For a given rational number r, a classical theorem of Niven asserts that if cos(rp) is rational, then cos(rp) [element-of] {0,±1,±1/2}. In this note, we extend Niven's theorem to quadratic irrationalities and present an elementary proof of that.

In this essay, Ross Collin offers ethics-focused readings of Anton Chekhov's popular short stories "The Schoolmistress" and "The Teacher of Literature." Chekhov shows in the two stories how teaching can inhibit teachers' flourishing. That is to say, teaching under bad conditions can draw teachers into moral…

Science learning requires students to build new mental models of imperceptible mechanisms (photosynthesis, circadian rhythms, atmospheric pressure, etc.). Since mechanisms are structurally complex and dynamic, building such mental models requires mentally simulating novel structures, their state changes, and higher-order transformations…

"What 'is' marketing?" Perusal of the marketing literature reveals that "marketing" has been defined and characterized in multiple, often inconsistent but typically ambiguous, ways that have evolved over time. The present essay argues that characterizing marketing as a transdisciplinary body of knowledge formally captures its…

This article presents a challenge to notions of clarity--and its relation to understanding--within the college composition classroom by relying on Lacanian pedagogical theory. While the field of composition has issued criticisms against clarity in student writing, there has been less emphasis on interrogating clarity in instruction. By delineating…

In this paper, the author will develop a more comprehensive notion of truth, one that goes beyond the epistemological correspondence theory, and the author will argue for the importance of authentication as a crucial extension of truth, especially in a posttruth climate. Hannah Arendt observes, "facts need testimony to be remembered and…

In "Reel to Real: Race, Class, and Sex at the Movies," a collection of profound and paradigm-shifting essays on film, Bell Hooks (1996) writes, "Whether we like it or not, cinema assumes a pedagogical role in the lives of many. It may not be the intent of a filmmaker to teach audiences anything, but that does not mean that lessons…

While textbooks may remain important tools for information delivery, how can educators find and present interesting and relevant content to eighteen to twenty-something-year-olds? If learning is to take place, capturing and maintaining student attention, interest, and active engagement is a primary challenge in the classroom. Given this reality,…

High expectations are placed on Climate Change Education (CCE), ranging from emotionally and practically preparing young people for the changes ahead, to supporting them in becoming climate-friendly actors. To address these challenges and inspire new approaches, this paper introduces a typology of utopian knowledge into the practice of CCE. It…

This article provides insight into the process and implementation of a professional development workshop that was created for and provided to educators who were interested in implementing more playful pedagogies in their educational settings. The workshop focused primarily on meeting the needs of all learners through meaningful and engaging…

As the "Journal of Museum Education" reaches its fifty-year publication milestone, this article traces the roots of the Museum Education Roundtable (MER) and the organization's resulting journal, both critical to professionalizing and shaping the field of museum education. Central to this publishing effort were the relationships amongst…

Can Aristotle's idea of practice be made fruitful for music pedagogical action in schools? That this is the case is repeatedly asserted in the music pedagogical discussion. This article takes up this assertion and develops a proposal for class music making based on Aristotle's theory of action.

In this paper, Katja Castillo approaches the phenomenon of teaching through an analysis of Emmanuel Levinas's unedited conference notes titled "Les nourritures," "Les enseignements," and "L'écrit et l'oral." Levinas's thinking prior to the publication of his major works provides an entry point to his philosophy. In…

This paper initiates a teaching sequence that focuses on building up equivalent definitions to the standard ones for the limit concept in Real Analysis. It comprises two parts: The first provides a classroom assignment where students, guided by Analysis lecturers, are led to develop an alternative definition to the [epsilon] - [delta] one for…

This discussion introduces a heuristic to guide writing instruction with adolescents and young adults. Our framework, called "Open World Writing," consists of six writing territories (vision, material, design, voice, flow, polish) that provide focus and clarity for writing and educators working across academic and creative writing…