Communications

The expectations I set in my classroom revolve around a central principle: mathematical communication. I firmly believe that a student’s ability to learn mathematics is closely tied to their ability to articulate and write about mathematical concepts. I’ve noticed that many students struggle to find the right words when trying to express a point of confusion. A particularly positive moment in one of my classes occurred when I encouraged a student to express their question by writing on the board. This experience was significant to me because it underscored the importance of focusing on the communication aspect of mathematics itself. In that situation, I guided the student in phrasing their question clearly and ensured the rest of the class followed along. Afterward, I set a goal to explore teaching methods that emphasize mathematical communication while also providing clear and reasonable expectations.

Expectations

I begin each semester by setting expectations for attendance, engagement, and participation—expectations that are not directly tied to their grades. The goal is to foster a sense of personal responsibility in my students. To achieve this, I emphasize that learning happens both inside and outside the classroom by encouraging them to start homework assignments early, work on them gradually, and regularly read the textbook. Early on, I also stress the importance of mathematical articulation and writing. For example, I expect students to actively participate in discussions and practice sharing their thoughts on core concepts. It’s common for me to ask students to make observations or propose solutions to the current problem.

In addition to these general expectations, I establish clear guidelines explicitly related to their grades. Alongside T.I.L.T. (Transparency in Learning and Teaching) assignments, I provide lab exercises designed to teach students how to produce high-quality written solutions for homework, quizzes, and exams. I distribute a grading rubric and a problem set featuring multiple solutions for students to evaluate. Together, we discuss how they would grade these sample solutions, helping them develop a stronger understanding of what constitutes a well-written response. Following this discussion, students complete their own written problems, which I grade and comment on.

By emphasizing communication skills in mathematics, I set clear expectations for the quality of their work. As a result, I’ve observed significant improvements in the clarity and organization of their exams. This focus not only benefits my students but also makes me a more efficient grader. It allows me to provide precise feedback on both the correctness of their solutions and the structure of their written work, helping them continually improve.

Transparency

Transparency is the glue that holds my first two philosophies together. From the very beginning of each semester, I frequently use the words "communication," "expectations," and "transparency" to set the tone. Early on, I provide my students with a grading assignment to give them a glimpse behind the curtain. I want them to clearly understand what is expected of them and why I approach teaching the way I do. I believe it’s empowering for students to grasp the "why" behind my choices, as it helps them take ownership of their learning experience.

Ultimately, I strive to ensure that my students never feel caught off guard. By being transparent about my teaching methods, I make it clear how they will be assessed and what they are meant to gain from each assignment and exercise. This approach fosters trust and allows students to focus on developing the skills and understanding they need to succeed.

From Fall 2021 to Spring 2023, I was responsible for coordinating the lecture sections of MAT 190 Precalculus at UNC Greensboro. Prior to 2020, the math department offered both a year-long precalculus sequence and a version of MAT 190 with a different curriculum. This was later restructured so that MAT 190 became the sole precalculus course, now offered as a 4-credit hour course. Due to the COVID-19 pandemic, the newly restructured MAT 190 was initially offered only as an online course. In Fall 2021, I was assigned to teach the first lecture section.

My resources were limited to the online syllabus and the MyLab and Mastering homework assignments. I took on the responsibility of creating all class notes, exams, and lab assignments for the new computer lab component, which accounted for the additional credit hour. While the course had an official faculty coordinator, I was tasked with developing the course content from scratch. Additionally, I designed a Development Canvas Page, which has since been used by myself and all subsequent MAT 190 instructors. I added a personal touch to the Canvas page by drawing the banner featured above.

Because the materials from the previous iteration of MAT 190 were no longer relevant, this project proved challenging but also rewarding. It allowed me to apply my own teaching methods and philosophies to the course. My materials were thoroughly vetted by multiple faculty members in the math department, all of whom gave their approval.

In Spring 2022, I co-taught the two available lecture sections of MAT 190 alongside another graduate student. This experience gave me the opportunity to take on a leadership role. I gained valuable insight into the course’s effectiveness from another instructor’s perspective and implemented improvements and changes based on this feedback as I progressed.

I am proud to say that this continues to be a well functioning course at UNC Greensboro!