Partnering with Students to Build Community in an Upper Level Mathematics Course

Featured Faculty and CTL Student Pedagogical Partners

Ryan Alvarado photo

Ryan Alvarado





Tessa Levenstein Image

Tessa Levenstein '22





Stephanie Masotti image

Stephanie Masotti '22





Kriti Verma image

Kriti Verma '22





I taught Math 355 (Introduction to Analysis) during the Spring 2020 semester. This course is a 300-level math major course that serves as one of the two courses over which students may choose to take their comprehensive exam for the major. The focus of the course is to teach students how to apply formal, mathematical logic and articulate their step-wise, logical thinking to solve complex mathematical scenarios, using both narrative form and formal, mathematical proof structures [link to syllabus here]. In other words, this course asks students to demonstrate their ability to build complex arguments to connect seemingly disjointed mathematical claims. This semester, the course enrolled 26 students, primarily sophomores and juniors, with a wide range of experience in upper-level math courses.

I was so grateful to have partnered with three Center for Teaching and Learning Pedagogical Consultants this semester (Kriti Verma, Steph Masotti, and Tessa Levenstein), who provided weekly, up-to-date feedback from other students in the course, administered class surveys, and conducted focus groups. The partners helped me work through many of the ongoing questions that I had about the course design and structure, especially during the shift to remote teaching and learning, such as: 

  • What is the best format for assessment (e.g., in-class exams, take-home, open-book exams, an entirely different approach to evaluating student comprehension)? 
  • What is the appropriate workload for this course, given student background knowledge. After shifting to remote teaching, the question of workload also related to variable home learning situations.
  • How can we maintain a sense of community throughout the semester, especially in remote contexts? 

I think that the most successful impacts of our partnership emerged from the fact that we were able to gather and engage with the opinions of the students directly and have ongoing, face-to-face communication about what students were thinking and feeling about the class and the assignments that were offered. Especially given the transition to remote learning, this direct line of communication to student experience was critical to my ability to be responsive.

As I worked in partnership with my student consultants to adapt the course to remote teaching and learning, I sought to balance three priorities: 

  1. How to maintain rigor, so that students continued to develop their high-level mathematical analysis skills,
  2. How to ensure a sense of familiarity and thus, stability in the class climate, and
  3. How to build in appropriate flexibility in order to account for students’ variable home learning climates and demands on their time and psychological energy.

Some direct impacts of this partnership on course design include: 

  • Exam Structure. After much deliberation with my student partners, I decided to maintain the in-class exam format (so as to maintain the familiarity of assessment style that students had previously experienced and will experience on the comprehensive exam) for all exams except for a final, take-home exam. At the same time, I allowed students to submit re-writes on their exams for problems on which they had struggled (so as to provide flexibility in how students’ demonstrated that they had developed the rigorous analytic skills of the course). 
  • Building and Maintaining Community. Drawing on recommendations from my student partners, I incorporated several practices aimed at building community, especially during the remote teaching portion of my course: 
    • I created breakout rooms for the students to convene at the start of each week, to discuss both academic and nonacademic prompts without an instructor presence. 
    • During synchronous lectures, which were recorded for students to use for review, I asked students to turn on their videos, which allowed me to quickly call on students after I posed a question to or ask for input from students in the class. Students remarked about how they appreciated being able to see other students and hear questions from their colleagues. For a demonstration of this process during remote learning, see the video clip included below.
    • Chat Feature in Zoom. While I had initially disabled this feature in Zoom, I found out that students really enjoyed the opportunity to say “hi” to their friends in class and this social connection provided them with an important mental break during lectures.
    • Music playlist and pre-lecture Djing. I made a collaborative playlist on Spotify and asked students to add some of their favorite songs to the playlist. At 10 minutes before the start of class, and during any lulls in lecture, I played the playlist. It  was great to see them bob their head in the beat as they prepared for class.

