How did it go? Reflections on teaching college math during a pandemic, by Allison Henrich and Matthew Pons

“Overwhelmed.” 

“Drowning.” 

“Exhausted.”

This is how math faculty were doing as they finished up their fall terms in one of the most challenging years that many people on this planet have ever endured. We asked several math professors to respond to a survey reflecting upon their teaching experiences and, more broadly, their experiences working in the middle of a pandemic. Twenty mathematicians responded. Here’s what we learned.

The most common challenge that more than half of our respondents acknowledged was the blurred lines between work and other aspects of life. Many of us are parents, working from home with our children and perhaps a partner who is also trying to fulfil the duties of a full time job. Others of us don’t have children or other family members to care for, and work expands to fill all of our time.

“My biggest challenge was making lecture videos with a 5-year-old and a 1-year-old playing in the background and interrupting me. To deal with this challenge, I went to the car to make videos, borrowed a colleague’s basement to make some videos, and timed making videos with my husband taking the kids to the park on weekends.” 

“My biggest challenge was having enough time to devote to my job while also having a toddler at home. The time I would usually commit to work changed dramatically and lessened quite a bit.” 

“The biggest challenge for me is work life balance. Being in a support role to so many people through such a stressful time takes its toll. Sometimes I feel like the giving tree.” 

Whether or not we have a full or an empty house, working from home means there are no natural boundaries that separate work from non-work. As a response, one casualty of these blurred lines is our self care.

“I built up my body up through healthy habits over the summer, and then I coped with the challenges this fall by slowly destroying it through numbing booze during the semester.” 

“The combination of teaching more than normal, trying to be as flexible as possible with students with regard to due dates, and no longer having separate “work” and “home” spaces has made it more difficult than normal to turn off “work mode” and focus on self care.” 

Another casualty is our scholarship.

“To manage the reduced hours available (and the increased time teaching online demanded), I had to step back entirely from research, which meant papers not written, promotion not applied for, projects not started or continued. I had no choice—there are simply not enough hours in the day when the kids are not in school. Though it’s really frustrating and depressing, I’m on the other side of tenure, so restarting everything once the kids are back in school is not as fraught with pressure and panic as it must be for my junior colleagues in the same time-stricken situation.” 

Survey respondents were also challenged by either having too many people around at home, or too few.

“Working from home for me means that I don’t leave the house much. It is lonely.” 

“My biggest challenge is social isolation of self, friends/family/colleagues, and students.” 

“My biggest challenge is living and working from home with a husband also working from home, two kids in remote school, two pre-school aged kids, and a baby. I don’t sleep and the house is a mess.” 

The dearth or wealth of housemates aside, people found it difficult to mentally juggle work and thoughts about the pandemic, politics, and social justice issues.

“My biggest challenges have been no child care, no breaks from working, and worrying about my health and my family’s health. I don’t have pre-existing conditions, but since I’ve had bronchitis/pneumonia at least four times, I don’t really want to experiment with getting Covid. Plus, my emotional response to national events has been a challenge. Sometimes I read the paper and want to vomit.” 

“I’m not well. Family politics plus terrible teaching conditions are heartbreaking.” 

“My biggest challenge has been my grief (and sometimes anger) at the foolishness of people in this country.”

“My biggest challenge has been staying sane while loved ones and students make questionable decisions to gather and ignore science.”

Working at home during a time of national and international turmoil creates a variety of challenges, but for math professors, teaching mathematics remotely poses its own special set of problems. Some people are teaching face-to-face, some online, and there are some who teach using both modalities, or need to be prepared to pivot from one to another mode of instruction at a moment’s notice.

“My biggest challenge is the uncertainty from day to day. How many students will be in class today and how many out due to quarantine or isolation? What if I or anyone in my family wakes up sick? Can I quickly pivot to online class?” 

“I tried to set up course formats that would allow me some leeway (and the students  who might get sick or quarantined). I recorded lectures, realizing that some things would just have to be flexible during this semester. Amazingly, some of my colleagues were shocked when students started getting sick and quarantined. Some of my classes got moved to e-learning and some streamed. I had to do *stuff* to get my school to let me teach online. Being forced to teach face-to-face would have been a disaster because my kids had a grand total of 6 days of face-to-face school this semester.” 

For those teaching in person, fear of getting sick and potentially passing on the coronavirus to a family member is a significant factor in their lack of well being.

“(I have) anxiety over getting sick or bringing this home to my husband and kids.”

Regardless of how people are delivering content to their students, teaching in a pandemic has required a major redesign of courses and learning new skills. In some cases, this has had some positive results.

“I am proud of my decisions to (a) remove nearly all timed assessments from my courses, (b) incorporate a feedback and revision process into all written homework assignments in my courses, and (c) implement standards-based grading for the first time in a course (despite the pandemic). I feel like this helped reduce some of the increased student anxiety this term and helped us shift our focus away from grades and towards learning.” 

