The aim of this paper is to propose a method for solving head-on elastic collisions, without algebraic complications, to emphasize the use of the fundamental conservations laws. Head-on elastic collisions are treated in many physics textbooks as examples of conservation of momentum and kinetic energy.

Preparing students for the consequential ethical decisions that they will face in their careers is among the most difficult tasks of management education. I describe some of these challenges based on my book "Why They Do It: Inside the Mind of the White-Collar Criminal" and recent work in behavioral ethics. I explore why some decisions…

Wicked sustainability problems (WSPs) are an important and particularly challenging type of problem. Science and engineering education can play an important role in preparing students to deal with such problems, but current educational practice may not adequately prepare students to do so. We address this gap by providing insights related to…

What "gamification" means and what it doesn't has been addressed and described by many researchers from a variety of different perspectives in the past. Similarities and differences of the methods between "gamification" and "games" (as well as "gamification" and "game based learning") have also…

Theorists have argued instructional strategies that emphasize ill-structured problem solving are an effective means to support higher order learning skills such as argumentation. However, argumentation is often difficult because novices lack the expertise or experience needed to solve contextualized problems. One way to supplement this lack of…

"Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014) gives teachers access to an insightful, research-informed framework that outlines ways to promote reasoning and sense making. Specifically, as students transition on their mathematical journey through middle school and beyond, their knowledge and use of…

In human problem solving, there is a wide variation between individuals in problem solution time and success rate, regardless of whether or not this problem solving involves insight. In this paper, we apply computational and parameterized analysis to a plausible formalization of extended representation change theory (eRCT), an integration of…

In recent years most text books utilise either the sign chart or graphing functions in order to solve a quadratic inequality of the form ax[superscript 2] + bx + c < 0 This article demonstrates an algebraic approach to solve the above inequality. To solve a quadratic inequality in the form of ax[superscript 2] + bx + c < 0 or in the…

This article introduces a method to critical reviews and explores the ways in which problems have been formulated in knowledge production on career guidance in Denmark over a 10-year period from 2004 to 2014. The method draws upon the work of Bacchi focussing on the "What's the problem represented to be" (WPR) approach. Forty-nine…

This paper is concerned with developing a new class of generalized numbers. The main advantage of this class is that it generalizes the two classes of generalized Fibonacci numbers and generalized Pell numbers. Some new identities involving these generalized numbers are obtained. In addition, the two well-known identities of Sury and Marques which…

We articulate a student perspective on task design in mathematics education, foregrounding a dynamic relationship between intentions of task designers, teachers, and students. First, we characterize a student perspective on task design. Second, we provide theoretical perspectives that we use as tools to account for different facets of task design…

This theoretical paper suggests identity as a nexus of research on affect and discourse in mathematical learning. It broadens Sfard and Prusak's (2005) discursive definition of identity by building on an analytical framework that examines positioning of students at three levels: the objects described, the interactions achieved, and the alignment…

Eliciting and responding to student thinking are high-leverage practices that have powerful implications for student learning. However, they are difficult to enact effectively, particularly for novices, and more research is needed to understand how teacher education can support teachers in developing these skills. This study examined ways…

The advancement of computer and communication technologies has enabled researchers to conduct and analyze the learning process of posing problems. This study investigates what learners think while posing problems as sentence integration in terms of intermediate products as well as the posed problems as the resultant product. Problem posing as…

A commonly accepted claim in mathematics education is that there is a relationship between the cognitive demand of mathematical task enactments and students' subsequent learning. One study often cited to support this claim is Stein and Lane (1996), and in 44% of those citations, Stein and Lane (1996) is the sole reference provided. Citation…