One of the main goals of an individual participant data meta-analysis (IPD-MA) of intervention studies is to investigate whether treatment effect differences are present, and how they are associated with patient characteristics. Examining treatment heterogeneity due to a continuous covariable (e.g., BMI or age) may be challenging, since there is…

Approximate mathematical treatments are commonly taught in undergraduate chemistry, but the validity ranges of these approximations have rarely been properly defined. We present error contour plots of commonly used quadratic approximations for calculating equilibrium proton concentrations of monoprotic acids. Students and instructors can easily…

With the increased number of MOOC offerings, it is unclear how these courses are related. Previous work has focused on capturing the prerequisite relationships between courses, lectures, and concepts. However, it is also essential to model the content structure of MOOC courses. Constructing a precedence graph that models the similarities and…

Word-problem features such as text complexity, charts and graphs, position of the unknown, calculation complexity, irrelevant information, and schemas impact word-problem performance. We compared the word-problem performance of typically achieving (TA) students and students with mathematics difficulty (MD). First, we measured the word-problem…

The authors take a mathematical journey into polygonal chains to provide an algorithm that will construct a closed polygonal chain where the lines intersect exactly an exactly an odd number of times.

Several researchers have promoted reimagining functions and graphs more quantitatively. One part of this research has examined graphing "conventions" that can at times conflict with quantitative reasoning about graphs. In this theoretical paper, we build on this work by considering a widespread convention in mathematics teaching: putting…

This study aims to describe how preservice secondary mathematics teachers (PSMTs) reason about different function representations. The study focuses on two PSMTs' reasonings across static and dynamic representations of functions. Sfard's (2008) Theory of Commognition guided our analysis. Findings indicate that while static representations restrict…

A growing emphasis on computational thinking worldwide necessitates student proficiency in creating algorithms. Focusing on the use of counterexamples for developing student-invented algorithms, I reanalyze two pieces of data from previously published research, pertaining to two different cases of students' algorithmatizing activity. In both…

Aim/Purpose: This study seeks to present a learning model of discrete mathematics elements, elucidate the content of teaching, and validate the effectiveness of this learning in a digital education context. Background: Teaching discrete mathematics in the realm of digital education poses challenges, particularly in crafting the optimal model,…

A simple in-class demonstration of integral Calculus for first-time students is described for straightforward whole number area magnitudes, for ease of understanding. Following the Second Fundamental Theorem of the Calculus, macroscopic differences in ordinal values of several integrals, [delta]"F"(x), are compared to the regions of area…

Graphical representations of data are common in many disciplines. Previous research has found that physics students appear to have better graph comprehension skills than students from social science disciplines, regardless of the task context. However, the graph comprehension skills of physics students have not yet been compared with (veterinary)…

The paper discusses a certain type of competitions based on distance interaction of a participant with simulation models of concepts from discrete mathematics and computer science. One of them is the "Construct, Test, Explore" (CTE) competition, developed by the authors, the other is the Olympiad in Discrete Mathematics and Theoretical…

The author focused on solving problems of third-degree price discrimination under a monopoly by integrating microeconomic theory and spreadsheet modeling. Price discrimination refers to a firm situation in which the same good is sold to different groups of consumers at different prices. First, the author included an introductory math background…

Studying students' performance in learning differentiability is essential since it requires them to perform proceptual thinking. This case study research investigates students' proceptual thinking outcomes in learning the differentiability concept using Desmos Classroom Activities (DCA) based on the Three Worlds of Mathematics (TWM) framework. In…

Current network design problems can be solved by offline or online methods. Offline methods are criticized for their complexity and in flexibility, whereas online methods lack guaranteed optimality. Non-blocking properties, which are typically studied in switching structures, could be used to evaluate the capability of a switching structure to…