This study explores three aspects of a math emporium (ME), a model for offering introductory level college mathematics courses through the use of software and computer laboratories. Previous research shows that math emporia are generally effective in terms of improving final exam scores and passing rates. However, most research on math emporia…

This article proposes a new model of human concept learning that provides a rational analysis of learning feature-based concepts. This model is built upon Bayesian inference for a grammatically structured hypothesis space--a concept language of logical rules. This article compares the model predictions to human generalization judgments in several…

Challenges Smolensky's theory that human intuitive/nonconscious cognitive processes can only be accurately explained in terms of subsymbolic computations in artificial neural networks. Symbolic learning models of two cognitive tasks involving nonconscious acquisition of information are presented: learning production rules and artificial finite…

Learnability theory involves the construction of formal mathematical proofs whose goal is to demonstrate how the child can successfully induce a mature grammar. An empirically adequate learnability proof constitutes a detailed hypothesis concerning the boundary conditions within which acquisition proceeds and can provide a general framework for…