In this article, we consider certain minimization problems. If d[subscript 1], d[subscript 2] and d[subscript 3] are the distances of a boundary or inner point to the sides of a given triangle, find the point which minimizes d[subscript 1][superscript n] + d[subscript 2][superscript n] + d[subscript 3][superscript n] for positive integer n. These…

Strategies are proposed that promote use of an Integrated Applied Mathematics (IAM) approach to enhance teaching of advanced problem-solving and analysis skills. Three scenarios of 1-dimensional transport processes are presented that support using Error Function analyses when considering short time/small penetration depths in finite geometries.…

The purpose of this study was to investigate university students' conceptions of the definite integral in the process of finding the volume of a solid of revolution. The participants were four students enrolled in a university calculus course in Turkey. Data were obtained by task-based interviews, in which the participants had to work on a problem…

Despite the increasing amount of research on students' quantitative reasoning at the secondary level, research on students' quantitative reasoning at the undergraduate level is scarce. The present study used task-based interviews to examine 16 high-performing undergraduate calculus students' quantitative reasoning in the context of solving three…

The ability to solve mathematical problems has been an interesting research topic for several decades. Intuition is considered a part of higher-level thinking that can help improve mathematical problem-solving abilities. Although many studies have been conducted on mathematical problem-solving, research on intuition as a bridge in mathematical…

The purpose of these notes is to generalize and extend a challenging geometry problem from a mathematics competition. The notes also contain solution sketches pertaining to the problems discussed.

The home confinement that was imposed to reduce and control the spread of COVID-19 pandemic led educational systems to implement changes in many school activities. Teachers moved to remote teaching and relied on digital apps to present and discuss learning activities with their students. Likewise, they looked for new routes and means to follow up…

Visual thinking plays an essential role in solving problems and in learning mathematics. Many students do not understand how to graphically or geometrically represent problems and solve algebra problems. Visual thinking is the ability, process, and results of creating, interpreting, using, and imagining images and diagrams on paper or with…

Previous work has looked at the relationship between high school preparation and student performance in calculus-based introductory mechanics (physics 1) courses. Here, we extend that work to look at performance in introductory calculus-based electricity and magnetism (physics 2), and we look at the significance of what college math courses have…

Although numerous studies have investigated how technology affects academic achievement, very few have focused on the purpose of the use of technology in mathematics education. This current study examines how student teachers (STs) benefit from GeoGebra as one of the Dynamic Geometry Software (DGS) while solving continuity problems. In order to…

This study consisted of two stages. In stage A, 38 students were divided randomly into an experimental and a control group. The experimental group received lectures assisted by dynamic geometry software (DGS) and the control group received lectures using chalk and blackboard. The effects of DGS on metacognition and its components were…

The article is dedicated to solving extrema problems in teaching mathematics, without using calculus. We present and discuss a wide variety of mathematical extrema tasks where the extrema are obtained and find their solutions without resorting to differential. Particular attention is paid to the role of arithmetic and geometric means inequality in…

This study aims to explore a phenomenon of a one-off manifestation of mathematical creativity on the part of a student, against the background of her normative and not especially creative behavior--a flash of creativity. We seek to elaborate on this phenomenon in terms of the 4P (person, press, process and product) model of creativity. Namely,…

As mathematics educators we want our students to develop a natural curiosity that will lead them on the path toward solving problems in a changing world, in fields that perhaps do not even exist today. Here we present student projects, adaptable for several mid- and upper-level mathematics courses, that require students to formulate their own…

The paper investigates geometric errors students made as they tried to use their basic geometric knowledge in the solution of the Applied Calculus Optimization Problem (ACOP). Inaccuracies related to the drawing of geometric diagrams (visualization skills) and those associated with the application of basic differentiation concepts into ACOP…