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.

Appendix A. Problem statements

Boeing versus Airbus

The Boeing Company faces a critical strategic choice in its competition with Airbus Industries for the long-haul flight segment: should it design and build a super-747 model that can carry 550 passengers at speeds around 350 mph, or a plane that can fly at 95% of the speed of sound but carry only about 350 passengers? As a member of Boeing's Planning Group, your task is to build a model to investigate the trade-offs involved in this decision.

Red Cross

The Red Cross provides about 40% of the replacement blood supply for the United States. The available donor base has been shrinking for years, and although increased advertising has kept Red Cross supplies adequate, the time is approaching when demand will outstrip supply. For many years, the Red Cross has refused to pay donors for blood, on the grounds that to do so would ‘put the blood supply of the country at risk.’ However, Red Cross management has begun to consider changing its policy. Evaluate the impacts of a policy under which the Red Cross would pay each of its donors a set fee.

Alumni Giving

Your client is the planning office of a major university. Part of the job of the planning office is to forecast the annual donations of alumni through the university's long-established giving programme. Until now, the forecast has been made subjectively. The client wants you to develop a more objective approach. Your client has provided the attached sample of one of the annual reports produced by the planning office. The reports show, for each alumni class in that year:

• number of alumni in class (Class Roll),

• number of givers,

• per cent of class giving,

• total direct donations from class,

• other gifts for class (eg, employer matching), and

• class total.

Your client has also provided the attached graph of a recent year's class totals. Develop a model to estimate how much money the university's alumni will donate in each of the next 5 years.