We demonstrate the Stirling formula, approximating the factorial, utilising accessible and elementary methods in an engaging manner.

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…

This study aims to suggest a generalized class of estimators for population proportion under simple random sampling, which uses auxiliary attributes. The bias and MSEs are considered derived to the first degree approximation. The validity of the suggested and existing estimators is assessed via an empirical investigation. The performance of…

We consider Bayesian estimation of a hierarchical linear model (HLM) from partially observed data, assumed to be missing at random, and small sample sizes. A vector of continuous covariates C includes cluster-level partially observed covariates with interaction effects. Due to small sample sizes from 37 patient-physician encounters repeatedly…

Background: Many students face difficulties with algebra. At the same time, it has been observed that fraction understanding predicts achievements in algebra; hence, gaining a better understanding of how algebra understanding builds on fraction understanding is an important goal for research and educational practice. Objectives: However, a wide…

We propose new ways of robustifying goodness-of-fit tests for structural equation modeling under non-normality. These test statistics have limit distributions characterized by eigenvalues whose estimates are highly unstable and biased in known directions. To take this into account, we design model-based trend predictions to approximate the…

Simulation studies are the basic tools of quantitative methodologists used to obtain empirical solutions to statistical problems that may be impossible to derive through direct mathematical computations. The successful execution of many simulation studies relies on the accurate generation of correlated multivariate data that adhere to a particular…

In this study, we focus on a specific visual representation that is used across several mathematics and science content areas: the 'partitioned square' (PS). Previous research has examined PSs in single content areas in isolation, such as for mathematics polynomials or biology random mating, where the PS was generally in the service of other…

The most common challenges students face in solving first-order ordinary differential equations (ODEs) can be overcome by identifying the types of errors, understanding the factors that cause difficulties, and finding appropriate solutions. Therefore, this research aimed to adopt a descriptive qualitative approach, including nine sixth-semester…

For randomized trials that use text as an outcome, traditional approaches for assessing treatment impact require that each document first be manually coded for constructs of interest by trained human raters. This process, the current standard, is both time-consuming and limiting: even the largest human coding efforts are typically constrained to…

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…

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.…

Structural equation models offer a valuable tool for delineating the complicated interrelationships among multiple variables, including observed and latent variables. Over the last few decades, structural equation models have successfully analyzed complete and right-censored survival data, exemplified by wide applications in psychological, social,…

Algebra has been identified as a gatekeeper to careers in STEM, but little research exists on how algebra appears for practitioners in the workplace. Surveys and interviews were conducted with 77 STEM practitioners from a variety of fields, examining how they reported using algebraic functions in their work. Survey and interview reports suggest…