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This dissertation proposes the Problem Map (P-maps) ontological framework. P-maps represent designers' problem formulation in terms of six groups of entities (requirement, use scenario, function, artifact, behavior, and issue). Entities have hierarchies within each group and links among groups. Variables extracted from P-maps characterize problem formulation.
Three experiments were conducted. The first experiment was to study the similarities and differences between novice and expert designers. Results show that experts use more abstraction than novices do and novices are more likely to add entities in a specific order. Experts also discover more issues.
The second experiment was to see how problem formulation relates to creativity. Ideation metrics were used to characterize creative outcome. Results include but are not limited to a positive correlation between adding more issues in an unorganized way with quantity and variety, more use scenarios and functions with novelty, more behaviors and conflicts identified with quality, and depth-first exploration with all ideation metrics. Fewer hierarchies in use scenarios lower novelty and fewer links to requirements and issues lower quality of ideas.
The third experiment was to see if problem formulation can predict creative outcome. Models based on one problem were used to predict the creativity of another. Predicted scores were compared to assessments of independent judges. Quality and novelty are predicted more accurately than variety, and quantity. Backward elimination improves model fit, though reduces prediction accuracy.
P-maps provide a theoretical framework for formalizing, tracing, and quantifying conceptual design strategies. Other potential applications are developing a test of problem formulation skill, tracking students' learning of formulation skills in a course, and reproducing other researchers’ observations about designer thinking.




Ultimate Frisbee or "Ultimate," is a fast growing field sport that is being played competitively at universities across the country. Many mid-tier college teams have the goal of winning as many games as possible, however they also need to grow their program by training and retaining new players. The purpose of this project was to create a prototype statistical tool that maximizes a player line-up's probability of scoring the next point, while having as equal playing time across all experienced and novice players as possible. Game, player, and team data was collected for 25 different games played over the course of 4 tournaments during Fall 2017 and early Spring 2018 using the UltiAnalytics iPad application. "Amount of Top 1/3 Players" was the measure of equal playing time, and "Line Efficiency" and "Line Interaction" represented a line's probability of scoring. After running a logistic regression, Line Efficiency was found to be the more accurate predictor of scoring outcome than Line Interaction. An "Equal PT Measure vs. Line Efficiency" graph was then created and the plot showed what the optimal lines were depending on what the user's preferences were at that point in time. Possible next steps include testing the model and refining it as needed.