Learning by Teaching: Service-Learning in a Precalculus Classroom

By Ekaterina Yurasovskaya, Seattle University

Mathematics is a beautiful subject that can easily become an ivory tower. There can be a temptation for teachers and students of mathematics to shy away from the role that mathematics plays as a social force and a barrier that can put a halt to a person’s career, security, and social mobility. The mathematics education community has been studying this situation for years – for example, see this article by Rochelle Gutierrez [1]. One way to include a focus on society and its problems in a mathematics classroom is by introducing service-learning into one’s course.

Service-learning is a pedagogy that combines the course content with community service that is directly tied to the material that students are studying inside the classroom. Service-learning has traditionally belonged to the domain of social sciences such as psychology, sociology, or social work, however interest in service-learning has recently increased in STEM disciplines as well. A special issue of PRIMUS [2] was entirely dedicated to mathematical service-learning projects; an interested reader will find a wealth of helpful practical information and project descriptions there, from math fairs and tutoring to running modeling projects for community organizations. In this post, I would like to share with you my own experience with service-learning, its effect on my students’ worldview and mathematical knowledge, as well as offer some suggestions for the instructor who would wish to introduce service-learning into a math course.

Personal experience and motivation

When I first learned about service-learning four years ago, I immediately wanted to try it – and my initial motivation was practical. Precalculus students are a mathematical population at risk. Weak algebra preparation invariably hinders progress of STEM students, and severely affects performance in Calculus, a major junction in the leaky STEM pipeline. As teachers, we know that one of the best ways to learn something is to teach it ourselves: “I hear and I forget. I see and I remember. I do and I understand”. This led me to ask myself: “What if university students in my classroom had to teach algebra prerequisites to someone else? Will it help them learn and understand that material themselves?”

Since 2015, I have implemented service-learning as a component of one of my winter precalculus classes, each section numbering 21-25 students. In addition to the regular lecture-homework-tests-problem-solving part of the course, students spent 2-3 hours each week tutoring mathematics to students in the community, an urban environment with a large immigrant and refugee population. In the past three years, students have served in local middle schools, a high school, a community college, and an elementary school. My goal was to place students at or above the middle school level, so that the mathematical content would be sufficiently challenging; the option to tutor at the elementary school was reserved for exceptional situations.

At the end of the course, I saw interesting results in my students’ course performance. During the first iteration in 2015, I saw a reduction in fundamental mistakes made on the final exams between service-learning and regular sections. Another time, a less-prepared service-learning group caught up in exam performance with the initially stronger regular section, and demonstrated a positive shift in beliefs about importance of conceptual understanding in mathematical problem-solving. The full description of the first iteration of the service-learning experiment and its results appeared in the RUME XIX Conference Proceedings [3].

In general, the atmosphere in the service-learning course seems different, with students being more focused and rarely slacking in their own work – perhaps because they feel they are role models for their own students. This is quite consistent with past experience of my colleagues who also found that service-learning produced an interesting effect in their classroom. For example, Allison Henrich [4] noted a decrease in math anxiety in service-learning students taking a math course for non-majors.

Student reflection

Reflection is an integral component of a service-learning course, because it serves as a tool for converting experience into knowledge (thank you, Jeffrey Anderson, for a great analogy!). In my class, students engaged in structured reflection to help them process their experiences. Twice during the quarter, we spent 40 minutes of class time talking about the students’ service-learning experiences. By talking to classmates who worked at the same location, students built a community and a support network, and resolved practical problems. The class discussions focused on questions raised by students themselves: “How would you explain to a student what a variable is?” “What do you do if someone is disrespectful?” “How do you motivate an unmotivated student?”

Students also kept a weekly reflection journal, and reading it was one of the most rewarding – and time-consuming – parts of my experience as instructor of a service-learning course. Each entry consisted of a mathematical and non-mathematical reflection. In the mathematical part, students analyzed their teaching interactions and reflected on the subject material that came up in the tutoring sessions. Students often noted parallels between the material we were covering in our class and their tutoring sessions, where they explained concepts of graphing and solving equations, and organizing data for word problems.

The optional non-mathematical part was free-form, and students could reflect on the human part of their experience, describing the kids they observed or the difficulties that immigrant students faced. One student reflected:

Oftentimes when a student is confused in class, it’s not that they don’t understand math, it’s that they are struggling translating the English being spoken.[…] If I wrote the problem out using numbers they could solve it immediately. They are astonishingly intelligent.

Quite often students saw themselves in the students they taught, which led them to recognize their own mal-adaptive mathematical strategies, such as not reading a problem or rushing through a solution. Some drew strength and inspiration from the personal struggles of their students, regardless of age, and witnessed how difficult life circumstances combined with poor math preparation put educational and career goals out of reach for their students.

Tutoring at Seattle Central Community College is really eye opening. It’s really made me think of my blessings and truly be grateful for them…Recently one of the people I tutor (let’s call her Hana) has dropped out of school. This was a woman that I admired and looked up to from the moment I met her. […] When she told me of her decision over the phone, I was surprised by how big the blow was to me. She was a 57 year old woman aiming to be a nurse. She showed me how determined a person can be even when the odds and/or circumstances are against them. She had dropped out due to medical reasons which really upset me due to how well she was picking up on her material in class.

Instructor experience

As the instructor of a service-learning course, one should be prepared for a time-consuming, rewarding, often intense, sometimes draining, unexpected and interesting experience. One should be aware that service-learning has potential to lead to lower overall course evaluations, despite the overwhelmingly positive student feedback on the tutoring experience. Service-learning introduces a potential for instability into the classroom, and the instructor has little control over the way this experience will unfold. I found myself addressing all sorts of matters, from practical to political. Seattle University has a wonderful Center for Community Engagement, which is instrumental in organizing student placement, arranging background checks, finding community partners, as well as providing cultural competence training to students. If a university does not have such an organization within its structure, the necessity to find community partners and build connections falls to the instructor, which is a large and time-consuming endeavor.

The instructor in a service-learning course has a responsibility to carefully frame the discussion about the experience so that service-learning does not end up reinforcing existing stereotypes and instill a “savior complex” in participating university students. The instructor should also provide some pedagogical training to students and discuss helpful tutoring strategies and the necessity to teach for understanding. Some pedagogical training can happen during regular lectures, while other discussions will fit well into the in-class reflection sessions.


Hopefully, the mathematical benefits can convince the more traditional and conservative math departments to implement some form of service-learning in their classes. A liberal arts or religiously-affiliated institution may follow a mission statement that aligns with a message of service and social justice, and so may be more open to service-learning as pedagogy. I would like to end this post with a quote from student reflection:

I believe that service-learning should be something that everyone should at least participate in at least once. Maybe it will be a hit or miss, but if it is a hit with some individuals, they can definitely devote their passion and their drive to teaching scholars and students who would greatly benefit from tutors.


[1] Rochelle Gutiérrez. (2013). The Sociopolitical Turn in Mathematics Education. Journal for Research in Mathematics Education, 44(1), 37-68.

[2] Special Issue on Service Learning. PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies 23:6

[3] Ekaterina Yurasovskaya. (2016) Service-learning in a precalculus class: Tutoring improves the course performance of the tutor. In (Eds.) T. Fukawa-Connelly, N. Infante, M. Wawro, and S. Brown, Proceedings of the 19th Annual Conference on Research in Undergraduate Mathematics Education, Pittsburgh, Pennsylvania. 496–505.

[4] Allison Henrich, and Kristi Lee.(2011) Reducing math anxiety: Findings from incorporating service learning into a quantitative reasoning course at Seattle University. Numeracy. 4(2).

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