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…

Spark, one of the products offered by MyQ (formerly Plethora), is a game-based platform meticulously designed to introduce students to the foundational concepts of computer science. By navigating through logical challenges, users delve into topics like abstraction, loops, and graph patterns. Setting itself apart from its counterparts, Spark boasts…

This paper argues that abductive reasoning has a central place in theorizing Health Professions Education. At the root of abduction lies a fundamental debate: How do we connect practice, which is always singular and unique, with theory, which describes the world in terms of rules, generalizations, and universals? While abduction was initially seen…

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…

During language acquisition children generalise at multiple layers of granularity. Ambridge argues that abstraction-based accounts suffer from lumping (over-general abstractions) or splitting (over-precise abstractions). Ambridge argues that the only way to overcome this conundrum is in a purely exemplar/analogy-based system in which…

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…

Previous research on open-mindedness, whether by critical thinking researchers, philosophers of education, or intellectual virtue theorists, has not sufficiently addressed the challenge posed by cognitive bias, particularly motivated reasoning. How can students develop their open-mindedness when they are often motivated to preserve their prior…

Kant's commitment to autonomy raises difficult questions about the very possibility of Kantian moral education, since appeal to external pedagogical guidance threatens to be in contradiction with autonomous virtue. Furthermore, moral education seems to involve getting good at something through repetition; but Kant seems to eschew the notion of…

Individuals draw conclusions about possibilities from assertions that make no explicit reference to them. The model theory postulates that assertions such as disjunctions refer to possibilities. Hence, a disjunction of the sort, "A or B or both," where "A" and "B" are sensible clauses, yields mental models of an…

The expectation for doctoral research to contribute to knowledge is closely related to examiners' attention to conceptual and theoretical components in the thesis. These components require abstract thinking and familiarity with a number of research ideas that are difficult to teach and learn. We argue that these can be made more accessible to…

Background: The term individual differences refers to the physical, behavioral, cognitive, social, and emotional attributes that make each human unique. Late adolescence to young adulthood represents a time of significant neurobiological and cognitive transformations that contribute further to human variability. Those transformations include an…

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…

Students' capacity for making evaluative judgements of their own work is widely acknowledged as central to their learning within programmes as well as being vital to their subsequent professional practice. In higher education literature, the act of evaluative judgement is usually portrayed as a process of deliberative, analytical reasoning…

The syntactic behaviour of human beings cannot be explained by analogical generalization on the basis of concrete exemplars: analogies in surface form are insufficient to account for human grammatical knowledge, because they fail to hold in situations where they should, and fail to extend in situations where they need to. [For Ben Ambridge's…