Out of over 1.9 million students in the 2018 ACT-tested graduating class, 44% took the full ACT® test at least twice in hopes of improving their scores. Camara and Allen (2017) support this practice, confirming that factors such as time in the classroom between test administrations are associated with increases in ACT Composite scores from the…

Pearson's product-moment correlation can be explained by means of the probability of concordant pairs of observations on two continuous variables (ie, the order of the observations from two randomly selected individuals is the same between the two variables). The probability of concordant pairs features relatively easy computation and offers an…

It is well known that two events A and B are independent if and only if . Here, we derive a condition for independence not well known. We then extend the condition for independence of n events.

Mathematical symbols, such as those embodying quantum concepts, are indispensable for conveying complex ideas and relationships in academic writing. However, some education researchers and students keep a distance from anything mathematical: algebraic equations, geometrical reasoning, or statistical symbols. How to lower the access threshold for…

Pedagogical content knowledge (PCK) traditionally has been used in research concerning prospective and practicing classroom teachers. This essay argues that PCK is also relevant to other professions including those advancing quantitative reasoning (QR). To illustrate, the case of PCK for teaching QR is considered. Those in fields such as public…

The American School District Panel (ASDP) is a nationally representative set of more than 1,000 school district leaders who agree to take surveys over time. RAND recruits ASDP members using probabilistic sampling methods, which allow researchers to weight survey results to generalize to the national population of school districts and charter…

This paper provides the first experimental evidence of how admission outcomes in centralized systems depend on strategic college choice behaviors. Centralized college admissions simplify the application process and reduce students' informational barriers. However, such systems also reward informed and strategic college choices. In particular,…

A modified and improved inductive inferential approach to evaluate item discriminations in a conditional maximum likelihood and Rasch modeling framework is suggested. The new approach involves the derivation of four hypothesis tests. It implies a linear restriction of the assumed set of probability distributions in the classical approach that…

The field of Linguistics has long been interested in the verb meanings of intransitive verbs and their argument structure, specifically the breakdown of intransitive verbs into unaccusative and unergative verb types. Despite extensive research, a universally applicable explanation for this breakdown remains elusive due in part to the variability…

As colleges and universities grapple with uncertainty around current and future enrollment as well as increasingly vocal questions about the value of postsecondary education, it is critically important that institutions ascertain and invest in the elements of campus learning and engagement that add value to the undergraduate experience. This study…

This article describes a hands-on geometric tiling art activity used in two third-grade classes and four fifth-grade classes in a rural public elementary school with class sizes of around 20 students each. The lesson investigates concepts in geometry, number sense, and probability. Examples of student work and takeaways for other teachers…

Longitudinal data structures are frequently encountered in a variety of disciplines in the social and behavioral sciences. Growth curve modeling offers a highly extensible framework that allows for the exploration of rich hypotheses. However, owing to the presence of interrelated sources of potential data-model misfit at multiple levels, the…

Although educational research and evaluation generally occur in multilevel settings, many analyses ignore cluster effects. Neglecting the nature of data from educational settings, especially in non-randomized experiments, can result in biased estimates with long-term consequences. Our manuscript improves the availability and understanding of…

This article provides conceptual ideas, data, and exercises, for integrating original sources of recent, state of the art, world-class life science research in the undergraduate mathematics curriculum and classroom. To this end, this article shows how one of the main goals of calculus in the life sciences, fitting parameters to data and assessing…

It is increasingly recognised that to be informed citizens and to participate fully in the workforce requires an understanding of statistical data and risk. Such understanding is underpinned by statistical reasoning. It has been shown, however, that students have difficulty moving from concrete representations and procedural mathematical…