The motion equations of a body under gravity and resistance linearly dependent on speed are usually analysed by solving differential equations. In this paper we report a derivation not explicitly involving differential equations but instead based on some elementary mathematical operations. The derivation uses only knowledge covered in a typical…

In the multivariable calculus course, a standard application of triple integration is to find volumes of bounded regions in R[superscript 3]. In this article, we consider the problem of computing volumes, by way of examples, of regions bounded by planes and quadric surfaces. For illustration, we present the solution to two basic but non-standard…

It is proposed a network approach for electric circuits simplification, that through a unified systematic procedure allows simplifying circuits of any complexity, and evaluation of the equivalent resistances, capacitors and inductors. Circuits to be simplified are characterized by their nodes, and by the elements of different types (resistances,…

In this work, a simple rocking pendulum, in a circular arc shape, is presented. The idea is to put a rigid arc on a clean flat surface of glass and leave it to oscillate under the effect of a little impulse. Then, the periodic time of this arc pendulum's motion is experimentally determined. The mathematical analysis of the arc's motion is derived…

Multidimensional Item Response Theory (MIRT) is widely used in educational and psychological assessment and evaluation. With the increasing size of modern assessment data, many existing estimation methods become computationally demanding and hence they are not scalable to big data, especially for the multidimensional three-parameter and…

Exploratory structural equation modeling (ESEM) allows for the estimation of all cross-loadings, which leads to the number of parameters estimated substantially greater than that in conventional SEM. This study examined the sensitivity of fit measures (CFI, RMSEA, AIC, BIC, SaBIC, LRT) to measurement noninvariance in ESEM. Results suggested that…

In this paper, we introduce novel instructional approaches to engage students in using modelling with data to motivate and teach differential equations. Specifically, we introduce a pedagogical framework that will execute instructional modules to teach different solution techniques for differential equations through repositories and notebook…

The consequence of a change in school leadership (e.g., principal turnover) on student achievement has important implications for education policy. The impact of such an event can be estimated via the popular Difference in Difference (DiD) estimator, where those schools with a turnover event are compared to a selected set of schools that did not…

As part of the effort to develop an improved oral reading fluency (ORF) assessment system, Kara et al. (2020) estimated the ORF scores based on a latent variable psychometric model of accuracy and speed for ORF data via a fully Bayesian approach. This study further investigates likelihood-based estimators for the model-derived ORF scores,…

As part of the effort to develop an improved oral reading fluency (ORF) assessment system, Kara et al. estimated the ORF scores based on a latent variable psychometric model of accuracy and speed for ORF data via a fully Bayesian approach. This study further investigates likelihood-based estimators for the model-derived ORF scores, including…

An alternating treatments design was used to analyze the effects of concrete and virtual manipulatives on the duration and number of correctly solved linear equations by three middle school students with cognitive disabilities. Participants physically manipulated algebra tiles to solve an equation during the concrete manipulative condition. During…

In mathematics education, students are repeatedly confronted with the tasks of interpreting and relating different representations. In particular, switching between equations and diagrams plays a major role in learning mathematical procedures and solving mathematical problems. In this article, we investigate a rather unexplored topic with…

This paper describes a way to simulate and visualise 3D representations of the resultant electric field vector propagation for plane, circular and elliptically polarised waves. These polarisation states are obtained by the superposition of two coherent linearly polarised waves oscillating in two mutually perpendicular directions. The required data…

This paper shows how the freely downloadable software package called "SMath Studio" can be used to solve the time-independent Schrödinger equation using a simple step-wise approximation. The solution is illustrated with reference to the hydrogen atom for which trial eigenvalues are supplied by the energy level formula of the Bohr atom.

Background: Many students solving quantitative problems in science struggle to apply mathematical instruction they have received to novel problems. The few students who succeed often draw on both their mathematical understanding of the equation and their scientific understanding of the phenomenon. Understanding the sensemaking opportunities…