The "object lesson" is a particular teaching method that was widespread in Europe and the westernised world during the nineteenth century, which was variously adapted according to national contexts under the name of "Anschauungsunterricht, leçon de choses, lezione di cose, and lección de cosas." Based on the intuitive…

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…

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,…

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…

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…

How should our students think about external forcing in differential equations setting, and how can we help them gain intuition? To address this question, we share a variety of problems and projects that explore the dynamics of the undamped forced spring-mass system. We provide a sequence of discovery-based exercises that foster physical and…

The formal acceptance of a mathematical proof is based on its logical correctness but, from a cognitive point of view, this form of acceptance is not always naturally associated with the feeling that the proof has necessarily proved the statement. This is the case, in particular, for proof by contradiction in geometry, which can be linked to a…

Taking as a point of departure that consciousness of time is pivotal to historical consciousness, this paper explores intuitive temporal experiences as opposed to the less intuitive temporal experience connected with historical consciousness. The intuitive daily/cyclic, social and mythical temporal awareness is being opposed to historical…

The purpose of this study is to explore the happiness principles and educational thoughts of Buddha and Laozi. The significance of the study is to provide the basic theories and the worthy resources of contemporary and future education, especially happiness education and moral education, for educational theorists and practitioners in the world. To…

Research in psychology and in mathematics education has documented the ubiquity of "intuition traps" -- tasks that elicit non-normative responses from most people. Researchers in cognitive psychology often view these responses negatively, as a sign of irrational behaviour. Others, notably mathematics educators, view them as necessary…

Structural concepts are fundamentals of civil engineering for students to learn, for lecturers to teach and for engineers to use. Many students however find it difficult to understand structural concepts due to their abstract nature. "Seeing and Touching Structural Concepts" has been developed as an approach to help civil engineering…

We use analogies to provide introductory laboratory students intuition into measurement uncertainties. Using a battery-resistor circuit we discuss uncertainty concepts and derive expressions for uncertainty of the mean and sums of uncertainties. Finally, we draw attention to the fact that the interpretation of standard deviation as uncertainty…

Recently, there has been increasing pedagogical interest in the qualities and characteristics of movement. This article examines these qualities and characteristics in terms of John Dewey's distinction between abstract, linguistic "significant" meanings and concrete, embodied "imminent" meanings. Imminent meanings are comprised…

In response to the authors, I demonstrate how threshold concepts offer a means to both contextualise teaching and learning of quantum physics and help transform students into the culture of physics, and as a way to identify particularly troublesome concepts within quantum physics. By drawing parallels from my own doctoral research in another area…