Computer Assisted Synthesis of Visual and Symbolic Meaning in Mathematics Education

Abstract

A number of factors pertaining to a wide variety of distinctions -- such as particular-general,arithmetic-geometry, sense-reference, procedural-declarative, concrete-abstract, object-attribute-- are implicated in developing a meaningful understanding of visual and symbolic aspectsof mathematics. A rather simplistic "association-abstraction" model of mathematical cognition, asit stands, appears inadequate to account for these factors, particularly with respect to instructionaldesign and assessment. Such fundamental inadequacies warrant better theory and more research.Methodology directed toward this end, drawing on digital video technology, is sketched out.