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)…

Teaching quantum physics (QP) to high school (HS) students is gaining momentum, necessitating the exploration of various effective methods. Specifically, the research on quantitative teaching methods is still in its early stages. Understanding the power of Dirac notation (DN) in teaching is crucial for grasping the complexities of QP, as it…

This work reports the results of a research aimed to know the probabilistic reasoning of high-school students when they deal with the notion of random intervals. An activity was carried out involving students between ages 16 and 17 who built random intervals through physical and computational simulations. The research question guiding this work…

We investigate the reliability of data from the Wage Indicator (WI), the largest online survey on earnings and working conditions. Comparing WI to nationally representative data sources for 17 countries reveals that participants of WI are not likely to have been representatively drawn from the respective populations. Previous literature has…

This article presents a latent class model for multilevel data to identify latent subgroups and estimate heterogeneous treatment effects. Unlike sequential approaches that partition data first and then estimate average treatment effects (ATEs) within classes, we employ a Bayesian procedure to jointly estimate mixing probability, selection, and…

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'…

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…

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…

The purpose of this study was to analyze the problem-solving techniques that students in a fifth-grade classroom applied while solving mathematical word problems. Fifth-grade students in a private school with Ministry of Education curricula in Al Ain, Abu Dhabi, were given a set of 15-word problems to solve with detailed justifications. The…

Mathematics educators and researchers have advocated for the use of manipulatives to teach mathematics for decades. The purpose of this article is to provide illustrative uses of a readily available manipulative rather than a complete list. From an Australian perspective, Pop-it fidget toys can be used across the mathematics curriculum. This paper…

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…

This article presents the results of a qualitative research with a group of 15 university students of social sciences on informal inferential reasoning developed in a computer environment on concepts involved in the confidence intervals. The results indicate that students developed a correct reasoning about sampling variability and visualized…

Inequalities do not end once students enter higher education. Yet, the majority of papers on the effectiveness of higher education aid examine its impact on college enrolment. In this paper, we provide evidence on the causal impact of means-tested but otherwise unconditional financial aid on the outcomes of students who have already enrolled in…

Working memory capacities are associated with mathematical development. Many studies have tried to improve working memory abilities through training. Furthermore, the central executive has been shown to be the component of working memory, which is the most strongly related to numerical and arithmetical skills. Therefore, we developed a training…

This article presents "The Two Children Problem," published by Martin Gardner, who wrote a famous and widely-read math puzzle column in the magazine "Scientific American," and a problem presented by puzzler Gary Foshee. This paper explains the paradox of Problems 2 and 3 and many other variations of the theme. Then the authors…