From literature, we know that making the connections between mathematics and physics is not trivial for most students, even at the advanced level. In the specific context of partial derivatives in thermodynamics, research suggests that making explicit connections between the mathematics and the physics is necessary to foster student understanding.…

Much of physics involves the construction and interpretation of equations. Research on physics students' understanding and application of mathematics has employed Sherin's symbolic forms or Fauconnier and Turner's conceptual blending as analytical frameworks. However, previous symbolic forms analyses have commonly treated students' in-context…

Despite its crucial importance in physics, there are not many studies focusing on student difficulties and teaching strategies related to the (1D) wave equation in the PER literature. In order to contribute to fill this gap, we conducted a study with university students which focused on specific aspects that are crucial for understanding this…

This paper aims to broaden the scope of the construct concept image by addressing the mathematically oriented notion of "solution of an algebraic equation." The notion solution of an algebraic equation is not mathematical per se, but it is most prevalent in mathematical communications and in mathematics education. The paper describes…

This article explores the conceptual challenges that engineering students encounter with double integrals in a vector calculus course. Drawing on previous literature and utilising APOS (Activity- Process- Objects- Schema) as a theoretical framework, this study investigates the difficulties that students face in understanding and applying double…

Single case experimental designs are an important research design in behavioral and medical research. Although there are design standards prescribed by the What Works Clearinghouse for single case experimental designs, these standards do not include statistically derived power computations. Recently we derived the equations for computing power for…

We first review existing literature on cumulative logit models along with various ways to test the parallel lines assumption. Building on the traditional frequentist framework, we introduce a method of Bayesian assessment of null values to provide an alternative way to examine the parallel lines assumption using highest density intervals and…

This paper describes two examples of teaching situations in which the idea of infinity arises, and supports the conclusion that infinity is not a physical reality but a very powerful and useful mathematical device which facilitates modelling and the solution of problems in physics.

Proposed is a new method of standard setting referred to as response vector for mastery (RVM) method. Under the RVM method, the task of panelists that participate in the standard setting process does not involve conceptualization of a borderline examinee and probability judgments as it is the case with the Angoff and bookmark methods. Also, the…

Objective: Determine whether the ACSM walking equations, which calculate caloric expenditure, were accurate for college-aged males and females. Participants: Between 2011 and 2016, 100 college-aged males, 20.24 ± 2.0 years old, and 100 college-aged females, 20.8 ± 1.3 years old, volunteered to participate. Methods: Participants walked on a…

In this paper, we present a novel solution of the quadrature of a parabola based on application of Ramanujan's formula for the partial sum of the square roots of the first "n" natural numbers. We also derive a new formula for calculating of area of a parabolic segment and we apply the result to a generalization of some classical theorems…

Optimal design of multisite randomized trials leverages sampling costs to optimize sampling ratios and ultimately identify more efficient and powerful designs. Past implementations of the optimal design framework have assumed that costs of sampling units are equal across treatment conditions. In this study, we developed a more flexible optimal…

A collision of one object with two or more objects is relatively complicated in general, but a simple example is provided by Newton's cradle since all the objects are identical and in line. In the present paper, an experiment is described where a heavy mallet collides head-on with two billiard balls. The two conservation equations indicate that…

An experiment is described where a pendulum bob was allowed to roll back and forth across an inclined plane. The period of oscillation is larger than that for oscillation in a vertical plane, in part because the effective value of "g" is reduced on an inclined plane. The experiment highlights the differences between all three common…

Gaining useful insight into real-world problems through mathematical modelling is a valued activity across several disciplines including mathematics, biology, computer science and engineering. Differential equations are a valuable tool used in modelling. Modelling provides a way for students to engage with differential equations within a…