Spontaneous Usage of Different Shortcuts Based on the Commutativity Principle

摘要: Based on research expertise a person can be said to possess integrated conceptual knowledge when she/he is able spontaneously identify task relevant information in order solve problem efficiently. Despite the lack of instruction or explicit cueing, should recognize which shortcut strategy applied – even context differs from one procedural about was originally acquired. For mental arithmetic, first signs such adaptive flexibility develop already primary school. The current study introduces paper-and-pencil-based as well an eyetracking-based approach unobtrusively measure how students spot and apply (known) options arithmetic. We investigated development relation spontaneous use two strategies derived mathematical concept commutativity. Children grade 2 7 university solved three-addends addition problems, are rarely used class. Some problems allowed either commutativity-based strategies. Results suggest that three onwards both shortcuts were application correlated positively with other. Rate usage substantial but smaller than instructed variant. Eyetracking data suggested similar fixation patterns for application. consistent principle so it different contexts