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…

Functions and formulas in spreadsheets provide an instructional opportunity to help students build their skills in identifying errors in their own work and identifying a path to go about correcting the errors. This paper provides examples of functions and equations used to create two approaches to calculating the solution to one problem, such as 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…

The authors describe and discuss an activity in which primary school students were instructed how to use graph theory to solve a spatial puzzle. This activity was aligned with the design principles of vicarious failure. They discuss how this impacted the type of dialogue observed in the classroom and found that students were more likely to focus…

Errors are inevitable in most learning contexts, but under the right conditions, they can be beneficial for learning. Prior research indicates that generating and learning from errors can promote retention of knowledge, higher-level learning, and self-regulation. The present review proposes an integrated theoretical model to explain two major…

The present study describes an R function that implements six corrective procedures developed by Bartlett, Swain, and Yuan in the correction of 21 statistics associated with the omnibus Chi-square test, the residuals, or fit indices in confirmatory factor analysis (CFA) and structural equation modeling (SEM).

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…

Despite strong theoretical and empirical evidence suggesting that word meaning knowledge plays a critical role in word reading, interventions for students with word reading difficulties and disabilities frequently target word reading instruction in isolation. This article connects reading theory to practice by describing one approach to integrate…

Practice-based pedagogies, such as representations of practice and approximations of practice, are increasingly common in mathematics teacher education. More needs to be known about how teacher candidates' (TCs') productions through such activities make visible the resources they bring to the work of teaching. In this paper, we highlight our use…

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…