Complexity of Geometry Problems as a Function of Field-Dependency and Asymmetry of a Diagram

Solving geometry problems is challenging for students of all ages. The complexity of geometry problems is multidimensional and is linked to visualization, auxiliary constructions required for solutions, computational and proof skills, and deep and robust knowledge of geometry concepts and their properties (definitions, axioms, and theorems). In this paper, we hypothesized that the field-(in)dependency and (a)symmetry of the geometric diagrams given in geometry problems affect the complexity of the problems. We designed 168 short verification problems: 21 sets of 4 geometric diagrams with a systematic variation of the examined conditions accompanied by a correct and an incorrect property. The hypotheses were examined using the accuracy and response times of 45 undergraduate and graduate Taiwanese students who were asked to solve these problems in a computerized setting. Based on the results of this test, we demonstrated that both asymmetry and field-dependency of diagrams increase problems’ complexity, as indicated by a decrease in the accuracy and an increase in reaction time of responses.