The ability to distinguish between exact and inexact differentials is an important part of solving first-order differential equations of the form Adx + Bdy = 0, where A(x,y) [not equal to] 0 and B(x,y) [not equal to] 0 are functions of x and y However, although most undergraduate textbooks motivate the necessary condition for exactness, i.e. the…

Many proofs of the arithmetic mean harmonic mean inequality have been proposed based on the rich connections between mathematics and physics. Sometimes the Arithmetic Mean Harmonic Mean inequality is proved by using electric networks. In this note, we use a simple set of two springs, instead of four springs which would be the equivalent set to…

Background: Diet quality assessment in community health settings is critical to reduce the incidence and improve management of diet-related chronic disease. Unfortunately, understandable and actionable brief dietary screening tools that empower individuals are nearly absent. Purpose: The purpose of this article is to describe two rigorous…

Despite the ease of accessing a wide range of measures, little attention is given to validity arguments when considering whether to use the measure for a new purpose or in a different context. Making a validity argument has historically focused on the intended interpretation and use. There has been a press to consider both the intended and actual…

As a follow-up to their article, "Emojis and Their Place in the Mathematics Classroom" (EJ1358586), the authors examine how emojis can be used as bridging representations to support student understanding of proof and algebra in upper primary school. They take a problem from reSolve, Level 3, (AAMT, 2020), look at it from the perspective…

This paper presents a novel figure for teaching multiple geometric proofs of the Pythagorean theorem. Because it consists only of congruent given right triangles, the figure can be constructed using a template of the given right triangle or, if available, a computer program. Within the figure, called a Pythagorean multi-proof square, there are…

There are many problems whose solution requires proof that a quadrilateral is cyclic. The main reason for writing this paper is to offer a number of new tools for proving that a particular quadrilateral is cyclic, thus expanding the present knowledge base and ensuring that investigators in mathematics and teachers of mathematics have at their…

Researchers need to know what is an appropriate sample size for interview work, but how does one decide upon an acceptable number of people to interview? This question is not relevant to case study work where one would typically interview every member of a case, or in situations where it is both desirable and feasible to interview all target…

Experimental psychology is witnessing an increase in research on individual differences, which requires the development of new tasks that can reliably assess variations among participants. To do this, cognitive researchers need statistical methods that many researchers have not learned during their training. The lack of expertise can pose…

Nurse educators at the undergraduate level spend significant time developing and revising exam questions. Following the exam administration, course faculty have the opportunity to complete an item analysis and question revision to improve reliability and validity. A challenge faculty face is tracking these exam changes when teaching as part of a…

Developed as an integral component of many higher education programs, internships provide a multitude of benefits for participating students. However, there is a lack of tools designed to measure internship-related learning outcomes. Therefore, this article will present the process of constructing and validating a scale that can be used to…

Cross-validation is a common statistical procedure applied to problems that are otherwise computationally intractable. It is often employed to assess the effectiveness of prediction procedures. In this report, cross-validation is discussed in terms of "U"-statistics. This approach permits consideration of the statistical properties of…

Connecting and comparing across student strategies has been shown to be productive for students in elementary and secondary classrooms. We have recently been working on a project converting such practices from the K-12 level to the undergraduate classroom. In this paper, we share a particular instantiation of this practice in an abstract algebra…

The Political Identity and Relational Impact Scale (PIRI) is a self-report scale of personal and relational responses to political conflict. This article describes the development and exploratory factor analysis of the scale. The selected model consists of 30 items and a four-factor structure with high internal consistency.

This article aims to share five practical approaches for how teachers can identify, adapt, and create their own writing prompts they assign to students: (1) Promote Students' Solution Paths; (2) Go beyond Asking Students to Simply "Explain"; (3) Prompt Students to Share Their Reasoning; (4) Have Students Consider the Validity of a Given…