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…

Most of the research on mathematical and scientific thinking has been concerned with uncovering knowledge structures and reasoning processes in people of different levels of competence. How these structures and processes are acquired has only recently become a major concern. Thus, some of the major research on mathematical and scientific thinking…

This paper presents a theoretical framework for investigating the role of algorithms in mathematical thinking using a combined ontological-psychological outlook. The intent is to demonstrate that the processes of learning and of problem solving incorporate an elaborate interplay between operational and structural conceptualizations of the same…

This paper describes the BUD project which surveyed childrens' conceptions of division, and of fractions and decimals. The lack of connection between counting skills and conceptual understanding is discussed. The expectations for new algorithms and the basic idea in planning the BUD project are summarized. Some previous studies on counting, the…

Compared and contrasted are the concepts intuition and logic. The ideas of conceptual thought and algorithmic thought are discussed in terms of the world as a labyrinth, intuition and time, and the structure of knowledge. (KR)