In end-of-course evaluations, students remarked that I “was always engaged with ideas that students brought to the table” and that the course structure allowed for the “finding [of] the root of the issues with students' ways of thinking, so as to improve learning.” Another student specifically remarked on the benefits of connecting with their peers in the course: “He would set up breakout rooms in classes to make sure our peers can talk to each other, so the sense of community in our class remained even though we were not in the classroom together.” 

Reflections of the CTL Student Pedagogical Partners

It is clear from the student pedagogical partners' reflections just how important an open dialogue with students is for their sense of connection and learning in the course. The positionality of the pedagogical partners, as students in the course themselves, allowed them to engage in authentic and direct conversations with their colleagues, which benefited our joint process and the ongoing course design, especially following the shift to remote teaching. The student partnership also had a profound impact on the partners themselves, as they developed a deeper understanding of the diverse needs of learners in the classroom and the multi-layered process of developing and delivering a course. Finally, the partners said that the insights and invigoration gained through this process will lead them to approach their future classes with a perspective.

When reflecting on the contributions of the student partners, Tessa wrote, “As for our contributions to classroom learning, I believe that before the move to remote learning, we reinforced the strategies that Professor Alvarado was using that were working really well. After the move to remote learning, I think that we played a much bigger role in figuring out how lectures and office hours should work and modifying testing. We ended up recommending the take home final, which was adopted, and after hearing from the students about testing, I am confident that a take home final was the right format to adopt.”

In order to gain insights into students’ experience with remote learning, the CTL student consultants employed two strategies: 1) they developed and administered a mid-semester survey, which asked for student feedback about their experiences of lecture content and pace, comfort asking questions in class, attendance and effectiveness of office hours, and any other feedback that they would like anonymously shared with the instructor; and 2) they conducted a focus group with students after the end of the course to get more in-depth feedback about remote learning and the assessment redesign. Kriti wrote that her position as a student consultant in these feedback sessions allowed students’ to communicate openly and honestly about their experiences in the course, which in turn improved the quality of the information that the professor received. She said, “I think that the most successful impacts of our partnership were that we got to express the opinions of the students directly and have face-to-face communication about what the students were thinking and feeling about the class and the assignments that were offered, rather than a more impersonal answer that could be collected through a survey, especially with the transition to remote-learning.” Stephanie also wrote about the benefits of this approach to gaining student feedback about their needs and challenges: “If a student is struggling in a course, the professor will not know how to help them unless they have an open dialogue about what they are struggling with. We received survey responses explaining student struggles that had never occurred to any of us in the partnership, so it was essential for us to gather this information.”

The student partners also reported that working with faculty in this role resulted in changes to how they view themselves as learning and how they view the hard work of teaching. Tessa said, “I felt that this partnership made me feel more responsible for and connected to my class than I have previously felt in my classes. I think that the partnership made me feel more accountable both to my professor and my classmates. It was incredibly helpful as a student to understand my professor’s motivations and to talk with him so frequently about the classroom experience… I felt an ownership in the class in a way that I wish I felt in more of my classes as a regular student.” Similarly, Stephanie said, “I am happy with what we were able to accomplish in terms of making adjustments to the structure of the course and the material we covered.  We successfully gained feedback from students and made adjustments to class structure that led to more effective learning for most of the students in the class. We received meaningful responses from surveys and focus groups.   I also gained a much deeper understanding of all the work that goes into teaching a course.  Prior to this partnership, I already appreciated and valued the work that professors put into their courses, but I was not aware of how difficult it is to design a course that actively meets the needs of every student in the class, covers all of the necessary material, and maintains the interest of the students.  I will approach my future classes with this new perspective.” Finally, Kriti wrote about how this partnership work shifted her awareness of the benefits of using a wide range of pedagogical approaches to support student learning. She said, “Because it is highly unlikely that every student will learn and understand the material using the same teaching techniques and the same assignments, the best way to reach all students is to give different things they can do to learn to reach as many students as possible.”