critical function of nurses in healthcare settings. An essential component of safe medication administration is accurate drug-dosage calculation, but instruction in drug-dosage calculation methods…

The purpose of this study is through Monte Carlo simulation to compare several propensity score methods in approximating factorial experimental design and identify best approaches in reducing bias and mean square error of parameter estimates of the main and interaction effects of two factors. Previous studies focused more on unbiased estimates of…

We consider the effect on estimation of simultaneous variable centering and interaction effects in linear regression. We technically define, review, and amplify many of the statistical issues for interaction models with centering in order to create a useful and compact reference for teachers, students, and applied researchers. In addition, we…

This study examined estimation and accuracy of normative perceptions for students during one celebratory drinking occasion. Students who drank on St. Patrick's Day overestimated the percentage of others who also drank, whereas the students who did not drink on St. Patrick's Day underestimated the percentage of others who also did not drink. The…

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This seventh installment of "Explorations in Statistics" explores regression, a technique that estimates the nature of the relationship between two things for which we may only surmise a mechanistic or predictive…

Here, we present complex resonance states (or Siegert states) that describe the tunnelling decay of a trapped quantum particle from an intuitive point of view that naturally leads to the easily applicable Siegert approximation method. This can be used for analytical and numerical calculations of complex resonances of both the linear and nonlinear…

Sensitivity analysis is the study of how the different input variations of a mathematical model influence the variability of its output. In this paper, we review the principle of global and local sensitivity analyses of a complex black-box system. A simulated case of application is given at the end of this paper to compare both approaches.…

We examine a generalization of the one-dimensional Ising model involving interactions among neighbourhoods of "k" adjacent spins. The model is solved by exploiting a connection to an interesting computational problem that we call ""k"-SAT on a ring", and is shown to be equivalent to the nearest-neighbour Ising model in the absence of an external…

Although nowadays there are mythbusting teams ready to empirically confirm or deny advertising claims that may seem too good to be true, it is often economically prohibitive to perform the kinds of experiments that are called for. It is therefore sometimes more sensible and efficacious to perform a thought experiment instead, especially if the…

Targets presented just beyond arm's reach look closer when observers intend to touch them with a reach-extending tool rather than without the tool. This finding is one of several that suggest that a person's ability to act influences perceived distance to objects. However, some critics have argued that apparent action effects were actually due to…

In randomized control trials (RCTs) in the education field, the complier average causal effect (CACE) parameter is often of policy interest, because it pertains to intervention effects for students who receive a meaningful dose of treatment services. This article uses a causal inference and instrumental variables framework to examine the…

In this activity, I show how high school students apply their knowledge of density to solve an unknown variable, such as thickness. Students leave this activity with a better understanding of density, the knowledge that density is a characteristic property of a given substance, and the ways density can be measured. (Contains 4 figures and 1 table.)