By: Lara Pudwell, Valparaiso University
What is the first meaningful mathematics problem you remember solving? For me, it was the nine dots, four lines puzzle. When my fourth grade teacher assigned it as an extra credit problem, I spent several days of recess scribbling out attempted solutions in the sandpit, erasing, and trying again until, at last, I found a solution!
I believe this geometric puzzle still sticks out in my memory nearly three decades later because it was one of the first experiences I had with trying to answer a question that didn’t simply involve mimicking previous work. For practitioners, informed trial-and-error is a key step in doing mathematics, so the idea of “thinking out of the box’’ (or in my case, literally thinking in the sandbox…) to build intuition seems natural. However, this is a far stretch from the view of many students who see mathematics as an opportunity to memorize formulas and execute repetitive tasks.
Where do students learn the process of refining mathematical conjectures? Certainly, teaching (via) inquiry in the mathematics classroom has generated much discussion, but often the conversation about inquiry is attached to particular material in the curriculum, with an inquiry-based approach to calculus or statistics, for example. Despite being fundamental to doing mathematics, the majority of the time the inquiry process is a means to an end, rather than a focus of an entire class, and it’s rarely addressed directly. In this environment, some students internalize the inquiry process by indirect exposure. Others finish their education without a true sense of how mathematics is actually developed.
Experimental mathematics courses are one answer to the need to celebrate and study inquiry for the sake of inquiry. In particular, an experimental mathematics course is not a course about a particular set of material; it is a course about a particular approach to doing mathematics.
Courses in experimental mathematics have been offered by at least 7 different colleges and universities . Outside of those who have taught or taken these courses, there is not widespread understanding of what “experimental mathematics” means in the undergraduate curriculum. My goal in this post is to give a better idea of what such a course looks like.