# A tradition of creative problem solving

**Author: Lona** | Image: Lona

**Author: Lona** | Image: Lona

Elgin Johnston, professor of mathematics and director of the Center for Undergraduate Mathematics Excellence at Iowa State University, loves to create problems and help others learn how to solve them. In fact, he has been writing mathematics problems for high school students to solve and coaching them to become better problem solvers for 30 years through the Mathematical Association of America.

Shortly after becoming a faculty member in 1977, Johnston began working with Iowa State students to coach them in preparation for the William Lowell Putnam Mathematical Competition, the preeminent mathematical competition for undergraduate students in the United States and Canada. His commitment to training students to be exemplary problem solvers helped the Iowa State Putnam Competition team rank as high as 22nd out of approximately 500 teams.

He wanted to instill the same appreciation he has for mathematical problem-solving in all Iowa State undergraduate mathematics students, so he created the “Problem of the Week.”

The Problem of the Week is a written problem that is posted online and around Carver Hall every Monday the first 14 weeks of each semester. Students submit their solutions to Johnston.

“One motivation for this was to get students interested in math beyond the classroom. Lots of students like to come up with solutions to problems,” said Johnston.

“Professor Johnston’s problem of the week was what first taught me how much fun proofs can be.”

The problems come from what Johnston wrote in his 30 years of coaching. He tailors the problems to the undergraduate students at Iowa State to be solvable by calculus or earlier skills, such as algebra, trigonometry and geometry.

Johnston’s commitment to engaging students shows, as the Problems of the Week bring in anywhere between 60 to 70 responses at the beginning of the semester, which Johnston reads each week.

The problems become increasingly difficult as the semester continues, and there may only be 10 to 12 responses by the end of the semester. Though the responses may dwindle, the impact is clear: students like solving problems, and coming up with interesting answers.

“Over the years, there have been some very creative solutions,” Johnston said. “I’m always interested in seeing how people look at a problem. Students have told me they look forward to the next problem coming out.”

Brantley Vose (’18 mathematics) started on the problems of the week before even attending Iowa State University.

“Professor Johnston’s problem of the week was what first taught me how much fun proofs can be,” said Vose. “When I was a high school junior, I emailed Professor Johnston with a solution to the current problem. He actually corresponded with me and sent me follow up problems. Those problems were what got me hooked on proofs in the first place.”

And it isn’t just students who are interested in solving the Problem of the Week.

“It is focused on undergraduates, but a lot of faculty also work on the problem and send a solution,” Johnston said.

After more than 40 years at Iowa State, Johnston plans to retire in 2020, but hopes that his Problem of the Week will live on.

“Our students write well, they’re interested in mathematics and they like solving problems,” Johnston said. “We have some very talented students.”