One of the key challenges of Engineering Education is developing students’ ability to navigate and solve moderately- or ill-structured problems with multiple solution paths. Existing theoretical and conceptual frameworks can provide a basis for understanding this challenge. In order to solve ill-structured problems, students may need to improve their ability to carry out self-regulated learning in order to plan, execute, and reflect on their problem solving efforts. For example, they might need to develop metacognition in order to direct their thinking. In addition, a student may progress via development stages: at first, they might attempt only one method to solve a problem; next, a student may resort to a simpler method if their first attempt failed; finally, a student might first start with an estimation to get a general idea of the answer before moving to a more detailed solution plan.
An experiment was performed to illustrate the possibilities of student problem solving activity on such a problem. The subject population consisted of 72 undergraduate and graduate students recruited from an engineering-focused university on the U.S. East Coast. The participants were given a problem with a well-defined goal but no well-defined method. The results were coded to extract the method used and the approximate time used for each method. Student performance was compared against school year, the choice of method, and the number of methods used. No significant differences in performance were found between students in different years. However, it was found that students who either 1) used simpler methods (methods with lower solve time) or 2) used more than one method tended to perform better than average, though the results are not statistically significant.
After performing the experiment, we realized that there could exist an “optimal” number of solution methods (more than one but not infinitely large) that would maximize problem solving success. In order to better understand this, we performed a simulation to better understand the interplay between multiple method use and problem solving effectiveness in a time-limited scenario. Each solution method was modeled with a different solve time. It was found that whenever there existed sufficiently short methods for solving a problem, using multiple methods (i.e. switching methods) can improve the problem solving outcome. The optimal number of methods is dependent on the methods’ solve times. This result is consistent with the outcome of the experiment and suggests several teaching strategies an instructor can use: 1) teach students low solve time methods and 2) teach students to switch methods when needed and 3) teach students how to select favorable (low solve time) starting methods.
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