Math capstone: Using equations to solve real-life issues

Math capstone: Using equations to solve real-life issues

W hat do COVID, taxicabs and mindsets have in common? The answer may surprise you: math.

Math is the abstract science of using calculations, shapes and quantity to solve a problem. But multiple steps, numbers and signs do more than complete mathematical equations.

They can be used to unravel everyday problems, as well.

The purpose is to synthesize ideas learned in previous coursework to go beyond the prescribed curriculum in terms of content, depth and approach and help our students develop the ability to work independently on a project of their choosing.
– Dr. Robert Blumenthal
That’s exactly what three seniors did in November for their capstone projects. They used statistics and data to answer real-life challenges like discovering a direct taxicab distance between two coordinates; seeing if students develop the mindset they’re not good at math; and whether the COVID shutdown effected grades at Georgia College.  

“The purpose is to synthesize ideas learned in previous coursework to go beyond the prescribed curriculum in terms of content, depth and approach and help our students develop the ability to work independently on a project of their choosing,” said Dr. Robert Blumenthal, chair of mathematics.

In the past four years, 62 math majors have presented capstone research. Each chose a topic of interest and a professor to mentor them. Students engage in a year of reading, research and working mathematical puzzles. It ends with the annual Capstone Day, where they present findings in front of faculty and family.  

Senior Seth Rozelle of Warner Robins is working on a degree in math with a minor in computer science. He chose to do his undergraduate research on COVID and whether online learning during lockdowns effected grades at Georgia College.

Senior Seth Rozelle presents his math capstone research.
Senior Seth Rozelle presents his math capstone research.

He thought it’d be a timely and popular topic. His research required rigorous data analysis, studying grade distribution in 19 areas of study across campus.

Overall, he learned students performed better in the spring months of the pandemic, than previously.

“We were observing whether the distribution of grades at Georgia College changed significantly in any way. The short answer is it did,” Rozelle said. “In spring of 2020, there were significantly more A's, less failing grades and slightly more withdrawals in most categories. Then, in spring 2021, grades seemed to come back to pre-COVID numbers.”

What gets me out of bed in the morning is I get to do work like this that substantially answers questions people want to know...
– Seth Rozelle
Rozelle said his research is “immediately relevant” and can shed light on academic learning during a global pandemic. Going forward, it can be used to determine if hybrid learning is better in emergencies.

This project will also help Rozelle when he applies to graduate programs for statistics or biostatistics. In April, he’ll present his work at the National Conference on Undergraduate Research (NCUR).

“I’ve always had a knack for numbers. I want to be a statistician. Georgia College was the university with the most opportunities, conveniency and affordability for me,” Rozelle said.

“What gets me out of bed in the morning is I get to do work like this that substantially answers questions people want to know,” he said. “This project gave me priceless experience and insight on the kind of work I want to do.”

Dr. Jebessa Mijena listens recently to capstone presentations.
Dr. Jebessa Mijena listens recently to capstone presentations.
His mentor, Dr. Jebessa Mijena, associate professor of math, teaches courses in statistics, calculus sequences and differential equations. Capstone students interested in statistics, data science and machine learning generally come to him for direction.

It’s his job to offer suggestions and guidance but otherwise step back.

“These types of capstone projects teach our students about completing tasks independently without much help from the professors,” Mijena said.

Another senior math major, Natalie Taylor of Rossville, Georgia, did her capstone under the direction of Dr. Rodica Cazacu. Most people think the distance between two destinations is the mileage given by Google Maps––a direct line, what’s known in math as “Euclidean distance.” But traveling to another place often involves twists and turns. Taylor used horizontal and vertical distance between two points to find what’s called “taxicab distance.”

Senior math education major Morgan Grey of Dacula, Georgia, studied the stigma around math. She met several times a week with Dr. Doris Santarone, assistant professor of math education, for assistance. Grey was deeply interested in why some people believe their math abilities are predetermined and cannot change.

She collected data from hundreds of students in grades K-12 to determine their “mindsets.” She also looked at teaching methods to see if attitudes can be altered.

“From a young age, I wondered why some people called themselves a math person, meaning they could do math well, or why they weren’t a math person,” Grey said. “Contrary to this is a ‘growth mindset,’ when people believe they’re born with a set of basic qualities that can be changed and improved through hard-work and strategies that foster growth.”

Senior Morgan Grey presents her capstone research.
Senior Morgan Grey presents her capstone research.
Grey found most children start out with healthy mindsets. As grade levels increase in math, however, this positive attitude declines. A significant decrease occurs between kindergarten and 3rd grade, Grey learned, when multiplication and fractions are introduced and “students begin to doubt their abilities.”

She was surprised to find a similar problem with the mindsets of teachers. Teachers in higher grade levels are less convinced students can overcome difficulties in math.

This discovery could lead to finding out why and ways to fix it, Santarone said. Real-life problems are challenging to solve––and that’s why Santarone loves math. It’s also why so many students consider the math capstone to be the highlight of their college experience.

“When you’re given a problem and you don’t know how to solve it,” Santarone said, “you have to use problem solving skills, logic and critical thinking to apply what you know to find a solution.”

In his department, Blumenthal emphasizes critical thinking and making informed decisions based on evidence. Faculty focus on interdisciplinary work and making connections between disciplines.

The math capstone is the crowning glory.

“This is just one of the things that makes Georgia College such a great place for our students and faculty,” Blumenthal said. “It’s very rewarding to work with such talented and dedicated students.”

Grey hopes to take what’s she learned during her capstone experience and become a 6th-12th grade math teacher. She wants to show others they can tackle math and succeed.

Math can be rigorous and challenging, but it’s not impossible. That's what is so exciting about it. The challenges we face in math can also prepare us for any hardships life throws at us, so that we can persevere.
– Morgan Grey

“I 100% believe this capstone has been nothing but a positive experience for me at Georgia College,” Grey added. “It’s taught me proper research skills and time management techniques, plus it helped me become more professional. I’m very thankful to have had this opportunity.”