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How do problem solvers represent visual-spatial information in complex problem solving tasks? This paper explores the predictions of symbolic computation, embodied problem solving and a neurocomputational theory for what factors influence internal representation choices. Across two studies, data are collected from experts and novices in three different, complex visual-spatial problem-solving domains (weather forecasting, submarine target motion analysis, and fMRI data analysis). Internal spatial representations are coded from spontaneous gestures made during cued-recall summaries of problem solving activities. Analyses of domain differences, expertise differences, and changes over time with problem solving suggest that neurocomputational constraints play a larger role than the nature of the visual input or the nature of the underlying real world being examined through problem solving, especially for expert problem solvers. The particular neurocomptuational feature that was found to drive internal representation choice is the required spatial precision of the main goals of problem solving.