This theoretical paper sets forth two "aspects of predication," which describe how students perceive the relationship between a property and an object. We argue these are consequential for how students make sense of discrete mathematics proofs related to the properties and how they construct a logical structure. These aspects of…

Inquiry is promoted as a way to engage students so that they learn more deeply; inquiry is also an end in itself, introducing students to the research process and the behaviors of a mathematician. This article reflects on an individual exploratory project used in a sophomore-level number theory course, examining how it supported student inquiry…

A number of quality theories have been utilized to provide a framework or background for studies of online learning and instruction. While many of these theories have been useful, several have been modified as new technologies have been invented and adopted in schools. This paper examines some of the most prominent theories of online learning and…

In the Spring of 2011, two of the authors of this paper taught number theory courses at their respective institutions. Twice during the semester, students in each class submitted proofs of two to three theorems to be peer reviewed by students in the other class. Each student wrote anonymous and formal referee reports of the submitted theorems,…

Discusses the importance of the early history of Greek mathematics to education and civic life through a study of the Parthenon and dialogues of Plato. "The Parthenon and Liberal Education" seeks to restore the study of mathematics to its original place of prominence in the liberal arts. To build this case, Geoff Lehman and Michael…

The use of established and discipline-specific theories within research and practice is an indication of the maturity of a discipline. With computing education research as a relatively young discipline, there has been recent interest in investigating theories that may prove foundational to work in this area, with discipline-specific theories and…

Recent educational studies in mathematics seek to justify a thesis that there is a conflict between students' intuitions regarding infinity and the standard theory of infinite numbers. On the contrary, we argue that students' intuitions do not match but to Cantor's theory, not to any theory of infinity. To this end, we sketch ways of measuring…

This paper deals with a brief history of probability theory and its applications to Jacob Bernoulli's famous law of large numbers and theory of errors in observations or measurements. Included are the major contributions of Jacob Bernoulli and Laplace. It is written to pay the tricentennial tribute to Jacob Bernoulli, since the year 2013…

This paper explores the development of the method of partial fraction decomposition from elementary number theory through calculus to its abstraction in modern algebra. This unusual perspective makes the topic accessible and relevant to readers from high school through seasoned calculus instructors.

Accepted definitions of educational leadership practice typically view it as influence to achieve organisational goals. Such definitions have been widely used over the last 30 years. During that time, the number of educational leadership theories/models has increased and cover the many aspects of educational leadership all of which implicitly or…

This article builds on conclusions drawn in the article "Eyeless in America," by the same author and considers how 50 American films about the wars in Iraq and Afghanistan intended to function as what Jacques Ellul called "integration propaganda" fared. This article considers and rejects a number of theories about why most…

Emerging technologies offer an opportunity for the development, at the institutional level, of quality processes with greater capacity to enhance learning in higher education than available through current quality processes. These systems offer the potential to extend use of learning analytics in institutional-level quality processes in addition…

Larry Nucci, in his article "Character: A Multifaceted Developmental System," has outlined a model of character that focuses on 4 domains of the moral system. This response focuses on 2 issues. The first is Nucci's equation of character with moral functioning. My research has led me to propose that 3 elements are essential to any…

Career development for university research managers and administrators (RMAs) is inherently challenging in small island states. In this article, we argue that by acquiring career adaptability resources, university RMAs can address their career development needs even in contexts with a restricted labor market. We do this by first identifying the…

Avalanche studies have undergone a transition in recent years. Early research focused mainly on environmental factors. More recently, attention has turned to human factors in decision making, such as behavioural and cognitive biases. This article adds a "social" component to this human turn in avalanche studies. It identifies lessons for…