Cheating attracts a significant amount of attention in conversations about assessment, and with good reason: if students cheat, we cannot be sure they have met the learning outcomes of their course. In this conceptual article we question the attention given to cheating as a concept and argue that the broader concept of validity is a more important…

Across the world, teacher quality has come to be recognised as one of the most important variables affecting student outcomes; consequently, the regulation of entry into the profession is the subject of iterative review. The traditional 'one-off' interview, involving an interviewee and two or more interviewers, is a common, but not unproblematic,…

This paper introduces the concept of logical consistency in students' thinking in mathematical contexts. We present the Logical in-Consistency (LinC) instrument as a valuable assessment tool designed to examine the prevalence and types of logical inconsistencies among undergraduate students' evaluation of mathematical statements and accompanying…

This article presents an inquiry-oriented lesson for teaching Lagrange's theorem in abstract algebra. This lesson was developed and refined as part of a larger grant project focused on how to "Orchestrate Discussions Around Proof" (ODAP, the name of the project). The lesson components were developed and refined with attention to how well…

In this paper, a simple proof of the Morley's Trisector Theorem is presented which involves basic plane geometry only. The use of backward geometric approach, trigonometry or advanced mathematical techniques is not required. It is suitable for introducing to secondary or undergraduate students, as well as teachers or instructors for learning or…

As new technological developments continue to change the educational landscape, it is not an exception in the area of proof and proving. This classroom note introduces the use of one of the trending proofs assistants -- the Lean theorem prover. We first provide a technical account of Lean, then exemplify Lean proofs in propositional logic, number…

Recent research in university mathematics education has moved beyond the traditional focus on the transition from secondary to tertiary education and students' understanding of introductory courses such as pre-calculus and calculus. There is growing interest in the challenges students face as they move into more advanced mathematics courses that…

Aspiring teachers must develop an in-depth understanding of high-quality instructional practices. In order to prepare, instruct, and coach aspiring teachers, the National Institute for Excellence in Teaching (NIET) has developed a the NIET Aspiring Teacher Rubric (ATR) based on principles of excellence in instruction. This research brief…

Courses: This activity can be used in writing-based (communication) courses across various disciplines including, but not limited to, introduction to writing and rhetoric, business communication, and communication research methods. Objectives: On completion of this activity, students will develop critical reading, thinking, and writing skills as…

In mathematics education, the research on proof by contradiction (PBC) often claims that this activity is more difficult for students than direct proof, or simply difficult in general. Many hypotheses have been offered to support or explain this belief, yet they span a disorientingly wide swath of journal articles, conference papers,…

Calculating analytical uncertainties as a part of method validation is a relevant aspect of field and laboratory practices in instrumental analytical chemistry subjects, which usually require complex algorithms. This work describes the development and didactic use of an automatic and straightforward informatics tool, implemented in an Excel macro,…

Postsecondary institutions generally exist with student and academic affairs working in silos, which creates a fragmented experience for students. Reduced state and federal funding mean that institutions cannot invest in costly new programs or initiatives. The article provides a research-informed approach with practical advice about how…

We present an investigation of the infinite sequences of numbers formed by calculating the pairwise averages of three given numbers. The problem has an interesting geometric interpretation related to the sequence of triangles with equal perimeters which tend to an equilateral triangle. Investigative activities of the problem are carried out in…

The paper argues that contemporary test validity theory places the consequences of testing on the lives of all college applicants at the back of the test validation argument. It introduces the notion of test efficacy as a process to gather evidence on claims on consequences of testing on all college applicants that can be traced back to validity.…

An online intro-to-proof course provided an unexpected opportunity for a series of email exchanges that yielded insights into one student's mathematical thinking and the ambiguous role of mathematical jargon in miscuing this student's reasoning. The jargon deals with the notation [limit value of a function], which encapsulates multiple conceptual…