The Gauss-Lucas Theorem is a classical complex analysis result that states the critical points of a single-variable complex polynomial lie inside the closed convex hull of the zeros of the polynomial. Although the result is well-known, it is not typically presented in a first course in complex analysis. The ease with which modern technology allows…

From the late eighteenth through the end of the nineteenth century, educational philosophers and practitioners debated the benefits and shortcomings of the use of emulation in schools. During this period, "emulation" referred to a pedagogy that leveraged comparisons between students as a tool to motivate them to higher achievement. Many…

Physics education research has a tradition of studying problem solving, exploring themes such as physical intuition and differences between expert and novice problem solvers. However, most of this work has focused on traditional, or well-structured, problems, similar to what might appear in a textbook. Less work has been done with open-ended, or…

In this article, Monica Housen describes how she uses Guess the Number of . . . , a game that develops estimation skills and persistence to provide a fun, to provide a meaningful experience for her high school students. Each week she displays objects in a clear plastic container, like those for pretzels sold in bulk. Students enter a…

This paper proceeds from the premise that film can be educational in a broader sense than its current use in classrooms for illustrative purposes, and explores the idea that film might function as a form of education in itself. To investigate the phenomenon of film as education, it is necessary to first address a number of assumptions about film,…

Creativity and giftedness in mathematics education research are topics of an increased interest in the education community during recent years. This introductory paper to the special issue on Mathematical Creativity and Giftedness in Mathematics Education has a twofold purpose: to offer a brief historical perspective on the study of creativity and…

STEAM, where the "A" represents arts and humanities, is considered a transdisciplinary learning process that has the potential to increase diverse participation in science, technology, engineering, and math (STEM) fields. However, a well-defined conceptual model that clearly articulates essential components of the STEAM approach is…

What is relational reasoning? Why is it critical to consider the role of relational reasoning in students learning and development in science, technology, engineering, and mathematics (STEM)? Moreover, how do the particular contributions populating this special issue address the pressing societal needs and offer guidance to researchers and…

The use of free energy plots to understand the concept of thermodynamic equilibrium has been shown to be of great pedagogical value in materials science. Although chemical equilibrium is also amenable to this kind of analysis, it is not part of the agenda of materials science textbooks. Something similar is found in chemistry branches, where free…

Constructivist learning theories have become the dominant ideology in educational circles, in part, because there is a primacy on the agential individual with its definite identity. However, precisely because "to construct" is a "transitive" verb, it occludes the fact that in learning and development, we come to know something…

Objective assessment of the quality of available educational resources presupposes the existence of specific quality standards and specific evaluation tools which consider the specificities of digital products with educational ambitions. The study presents the results of research conducted on a representative sample of teachers who commented on…

An instructional designer's values about instructional methods can be a curse or a cure. On one hand, a designer's love affair for a method may cause them to use that method in situations that are not appropriate. On the other hand, that same love affair may inspire a designer to fight for a method when those in power are willing to settle for a…

Successful inquiries using the C3 Framework depend on compelling questions that structure an inquiry and supporting questions that allow the inquiry to unfold coherently. The Inquiry Design Model (IDM) reflects the three elements common in inquiry teaching and learning. Those elements--questions, tasks, and sources--are represented in a one-page…

Little research has been done on philosophical implications of the middle voice of early Greek and certain non-Western indigenous languages. In particular, the potential of such a medial ontology has yet to be even explored, much less realized, within the context of interdisciplinary studies. As a linguistic structure indicating an ambiguous…

This chapter introduces gamification and a model for utilizing game design elements for leadership competency development.