Oxidation number (ON) is taught as an electron-counting concept for redox reactions in chemistry curriculum. The molecular formula method, the Lewis formula method, and the structural formula method have all been used to determine ON. However, the task of assigning ON still poses problems for some teachers and students. This paper explores a new…

In this article, we present a two-stage estimation approach applied to multilevel latent class analysis (LCA) with covariates. We separate the estimation of the measurement and structural model. This makes the extension of the structural model computationally efficient. We investigate the robustness against misspecifications of the proposed…

Any quadratic function has a line of symmetry going through its vertex; any cubic function has 1800 rotational symmetry around its point of inflection. However, polynomial functions of degree greater than three can be both symmetrical and asymmetrical (Goehle & Kobayashi, 2013). This work considers algebraic conversions of symmetrical quartic…

In this paper, we first focus on the sum of powers of the first n positive odd integers, T[subscript k](n)=1[superscript k]+3[superscript k]+5[superscript k]+...+(2n-1)[superscript k], and derive in an elementary way a polynomial formula for T[subscript k](n) in terms of a specific type of generalized Stirling numbers. Then we consider the sum of…

In parallel process latent growth curve mediation models, the mediation pathways from treatment to the intercept or slope of outcome through the intercept or slope of mediator are often of interest. In this study, we developed causal mediation analysis methods for these mediation pathways. Particularly, we provided causal definitions and…

While research on the opportunity to learn about mathematics concepts provided by textbooks at the secondary level is well documented, there is still a paucity of similar research at the undergraduate level. Contributing towards addressing this knowledge gap, the present study examined opportunities to engage in quantitative and covariational…

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,…

How long will it take to get from "Point A" to "Point B"? Estimating the answer to this question is essential for outdoor leaders to accurately and safely manage their outdoor adventure education course. By being able to carefully estimate the amount of time needed to travel a particular route, over the course of a day or an…

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…

The article shows that even a small number of iterations give a very large length of the Koch Curve. The overall purpose of this work is to show that even a small number of iterations can give a very complex fractal structure. In this case it is the very big length of Koch's curve. As examples, the distance from the Earth to the Moon and from the…

Conducting research with human subjects can be difficult because of limited sample sizes and small empirical effects. We demonstrate that this problem can yield patterns of results that are practically indistinguishable from flipping a coin to determine the direction of treatment effects. We use this idea of random conclusions to establish a…

Data harmonization is an emerging approach to strategically combining data from multiple independent studies, enabling addressing new research questions that are not answerable by a single contributing study. A fundamental psychometric challenge for data harmonization is to create commensurate measures for the constructs of interest across…

This study used the RBC+C model to reveal the abstractions of the 6th-grade students in the process of transition to the parallelogram area formula. Also, constructing parallelogram area information was employed as a teaching experiment based on the basic interpretive approach, one of the qualitative research methods. The study participants…

Assessing sensitivity to unmeasured confounding is an important step in observational studies, which typically estimate effects under the assumption that all confounders are measured. In this paper, we develop a sensitivity analysis framework for balancing weights estimators, an increasingly popular approach that solves an optimization problem to…

Alpha-particle sources are widely used in industrial and medical applications. Such applications include smoke detectors, static charge eliminators, and radiation therapy. This paper is concerned with the detection of alpha particles. A number of techniques are known for the detection of alpha particles. Those techniques include the Geiger-Müller…