O.R. course ‘brings math to life’ for high school students

O.R. course ‘brings math to life’

By Thad Wilhelm

Teaching mathematics through meaningful and relevant problems has been inspiring. I’ve been teaching teenagers for 19 years and have been constantly bombarded with the question, “When am I ever going to use this?” As a novice teacher, with a freshly minted bachelor’s degree in mathematics, I tried convincing my students that mathematics is beautiful and should be appreciated as such. Predictably, this line of reasoning largely fell on deaf ears. After several years of my students rolling their eyes at my fascination with the elegance of pure mathematics, I began to concede that the primary use for what I was teaching them was to help them be successful in future mathematics classes.

The realization that the purpose of the vast majority of the mathematics I taught was merely preparation for more advanced, and equally esoteric, mathematics was disillusioning. It became more difficult for me to muster much enthusiasm for teaching topics that I didn’t believe had much practical value for my students’ future lives as citizens, professionals or consumers. Teaching a traditional, algebra-based and calculus-oriented mathematics curriculum to all students disenfranchises most kids and all but guarantees they’ll never get to a point in their mathematics education where they can appreciate the beauty and elegance. I only got to that point near the end of my undergraduate career as I completed my mathematics major.

I enjoyed mathematics as a younger student, mostly because it came relatively easy to me. When I went to college, I was taught by academic mathematicians. I learned to appreciate mathematics for its own sake. I came to see science, engineering, economics and other more pragmatic disciplines merely as interesting applications of mathematics. Now I realize a much more productive outlook is to see mathematics as a powerful set of tools for understanding, improving and predicting systems in the real world.

It wasn’t until I started teaching mathematics as a tool for making decisions and solving meaningful problems that the subject truly came to life for my students. I mostly teach juniors and seniors in high school. They all dutifully take mathematics classes because: (a) they have been told by their parents, teachers and guidance counselors that mathematics is important, and/or (b) they are required to do so if they want to graduate from high school. In my pre-calculus classes, my students hone their skills at algebraic manipulations by solving problems that have absolutely no practical value. I tell myself that they’re learning valuable problem-solving and strategic-thinking skills, and perhaps they are; but when I give them novel problems to solve independently, the results are not encouraging.

When these same students take my operations research class the following year, however, they are engaged much more actively. We spend a great deal of time trying to understand the problem context in order to model it. Students all have relevant experiences and perspectives and are eager to share them as we discuss what facets of the scenario to include in our model, what assumptions are reasonable and the reliability of the data we use. Having seen these same students passively trudge through my pre-calculus curriculum, it’s remarkable to see how energetically they discuss and debate the models we build.

To solve the models, we need some mathematics. For the first time in their mathematics educations, the students see an actual need to develop and deploy mathematics. They engage in high-level quantitative reasoning. They define variables (after finally coming to terms with what a variable truly is). They use those variables to write functions, equations and inequalities to model objectives and constraints. My students quickly come to see the shortcomings of an education that focuses primarily on paper-and-pencil manipulations when realistic problems become much too large to solve by hand. They come to see the value they bring to the world is not their facility with symbolic manipulations but their ability to conceptualize a problem, model that problem mathematically, program a computer to solve the problem, and then interpret the solution.

Along the way, they ask innumerable “What if?” questions that we can investigate both in the context of the problem and in our mathematical model of it. Developing models was interesting and involved rich discussion, but interpreting the solution and discussing how the solution would be implemented and its implications are the subjects of much more heated debate. The level of interest and engagement I see from students in my operations research class far exceeds what I see even in my honors-level traditional mathematics classes. My students were beginning to see the powerful utility of mathematics to help make better decisions in authentic contexts from business, industry and public policy, as well as their own lives.

As a teacher, this class is a joy to teach. After teaching pre-calculus for more than a decade, there’s very little that can surprise me when it comes to the questions students ask. Their questions are usually about skills, techniques or well-defined concepts. In the operations research classes, students constantly bring their own sets of experiences and insights to bear on the problems and ask questions I’ve never considered. The result is a fast-paced and more genuine dialogue within the class with vastly more student-to-student interaction than in traditional classes where I am involved in almost every exchange. ORMS

Thad Wilhelm (twilhelm@birmingham.k12.mi.us) teaches mathematics and operations research at Seaholm High School in Birmingham, Mich.