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?”

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On the Culture of Making Things

By Nicholas Long, Stephen F. Austin State University

In one of life’s weird coincidences, when I moved to a small town in East Texas to start my academic career at Stephen F. Austin State University (SFA) ten years ago, I didn’t know that I would be working with someone from my high school graduating class of about 150 people. Through that small quirk of life, I met a lot of the art faculty and local artists in the Nacogdoches area. I love that I get to hang out with artists and art educators. They are really cool people and they MAKE THINGS. Things that people want to look at, things that people want to discuss, and sometimes, things that people even buy.  

The idea I want us all to consider is: “How do we grow and improve the culture of making and improving things for our teaching?” When I say things for our teaching, I mean much more than just textbooks and notes for lecture; I mean software and technology that adds meaning and value for our students; I mean activities that can change the attitudes, habits, and practices of our students; I mean the many other materials and resources that will transform students and mathematics classrooms. While I will cite some examples below of projects and resources that I think are doing good things, I genuinely think we need to not compartmentalize these practices, but make them part of what we as a community do. Continue reading

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Pursuing Our Mission to Support All Students at All Ages

By Priscilla Bremser, Contributing Editor, Middlebury College

The more I teach and learn mathematics, the more I regard the subject as a powerful resource that is unfairly distributed. Clearly, I’m not alone. Search for “underrepresented” on the American Mathematical Society website and you’ll find the inclusion/exclusion blog and the Director of Education and Diversity at the AMS, for example. While it is vital to build on the work of exemplary programs at the university level, we cannot fully address the inequities in access to mathematics, and to fields that require mathematics, unless we also examine and address inequities in pre-college education.

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Students Find Their Fit in the Mathematical Community at the Marshall University REU

By Stacie Baumann, 2017 graduate of West Virginia Wesleyan College, currently a doctoral student at Auburn University, and Matthew Jones, Virginia Tech, class of 2018

Editor’s note: The editors thank Stacie and Matthew for taking the time to share their thoughts and insights with us about their REU experiences. For students who are interested in applying for an REU, lists of programs can be found here and here. To read more about student and faculty experiences with REUs, see our other articles on this topic.


I did not know what a Research Experience for Undergraduates (REU) was until one of my professors suggested I apply to REUs at a few different institutions. I went to a small liberal arts college with few research opportunities. I applied to a handful of different REUs and was excited when I received my acceptance from Marshall University. I was excited to spend eight weeks of my summer at a different institution and to learn what mathematical research really looked like. I was also nervous that I would be behind the other students academically. When I arrived, my nerves were calmed and the excitement continued.


If I learned anything from participating in the REU at Marshall University, it was how to be frustrated. Before the REU, I had certainly encountered a few difficult proofs in my courses, some of which I spent a couple of days thinking about. However, I had never spent an entire summer obsessed on one seemingly tiny mathematical problem. Throughout the months of June and July, I thought about mathematics at breakfast while drinking my coffee. I thought about mathematics while sitting in a classroom at Marshall. I thought about mathematics while playing cards in the evening. I went as far as to buy a 3-foot-wide whiteboard to keep beside my bed that I could grab in the middle of the night and test out propositions.

When I describe that experience to my friends outside of the mathematics community, they usually say, “That sounds awful”. But in actuality, it was the most exciting experience of my brief mathematical career. In a short span of time, I learned a great deal of exciting new mathematics that I would not have been exposed to in a normal course at my home institution. I learned a great deal more about the mathematical community in general, how research works and where I might fit in. Most importantly, I learned how exhilarating the process of figuring things out mathematically can be. Continue reading

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They Taught Me by Letting Me Wonder

By Dr. Nafeesa H. Owens, Ph.D., Program Director/PAEMST Program Lead, Presidential Awards for Excellence in Mathematics and Science Teaching, National Science Foundation*

Today we celebrate the story of Marizza Bailey, who was honored last year by the White House with one of its Presidential Awards for Excellence in Mathematics and Science Teaching (PAEMST).

Marizza Bailey (top right), with her grandmother Luz Mendizabal, her mother, and her daughter, in a newspaper clipping from 1997, when Luz was given an award by Lima, Peru, for her advancement of education in the city.

When Marizza Bailey was 12, her grandmother, Luz Mendizabal, came to live with her in California. Born in Peru, Luz put herself through graduate school to earn a doctorate degree in Mathematics Education, all while teaching full-time and raising eight children. She brought many things with her when she arrived in California: her voracious appetite for learning, her vast knowledge of mathematics, history and literature, but what Marizza appreciated most were the questions. “Why do you think that?” “What makes you say that?” “How do you know that?” A conversation with Luz was a series of questions and answers that stimulated critical thinking.

With a grandmother who was a mathematics teacher and who inspired thoughtful dialogue with her children and grandchildren, it’s no wonder that Marizza followed Luz’s footsteps and became a mathematics educator, as did Marizza’s mother before her. For this family, mathematics was not so much a career or a school subject, but a way of viewing and interpreting the world. Marizza says of her family, “They taught me by letting me wonder and allowing me to draw my own conclusions.”
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Do We Get to Work at the Board Today?

By Steven Klee, Contributing Editor, Seattle University

When I first started incorporating active learning in the classroom, I struggled with getting my students to buy into being active.  I made worksheets, put the students in groups, and excitedly set them off to discover and play with mathematical ideas.  Despite this, many students were inclined to sit silently in a group of four and work on the problems on their own.

But really, who can blame them? First, this propensity towards solitude can be explained by basic human nature: specifically, the fear of being wrong.  We don’t want to be wrong. At least, we don’t want to be wrong in front of other people.  From that perspective, working alone is safe and comfortable.  We should view our job as teachers as one of helping our students overcome this basic human inclination, as opposed to viewing it as a failure or shortcoming on their part.

