In classical calculus textbooks, the existence of primitive functions of continuous functions is proved by using Riemann integrals. Recently, Patrik Lundström gave a proof via polynomials, based on the Weierstrass approximation theorem. In this note, it is shown that the proof will be easy by using continuous piecewise linear functions.

A fascinating and catchy method for proving that a number of special lines concur is using the concept of locus. This is now the classical method for proving the concurrency of the internal angle bisectors and perpendicular side bisectors of a triangle. In this paper, we prove the concurrency of the altitudes and the medians by showing that they…

Using the basic properties of the base-b representation of rational numbers, we will give an elementary proof of Gauss's lemma: "Every real root of a monic polynomial with integer coefficients is either an integer or irrational." The paper offers a new perspective in understanding the meaning of 'irrational numbers' from a deeper…

We present a method to compute the power series expansions of e[superscript x] ln (1 + x), sin x, and cos x without relying on mathematical analysis. Using the properties of elementary functions, we determine the coefficients of each series through the method of undetermined coefficients. We have validated our formulae through the use of…

In this article, we state an interesting geometric conservation property between the three angle bisectors of three similar right triangles and provide a proof without words for its justification. A GeoGebra applet is also presented to help with the understanding of the progression of the proof from inductive to deductive stage.

Personalized assessments are of increasing interest because of their potential to lead to more equitable decisions about the examinees. However, one obstacle to the widespread use of personalized assessments is the lack of a measurement toolkit that can be used to analyze data from these assessments. This article takes one step toward building…

Validity is a key element of many forms of research--particularly surveys, which are often used in health professions education research. A survey must accurately measure what it is intended to measure to be considered valid. This is becoming increasingly difficult in the age of artificial intelligence (AI), where "bots" (short for…

Inquiry-based instruction in undergraduate mathematics is commonly characterized by students producing mathematical content (e.g., definitions, theorems, or proofs) rather than consuming it. In this paper, we argue that a production-centered view of inquiry is unnecessarily restrictive and limits the full range of disciplinary activity available…

This is the second article in a series of three in this special issue on establishing a boundary object to foster network health and development. The first article laid out the theoretical rationale for an Improvement Network Health and Development Framework. This article details the efforts to develop a set of practical measures tied to this…

There is increasing interest in health professions education (HPE) in applying argument-based validity approaches, such as Kane's, to assessment design. The critical first step in employing Kane's approach is to specify the interpretation-use argument (IUA). However, in the HPE literature, this step is often poorly articulated. This article…

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…

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…

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…