The Classroom is a Social Learning Community

I think the ability to communicate mathematics, in both spoken words and writing, is a foundational practice of the discipline at any level, so group work is a critical component of my teaching that I incorporate in every class I teach. Good group work facilitation requires active instructor preparation; I usually lead my class in a discussion during the first week about their prior experiences working with peers. I’ve found that generating group work norms together with my students gives students agency in influencing classroom culture and increases their buy-in to group work. I communicate to my students that I believe every person has something valuable to offer their group and that although their contributions might all look different, every group member should feel like they have a better understanding of the problem by the end of a work session. I emphasize this because I want myself and my students to honor the depth and diversity of ideas that our collective community brings to group discussions. I take care to plan group work before class, keeping in mind the wide array of mathematical backgrounds that are present in my class, particularly in a zero-entry class like QL where some students come fresh out of high school calculus and others haven’t taken a math course in more than a decade. During group work, I act as facilitator in many student conversations. Sometimes, my goal is to help a quiet student bring their thinking forward to the larger group. Other times, I’ve helped students navigate team communication conflicts.

When group work is incorporated into a class effectively, it has the potential to help students develop strong social bonds that benefit them in areas of their college experience outside of learning mathematics [1]. I ask my students to exchange contact information with someone else to give them another resource in my class, but also to model why having class connections is important throughout the rest of their college careers. An exchange in my QL class that left a deep impression on me occurred when a student who had been absent for a couple weeks returned to class and his group immediately greeted him, saying that they missed him, and offered to catch him up on the work. I make an effort to reach out personally to any students struggling with attendance but I think there’s great power in feeling needed and valued by your peers in the classroom community. This sense of belonging can be the nudge a student needs to stay the course and not drop or withdraw from a class.

I want my students to feel that their contributions to their classroom community (and to the other communities they belong to outside of school) are valued and respected. Underlying this value is a desire to help my students think positively of themselves as practicing mathematicians. Although this looks quite different across the breadth of classes and student populations that I’ve taught, a strategy I’ve employed to do this is to incorporate relevant and contextual content tailored to the students in that particular course. Researchers have shown that many students who take QL (and similar zero-entry courses such as college algebra) enter the classroom with high levels of math anxiety and a belief that mathematics is disconnected from their lived experiences and future careers [2], [3]. The literature surrounding pre-service teachers also reports high math anxiety in this population [4]. These findings are echoed by my own students in an activity I give my class on the first day of the semester. When I ask them to share something they’re worried about regarding the course, a repeated sentiment that appears is that students are nervous about their performance because they just “aren’t math people.”

My strategy is to draw upon students’ personal experiences and funds of knowledge [5] to help them gain confidence in math. Michigan State’s QL course is required for students of the residential political science college and they make up a significant proportion of my QL students each semester. When teaching a unit on estimation, I lead the class in a discussion about whether it is reasonable for a congressional candidate to knock on the door of every voter in their district. This excites my political science students who have knocked doors in campaigns like this because the class relies on their personal knowledge and experience to move forward with our estimation. This taps into their leadership roles in communities outside our classroom and allows them to leverage that knowledge and experience to make quantitative judgements. I’ve employed a similar foregrounding of relevance with my pre-service teachers. Many of the longer, reflective tasks that I asked them to complete involved thinking with their “teacher hats,” such as giving feedback on a sample student solution. I found that this was a useful reframing that asked students to assume a role they were more confident in and positioned them as the experienced knower in this scenario.

While teaching transition to proofs, I focused on developing policies and assignments to introduce students to the community of professional mathematics by structuring my class in a way that reflects the practices of the discipline. In transition to proofs, I felt it was important to offer revisions on all homework and proof quiz assessments to emphasize the reality of proof writing as an iterative process that often requires a mathematician to revisit and revise their ideas. I also assigned a proof portfolio project rather than a traditional midterm or final exam, where students practiced typing up proofs in formality and met with me one-on-one in an oral portfolio defense. Again, this project was designed to be a more authentic reflection of a mathematician's work, including the practice of creating oral presentations to share math in seminars and it gave students the chance to express their mathematics in multiple modalities.

Teaching in online and hybrid settings prompted many undergraduate educators to rethink what a college math course should look like, and I reflected a lot on my own practices during this period. I think highlighting the manifold ways that we communicate mathematics has always been a part of my teaching philosophy, but I began to prioritize this in my course design by incorporating multiple methods of engagement. When designing curriculum for QL, I worked on both individual, timed, online assessments connected to news articles as well as multiple group projects that concluded long-form writing assignments where students were tasked with communicating quantitative thinking to a targeted audience. In the weekly assessments, I asked students to use their quantitative skills to engage with a popular news story that I chose for its timeliness and potential interest to students. I built these assessments around a variety of sources and articles that students would find interesting and relevant to their lives, such as an exploration of weighted ranking systems in an article explaining why college ranking lists name different schools as the “best” university. In one of the longer-form projects I helped develop, students explored percent change by looking at how the cost of living compared in different cities and how cities scored on various quality of life metrics. They summarized their learning in an assignment that asked them to write an email to their boss negotiating costs related to relocating for a new job. These two assignments are examples of a course design that allows students to communicate their quantitative understanding in multiple ways that are all relevant to the mission of the course.

Ultimately, my goal is to build community with my students and for them to feel like they have a respected voice in that community. I offer anonymous feedback surveys at various points in the semester to check in with my students about their experience in class and use those survey results to inform my teaching. I also created a journaling assignment for my transitions to proof class where I had students engage in reflective writing tasks about the mathematics they were learning, their workload and progress through the semester, as well as giving them an open space to share whatever was on their mind. I thought this was especially helpful in a hybrid setting where we didn’t have the benefit of being present in the same physical space, and this assignment gave me good insights into how to help both my high-achieving and struggling students achieve success in the course.

References

[1] Springer, L., Stanne, M. E., & Donovan, S. S. (1999). Effects of small-group learning on undergraduates in science, mathematics, engineering, and technology: A meta-analysis. Review of educational research, 69(1), 21-51.

[2] Wismath, S. L., & Worrall, A. (2015). Improving University Students' Perception of Mathematics and Mathematics Ability. Numeracy: Advancing Education in Quantitative Literacy, 8(1).

[3] Mayfield, B., & Stewart, A. (2019). Quantitative Literacy in the Core Curriculum of Hood College: Chapter II, Outcomes and Assessment. Numeracy: Advancing Education in Quantitative Literacy, 12(1).

[4] Bursal, M., & Paznokas, L. (2006). Mathematics anxiety and preservice elementary teachers' confidence to teach mathematics and science. School Science and Mathematics, 106(4), 173-180.

[5] Bartell, T., Wager, A., Edwards, A., Battey, D., Foote, M., & Spencer, J. (2017). Toward a framework for research linking equitable teaching with the standards for mathematical practice. Journal for Research in Mathematics Education, 48(1), 7-21.