The cosine theorem is used in solving triangulation problems and in physics when solving problems of addition of unidirectional oscillations. However, this theorem is used only for the analytical calculation of triangles or when solving problems of adding two oscillations. Here we propose a generalization of the cosine theorem for the case of…

In this regular "American Educator" column, findings from the field of cognitive science that are strong and clear enough to merit classroom application are considered. Individuals vary in their views of what students should be taught, but there is little disagreement on the importance of critical thinking skills. In free societies, the…

The distant magnetic field of a magnetic dipole is usually derived via the magnetic vector potential and substantial vector calculus. This paper presents an alternate proof that is less mathematically intensive, and that ties together various problem-solving tricks (the principle of virtual work, observation that only instantaneous quantities…

When students are solving problems they often turn to examples when they need assistance. Examples are helpful because they illustrate how a problem can be solved. However, when examples are very similar to the problems, students default to copying the example solutions, which hinders learning. To address this, prior work has investigated the…

The purpose of this note is to describe several challenging problems in Euclidean geometry. The note also contains author's solution sketches to the two problems.

Prior research has demonstrated the importance of forecasting to creative problem-solving performance. Less is known about how case analysis and outcome valence impact forecasting performance. In this study, 266 participants were asked to assume the role of a Marketing Director of a clothing company and develop a marketing campaign for entering a…

In a recent submission to "The Physics Teacher," we related how trigonometric identities can be used to find the extremes of several functions in order to solve some standard physics problems that would usually be considered to require calculus. In this work, the functions to be examined are polynomials, which suggests the utilization of…

Metacognition, or the ability to "think about thinking," plays a significant role in the performance of first-year design students. Although the number of studies that focus on metacognition has increased in the past decade, additional studies are needed to more fully investigate metacognition and the use of metacognitive strategies in…

There are many problems whose solution requires proof that a quadrilateral is cyclic. The main reason for writing this paper is to offer a number of new tools for proving that a particular quadrilateral is cyclic, thus expanding the present knowledge base and ensuring that investigators in mathematics and teachers of mathematics have at their…

This paper aims to provide a comprehensive analysis of publication patterns on computational thinking (CT) over two recent periods (period I: 2006-2012; period II: 2013-2018). Based on keyword analysis, a total of 3798 (period I) and 7175 (period II) keywords were found. Derived from the content analysis, a research typology of two-period keywords…

Purpose: The purpose of this paper is to discuss the possibilities of transcending individual, organizational and social problems through the prism of presence as suggested by Senge et al. (2012). Design/methodology/approach: The paper is based on the critical review of previous contributions. Findings: The idea of a learning organization seems…

This study analyses the view of students' mental models in solving mathematical problems. The study employed a literature review using well-accepted and robust guidelines. Data were collected by searching books and articles of journals. Data analysis techniques were done qualitatively. The finding of this study showed that the mental model is…

Purpose: The purpose of this practitioner paper is to explore whether the principles of Design Thinking and the Lean Startup could be employed in developing a disruptive model for delivering educational programs within higher education in a way that attempts to eliminate the multitude of problems facing this industry, while simultaneously adhering…

The present study aims to examine mathematical creativity in students' work in geometry. Research conducted was based on two aspects: (a) examining the influence of geometrical figure apprehension on the production of multiple solutions and (b) how the necessity to construct auxiliary lines in the given shape promotes the production of multiple…

The importance of mathematical problem posing has been acknowledged by many researchers. In this theoretical paper, we want to capture different meanings and aspects of problem posing by approaching it from three different levels: (1) by comparing definitions, (2) by relating it to other constructs, and (3) by referring to research and teaching…