Traditional physical chemistry conceptions of reaction mechanism are formulated in terms of stationary points of an Arrhenius-style "energy profile" that differs sharply (in purpose and form) from the corresponding Robinson-style "arrow-pushing" mechanistic conceptions of organic chemistry. We show here how these diverse…

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…

In this paper, we share the results of the piloting of national diagnostic assessments for strategic calculation with Grade 3 learners in South Africa. The diagnostic assessment pilot intervention was focused on promoting strategic use of calculation strategies and aimed to move learners on from the concrete one-to-one counting methods that…

In the era of the "reproducibility crisis" and the "P-value controversy" new ways of presentation and interpretation of the results of a meta-analysis are desirable. One suggestion that has been made for single studies almost six decades ago and taken up now and then is the P-value function. For a given outcome, this function…

The purpose of this research note is to introduce a latent growth curve reconstruction approach based on the Tabu search algorithm. The approach algorithmically enables researchers to optimally determine at both the individual and the group levels the order of the polynomial needed to represent the latent growth curve model. The procedure is…

The acid-catalyzed dehydration of regioisomeric methylcyclohexanols is a classic organic chemistry experiment featured in a variety of laboratory textbooks and literature. The mechanistic details of this reaction have received an inconsistent and occasionally inaccurate treatment, wherein the reaction has been described as a mix of E1, E2-like,…

Gaussian-2-Blender is an open-source application programming interface (API) written in Python that allows for the conversion of Gaussian input files to 3D objects of different formats. This new tool was developed in response to the shortcomings of available programs to import Gaussian calculations into augmented reality (AR) or virtual reality…

Inconsistent filtering of force plate data persists in published studies. Previous evidence suggests that low pass filtering produces the largest error when calculating jump height, but used jump height from unfiltered force plate data as the criterion. This study investigated the effects of low pass filtering on jump height calculated from force…

We propose an algorithm that allows calculating the remainder and the quotient of division between polynomials over commutative coefficient rings, without polynomial long division. We use the previous results to determine the quadratic factors of polynomials over commutative coefficient rings and, in particular, to completely factorize in Z[x] any…

A reference interval provides a basis for physicians to determine whether a measurement is typical of a healthy individual. It can be interpreted as a prediction interval for a new individual from the overall population. However, a reference interval based on a single study may not be representative of the broader population. Meta-analysis can…

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…

This article presents a case study of two Grade 5 boys' argumentation concerning addition and subtraction of negative numbers while using an interactive tablet-based application simulating positive and negative tiles. We examine the properties of integers they conjectured, and the kinds of evidence and arguments they used to support their…

Virtual reality has become a significant asset to diversify the existing toolkit supporting engineering education and training. The cognitive and behavioral advantages of virtual reality (VR) can help lecturers reduce entry barriers to concepts that students struggle with. Computational fluid dynamics (CFD) simulations are imperative tools…

Computational models are employed to study and respond to pressing environmental issues such as groundwater contamination. This use of computational models, which often involves algorithms and uncertainty that are hidden to the public, has implications for environmental science literacy. This study applies a design-based research approach to…