Mathematics is a creative process, and unfortunately, that process is often hidden from students of the discipline. This is certainly the case in the area of mathematics commonly referred to as abstract algebra. Current pedagogy conceals from the student many of the great ideas generated by significant problems in the history of the discipline. In…

The aim of this article is to establish some interesting inequalities involving arithmetic functions.

The standard approach to the general rules for differentiation is to first derive the power, product, and quotient rules and then derive the chain rule. In this short article we give an approach to these rules which uses the chain rule as the main tool in deriving the power, product, and quotient rules in a manner which is more student-friendly…

Fox, Ericsson, and Best's (2011) thoughtful justification of the use of think-aloud protocols for revealing the stream of consciousness comes on the centennial of the death of William James, history's greatest practitioner and advocate of introspection. This confluence naturally invites speculation about how James might have responded to the…

Youths in residential care have likely experienced trauma as they have had atypical and disruptive events occur in their lives that has contributed to their out-of-home placement. For people who have been traumatized, the regulation of emotions is an important feature of their recovery. This article presents a model that traces phases from…

This commentary highlights important contributions of four empirical investigations of how people sort through the masses of information that are now available to them and find what they need to solve some problem or make some decision. These studies demonstrate the impact of differences among information sources and the role that these…

Who, rather than what, decides what giftedness is? The academic world traditionally focuses on theoretical descriptors whereas society as a whole is more interested in practical function. This partly divided focus is becoming increasingly critical and problematic as economies are becoming global and the political objective is to create a knowledge…

Johnnella Butler writes here that the title of this article "Two Steps Forward, One Step Backward," expresses the "wicked problem" of diversity as a concrete goal in higher education. The concept of the "wicked problem," is a term coined in the late 1960s by social planners. Consulting Wikipedia, as so many of our…

The full promise of class room learning is dependent on its ability to incorporate 21st century skills in its instructional design, delivery and implementation. In this increasingly competitive global economy, it is not enough for students to acquire subject-level mastery alone. Skills like creative thinking, problem-solving, communication and…

This study investigated the effects of working in dyads and their associated gender composition on performance (solution rate and time) and process variables (number of impasses, number of passed solutions, and number of problem solving suggestions and interactions) in a set of classic insight problem solving tasks. Two types of insight problems…

To what extent can instructional design be based on principles for instilling a culture of problem solving and conceptual learning? This is the main focus of the study described in this paper, in which third grade students participated in a one-year course designed to foster problem solving and mathematical reasoning. The design relied on five…

This study examined the knowledge levels of prospective mathematics teachers about the concepts of degree and radian, which are among the angle measuring units that constitute the basis of trigonometry, and the relationships between those concepts. The study group consisted of 93 prospective mathematics teachers attending a state university in…

The past two decades have witnessed increasing global acceptance of the important role that capable leadership plays in education reform and school improvement. Consequently, policymakers internationally have actively sought means of strengthening capacity for school-level leadership, with a particular focus on the design of more effective…

This study investigated the relationship between problem familiarity and students' learning in a problem-based course. Problem familiarity in this study refers to the extent to which a problem fits with students' prior knowledge and experiences. As part of regular course work, 172 students were given two problems on different occasions.…

Problem-Based Learning (PBL) has been one of the popular pedagogical strategies these years. PBL is about students connecting disciplinary knowledge to real-world problems--the motivation to solve a problem. To recognize general elements and typological differences of language in translation is the motivation to solve real problems such as…