The goal of our research program is to explicate the learning of mathematical concepts in ways that are useful for instructional design and to develop design principles based on those explications. I review one type of concept and our elaboration of reflective abstraction, coordination of actions (COA) that accounts for its construction. I then…

Human thought can be characterised as being situated in the 'space of reasons'. That is to say that human thought is guided by the norms of theoretical and practical rationality which, in turn, enable autonomous thinking. But how do children learn to navigate the space of reasons? Building on the work of Tugendhat and Bakhurst, among others, we…

This article reviews two aspects of human learning: (1) people draw inferences that appear to rely on hierarchical conceptual representations; (2) some categories are much easier to learn than others given the same number of exemplars, and some categories remain difficult despite extensive training. Both of these results are difficult to reconcile…

Humans are sensitive to the properties of individual items, and exemplar models are useful for capturing this sensitivity. I am a proponent of an extension of exemplar-based architectures that I briefly describe. However, exemplar models are very shallow architectures in which it is necessary to stipulate a set of primitive elements that make up…

The construct of metacognition appears in an ever increasing number and range of contexts in educational, developmental, and cognitive psychology. Can it retain its status as a useful construct in the face of such diverse application? Or is it merely an umbrella term for diverse mental phenomena that are loosely if at all connected? Here I argue…

Ambridge argues that the existence of exemplar models for individual phenomena (words, inflection rules, etc.) suggests the feasibility of a unified, exemplars-everywhere model that eschews abstraction. The argument would be strengthened by a description of such a model. However, none is provided. I show that any attempt to do so would immediately…

It's not uncommon for people to make reference to atmospheres, including in relationship with educational spaces. In this article, we investigate educational atmospheres by turning to Western and Chinese literature on the air and wind. We pursue this task in three phases. First, we examine the Western literature to see the possible strings of…

After describing Wittgenstein's notion of "certainty", in this article I provide four arguments to demonstrate that no certainty can be acquired at will. Specifically, I argue that, in order to assimilate a certainty, it is irrelevant whether the individual concerned (1) has found a ground that seemingly justifies that certainty; (2) has…

Conventional coordinate systems are often considered representational tools for reasoning about mathematical concepts. However, researchers have shown that students experience persistent difficulties as they engage in graphing activity. Using examples from research and textbooks, we present a framework based on a conceptual analysis of the use of…

Ambridge argues that there is widespread agreement among child language researchers that learners store linguistic abstractions. In this commentary the authors first argue that this assumption is incorrect; anti-representationalist/exemplar views are pervasive in theories of child language. Next, the authors outline what has been learned from this…

Two key research issues in the field of causal learning are how people acquire causal knowledge when observing data that are presented sequentially, and the level of abstraction at which learning takes place. Does sequential causal learning solely involve the acquisition of specific cause-effect links, or do learners also acquire knowledge about…

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…

Purpose: The purpose of this paper is to illustrate how associationism mistakenly assumes that direct experience is possible; that is, there is expectation-free observation and association without prior expectation. Thus, associationism assumes that learning involves the absorption of information from the environment itself. However, contrary…

Many technological artifacts (e.g., humanoid robots, computer agents) consist of biologically inspired features of human-like appearance and behaviors that elicit a social response. The strong social components of technology permit people to share information and ideas with these artifacts. As robots cross the boundaries between humans and…

The ability to cite reasons, to justify claims and give support to arguments is seen as primary characteristics of a critical thinker. This paper discusses how the "Elements of Reasoning" is employed with Socratic Questioning to develop critical thinking in the language classroom. The principles that guide the questioning are laid out…