The formula for the variance of a binomial distribution is both concise and elegant. However, it is often taught without reference to the underlying reasoning. That being the case, is it important, or useful, to understand why this formula can be used to calculate the requisite result? In this article, the author demonstrates a teaching sequence…

The college experience involves much more than credit hours and degrees. Students likely derive utility from in-person instruction and on-campus social activities. Quantitative measures of the value of these individual components have been hard to come by. Leveraging the COVID-19 shock, we elicit students' intended likelihood of enrolling in…

The purpose of this quantitative study was to determine if students' participation in the ALP co-requisite developmental English program relates to the likelihood of passing gateway college-level English. Data was collected to allow for analysis of gateway college-level English passing probability for all students who participated in gateway…

A growing body of research has provided evidence for the foreign language effect on thinking, notably decision-making. Our prior work found reduction of recency effect following positive feedback in a foreign language as compared to the native tongue during even-probability gambling. However, the fundamental mechanisms underlying this effect…

For Freudenthal, the practice of mathematics in the curriculum is not a set of predetermined theories, goals and means. On the contrary, it is always associated with positively understood phenomenological processes in mathematics, as the curriculum is often used in conjunction with the transformation or development of practice. For Freudenthal…

Word spacing is important in guiding eye movements during spaced alphabetic reading. Chinese is unspaced and it remains unclear as to how Chinese readers segment and identify words in reading. We conducted two parallel experiments to investigate whether the positional probabilities of the initial and the final characters of a multicharacter word…

We tested predictions of fuzzy-trace theory that qualitative health status and gist representations (ordinal and categorical) of risks contribute to willingness to start medications, beyond effects of objective risk, emotion (worry), and numeracy. Adults in two experiments were given hypothetical scenarios based on actual medications, varying…

Network meta-analysis (NMA) is gaining popularity for comparing multiple treatments in a single analysis. Generalized linear mixed models provide a unifying framework for NMA, allow us to analyze datasets with dichotomous, continuous or count endpoints, and take into account multiarm trials, potential heterogeneity between trials and network…

The treatment of kurtosis in textbooks is both sparse and contradictory with applications rarely discussed. To address this, an easily understood definition of kurtosis is introduced and important applications are demonstrated. Two different approaches to teaching kurtosis are presented based on a financial application.

Predictive validity considerations in selection dictate choice of the predictor with the highest predictive validity. Implementation of this principle in any specific selection process inevitably entails choice between imperfectly correlated alternative predictors, real or hypothetical, which are equivalent in terms of predictive validity. We show…

The present research examined the consequences of telling young children they have a reputation for being smart. Of interest was how this would affect their willingness to resist the temptation to cheat for personal gain as assessed by a temptation resistance task, in which children promised not to cheat in the game. Two studies with 3- and…

Propensity and prognostic score methods are two statistical techniques used to correct for the selection bias in nonexperimental studies. Recently, the joint use of propensity and prognostic scores (i.e., two-score methods) has been proposed to improve the performance of adjustments using propensity or prognostic scores alone for bias reduction.…

This study examines Mood, Modality, and Attitude as a part of Appraisal theory in the Editorial News of the "Sydney Morning Herald" Interpersonal Meta function Analysis. Three methods were used, including (1) Indicative (Declarative and Interrogative) mood, (2) Modalization (Indicative Type), Probability (may be) and Usuality…

This case study carried out during the 2020 coronavirus disease of 2019 (COVID-19) lockdown used online data collection means to investigate the distribution of cognitive demand levels of probability and counting principles (PCP) learning tasks in a popular online Grade 12 mathematics textbook, based on the PCP teachers' rating. The teachers'…

Probability signifies a mainstream strand in mathematics curricula. Nonetheless, many curricular documents prepared for teachers might not offer enough support. In such a situation, a further reflection on teachers' professional knowledge for teaching probability is demanded; especially, from the perspective of probabilistic reasoning (PoPR) that…