Towards Spatial Reasoning with Strings and Pins

Spatial problems and a variety of abstract problems can be solved by humans with more ease if the problem can be visualized and/or manipulated. Elaborating on the differences and interplay between representing spatial problems and solving them, this paper focuses on exploring the qualities of a strings and pins problem solving domain. This domain is compared to the straightedge and compass domain of Euclidean geometry. The strings and pins domain is described and two case studies are analyzed: (i) a strings and pins solution of the shortest path problem and (ii) a strings and pins solution to the Voronoi diagram problem; both approaches are compared to a formal solution. Differences and similarities between the straightedge and compass domain and the strings and pins domain are analyzed, and features and limitations of constructive and depictive geometry are discussed. Different problem solving phases are distinguished. Furthermore, cognitive aspects of different problem solving approaches are discussed.