莎拉的火花' fascination with mental processing has led her to research math students' metacognition during proof writing — a vital mathematical process to convince others that their 演绎论点是准确的. Sparks is in her final year of studies 在 教育al 数学(现在 数学教育) Ph.D. 北科罗拉多大学的项目.

Sparks 说 her dissertation research boils down to communications.

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. 学生们并不总是准备充分 为了它，”她说.

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. 而 much of the metacognitive research in mathematics focuses on problem-solving strategies, Sparks' research is poised to push boundaries by examining metacognitive processes 特别是在证明写作任务中.

"I had two pairs of students work on two proof tasks together while I recorded them 博天堂官方网站音频和视频. 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 说.

Sparks anticipates the research contributing to conversations about the skills students 需要沟通逻辑推理和想法. 除了帮助支持数学 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," 她说.

She garnered a department 教学 award early in her Ph.D. 程序. 基尔德Karakok他是 数学科学 在 自然与健康科学学院 和Ph值.D. 程序 co-coordinator, 说 this award speaks to Sparks' dedication to 教学.

“她把学生放在第一位. She's using newer 教学 techniques and supporting students so that they can best learn mathematics," Karakok说. “评奖委员会 她对学生友好的教学大纲也给我留下了深刻的印象. 作为一名教师，她总是在努力 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 在会议结束时.

"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 “应该有所改善，”她说.

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. 她也帮助了我 learn time management skills and how to set myself up for success," 她说. “我看 forward to continuing to work with her post-graduation."

Karakok说 Sparks' research will extend beyond mathematical proofs to other written communication in mathematics courses that involve understanding how people process 他们怎么想，怎么写.

"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说.

Sparks plans to keep 教学 after she graduates in May 2025. 她喜欢教书 undergraduate and higher-level math courses as well as pre-service elementary and 中学教学课程.