In the context of an analytical geometry, this study considers the mathematical understanding and activity of seven students analyzed simultaneously through two knowledge frameworks: (1) the Van Hiele levels (Van Hiele, 1986, 1999) and register and domain knowledge (Hibert, 1988); and (2) three action frameworks: the SOLO taxonomy (Biggs, 1999;…

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,…

We introduce a novel measure of abstractness based on the amount of information of a concept computed from its position in a semantic taxonomy. We refer to this measure as "precision". We propose two alternative ways to measure precision, one based on the path length from a concept to the root of the taxonomic tree, and another one based…

This study investigated the roles of different executive function (EF) components (inhibition, shifting, and working memory) in 2-step arithmetic word problem solving. A sample of 139 children aged 8 years old and regularly attending the 3rd grade of primary school were tested on 6 EF tasks measuring different EF components, a reading task and a…

Post-problem reflective tutorial dialogues between human tutors and students are examined to predict when the tutor changed the level of abstraction from the student's preceding turn (i.e., used more general terms or more specific terms); such changes correlate with learning. Prior work examined lexical changes in abstraction. In this work, we…

Attempts to ascertain whether class inclusion behavior is enhanced when children are first asked to compare the subclasses appearing in the class inclusion task and whether such an effect could be due to simple comparisons among the vocabulary terms differentiating the questions. Subjects were second, third, and fourth grade children. (BD/BR)