Beyond this, the desire to work alone can be attributed to culture and expectations.  Many students’ formative educational years have been spent sitting silently in desks passively absorbing lectures.  If they feel this is what is expected of a math class, then it is natural for them to continue to sit silently, even if the environment is meant to be collaborative.  Of course, it is not my intention to imply that this is an issue that is entirely the students’ fault – maybe my questions weren’t sufficiently open-ended, maybe I wasn’t doing a good enough job at “selling it,” maybe the students just like working alone, maybe, maybe, maybe… The list goes on.

I tried some of my standard tricks to foster communication among the students.  I would prepare impassioned pep talks about the benefits of working with your peers. This technique flopped for obvious reasons – no one wants to listen to what they are told is good for them.  Otherwise, cigarette companies and fast food restaurants would go bankrupt and I would be much more diligent about flossing.  I’d try to lighten the mood, saying “this isn’t a library, you’re welcome to talk to one another.” I’d give a difficult problem and leave the room to get a drink of water, forcing the students to rely on one another. These strategies helped, but never served to create the classroom of my dreams – one where students discuss math problems at such a frenzied pace that time ceases to exist; one that causes passersby to wonder whether we are having a math class or developing some bizarre scientific improv comedy troupe.

Over time, I continued to reflect on my own teaching and sought advice from more experienced practitioners of active learning.  As a result, I have developed a few strategies that have been effective in my classrooms. One of the most effective strategies for me has come from eliminating those pesky desks that keep getting in the way of my students’ learning.

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The Third Year of “On Teaching and Learning Mathematics”

By Benjamin Braun, Editor-in-Chief, University of Kentucky

Summer 2017 brought the third anniversary of On Teaching and Learning Mathematics and with it our annual review of the articles we have published since our previous year in review article. Over the past year, our articles have covered a range of topics and ideas, and I have loosely collated them by the following topics: active learning, K-12 education, summer experiences, assessment, diversity and inclusion, curricular issues, and mathematical culture. As we begin a new academic year, we hope you will take some time to read them (or read them again!) and be inspired. Continue reading

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Call for Nominations: Editor-in-Chief

Applications and nominations are invited for the position of Editor-in-Chief of the American Mathematical Society blog On Teaching and Learning Mathematics. The Society seeks a college or university mathematician or mathematics educator with at least five years of experience. Applicants should be familiar with issues in mathematics education at both the postsecondary and K-12 level, and have ideas for contributors who can write knowledgeably about those issues from a variety of pedagogical and institutional perspectives.

The Editor-in-Chief is assisted by a board of Contributing Editors, selected by the Editor-in-Chief, who help to create the contents of the blog and solicit material for publication. The goal for this blog is to stimulate reflection and dialogue by providing mathematicians with high-quality commentary and resources regarding teaching and learning. This blog serves as a big tent, giving voice to multiple contributors representing a wide range of ideas. The AMS provides support to this mission through social media promotion.

The responsibilities of the Editor-in-Chief are: to create and maintain an annual publication schedule (typically 24 articles per year), edit/review/approve articles prior to publication (in collaboration with editorial board members), solicit or write between 4 and 6 articles per year, lead editorial board conference calls, and recruit new editorial board members when needed. The average time commitment is 2-4 hours per week.

Nominations and applications should be sent to web-editor@ams.org by September 15, 2017, and should include the following information regarding the nominee/applicant: name, contact information, curriculum vitae, and past editorial and/or blog experience. Applicants are encouraged to submit a statement discussing the direction they would like to take the blog in the future.

Note from Ben Braun, current Editor-in-Chief:

Since we began On Teaching and Learning Mathematics in June 2014, I have had an amazing experience working with fantastic editorial board members and contributing authors. I believe that the commitment to excellence by our board members and contributors is the reason our blog attracts over 5,000 unique page views every month. For anyone who is interested in deepening their knowledge regarding the teaching and learning of mathematics, and in contributing to the improvement of postsecondary mathematics education, I encourage you to apply for this position.

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To Active Learning and Beyond: Attending to Student Thinking AND Student Experience in Active-Learning Math Classes

By Jess Ellis Hagman, Contributing Editor, Colorado State University

On a recent trip to Santa Fe, New Mexico, I met a really cool woman named Anna Sale who runs a podcast called Death, Sex, and Money (check it out). In this podcast she interviews people about things she is curious about. We talked about how her work is similar to research (come up with something you want to know more about, then go learn about it), except much less rigorous and you get answers much more quickly.

One thing I am very curious about is how students from marginalized populations experience active-learning classes. I believe deeply in teaching in a more active way, and I also believe deeply in teaching so that all of my students have the best opportunity to succeed, and sometimes I wonder if all my active-learning moves are enough to support all of my students. So, taking inspiration from Anna, I decided to interview some experts. (I am also working on a grant proposal to look at this in a much more rigorous/slow way). Continue reading

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The Mathematical Encounter That Changed My Life

By Art Duval, Contributing Editor, University of Texas at El Paso

I just returned from an all-years reunion of the Hampshire College Summer Studies in Mathematics (HCSSiM) program, a six-week program I attended during the summer between my sophomore and junior years of high school.  It has been run by David C. Kelly, whom everyone refers to just as Kelly, since he started it in 1971.  There are several other summer high school math programs around the country (a good start is this list from the AMS), which likely share some characteristics with Hampshire, but since Hampshire is the one I have personal experience with, this is the one I am compelled to talk about.  And while several people and experiences were instrumental in my path to becoming a mathematician, Hampshire is the one that stands out most prominently in my mind, the one mathematical encounter that changed my life.  And from talking to other people at the reunion last weekend, I know that many other program alumni feel the same way.

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