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Research in Cognition and Metacognition Aims to Improve Mathematical Communication

Graduate students' research is poised to push boundaries by examining metacognitive processes specifically during mathematical proof writing tasks.

Sarah Sparks' fascination with mental processing has led her to research math students' metacognition during proof writing — a vital mathematical process to convince others that their deductive arguments are accurate. Sparks is in her final year of studies in the Educational Mathematics (now Mathematics Education) Ph.D. program at the University of Northern Colorado.

Sparks said her dissertation research boils down to communications.

Sarah Sparks facing forward and smiling.
Sarah Sparks

"This is a broader conversation about how to communicate. It's applicable to a wide range of logical reasoning situations that aren't just computational. For example, going into a test, a student may feel confident on one type of question because they know that's something they understand. Metacognition encapsulates that ability to reflect on one's own understanding," Sparks said.

In higher-level mathematics, students transition from solving problems with specific approaches to developing proofs that show truth of mathematical statements.

"That can be a challenging shift for a lot of students. Students aren't always prepared for it," she said.

She explained it's especially important for students to meet the challenge of proof writing because mathematics is an intellectual gateway into a variety of fields. While much of the metacognitive research in mathematics focuses on problem-solving strategies, Sparks' research is poised to push boundaries by examining metacognitive processes specifically during proof writing tasks.

"I had two pairs of students work on two proof tasks together while I recorded them on audio and video. Then, I did two sets of follow-up interviews, where I showed them video clips and talked with them about things that happened during the tasks," she said.

Sparks anticipates the research contributing to conversations about the skills students need to communicate logical reasoning and ideas. Besides helping support mathematics students during their transition to proof writing, she believes it could impact curriculum development from grade school to undergraduate levels.

As a graduate part-time instructor, Sparks has taught or co-taught over 600 students at UNC, including math majors and liberal arts students.

"Students are creative, and they challenge me in my own understanding of mathematics. They all learn differently, so I learn new things about being a teacher every day," she said.

She garnered a department teaching award early in her Ph.D. program. Gulden Karakok, a professor in Mathematical Sciences in the College of Natural and Health Sciences and Ph.D. program co-coordinator, said this award speaks to Sparks' dedication to teaching.

"She's putting our students first. She's using newer teaching techniques and supporting students so that they can best learn mathematics," Karakok said. "The award committee also was impressed by her student-friendly syllabus. As a teacher, she's always trying to understand students and make connections with them."

As Sparks’ research advisor, Karakok mentioned the importance of aligning expectations. When both noticed their expectations weren't aligning, Sparks suggested a simple check-in at the end of their meetings.

"Sarah proposed this idea, which I'm going to do with my other graduate students. We tell each other what went well from our expectations and what are the things we should improve on," she said.

Sparks recalled struggling with her writing skills and navigating graduate school with attention-deficit/hyperactivity disorder (ADHD).

"Dr. Karakok went out of her way to support me in strengthening my writing skills and taking the skills that I did have and helping me grow them. She also helped me learn time management skills and how to set myself up for success," she said. "I look forward to continuing to work with her post-graduation."

Karakok said Sparks' research will extend beyond mathematical proofs to other written communication in mathematics courses that involve understanding how people process what they think and write.

"Once we understand how this writing process works with metacognition, we can think about how we can bring those skills into other forms of writing in other classes," Karakok said.

Sparks plans to keep teaching after she graduates in May 2025. She loves teaching undergraduate and higher-level math courses as well as pre-service elementary and secondary teaching courses.

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