Not knowing the population size is a common problem in data-limited contexts. Drawing on work in Sierra Leone, this short take outlines a four-step solution to this problem: (1) estimate the population size using expert interviews; (2) verify estimates using interviews with participants sampled; (3) triangulate using secondary data; and (4)…

This is the third in a series of articles describing CODAP and where it might be used to address content in the "Australian Curriculum: Mathematics" v9.0 (ACARA, 2022). We've talked before about model-ling and about statistics; this time, we'll talk about exploring probability using CODAP. As before, we have also prepared online pages…

This survey paper presents recent relevant research in mathematics education produced in Spain, which allows the identification of different broad lines of research developed by Spanish groups of scholars. First, we present and describe studies whose research objectives are related to student learning of specific curricular contents and…

This article is motivated by the importance of developing statistically literate students. The authors present a selection of problems that could be used to motivate student interest in probability as well as providing additional depth to the curriculum when used alongside traditional resources. The solutions presented utilise natural frequencies…

This article describes the adaptation and use of the Monopoly® board game as a simple simulator to help introduce the principles of probability and risk. It focusses on teaching experiences in an undergraduate business program and offers a new approach to teaching probability and risk with dice to produce a collaborative simulated gaming…

The aim of this paper is to approach the teaching of the Poisson distribution in a friendly and amusing way. It constitutes a common practice to adopt the main probability distributions in order to predict results of sport events and to estimate the win return of betting activities (Chalikias 2009). In particular, by using the Poisson…

In a signal detection theory (SDT) approach to multiple choice exams, examinees are viewed as choosing, for each item, the alternative that is perceived as being the most plausible, with perceived plausibility depending in part on whether or not an item is known. The SDT model is a process model and provides measures of item difficulty, item…

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…

Curriculum prerequisite networks have a central role in shaping the course of university programs. The analysis of prerequisite networks has attracted a lot of research interest recently since designing an appropriate network is of great importance both academically and economically. It determines the learning goals of the program and also has a…

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…

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.

Mathematics curricula have traditionally focused on content knowledge, often in the form of a scope and sequence of increasingly difficult mathematics. The importance of using and applying mathematics is recognised in the current Australian Curriculum Mathematics (AC: M) as 'proficiencies' that are intended to be integrated with the content. There…

In this article, we outline several activities revolving around soccer players who participated in the 2018 FIFA World Cup and 2019 FIFA Women's World Cup. Classroom activities are described from different perspectives, useful for a range of different statistics courses. In a first semester probability theory course, students investigate the…

This paper describes an investigation looking at the underlying mathematics of poker machines. The aim of the investigation is for students to get an appreciation of how poker machines are designed to ensure that in the long-term players will inevitably lose when playing. The first part of this paper describes how students can model a simple poker…

This paper compares the use of confidence intervals (CIs) and a sensitivity analysis called the number needed to disturb (NNTD), in the analysis of research findings expressed as 'effect' sizes. Using 1,000 simulations of randomised trials with up to 1,000 cases in each, the paper shows that both approaches are very similar in outcomes, and each…