This work provides a characterization of the learning of graph theory through the lens of the van Hiele model. For this purpose, we perform a theoretical analysis structured through the processes of reasoning that students activate when solving graph theory problems: recognition, use and formulation of definitions, classification, and proof. We…

Both scientists and children make important structural discoveries, yet their computational underpinnings are not well understood. Structure discovery has previously been formalized as probabilistic inference about the right structural form--where form could be a tree, ring, chain, grid, etc. (Kemp & Tenenbaum, 2008). Although this approach…

We report our qualitative study of twenty-four students enrolled in the second-semester of a second-year undergraduate (sophomore-level) organic chemistry course, Organic Two. We asked the research participants to propose the product and electron-pushing mechanism of elementary mechanistic steps in the absence and presence of the corresponding…

In recent years, ample research has shown that preschoolers choose selectively who to learn from, preferring, for example, to learn novel words from a previously accurate over a previously inaccurate model. But this research has not yet resolved what cognitive foundations such selectivity builds upon. The present article reports 2 studies that…

Negation, conjunction, and disjunction are major building blocks in the formation of concepts. This article presents a new model-based theory of these Boolean components. It predicts that individuals simplify the models of instances of concepts. Evidence corroborates the theory and challenges alternative accounts, such as those based on minimal…

Teaching students to doubt, that is, to "test," theological arguments as one might test any other kind of knowledge is challenging in that the warrant for such testing is not immediately clear. Stephen Toulmin, Richard Rieke, and Allan Janik's model of reasoning provides a conceptual framework that demonstrates the logical relationships between a…

The author suggests that educational philosophy should benefit from addressing questions traditionally asked within discourse in the philosophy of mind, namely: the relation between the mind and world and the problems of intentionality (or aboutness), meaning, and representation. Peirce's semiotics and his category of creative abduction provide a…

This description of the Structure-Mapping Engine (SME), a flexible, cognitive simulation program for studying analogical processing which is based on Gentner's Structure-Mapping theory of analogy, points out that the SME provides a "tool kit" for constructing matching algorithms consistent with this theory. This report provides: (1) a…

The challenge to the dominance of rationality in educational philosophy presented by John Dewey and Donald Schon is examined in this paper. The paper identifies basic assumptions of their perspective and explains concepts of reflective thinking, which include biography, context of uncertainty, and "not-yet." A model of reflective thought…

This paper describes the Structure-Mapping Engine (SME), a cognitive simulation program for studying human analogical processing. SME is based on Gentner's Structure-Mapping theory of analogy, and provides a "tool kit" for constructing matching algorithms consistent with this theory. This flexibility enhances cognitive simulation studies by…

Presents a view of the relative roles of logical presupposition and shared knowledge in "it"-cleft constructions. Indicators of shared knowledge relate to a speaker's "assumptions" about the state of the hearer's knowledge, whereas presuppositions indicate a speaker's "requirements" for what should be included within…

Described is research which sought to prove the hypothesis that mental models tend to preserve their autonomy with regard to the originals they are meant to represent. The results of this investigation involving 200 Israeli students are presented. (CW)

Chemistry is commonly portrayed at three different levels of representation--macroscopic, submicroscopic and symbolic--that combine to enrich the explanations of chemical concepts. In this article, we examine the use of submicroscopic and symbolic representations in chemical explanations and ascertain how they provide meaning. Of specific interest…

The purpose of this study was to investigate the effect of an eclectic thinking processes model on the logical reasoning abilities of students in grades six through twelve. The experimental school consisted of 159 students whereas the control school had 111 students. The Group Assessment of Logical Thinking (GALT) was administered to the sample as…

The mathematical experiences of elementary students often focus on memorizing facts and rules as opposed to making sense of the subject and developing problem solving skills. Students spend large amounts of time processing, memorizing and sorting collections of data which are tasks well performed by computer technology. To correct this situation,…