We present the theoretical argument that the use of mathematics in physics can be productively conceptualized as using a language and that learning to make sense of physics equations and appropriating them into novel scientific inquiry can be understood as a process of learning to read fluently with a high level of reading comprehension and to…

By telling autoethnographic stories, the author reflects upon her 16 years of EFL teaching and four years of MSc TESOL and PhD Education studies. Teacher intuition has played an important role in guiding her to make pedagogical decisions and judgments. Several teaching activities and designs are presented to demonstrate how the author followed her…

To design and improve instruction in mathematical proof, mathematics educators require an adequate definition of proof that is faithful to mathematical practice and relevant to pedagogical situations. In both mathematics education and the philosophy of mathematics, mathematical proof is typically defined as a type of justification that satisfies a…

In the first 20 years of the 21st century, research on morality grew exponentially in social sciences and related fields. A corresponding upsurge in the field of moral education has not been observed. It appears that there is a widening gap between the science of morality and the field of moral education, which once were closely interconnected…

Students often struggle with the concept of dependence of events or random variables. We present a simple coin flipping game that yields surprising results due to the dependencies within the game. The game is simple enough for young children to understand and play, yet complex enough to yield results that are counterintuitive to even most graduate…

This article contains 15 "takeaways" about how to teach organic creativity, from actual teachers with several hundred total years of experience. Teachers of English, physics, Advanced Placement Calculus, science, theater, the visual arts, dance, school administration, school counseling, educational psychology professing, world languages,…

Structural reasoning is a combined ability to "look for structures, recognize structures, probe into structures, act upon structures, reason in terms of general structures, and see how a piece of knowledge acquired resolves a perturbation experienced" (Harel and Soto, 2017). The purpose of this study was to explore the cognitive…

This paper describes our work to determine the naturalistic images that first-time second-semester university calculus students possess for series convergence. We found that the students we interviewed most frequently determined whether a series converged by imagining a process of appending summands into a running total and examining whether this…

Young children encounter uncertainty and challenges on a daily basis; through their intuitions, experiences and experimentation they construct knowledge, skills and dispositions towards probabilistic concepts. The aim of this exploratory ethnographic study is to identify how young children engage with probabilistic thinking and reasoning while…

Students' understanding of forces in circular motion is often incomplete. The problems are not limited to confusions about centripetal acceleration and centrifugal forces. This paper considers possible effects of different interventions by a teacher who has discovered the many types of free-body diagrams drawn by students for circular motion in a…

Aristotle argued that emotions should be controlled according to the principle of moderation to realize virtue (human excellence). This study examines moral education in Korea, which is grounded in the ethics of Aristotle and values reason in moral judgment. The advantages and disadvantages of specific approaches are analyzed by categorizing moral…

Teacher empathy has proven to be highly relevant for the educational process and for educational outcomes, while integrating it into the teacher practicing process is challenging. This study suggests using PSTs' (pre-service students) incorrect responses as a pedagogical tool for improving empathy awareness among them so that PSTs can feel empathy…

One goal of inquiry-oriented instruction is student engagement with others' mathematical ideas. This paper analyzes a relatively short episode in which students engaged with others' ideas; the instructor facilitated engagement in order to support students in making mathematical progress. Students expressed some bafflement pertaining to the…

This scholarly personal narrative explores the use of contemplative practices by teachers to support the development of authentic relationships with their students. The narrative demonstrates the value of contemplative practices in education by telling the story of the author's first seven years as a Waldorf teacher and the contemplative practices…

Continuing our critique of the classical derivation of the formula for the area of a disk, we focus on the limiting processes in geometry. Evidence suggests that intuitive approaches in arguing about infinity, when geometric configurations are involved, are inadequate, and could easily lead to erroneous conclusions. We expose weaknesses and…