This study investigated the effects of a place value intervention with third-grade students with learning disabilities. The intervention added content to a research-based intervention using the concrete-representational-abstract (CRA) sequence. The added content reflected current mathematics standards for third grade. Students' place value…

Cluster randomized control trials often incorporate a longitudinal component where, for example, students are followed over time and student outcomes are measured repeatedly. Besides examining how intervention effects induce changes in outcomes, researchers are sometimes also interested in exploring whether intervention effects on outcomes are…

This article presents a task providing college students opportunities to build on their high school knowledge of trigonometry to explore parametric equations and inverse trigonometric relationships within a contextual learning ladder problem.

Error analysis is an instructional strategy that can assist teachers to identify learners' areas of weakness in mathematics and that can point to remediation of those errors. This article explores the errors learners exhibit when solving quadratic equations by completing the square using Newman's Error Analysis Model. A research study explored the…

The major challenge of most basic schools is inadequate educational resources despite a conscious effort to constantly provide. This is a result of inaccurate data management leading to inappropriate predictions for effective planning. The actual efficiency of a system is determined by its ability to predict real-life data with speed and accuracy.…

Density functional theory (DFT) is indubitably the most popular and among the most successful approaches for approximately solving the many-electron Schro¨dinger equation. The level of understanding on the part of both researchers and students using DFT, however, is lacking, given the availability of black-box software. The present work addresses…

Contribution: This article compares student success via different pathways in which students take mathematics courses required for engineering degrees. Background: Mathematics courses are an integral part of engineering curriculum. Many institutions require or recommend the order in which students take Calculus II, Multivariable Calculus,…

We report an educational tool for the upper level undergraduate quantum chemistry or quantum physics course that uses a symbolic approach via the PySyComp Python library. The tool covers both time-independent and time-dependent quantum chemistry, with the latter rarely considered in the foundations course due to topic complexity. We use quantized…

The ability to distinguish between exact and inexact differentials is an important part of solving first-order differential equations of the form Adx + Bdy = 0, where A(x,y) [not equal to] 0 and B(x,y) [not equal to] 0 are functions of x and y However, although most undergraduate textbooks motivate the necessary condition for exactness, i.e. the…

The calculation of the magnetic field produced by a loop current using the Biot-Savart law is a very typical exercise in introductory university physics. However, the cases studied are limited, in most textbooks, only the circular arrangement is treated. In this article, we calculate the magnetic field of an elliptical loop current along an axis…

In this paper, I propose a new construct named "analytic equation sense" to conceptually model a desired way of reasoning that involves students' algebraic manipulations and use of equivalent expressions. Building from the analysis of two existing models in the field, I argue for the need for a new model and use empirical evidence to…

High school math projects center on solving real-world examples in a wide variety of situations that require a creative skill set. Creativity in high school mathematics takes place in a subtle form. In contrast, creativity presents itself conspicuously in art. Therefore, this paper will explore the utilization of polynomial equations in drawing…

The aim of this study is to investigate the effect of digital gamification-based instruction on the attitudes towards mathematics and anxiety of seventh-grade gifted students in the "Equation and Equation" unit. In this study, pretest-posttest unbalanced group experimental design was used. The study was conducted in the 2022-2023…

Research shows the salient place of mathematical teaching talk, including the mathematical-linguistic practices of naming and explaining, in the enactment of students' mathematical talk and learning with understanding in the classroom. Our study was developed to examine the noticing of two groups of secondary-school mathematics teachers in one-day…

The teaching of first-degree equations is a key point in secondary school curricula and requires the careful planning and selection of appropriate teaching materials. On the other hand, dyslexia, a specific learning disability, is increasingly common in the classroom. Thus, in the context of inclusion, the teaching methodology used by the…