The goal of this article is to make the case for a radical exemplar account of child language acquisition, under which unwitnessed forms are produced and comprehended by on-the-fly analogy across multiple stored exemplars, weighted by their degree of similarity to the target with regard to the task at hand. Across the domains of (1) word meanings,…

Making sense of mathematical concepts and solving mathematical problems may demand different forms of reasoning. These could be either domain-based, such as algebraic, geometric or statistical reasoning, while others are more general such as inductive/deductive reasoning. This article aims at giving visibility to a particular form of reasoning…

Linear functions are an important part of the middle school mathematics curriculum. Students in the middle grades gain fluency by working with linear functions in a variety of representations (NCTM 2001). Presented in this article is an activity that was used with five eighth-grade classes at three different schools. The activity contains 15 cards…

What is involved in consolidating a new mathematical abstraction? This paper examines the work of one student who was working on a task designed to consolidate two recently constructed absolute function abstractions. The study adopts an activity theoretic model of abstraction in context. Selected protocol data are presented. The initial state of…

An inquiry attempted to build an agenda for research that would result in a cognitive theory of instruction capable of informing educational practice and extending the limits of knowledge about how people learn and develop. What would such a theory look like, how close are we to having one, and what directions must be followed to further its…