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.

Feedback is an essential aspect of the teaching and learning process since it can objectively describe the learner's performance and guide him through revising their work to improve their academic performance. Studies regarding its application in education have recorded significant pedagogical benefits at the teaching and learning levels. The…

This flash report presents the finding concerning duplicate Higher Education Emergency Relief Fund (HEERF) grant awards to institutions of higher education. It includes a recommendation to enhance the U.S. Department of Education's (Department) ability to prevent, identify, and correct duplicate HEERF grant awards. While analyzing HEERF program…

The difference between students' ideas and scientific conceptions, is called misconceptions. Physics learning needs to be designed by teachers to eradicate misconceptions. This paper provides a review of 72 international journal articles on diagnosis methods, causes, and ways of remediating misconceptions that have been published between…

The quality of teaching mathematics and science depends on the teachers' competencies about instant feedback to mistakes. Instant feedback is some kind of feedback used whenever a mistake occurs. Mistakes are a starting point for learning; a chance to construct new knowledge or describe the misconceptions. Therefore studies on mistakes and instant…

The majority of foreign language learning (FLL) has recently been conducted online due to unprecedented changes in society and this trend seems to be global and perpetual even if the situation changes. Unfortunately, there is still low awareness among language instructors of the impact it may have on the corrective feedback they provide to their…

Many language teachers spend countless hours correcting student writing in hopes of improvement in accuracy, but as of yet, there has been little consensus regarding the efficacy of written corrective feedback (CF) or the type of CF that is most efficient. Although many studies have been conducted on the topic, conflicting results have arisen. In…

This article emphasizes the importance of embracing and mobilizing students' linguistic practices, particularly in bilingual settings. The authors reflect on their experiences as bilingual teachers, initially correcting students' use of regional Spanish variations and translanguaging (mixing English and Spanish). However, through advanced studies,…

Misconceptions are persistent beliefs that contradict the accepted scientific views, impacting how subsequent information is interpreted. Research to date has not examined the sources, or prevalence of, fundamental exercise science misconceptions in higher education (HE) or vocational education (VET) students. Both HE and VET educators were…

In this article, we focus on the design of a second language (L2) formative feedback system that provides linguistic complexity graph reports on the writings of English for special purposes students at the university level. The system is evaluated in light of formative instruction features pointed out in the literature. The significance of…

This paper describes the rationale, design and implementation of a short private online course (SPOC) on data-driven learning (DDL) (Johns, 1991), focusing on L2 error correction in postgraduate academic writing and involving over 300 registered users. I discuss the affordances of using a SPOC platform (namely "EdX") for online DDL…

As our post-secondary landscape evolves to address the needs of the next generation of learners and future educators, it is important to explore the potential conflict between the teaching methods employed by teacher educators and what we ask our pre-service teachers to enact. Amid the challenges facing many teacher preparation programs (including…

With the advent of web 2.0 and the ease of use of many hand-held devices, access to the internet has never been easier. This has been accompanied by a growing range of sites available for learning an L2. These sites offer lessons, explanations, exercises, corrections and feedback. It now becomes time once again to question whether physical bricks…

Utilizing the framework of educational linguistics, we investigate ways to foster greater awareness of, and facility with, academic English for educators and students across disciplines by maximizing the popularity of language-related software packages, applications and websites, those already commonly found in and out of the classroom. Our work…

The current volume aspires to add to previous research on the connection between writing and language learning from a dual perspective: It seeks to reflect current progress in the domain as well as to foster future developments in theory and research. The theoretical postulations contained in Part I identify and expand in novel ways the diverse…