# Analytical Problem Solving: A Prototype for Curriculum Restructuring

For six years, Daniel Maki (Mathematics) and Wayne Winston (Business) of IU-Bloomington have been team-teaching a successful, practical, tool-oriented course, entitled Analytical Problem Solving. The majority of the students who take this course are liberal arts majors (English, foreign languages, history, social sciences, etc.) in the Liberal Arts in Management Program (LAMP) who wish to learn how mathematics is used in business. The course is based on the idea that most students will appreciate mathematics more if they see an immediate use for it. With this in mind, the entire course is built around group projects. In addition, it has the following distinctive features which students find especially appealing:

• Real problems, obtained from businesses and governmental units, are used to motivate the mathematical topics covered. The course is project-driven with topics covered matching the knowledge needed to complete the projects;

• All mathematical topics taught in the course are then used immediately in the projects; thus, the students see the usefulness of mathematics in solving a diverse set of real-life problems;

• Students work in teams using technology to implement the mathematical tools developed in the class for the projects;

• Students are required to document, explain, and defend their mathematical work, thereby honing their communications skills and providing them with a sense of closure and accomplishment.

An example of a project is the scheduling of tellers at a local credit union. Students began by collecting data on service times. Then they used hourly and daily customer data to develop a model that could be used to forecast the workload at the credit union at any time. Next queuing theory was used to determine, as a function of the forecasted workload and service rate, the number of tellers needed at any given time. Then a user-friendly spreadsheet was developed that could be used by the credit union personnel manager to determine her manpower needs at any time. Finally a linear programming model was developed to help determine the minimum cost of scheduling tellers to meet forecasted manpower needs. This single project required the students to utilize basic statistics, regression analysis, queuing theory, advanced spreadsheet techniques, and linear programming.

The project-oriented structure of Analytical Problem Solving also suggests that it can be transplanted easily and naturally if well-documented teaching modules are developed. Indeed, a library of such teaching modules, built up and shared by members of ICUE-Math, would provide a rich source of materials with which any instructor could construct a similar course to suit the special needs and background of his or her students.

As we proceed with interdisciplinary course development and curriculum restructuring, we will draw on the experience and lessons learned from Analytical Problem Solving during the past six years. It is clearly not always possible, nor is it desirable, to make every course totally project-oriented. Nevertheless, the steering committees of the project will make every effort to ensure that the basic idea which makes Analytical Problem Solving so successful-i.e., most students will appreciate mathematics more if they see an immediate use for it-will be used as guidepost in our course development effort.