Mathematics senior finds effective teaching strategies on her path to a graduate degree

Mathematics homework in 2023 often has parents scratching their heads and admitting defeat. Oregon State University senior Madison Collins knows that feeling all too well.

At the dinner table growing up she disagreed with her parents on how to break up numbers for addition and multiplication problems. “My mother had different methods of math that she learned,” she said. “I went, ‘Mom, that’s not how my teacher told me to do it.’” Luckily for Collins, math came naturally, and her parents tried to keep her on her toes with new academic topics.

Until one day, she surpassed her father, an important figure in her life who encourages and challenges her academically.

“It was fun when I was talking to him about math content and he said, ‘I have no idea what you’re talking about.’” That’s when Collins realized, after all these years, she finally surpassed her father at a higher level of mathematics.

Modernizing the education process

A third-year student graduating with a bachelor's degree in mathematics with the mathematical biology option and a minor in chemistry, Collins plans to hit the ground running by starting her master's degree in math education at Oregon State in fall 2023. Even though 1+2 will always be equal to 3, Collins strives to teach math differently so that students can learn better and discover something new along the way.

“I want to help students from multiple backgrounds see that learning math and succeeding in a college math course is possible for them. I want to be able to communicate math well to students so they can learn the content and gain confidence in their mathematical abilities,” she said. “In college, a lot more students don’t feel like they can connect to the teachers personally, so I definitely want to try to build up the community in that way while teaching.”

Collins has already started analyzing how the college-level calculus curriculum is being taught in the classroom for her honors thesis. Her curriculum curiosity dates back to the table in her childhood kitchen.

Whenever she and her sister got stuck on a math problem, her parents paused dinner to get them back on track. Sometimes, this meant her parents teaching them ‘weird’ and ‘wacky’ methods that aren’t taught in school anymore. To Collins, this is a typical part of the education process.

“While parents being able to help kids with homework is really important, a lot of research has gone into improving education with new teaching strategies and ways of communicating certain ideas,” she said. “New advances are being made in math education theory all the time so the content delivery is changing. It is unrealistic not to change math to keep up with new understandings of concepts. With that said, many math curricula, especially calculus, have remained largely unchanged for decades.”

When Collins entered high school, she loved to ‘move pieces around’ to solve puzzle-like math problems in her calculus courses. Outside of the classroom, she chose to do sports instead of working a job, a choice that greatly impacts how she views the education experience. Joining the cross country, swimming and track teams helped her grow and prepare for the rigor of college courses early on.

Even though she didn’t continue sports at Oregon State, Collins kept running on her own during college. She competed in the April 2023 half marathon in Corvallis alongside her boyfriend while her uncle and mother ran the 5k.

Training for 13.1 miles, spending time with her family and developing a thesis in the same term required a work-hard-play-hard attitude. Especially when that workload also included tutoring.

$Four people stand with running bibs in front of the OSU football stadium.$

Madison Collins (#608) spent time with her uncle, mother and boyfriend after completing the April 2023 half marathon in Corvallis.

Building new communities with math

Sometimes, student-athletes struggle with maintaining satisfactory grades while trying to maintain a busy schedule, so Oregon State Athletics has a special tutoring program designed for them. As a tutor, she got these students back on track when they struggled with their college courses.

After a year, she switched to the Supplemental Instruction (SI) program. The program is a free resource that students at Oregon State utilize to learn key concepts in a group environment. Leaders come prepared with a lesson plan full of practice problems and interactive activities and implemented them in peer-led, group study tables.

This was her chance to practice shaking up the curriculum. Collins designed a BINGO activity that aided students with reviewing vocabulary. She also put together problem sets that they solved together at the study table. This way, she was able to not only host student-led lessons but encourage collaboration.

While an employee, she started chatting about what she wanted to research for her honors thesis with SI Coordinator Chris Gasser. He acted as a mentor by encouraging Collins to be resilient while taking tough academic courses. Before long, she stumbled upon her honors topic of choice - analyzing curriculum implementation.

Uncovering how calculus is taught

At the end of her third year, Collins devoted the majority of her time to developing her honors thesis with Oregon State Mathematics Instructor Elizabeth Jones. Collins visited different sections of MTH 252 Integral Calculus at Oregon State and recorded observations.

She sat with the students and jotted down different teaching strategies she saw implemented by a variety of instructors. Using her observations, she developed a framework for analysis in order to find the most effective ways to continue implementing the calculus curriculum in college-level courses.

$Madison Collins standing in front of a poster presenting her honors thesis.$

Madison Collins presented her honors thesis on how the calculus curriculum is implemented in the college classroom.

She enjoyed chatting with Jones about the different classroom, assessment, design and course support strategies she chose to analyze. But occasionally, their math education preferences diverged.

While talking about trigonometry substitution, they discussed different mathematical notations and the confusion that comes with non-standard notations. Variables are written with alphabetical characters. For instance, pertaining to trigonometric substitution, Collins prefers to use a ‘u’ whereas Jones prefers to use an ‘x’.

Sometimes, the same symbol can have different meanings in various areas of math. For example, absolute value bars, IVI, can denote other operations including vector magnitude, IVI. It’s a subtle detail, but can have a major impact on how variables are communicated to the students.

"I hope that by going into teaching, I can help people get through a typically difficult subject and make it more enjoyable for them."

Now that her first thesis is complete, Collins wants to put what she learned into practice by teaching in a college setting that is approachable for students. When students walk into her future office, she wants to address the little questions and not have students be hesitant to ask a question that is ‘too simple’ to answer.

“I get really excited when I am helping someone and can see them putting the pieces together in their head. When they reach the final answer in a ‘lightbulb moment,’ they get super excited,” she said. “I don’t just want to lecture students. I want to teach them how to approach math and build confidence in their skills.”

Being able to learn how to be the teacher she wants to be came at a cost. Luckily, when her academic experience got a little bumpy, she wasn’t alone.

Persevering in the face of failure

For Collins, being a Beaver at Oregon State came with the pressure to succeed. “The biggest challenge I've had growing up through school was that I put a lot of academic pressure on myself,” she said.

$Madison Collins standing in front of a white board.$

Madison Collins demonstrates how to solve a problem using calculus at the front of the classroom.

After her official advisor left the university, she met Oregon State Mathematics Professor Nathan Gibson who became her advisor, professor and mentor. He taught MTH 323 Mathematical Modeling, which turned out to be a tough class for Collins. She wrote a 10-page report talking about the errors that happen when modeling basic electrical circuits and how the different components differed from each other.

“I ended up using a little bit of electrical engineering from that one class I took in my first year. I’m pretty sure my simulation failed, but I still got an A on the paper,” she said. It takes encouragement to agree to finish a difficult course, especially when it comes to learning how to use differential equation systems in the real world. This was the type of mentorship Gibson provided when Collins needed it most. Now, she can apply what she learned in a classroom setting.

“A lot of people are told they aren’t a math person,” she said. “I totally agree that math is not something many people want to study, but I really enjoy it and the problem-solving aspect of it. I hope that by going into teaching, I can help people get through a typically difficult subject and make it more enjoyable for them.”

Collins is now able to teach others in a way she wishes she was taught – and it all started with math homework at the dinner table.