Research Findings: This study examined age-based developmental trajectories of four key number sense (NS) skills within an accelerated longitudinal design. Using data from 408 preschoolers, ages 45 to 68 months, linear and latent basis growth curves were evaluated. Results indicated growth across NS skills was best represented as nonlinear for all…

Previous research into the teaching and learning of surface area emphasises the use of nets and formulae to calculate the total surface area of three-dimensional objects despite enduring student difficulties. This study investigated an instructional intervention for Year 8 mathematics students (n = 47; 13-14 years old) designed to elicit multiple…

High-school mathematics teachers tend to use computational, constructed response questions in their classroom tests. However, the rapid shift to distance learning resulting from the COVID-19 pandemic created technological obstacles to using these items. This study investigated teachers' reasons for using particular items and how they adapted their…

Evidence in South Africa of poor performance on word problems points to particular challenges among learners relating to difficulties with, on the one hand, making sense of mathematical word problems and, on the other, moving beyond inefficient counting based calculation methods. While many studies in mathematics education in South Africa have…

The introduction of Computational Chemistry via "Molecular Modelling and Drug Design" course at undergraduate level has opened wide possibilities for students to expand their knowledge of quantum chemistry, organic reaction mechanisms, protein-ligand interactions, drug design, and probable "in vivo" behavior of drug candidates.…

This review describes a computational chemistry exercise aimed at enhancing the understanding of upper-division undergraduates in organic chemistry and physical chemistry regarding the structures and aromaticities of cyclobutadiene and cyclooctatetraene. This exercise exposes students to chemical problems that require computational methods as a…

Units coordination, defined by Steffe (1992) as the mental distribution of one composite unit (i.e., a unit of units) "over the elements of another composite unit" (p. 264) is a powerful tool for modeling students' mathematical thinking in the context of whole number and fractional reasoning. This paper proposes extending the idea of a…

The concept, development and assessment of computational thinking have increasingly become the focus of research in recent years. Most of this type of research focuses on older children or adults. Preschool age is a sensitive period when many skills develop intensively, so the development of computational thinking skills can already begin at this…

In this article the author describes an intervention program for students who were approximately six months behind expected standards. The program, "Prepare 2 Learn," had four components: building prior knowledge; developing mental computational fluency; encouraging a growth mindset; and meta-cognitive strategies. The qualitative data…

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…

A computational experiment investigating common organic chemistry mechanisms has been developed and implemented in a junior/senior-level physical chemistry laboratory course at two institutions. Students investigated various reactions that proceed via S[subscript N]1, S[subscript N]2, E1, and E2 mechanisms using hybrid Density Functional Theory…

Solution equilibria diagrams are excellent tools for understanding chemical speciation in multireaction chemical systems. They are usually plotted using software packages that efficiently perform advanced calculations, giving the possibility to graphically visualize thermodynamic and composition information. However, this approach frequently…

Purpose: The purpose of this study was to determine whether estimates of glottal aerodynamic measures based on neck-surface vibration are comparable to those previously obtained using oral airflow and air pressure signals (Espinoza et al., 2017) in terms of discriminating patients with phonotraumatic and nonphonotraumatic vocal hyperfunction (PVH…

In studies where the response variable is measured on a ratio scale, a ratio of means or medians provides a standardized measure of effect size that is an alternative to the popular standardized mean difference. Confidence intervals for ratios of population means and medians in independent-samples designs and paired-samples designs are proposed as…

Pre literacy skills in young children have been well established. Explorations of the parallel concept of pre mathematic skills in young children are minimal. Recommendations for how to engage young children, specifically infants, in math have been limited to caregiver counting games. This colloquium presents an example of how an 11-month-old is…