identifying the factors of problem complexity
Authors:Jeff Phillips, Dante Sblendorio
Mentor:Jeff Phillips, Associate Professor of Physics, Loyola Marymount University
The challenge of quantifying the complexity of problems encountered within STEM disciplines has been approached in a variety of ways. Typically, problems are characterized as either well-structured or ill-structured; determined by the ambiguity of the language used to convey the necessary information (knowns) needed to find a solution. Well-structured problems have clearly stated goals and parameters while ill-stated problems do not. While this single dimensional, if not binary, portrayal of problem difficulty is common, it does not completely capture all of the variations in problem complexity. We developed a reliable objective coding scheme that defines a three-component value that captures the amount of stated conditions within the problem, the number of necessary assumptions and physics concepts and the mathematical complexity. For example, problems with explicitly stated assumption (e.g. assume constant gravity) within the problem have a lower complexity rating than problems that do not give assumptions, and thereby force the solver to decide what to assume. We will present this coding scheme itself, results from when it is applied to popular physics texts and ideas for future studies such as comparing these results to student perceptions of difficulty, which often focus on superficial features.