Beyond categories: Dynamic qualitative analysis of visuospatial representation in arithmetic

Visuospatial representations of numbers and their relationships are widely used in mathematics education. These include drawn images, models constructed with concrete manipulatives, enactive/embodied forms, computer graphics, and more. This paper addresses the analytical limitations and ethical implications of methodologies that use broad categorizations of representations and argues the benefits of dynamic qualitative analysis of arithmetical-representational strategy across multiple semi-independent aspects of display, calculation, and interaction. It proposes an alternative methodological approach combining the structured organization of classification with the detailed nuance of description and describes a systematic but flexible framework for analysing nonstandard visuospatial representations of early arithmetic. This approach is intended for use by researchers or practitioners, for interpretation of multimodal and nonstandard visuospatial representations, and for identification of small differences in learners’ developing arithmetical-representational strategies, including changes over time. Application is illustrated using selected data from a microanalytic study of struggling students’ multiplication and division in scenario tasks.