How novices formulate models. Part I: qualitative insights and implications for teaching

Abstract

Teaching novices how to formulate mathematical models for ill-structured problems is a challenging task. Little is known about how novices approach ill-structured problems and how their performance differs from that of experts. We audiotaped 28 MBA students while they worked through four ill-structured modelling problems. The task in each problem was to begin to develop a model that could ultimately be used for forecasting or analysis of alternative courses of action. We analysed transcripts of these think-aloud protocols both quantitatively and qualitatively. We observed five behaviours that are not typical of experts and that limit the effectiveness of our subjects. These include: over-reliance on given numerical data, taking shortcuts to an answer, insufficient use of abstract variables and relationships, ineffective self-regulation, and overuse of brainstorming relative to structured problem solving. We conclude that an effective modelling pedagogy should teach how to: formulate models both in the presence and the absence of data, abstract variables and relationships, employ control strategies for self-regulation, and use structured problem-solving methods.