Two novel proofs show that the sum of a specific pair of normal random variables is not normal are established in this note. This is one of the most often misunderstood facts by first-year students in probability theory and statistics. The first proof is concise using the moment generating function. The second proof checks whether the moments of…

Binary logistic regression is one of the most widely used statistical tools. The method uses odds, log odds, and odds ratios, which are difficult to understand and interpret. Understanding of logistic regression tends to fall down in one of three ways: (1) Many students and researchers come to believe that an odds ratio translates directly into…

Common sense is a dynamic concept and it is natural that our (statistical) common sense lags behind the development of statistical science. What is not so easy to understand is why common sense lags behind as much as it does. We conduct a survey among Japanese students and provide examples and tentative explanations of a number of statistical…

In recent years, converging evidence has suggested that prediction plays a role in language comprehension, as it appears to do in information processing in a range of cognitive domains. Much of the evidence for this comes from the N400, a neural index of the processing of meaningful stimuli which has been argued to index the extent to which a word…

This paper reports the statistical and probabilistic reasoning of young children in terms of randomness, variability, and data representations in the context of informal inferential reasoning (IIR). Using the IIR approach, a task was designed and conducted one-on-one with 28 children aged 5 to 6 years old, in a case study setting. The researcher…

A commonly-held belief is that many university students are 'assessment-driven'; that is, students engage more with activities that are assessed compared with those that are not. 'Incentivised engagement' includes the practice of providing incentives (such as marks or otherwise) for students to engage in particular activities. Perusall is a social…

Sequence learning is fundamental to a wide range of cognitive functions. Explaining how sequences--and the relations between the elements they comprise--are learned is a fundamental challenge to cognitive science. However, although hundreds of articles addressing this question are published each year, the actual learning mechanisms involved in the…

This study investigates a range of non-normative ideas that pre-service teachers (PSTs) employ in reasoning about sampling variability. This issue was studied in the context of a content course on statistics and probability for pre-service middle grade teachers at a Midwestern American university. Analysis of seven PSTs' video and screen records…

This research presents the results of the implementation of a model-eliciting activity called Brickyards, designed to promote the learning of the binomial distribution. The theoretical framework used was the Models and Modeling Perspective, and the participants were undergraduate students enrolled in a probability and statistics course of the…

Take a family of independent events. If some of these events, or all of them, are replaced by their complements, then independence still holds. This fact, which is agreed upon by the members of the statistical/probability communities, is tremendously well known, is fairly intuitive and has always been frequently used for easing probability…

The typical collegiate introductory statistics course poses significant challenges for students. Many do not fully comprehend key course skills, and it is common for students to exit the class with a neutral or negative attitude toward statistics. To measure the impact of using relevant contextual examples as an instructional strategy during a…

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…

An international comparative study of mathematics textbooks is essential in identifying trends in international mathematics education, developing textbooks and improving the quality of teaching and learning in mathematics. This study analyses and compares the contents of the probability and statistics curricula in the high school textbooks of…

In this literature review, we survey student naïve ideas (frequently referred to as 'misconceptions') that plausibly relate, at least in part, to difficulty in understanding probability. We collected diverse naïve ideas from a range of topics in physics: Non-linear Dynamics; Cosmology; Thermal Physics; Atomic, Nuclear, and Particle Physics;…