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…

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…

We conducted a comprehensive synthesis of computer-assisted instruction (CAI) research that aimed to facilitate the learning of mathematical word problem solving involving elementary and secondary school students with learning disabilities or difficulties in mathematics. We examined a total of 13 studies under the four instructional categories:…

In this paper we examine how facilitators' prior experiences as mathematics teachers frame their work when facilitating a practice-based professional development (PD) for the first time. We focus on the experiences of a novice facilitator of StoryCircles, a professional learning process in which teachers collectively script and visualize a…

Hull-House was a unique social experiment by which Jane Addams realized her egalitarian vision for a shared civic life. Facing soaring social problems of the early twentieth century, Hull-House's most important mission was to help new immigrants learn the rule of self-government and become successful drivers of it. Hull-House was an unusual group…

Complexities of social problems in our globalised world pose new educational challenges, including how to empower citizens for active engagement with socioscientific issues. This study describes the analysis and discussion of an activist video as the first phase in an activist education programme. Participants were 104 preservice primary teachers…

Basic mathematic skills at the early age are foundational for later learning. Many students with autism spectrum disorder (ASD) struggle in academic learning without sufficient support. Research in the area of concrete manipulatives--tangible representations of abstract concepts--has been found effective. In addition, promising research has…