The second leg home advantage: evidence from European football cup competitions

The home advantage is a widely acknowledged sporting phenomenon, especially in association football. Here, we examine the second leg home advantage, an effect that is discussed in the public domain but which has received very little scientific attention. The second leg home advantage effect occurs when on average teams are more likely to win a two-stage knock-out competition when they play at home in the second leg. That is, both teams have a home advantage but this advantage is significantly greater for the team that plays at home second. Examining data from three different European Cup football competitions spanning 51 years, we show that the second leg home advantage is a real phenomenon. The second leg home team has more than a 50% probability to qualify for the next round in the competition even after controlling for extra time and team ability as possible alternative explanations. The second leg home advantage appears, however, to have decreased significantly over the past decade. Possible reasons for its existence and subsequent decline are presented.     

Unders and Overs: Using a Dice Game to Illustrate Basic Probability Concepts

In this paper, the dice game Unders and Overs is described and presented as an active learning exercise to introduce basic probability concepts. The implementation of the exercise is outlined and the resulting presentation of various probability concepts are described.     

The impact of the first COVID-19 lockdown in the UK for doctoral and early career researchers

Higher Education - Doctoral researchers and early career researchers (ECRs) are crucial to producing scientific advancements and represent the future of academic leadership. Their research...     

M in CoMputational thinking: How long does it take to read a book?

Even at the primary level, computational thinking (CT) can support young students to prepare for participating in futures that are immersed in data. In mathematics classrooms, there are few explanations of the ways CT can support students in formulating and solving complex problems. This paper presents an example of a primary classroom investigation (8-9 year olds) over seven lessons of the problem “How long does it take to read a book?” The aim is to illustrate ways a statistical investigation can provide context for CT and demonstrate how the two complement each other to solve problems involving mathematics. The findings highlight opportunities and challenges that students face across the elements of CT—decomposition, abstraction, pattern recognition and modelling, and generalization and algorithmic thinking, including recommendations for teaching.     

Hands-On: Investigating the role of physical manipulatives in spatial training

Studies show that spatial interventions lead to improvements in mathematics. However, outcomes vary based on whether physical manipulatives (embodied action) are used during training. This study compares the effects of embodied and non-embodied spatial interventions on spatial and mathematics outcomes. The study has a randomized, controlled, pre-post, follow-up, training design (N = 182; mean age 8 years; 49% female; 83.5% White). We show that both embodied and non-embodied spatial training approaches improve spatial skills compared to control. However, we conclude that embodied spatial training using physical manipulatives leads to larger, more consistent gains in mathematics and greater depth of spatial processing than non-embodied training. These findings highlight the potential of spatial activities, particularly those that use physical materials, for improving children's mathematics skills.     

Departmentalized,Self-Contained,or Somewhere in Between: Understanding Elementary Grade-Level Organizational Decision-Making

Recent trends indicate a move away from self-contained classrooms and toward content-focused departmentalization in elementary schools. This study takes a snapshot of the existing organizational structures used in elementary schools in one district and explores administrators’ beliefs and practices regarding this phenomenon. Our findings suggest administrators base their decisions to organize grade levels on various factors, including their own experiences, contextual dynamics, and personal perceptions of outcomes for students and teachers.