This paper examines prospective mathematics teachers' knowledge of asymptotes and asymptotic behaviour of functions in calculus. They are university students and future facilitators of knowledge in upper secondary education. We constructed a "reference epistemological model" to describe the knowledge about asymptotes for upper secondary…

The present study investigates the effect of the separator lines on the learning of 8th grade students in simplifying algebraic expressions with parenthesis. An experimental study was designed to achieve this goal involving 60 girl students in 8th Grade (13 and 14 years old) randomly selected and assigned to two experimental and control groups.…

There is a close connection between simple harmonic motion and uniform circular motion. This connection is widely taught and included in standard textbooks. Here, we exploit this connection to simultaneously derive two results from introductory mechanics: the period of a mass-spring system and the centripetal acceleration formula. Previously…

The variation of the period of oscillation of a pendulum with the amplitude is known as "circular error" to clockmakers, and can easily be observed even without modern laboratory instruments. There have therefore been many approximate formulae for the pendulum period as a function of the amplitude, but the simple equation due to Denman,…

Moderated multiple regression (MMR) has become a fundamental tool for applied researchers, since many effects are expected to vary based on other variables. However, the inherent complexity of MMR creates formidable challenges for adequately performing power analysis on interaction effects to ensure reliable and replicable research results. Prior…

This study builds on the simulation framework of a recent paper by Stanley and Doucouliagos ("Research Synthesis Methods" 2023;14;515--519). S&D use simulations to make the argument that meta-analyses using partial correlation coefficients (PCCs) should employ a "suboptimal" estimator of the PCC standard error when…

Model evaluation is a crucial step in SEM, consisting of two broad areas: global and local fit, where local fit indices are use to modify the original model. In the modification process, the modification index (MI) and the standardized expected parameter change (SEPC) are used to select the parameters that can be added to improve the fit. The…

Real data are unlikely to be exactly normally distributed. Ignoring non-normality will cause misleading and unreliable parameter estimates, standard error estimates, and model fit statistics. For non-normal data, researchers have proposed a distributionally-weighted least squares (DLS) estimator to combines the normal theory based generalized…

This article aims to clarify fundamental aspects of the process of assigning fuzzy scores to conditions based on family resemblance (FR) structures by considering prototype and set theories. Prototype theory and set theory consider FR structures from two different angles. Specifically, set theory links the conceptualization of FR to the idea of…

Properties of curved functions considered to be parallel over their domains are investigated. Parallel curves in a given plane may appear identical but are actually not superimposable and thus are not congruent. Translational shifted functions in a plane are not parallel curves because the shortest perpendicular distance between them is not…

Every application of integration by parts can be done with a tabular method. The trick is to identify and consider each new integral in the table before deciding how to proceed. This paper supplements a classic introduction to integration by parts with a particular tabular method called Row Integration by Parts (RIP). Approaches to tabular methods…

Linear panel models featuring unit and time fixed effects appear in many areas of empirical economics. An active literature studies the interpretation of the ordinary least squares estimator of the model, commonly called the two-way fixed effects (TWFE) estimator, in the presence of unmodeled coefficient heterogeneity. We illustrate some…

In undergraduate university courses, the assessment methods often lack variety, which can lead to significant stress for both students and educators. It is becoming increasingly apparent that incorporating a range of assessment types could alleviate this stress and better accommodate diverse learning styles (Leite et al., 2010). Elective Grading…

The ability to relate physical concepts and phenomena to multiple mathematical representations--and to move fluidly between these representations--is a critical outcome expected of physics instruction. In upper-division quantum mechanics, students must work with multiple symbolic notations, including some that they have not previously encountered.…

This article presents some equivalent forms of the common Kuder-Richardson Formula 21 and 20 estimators for nondichotomous data belonging to certain other exponential families, such as Poisson count data, exponential data, or geometric counts of trials until failure. Using the generalized framework of Foster (2020), an equation for the reliability…