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…

Combining methods from earlier content validity and more contemporary content alignment studies may allow a more complete evaluation of the meaning of test scores than if either set of methods is used on its own. This article distinguishes item relevance indices in the content validity literature from test representativeness indices in the…

Although school psychologists often comment on examinee motivation in their reports, systematic evaluation of effort is not common practice. Empirical assessment of performance effort provides critical evidence for the validity of evaluations and will likely lead to more valid assessments, recommendations, and placements. This article focuses on…

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…

Though previously unacknowledged, a SMART (Sequential Multiple Assignment Randomized Trial) design uses both regression discontinuity (RD) and randomized controlled trial (RCT) designs. This combination structure creates a conceptual symbiosis between the two designs that enables both RCT- and previously unrecognized, RD-based inferential claims.…

Qualitative thematic analysis is a commonly used and widely applicable form of qualitative analysis, though it can be challenging to implement. Due to its use across research questions, qualitative traditions, and fields, thematic analysis is also prevalent in mixed methods studies. Despite its widespread use, the term "thematic…

Problem solving and proofs have always played a major role in mathematics. They are, in fact, the heart and soul of the discipline. The using of a number of different proof techniques for one specific problem can display the beauty, and elegance of mathematics. In this paper, we present one specific, interesting geometry problem, and present four…

This module is designed for educators, educational researchers, and psychometricians who would like to develop an understanding of the basic concepts of validity theory, test validation, and documenting a "validity argument." It also describes how an in-depth understanding of the purposes and uses of educational tests sets the foundation…

Since 2018, institutions of higher education have been aware of the "enrollment cliff" which refers to expected declines in future enrollment. This paper attempts to describe how prepared institutions in Ohio are for this future by looking at trends leading up to the anticipated decline. Using IPEDS data from 2012-2022, we analyze trends…

A critical revisiting of research methods with multilingual learners raises issues of validity that are often unaddressed in current discussions of research quality. Though validity is conceptualized and assessed differently across research traditions, validity broadly describes the production of findings that are credible and trustworthy. The…

Education researchers often encounter scenarios where an abrupt policy change occurs within or across jurisdictions or populations that affect key student outcomes. Difference-in-differences is a research design analysts can use to estimate causal effects of these "natural experiments." This article introduces education researchers to…

Most existing solutions to the current replication crisis in science address only the factors stemming from specific poor research practices. We introduce a novel mechanism that leverages the experts' predictive abilities to analyze the root causes of replication failures. It is backed by the principle that the most accurate predictor is the most…

For medical educators, autoethnography as a research methodology provides a means of active engagement in reflective practice, ranging from teaching and educational innovation to interactions with patients and colleagues. In this way, they may benefit from the systematic reflexivity required, improve their interactions with the people around them,…