Since statistical inference is a probabilistic generalization about a population analyzed on the basis of a sample, inferential reasoning demands producing reasons ("statistical" and "contextual") to substantiate and validate generalizations. To convey an understanding of students' inferential reasoning, we present a…

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…

A key property of relational representations is their "generativity": From partial descriptions of relations between entities, additional inferences can be drawn about other entities. A major theoretical challenge is to demonstrate how the capacity to make generative inferences could arise as a result of learning relations from…

Learning trajectories are built upon progressions of mathematical understandings that are typical of the general population of students. As such, they are useful frameworks for exploring how understandings of diverse learners may be similar or different from their peers, which has implications for tailoring instruction. The purpose of this…

Successful analogical reasoning requires an analogue in a source domain to have high degrees of structural and surface similarity with a learning task in a target domain. It also requires learners to have sufficient source- and target-domain knowledge. We review the literature and speculate that "less" might create "more"; in…

There are many reasons to be curious about the way people learn, and the past several decades have seen an explosion of research that has important implications for individual learning, schooling, workforce training, and policy. In 2000, "How People Learn: Brain, Mind, Experience, and School: Expanded Edition" was published and its…

This article demonstrates the potential of using hierarchical Bayesian methods to relate models and data in the cognitive sciences. This is done using a worked example that considers an existing model of category representation, the Varying Abstraction Model (VAM), which attempts to infer the representations people use from their behavior in…

Children ages 3 to 5 years old are observed in a series of 3 experiments assessing their use of counterfactual thinking in causal reasoning. Results suggest that young children readily interpret the cause of an outcome in terms of a contrast between the observed sequence of events, and a counterfactual alternative in which the outcome did not…