The template-based automated item-generation (TAIG) approach that involves template creation, item generation, item selection, field-testing, and evaluation has more steps than the traditional item development method. Consequentially, there is more margin for error in this process, and any template errors can be cascaded to the generated items.…

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.

Graded Troubleshooting (GTS) is a powerful routine that teachers can use easily to engender students' metacognitive thinking and boost their understanding of mathematics concepts and procedures. This article describes a new GTS activity designed to prompt students to efficiently exploit worked examples when asked to diagnose erroneous examples…

It is widely recognised that feedback is an important part of learning: effective feedback should result in a meaningful change in student behaviour (Morris et al., 2021). However, individual feedback takes time to produce, and for large cohorts -- typified by the North of 300 challenge in computing (CPHC, 2019), it can be difficult to do so in a…

Barlow et al. (2018) discussed three types of mistakes worthy of inspection: procedural errors, inappropriate solution processes, and misconceptions. Here, the authors focus on procedural errors, as these often led the teachers in their professional development project to limit their inspection of mistakes to correcting. Despite this narrow focus,…

The past few decades have witnessed a remarkable surge of research interest in written corrective feedback (WCF). Given its pivotal role in the writing classroom, WCF has remained one of the most vibrant and dynamic areas for scholarly investigations. The aim of this article is to chart future directions for WCF research. To do this, it first…

Teachers can make number talks more ambitious and increase learning opportunities for students by debugging errors, promoting multi-student thinking, and orienting to make connections. This article describes the basic number talks routine and examines some common tendencies, such as "Serial Sharing." It concludes with a vignette to…

Automatic question generation and the assessment of procedural knowledge is still a challenging research topic. This article focuses on the case of it, the techniques of parsing grammars for compiler construction. There are two well-known techniques for parsing: top-down parsing with LL(1) and bottom-up with LR(1). Learning these techniques and…

Productive struggle is a process in which students expend effort to grapple with perplexing problems and make sense of something that is not immediately apparent and beyond their current level of understanding and capacity. The experience encourages students to reflect on and restructure their existing knowledge toward a new understanding of…

Since the publication of Pedagogy of the Oppressed, Paulo Freire has been important for disseminating the concept of dialogue in education. Dialogue is often framed as the kind of interaction that educators should enact in their practice, to right historical and socio-political wrongs. With this, speaking and assuming one's voice has a special…

Due to the nature of the teaching environment, students may often develop perceptions of their lecturers' ability as mathematicians, based on the pre-prepared and well-rehearsed content they present. In reality, performing mathematical calculations and solving problems is a difficult skill, and students may compare their own experiences…

With the recent rapid technological advance, second language (L2) educators have increasingly incorporated technologies into writing pedagogy. Two of the major technologies to promote L2 writing are e-portfolios and automated written corrective feedback (AWCF). Notably, feedback-rich portfolios facilitate L2 learners' self-regulation and writing…

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,…