The Gauss-Lucas Theorem is a classical complex analysis result that states the critical points of a single-variable complex polynomial lie inside the closed convex hull of the zeros of the polynomial. Although the result is well-known, it is not typically presented in a first course in complex analysis. The ease with which modern technology allows…

Although visual analysis has been the primary method of analysis in single-case designs (SCD), numerous statistical analyses have been developed to quantify SCD intervention effects and enable SCDs to be included in evidence-based practice reviews. This study investigated the correspondence between expert visual analysis and three effect sizes for…

We posit a dual approach to digital task design: to engineer opportunities for students to conceive of graphs as representing relationships between quantities and to foreground students' reasoning and exploration, rather than their answer-finding. Locally integrating Ference Marton's variation theory and Patrick Thompson's theory of quantitative…

This article describes the implementation of an activity with a Predict-Observe-Explain (POE) learning cycle to teach the concepts of velocity and acceleration to physics students aged 17-19. The study indicates how the instructor enacted the activity and provides sample student responses and group discussions. The description includes an example…

The study presented investigates the effects of supportive graphical interventions on the graphing skills and conceptual understanding of students in physics. In this study, the first group of participants was presented with ready-made graphs during the instruction, the second group was instructed on the proper construction and extraction of…

Teachers of students with visual impairments clearly have an important opportunity to promote graphics literacy skills for students with visual impairments through providing descriptions to make educational content accessible. Guidelines for appropriate image descriptions have been developed by the National Center on Accessible Materials (NCAM), a…

In this investigation, we (a) define the desirable features of publication-quality, single-case design graphs based on recommendations in the scholarly literature, (b) suggest GraphPad Prism as a suitable graphing program for creating graphs with those features, and (c) develop and validate a video-modeling tutorial designed to train behavior…

In understanding upper secondary school students' interpretations of information in graphical representations of a distance--time graph and an ECG graph, little attention has been paid to the analysis of the condition of the conceptual development related to their utterances. Understanding this better can help improve the teaching of…

Educational environments continue to evolve rapidly to address the needs of diverse, growing student populations while embracing advances in pedagogy and technology. In this changing landscape, ensuring consistency among the assessments for different offerings of a course (within or across terms), providing meaningful feedback about student…

Spontaneity criteria for processes with useful (especially electrical) work have been discussed based on total differentials of thermodynamic functions. Reaction Gibbs energy ([Delta][subscript r]G) and electrochemical reaction Gibbs energy ([Delta][subscript r]G~) have been juxtaposed. Three-dimensional graphs showing the dependencies of…

Single-case data are frequently used in school psychology. In research, single-case designs allow experimenters to provide rigorous demonstrations of treatment effects on a smaller scale and with more precise measurement than traditional group experimental design. In practice, single-case data are used to evaluate the effects of school-based…

All methodologies for detecting plagiarism to date have focused on the final digital "outcome", such as a document or source code. Our novel approach takes the creation process into account using logged events collected by special software or by the macro recorders found in most office applications. We look at an author's interaction…

It is common for high school physics teachers to comment on the challenges they face in supporting students' graph drawing skills, knowing their importance for the study of physics. This paper suggests a novel and alternative way to support students to develop their graph drawing skills as well as teach them about sound, frequency, and amplitude.…

Given the centrality of data visualizations in communicating scientific information, increased emphasis has been placed on the development of students' graph literacy--the ability to generate and interpret data representations--to foster understanding of domain-specific knowledge and the successful navigation of everyday life. Despite prior…

In this article, a numerical method integrated with statistical data simulation technique is introduced to solve a nonlinear system of ordinary differential equations with multiple random variable coefficients. The utilization of Monte Carlo simulation with central divided difference formula of finite difference (FD) method is repeated n times to…