“One silver lining is that all of the remote stuff has really forced my hand to adapt some new uses of technology.  I have a shared spreadsheet setup (using the “importrange” command) that allows me to share my homework grade book with students.  I will definitely use this again in the future!” 

“I am most proud of learning the new video technology, especially when I am teaching remotely to students in quarantine at the same time as teaching to the in-person students.  I also feel I am mastering the “art of the Chat”!  For example, the freshman engineers in Calculus who were hesitant to speak up in a Zoom classroom would answer questions readily in the Chat, and would post some really funny comments, too. The nonverbal banter was a delightful surprise!” 

A common complaint both about teaching in a remote setting or teaching in person with social distancing is that building community in a classroom and forming relationships with our students are incredibly difficult tasks.

“I’m relearning the basics of student-teacher interaction, as though I’m back in my first year. Video/Zoom/Email-based relationships are difficult for me, as I normally rely on the communal energy and subtle non-verbal language one receives (and gives) in a physical gathering.” 

“My university managed to stay in-person for the semester (masked and socially distanced, of course), so my biggest challenge in the classroom was the loss of group work for the in-person classes.  I love having students discuss the concepts and collaborate together, whether planned or spontaneous, and my classes felt empty without this communication.  The energy that comes from those interactions was gone, and I couldn’t read student’s facial expressions well when I was teaching, because of the masks.” 

“My biggest challenge has been student engagement during class. It’s hard to get students to talk during a normal semester sometimes but it’s even harder when 6 ft apart and in masks.” 

“My biggest challenge was the lack of energy that exists in all instructional formats. Remote teaching felt like a clinical means to an end, and in-person was stripped of a sense of warmth by the need for safety precautions and constant state of change and uncertainty.”

Some of us are also trying to chair departments during this pandemic. On top of teaching challenges, those of us who are also administrators lamented the lack of recognition of the massive amount of additional work and the added emotional strain that chairs face at this moment.

“Being a chair, I would like faculty to know that for as much as they are going through, their chairs have to go through the same and still must take on everyone’s issues and problems. If people could just say thank you for doing the job they didn’t sign up for, it would go a long way.” 

But there is more human connection for some during this time. Professors are reaching out to their students in ways that—for many—they never have before. Care for students has taken center stage.

“To help students who felt disconnected from and dispassionate about the class, I had flexible (almost 24/7) office hour availability, and encouraged students to reach out about class and non-class issues they may be having.” 

“I have been responding to student disengagement by reaching out to students who miss classes/assignments and offering sympathy, extensions, etc; using standards-based grading to get students to take ownership of their learning in key areas; and scheduling follow-up “oral make-up quizzes” on Zoom to force one-on-one discussions with struggling students who miss office hours and/or class.”

“I am proud of how I put the students first. I know that the leniency that I allowed in my classes was meaningful to them. I’m glad that I could offer them support in this really strange, stressful time.” 

This care for students is being felt. One of the most joyful experiences people have had this quarter is hearing their students’ appreciation.

“I’m most proud of the fact that the students responded positively in their end of the semester surveys (also known as “teaching evals” at some schools) and in their last emails to me. They clearly understood that I cared for them and saw me as an empathetic and supportive teacher.”

“I’m most proud when I receive emails of gratitude from students (more this semester than ever before) telling me how much they appreciated my effort and how they felt a part of the course, even when remote, or thanks for my patience with their individual needs. I told them on the first day of class that I would lead with patience and compassion, and I hope I was successful in doing so.” 

For many, it is challenging to find a silver lining. They just keep putting one metaphorical foot in front of the other. There’s something, though, about knowing that they’re not alone in their struggles. Sharing our challenges in teaching and in life right now is one of the best things we can do. One of our survey respondents said, “Completing surveys like this and talking to colleagues (especially at other schools) is therapeutic and helps me to feel like I’m not alone in this struggle.” 

You are not alone.

We would like to thank the following people for contributing to this blog post: Robert Allen, Jennifer Beineke, Heather Cook, Mike Diehl, Adam Giambrone, Katherine Heller, Emille Lawrence, Martin Montgomery, Emily Olson, Sara Quinn, Partick Rault, John Rock, Robert Rovetti, Anne Sinko, AJ Stewart, Sue VanHattum, Abigail Wacher, Marion Weedermann, Nancy Wrinkle

 

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Balancing the Love-Math Equation, by Anonymous

The different parts of a person’s life, such as family, friends, and careers, don’t exist in a vacuum. Disruptions in one area can have massive effects on another. For me, my personal life had almost catastrophic repercussions on my mathematics career.

When examining my romantic relationships from my early twenties, I find that I had often become the caretaker, filling the roles of girlfriend and mother to my boyfriends. And this was certainly the case with the partner I was with during the first couple years of my PhD. This person was brilliant, kind, and exciting, but also had a lot of deeply rooted issues that had me taking up a third role: therapist. At school, I would take classes, study, and teach. Then I would come home, work on homework, do all the cooking and cleaning, and help my partner work through whatever was affecting him that day.  Looking back on this experience, it is clear that this was an incredibly unhealthy and unbalanced relationship, but in the moment, I saw that the person I loved needed help, and so I helped. This “help” drained me, bit by bit.

