External Representations Contribute to the Dynamic Construction of Ideas

External representations such as diagrams, sketches, charts, graphs and scribbles on napkins play facilitatory roles in inference, problem-solving and understanding (e.g. [1],[2],[3],[4],[5],[6],[7],[8],[9]). How does the externality and visibility of representations facilitate inference and problem-solving__ __ One benefit of external representations is on memory. They reduce working memory load by providing external tokens for the elements that must otherwise be kept in mind. This frees working memory to perform mental calculations on the elements rather than both keeping elements in mind and operating on them [2],[9]. External representations also serve as visuo-spatial retrieval cues for long term memory, evoking relevant information that might not otherwise be retrieved. Another benefit of external representations is to promote discovery and inference, both visuo-spatial and metaphorical. Perceptual judgements about size, distance, and direction are easily made from external representations (e.g.[4]). In a Venn diagram, set relations such as inclusion are abstractly mapped onto visuo-spatial diagrammatic features, enabling direct perceptual calculation. Visuospatial features such as proximity, connectivity, and alignment provide useful hints to selection of appropriate inference paths (e.g.[1],[6],[8]) and to proper understanding of the structure of a target system (e.g.[5]). Calculations requiring counting, sorting, or ordering are easily made by rearranging external spaces (e.g. [7]).