The study outlines the early-stage development of a free-response General Relativity Concept Inventory (GRCI), an educational instrument designed to test for conceptual understanding of General Relativity. Data were collected for the study by having 26 participants from General Relativity courses work through the questions on the GRCI. Interviews…

Due to the learning paradox, students cannot have real difficulty in understanding a mathematical concept that they have not yet understood. There is a gap between real difficulties, directly experienced by students, and illusionary ones, only observed by researchers. This paper aims to offer a critical reflection on our understanding of the term…

An equal-armed balance at equilibrium--the bar is horizontal--tips into disequilibrium upon displacing a weight. Equilibrium is restored by reversing that move--putting the weight back where it was, or doing the same on the other side. Piaget adopted the idea of equilibration to describe how the intellect, in relating to the world, develops.…

When you look at an image, what do you see? What does the image say to you? What do you think about? What meaning do you infer? These questions may blur together, but they can be expanded individually and uniquely into a multitude of responses. Your initial thoughts are yours. You are silently debating meaning within yourself. If I interject a new…

Human creativity and ingenuity partly depend on divergent thinking -- the ability to generate many varied, original, and elaborate responses. Prior research has found ample evidence of an effect of cognitive factors, including the organization of semantic networks and associative ability, on divergent thinking. Less is known, however, about how…

This article presents a networking of two theories, the Extended Theory of Mathematical Connections (ETC) and the Onto-semiotic Approach (OSA). In particular, concordances and complementarities are identified in the respective conceptions of mathematical connections, as a result of applying these theoretical frameworks to a student's response…

Certain aspects of theoretical frameworks in mathematics education can remain unexplained in the literature, hence unnoticed by the readers. It is thus interesting to participate in a dialogue where they can be discussed and compared in terms of the aims, objects studied, results and their relation to teaching. This study is focused on how APOS…

Does language have a role to play in conceptual development, and if so, what is that role? Understanding the contents of another person's mind parallels the development in early childhood of mental state language. Does the conceptual understanding get reflected in and drive the language development, or does the language allow the representation of…

This study draws on four case studies of young children in order to explore the relationship between children's action schema [Athey, C. (1990). "Extending though in young children: A parent-teacher partnership." London: Paul Chapman] and their developing speech, language and communication. What emerged was a connection through…

Spatial thinking has roles to facilitate learners to remember, understand, reason, and communicate objects and the connections among objects that are represented in space. This research aims to analyze the spatial thinking process of students in constructing new knowledge seen from the field-independent cognitive style learners based on…

This study investigated the cognitive and social processes through which high school students acquire the differential concepts through communication in a dynamic geometry environment through some cases. Additionally, we observed how a dynamic geometry environment affects these processes. To achieve this objective, eight students were recruited by…

The reconciliation of theories of concepts based on prototypes, exemplars, and theory-like structures is a longstanding problem in cognitive science. In response to this problem, researchers have recently tended to adopt either hybrid theories that combine various kinds of representational structure, or eliminative theories that replace concepts…

The nature of knowledge in vocational education is often described in dichotomies such as theory versus practice or general versus specific. Although different scholars now acknowledge that vocational knowledge is more than putting bits of theoretical and practical knowledge together, it is still unclear how vocational knowledge should be…

For centuries, humans have contemplated the minds of gods. Research on religious cognition is spread across sub-disciplines, making it difficult to gain a complete understanding of how people reason about gods' minds. We integrate approaches from cognitive, developmental, and social psychology and neuroscience to illuminate the origins of…

One of the guiding questions in this discussion is how is it that certain ideologies become so ingrained and resistant to challenge and scrutiny? The central assumptions sustaining the argument conceive curriculum--the backbone of educational practice--to be an expression of ideological activity; the understanding of ideology as lived experience;…