Millie Johnson

In this colloquium, we will play with several original and I hope, “good” problems. Besides having fun, another goal is for you to leave with at least one problem to investigate on your own or with your students, regardless of whether you teach Math 099 or Math 599.

What's a “good” problem?

My current working definition is: An accessible, interesting problem that requires exploration, intuition, conjecturing, tinkering, and testing, with multiple approaches/strategies and opportunities for extension/challenge. Buzzwords: Low floor, high ceiling problems

How do you go about creating good problems? There is no cut and dried process, but it almost always involves asking “what if’s?” I will share some strategies used to create the problems posed, as time permits.

“In re mathematica ars proponendi pluris facienda est quam solvendi.”
“In mathematics the art of asking questions is more valuable than solving problems."                                         

~  Cantor’s doctoral thesis (1867)