The Miller-Rabin test is a useful probabilistic method for finding large primes. In this paper, we explain the method in detail and give three variations on this test. These variations were originally developed as student projects to supplement a course in error correcting codes and cryptography.

Core Maths (CM) qualifications were introduced into the post-16 curriculum in England in 2014, with first assessments in 2016. They are a suite of qualifications aimed at students who achieve a grade 4 (originally a grade C) or higher at GCSE Maths but do not go on to take AS or A level Maths. This group comprised around 40% of all students in…

Using software to teach statistical inference in introductory courses opens the door for methods and practices that are more conceptually appealing to students. With an increasing number of fields requiring competency in statistics including data science, natural and social sciences, public health and more, it is crucial that we as instructors…

Course dropout is a concern in online higher education, mainly in first-year courses when different factors negatively influence the learners' engagement leading to an unsuccessful outcome or even dropping out from the university. The early identification of such potential at-risk learners is the key to intervening and trying to help them before…

Grade retention and inequalities that derive from grade retention can influence student school trajectories and careers. Grade retention can discourage students from education, and increase school failure and dropout. This study explored the relationship between grade retention and student intentions to enrol in higher education. We also studied…

Tertiary mathematics has a central place in teacher education, yet in recent years there is growing evidence that realizing its potential affordances in secondary mathematics teaching is far from trivial. Research suggests that utilizing tertiary mathematics in secondary teaching requires interweaving it with knowledge for teaching secondary…

It is well established that participation in formal adult education varies by individual background characteristics. However, less attention has been paid to examining inequality in participation as a consequence of policy changes, such as educational expansion. This paper examines the process of tremendous expansion in Swedish Higher Vocational…

University students of all disciplines are expected to display critical thinking. Critical thinking may, however, be impeded by psychological and sociological factors such as: belief and confirmation biases, framing, social pressure to conform and poor assessment of probability and risk. These factors are rarely, if ever, thoroughly examined in…

We study how colleges shape their students' voting habits by linking millions of SAT takers to their college-enrollment and voting histories. To begin, we show that the fraction of students from a particular college who vote varies systematically by the college's attributes (e.g. increasing with selectivity) but also that seemingly similar…

This study employed design-based logistic regression to examine the extent to which attending a science, technology, engineering, and mathematics (STEM) magnet high school, school demographics, and student-level factors explain a student's intent to declare a STEM major in the first semester of college. The results show only student-level factors…

The internet has had a vast and pervasive effect on many industries. It has resulted in the creation of new industries and has overhauled the dynamics that governed existing industries. One of the most traditional industries that is now struggling to cope with the changes brought on by the internet is the industry of higher education. Students can…

Between 2001 and 2005, higher education in Italy went through a considerable process of reform according to the "Bologna Process." This paper evaluates the effects of this process on the academic performance of students. We estimate the difference in graduation probability between students who switched from pre-reform university courses…

The mass participation in higher education has led to greater spending by governments and students which has increased the focus on graduate outcomes. In England, the Office for Students (OfS) is planning to take regulatory action, using the Proceed metric, against universities and their courses which do not have 60% of students with positive…

The purpose of this quantitative study was to determine if students' participation in the ALP co-requisite developmental English program relates to the likelihood of passing gateway college-level English. Data was collected to allow for analysis of gateway college-level English passing probability for all students who participated in gateway…

In a study exploring how organizational identification impacted college retention and performance outcomes at a university in the United States, we found the mere act of taking the survey emerged as an unexpectedly strong result. Using propensity score matching, we found that those who took the voluntary survey during the first week of school were…