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.

False alarming, or detecting an error when there is not one, is a pervasive problem across numerous industries. The present study investigated the role of elaboration, or additional information about non-error differences in complex visual displays, for mitigating false error responding. In Experiment 1, learners studied errors and non-error…

This paper describes Alkaline, a size-reduced version of Kyber, which has recently been announced as a prototype NIST standard for post-quantum public-key cryptography. While not as simple as RSA, I believe that Alkaline can be used in an undergraduate classroom to effectively teach the techniques and principles behind Kyber and post-quantum…

This basic qualitative study explored the intercultural development and experiences of thirteen US undergraduate faculty members. It was grounded in the theoretical frameworks of intercultural development and constructive-developmental theory. Data included two Intercultural Development Inventories® 3-6 months apart; a Subject Object Interview;…

Adaptive action-related reactions to errors, i.e. (meta-)cognitive processes and behaviours directly aimed at overcoming an error, have been proposed to benefit learning outcomes. However, causally interpretable findings are sparse in the current literature. Addressing this research deficit, the present study aimed at investigating whether…

Background: Interest in the potential of learning from errors to benefit innovation and organizational and personal growth is currently increasing. In practice, individuals frequently do not appear to learn spontaneously from errors and setbacks without support. Based on prior work, this paper considers antecedents and consequences of adaptive…

This study, using a scriptwriting task, examines how 52 Czech pre-service mathematics teachers (PMTs) handled a situation in which a fictional pupil's incorrect reasoning resulted in a correct answer. The participants were asked to imagine and provide a script that reflects how the situation could evolve in response to the pupil's incorrect…

Aim/Purpose: This article investigates the process of identifying and correcting hallucinations in ChatGPT-4's recall of student-written responses as well as its evaluation of these responses, and provision of feedback. Effective prompting is examined to enhance the pre-evaluation, evaluation, and post-evaluation stages. Background: Advanced Large…

Many students struggle with making sense of feedback information and in applying and transferring it to new contexts. Research literature suggests that low-performing students are especially at risk because they often do not understand assessment criteria and cannot utilise information they receive. This paper addresses this problem through…

Perfectionism is widely recognised as a key factor in students' learning experiences, but such evidence is primarily derived from cross-sectional studies testing unidirectional links. To fill in the gap, our study used a longitudinal design and made the initial attempt to examine the bi-directional links between two types of perfectionism…

Mathematics is a core academic subject, regardless of grade level or setting. Everyone uses mathematics in their everyday life, so being competent in basic mathematics is critical to independent living. One thing teachers can do to ensure learners are learning the mathematics concepts being taught is to diagnose and remediate the errors they are…

Contribution: This study uses a qualitative research method to analyze interviews where participants simplified an electric circuit while explaining their thought process. Background: Rearranging circuit diagrams is a fundamental skill in electrical and electronic engineering, yet students can struggle with unfamiliar configurations. Current…

The study aimed to explore the perception of pre-service teachers regarding the use of the red pen for corrections. A non-random sample of twelve (12) respondents, consisting of three experienced tutors from the Mathematics, Science, and English Departments, along with nine pre-service teachers, were interviewed. The data was analysed…

Background: A solid conceptual understanding is essential for students to succeed in all academic disciplines. Student misconceptions are correlated with their poor academic performance and high attrition rates. It is especially important to correct student misconceptions in science-based undergraduate engineering mechanics courses that cover…

The study examined the influence of feedback features on revision uptake in dialogic peer feedback activities, and the moderating effect of self-efficacy and prior knowledge on this relationship. Data were collected over a 10-week course at a comprehensive university in China, involving 29 students and resulting in 242 revision-oriented comments.…