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…

In the paper a software solution is presented for the generation of instances of exercises. The focus is on education in mathematics but the approach can be adopted in other fields such as computer science and natural science. The present solution uses the R environment for the generation process and LaTeX for the content presentation. In the…

Most literature related to Benford's Law discusses what the law can be used for and how it works but fails to address effective methods and procedures for teaching the law to students. This article examines existing information resources to determine the most effective methods and procedures used to explain this Law to those who have no experience…

The Common Core State Standards for Mathematics have a widespread impact on children's statistical learning opportunities. The Grade 6 standards are particularly ambitious in the goals they set. In this critique, experiences helping children work toward the Grade 6 Common Core statistics expectations are used in conjunction with previous research…

Typical difficulties in learning probabilistic subjects are concerned with big data, complicated formulas and inconvenient figures in statistical analyses. The present research considers the usage of innovative teaching methods (e.g. electronic summary of lectures, presentations of lecture courses, task solution templates, electronic training…

White and Gorard make important and relevant criticisms of some of the methods commonly used in social science research, but go further by criticising the logical basis for inferential statistical tests. This paper comments briefly on matters we broadly agree on with them and more fully on matters where we disagree. We agree that too little…

As a component of the ongoing development of the mathematics curriculum in China, we compare the country's high school mathematics textbooks with those of several other countries. We base our analysis on the assumption that textbooks, as primary printed teaching resources, are key tools for interpreting educational policy. In this paper, we…

Recent concerns about a shortage of capacity for statistical and numerical analysis skills among social science students and researchers have prompted a range of initiatives aiming to improve teaching in this area. However, these projects have rarely re-evaluated the content of what is taught to students and have instead focussed primarily on…

We analyse the "two-dice horse race" task often used in lower secondary school, in which two ordinary dice are thrown repeatedly and each time the sum of the scores determines which horse (numbered 1 to 12) moves forwards one space.

Value-added models are being implemented in many states in an attempt to measure the contributions of individual teachers and schools toward students' learning. Scores from these models are increasingly used for high-stakes purposes such as setting compensation, hiring or dismissing teachers, awarding tenure, and closing schools. The statistician…

This paper presents discussions on stochastic education in early childhood, based on two doctoral research projects carried out with groups of preschool teachers from public schools in the Brazilian cities of Suzano and São Paulo who were participating in a continuing education program. The objective is to reflect on the analysis of two didactic…

In the nonequivalent groups with anchor test (NEAT) design, the standard error of linear observed-score equating is commonly estimated by an estimator derived assuming multivariate normality. However, real data are seldom normally distributed, causing this normal estimator to be inconsistent. A general estimator, which does not rely on the…

Since the introduction of the Common Core State Standards for Mathematics (CCSSM) in 2010, stakeholders in adopting states have engaged in a variety of activities to understand CCSSM standards and transition from previous state standards. These efforts include research, professional development, assessment and modification of curriculum resources,…

Statistics and probability have become an integral part of mathematics education. Therefore it is important to understand whether curricular materials adequately represent statistical ideas. The "Guidelines for Assessment and Instruction in Statistics Education" (GAISE) report (Franklin, Kader, Mewborn, Moreno, Peck, Perry, & Scheaffer, 2007),…

Student pathways through the American higher education system are complex and entail more than the choice between continuation and dropout. The four-year college system requires students seeking a bachelor's degree to pass through a series of transitions that are marked by the achievement of credit thresholds in each year of study. At those…