Even though I was exhausted, I did well in my classes. At the end of my second year in grad school, it was time to take the qualifying exams for the PhD program. These exams were traditionally held at the end of the summer, which was great because I had three months to study for the exams. I worked hard and studied as much as I could, but when you’re emotionally drained, there is only so much you can learn. By the end of the summer, I knew a lot, but it wasn’t enough.

The emotional rollercoaster I experienced during the qualifying exams is something that can hardly be expressed. I went into the exams nervous but hopeful; I thought I might be able to scrape by. The second I saw the exams, my hope diminished, but all I could do was go for it. Walking out of the exams, I knew I had not passed, and the devastation was overwhelming.

Then came the waiting: the formal results were sent out a week after the exams. During this time, the hope returned. Maybe I did better than I thought, maybe I had scraped by after all. I hadn’t.

With the fall semester beginning, I had to push off the fear and doubt, and gear up for taking the exams again in the winter. During this time, the emotional load of taking care of myself, my studies, and my partner started to have more significant effects. I lost a considerable amount of weight; I found it difficult to complete my school work; I slipped into a depression. I remained in denial for months. I blamed school for my struggles, when in reality the most exhausting part of my day was when I got home.

A few weeks before my second (and final) attempt at the qualifying exams, I was staying with my parents for the holidays and I came out of my denial. I began the heartbreaking and arduous process of ending the toxic relationship with my partner. A friend helped me move into her spare room. Studying for the qualifying exams was practically impossible, but I still tried. My second attempt at the exams wasn’t any better than the first.

Despite the misery of my situation, the math department was incredibly supportive. I talked to the professors about my situation, and they allowed me one final attempt at qualifying exams the following summer. During the spring and summer, I was able to get back on track, focusing on my work and my own well-being. By the end of the summer, I was feeling confident and knowledgeable. The third time was definitely a charm for me, as I passed the exams with high scores.

I still carry the lessons from this experience with me. I have learned what to look for in healthy relationships and not to act as my partner’s mother or therapist. I have come to a place of balance between my personal life and my career, making sure I put my needs before the desires of others.

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Celebrating Women in Mathematics, by Denise Rangel Tracy and Oscar Vega

The Association for Women in Mathematics (AWM) turns 50 next year, and in celebration a commemorative deck of cards has been created. Using one side of the cards, several different variations of a mathematical game called EvenQuads can be played. The other side of the deck features portraits and short biographies of 64 exceptional women mathematicians. This deck helps bring women mathematicians, both historical and modern, into the spotlight.

For many centuries, mathematics was a “boys club.” Women were not only not invited to participate in mathematical activities, but were actively discouraged from pursuing mathematics. Sofia Kovaleskaya had to fight against prejudice that closed the doors of universities to women in science. She ended up being the first woman to earn a Ph.D. in mathematics… less than 150 years ago. She went on to be the first woman to be appointed as a professor at a western university and had a successful career as a mathematician. Sophie Germain had to pretend she was a man to be taken seriously as a mathematician; she made great contributions to, for example, the advancement of the study of Fermat’s Last Theorem.

Stories like these are not restricted to historical women.  In 2018, Lenore Blum resigned her Distinguished Professor position at Carnegie Mellon University after unsuccessfully fighting systemic sexism caused by changes in the management structure of the Carnegie Mellon Center for Innovation and Entrepreneurship, an organization she co-founded. Maryam Mirzakhani is probably one of the most famous modern-day women mathematicians. She grew up during a war, in a country that frequently infringes on women‘s basic rights, and yet earned one of the most prestigious awards in mathematics, the Fields medal.

Thousands of women have had to persevere through systemic prejudice, ill advice from mentors and teachers, and general bias against women’s abilities in mathematics and other sciences. While times have changed and some things have improved, there is still more to do. The EvenQuads deck highlights women who have led the way and made contributions to the mathematical community. Help make women mathematicians known to the world. Learn more about the project at

https://awm-math.org/publications/playing-cards/

The Kickstarter campaign for the first EvenQuads deck (of four!) runs through November 18th.

https://www.kickstarter.com/projects/evenquads/evenquads

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The Best and the Brightest, by Pamela Pierce

I almost ended my study of mathematics after my bachelor’s degree. I am now grateful for the series of circumstances and decisions that led me to graduate school in mathematics, and ultimately to a fulfilling career at a school that is a perfect fit for me. Knowing how happy I am now, it would have been a shame had I given up on this dream.

I fell in love with mathematics during my college years. I was fortunate to attend a top-rated liberal arts college and to take classes with professors who were truly gifted at their craft. I enjoyed my classes and worked hard, but I was not a straight ‘A’ student; perhaps I was a “late bloomer”. I finally took Linear Algebra as a junior, and discovered that I loved writing proofs. What’s more—my professor noticed my interest, he saw potential in me, and he encouraged me to continue asking questions. My confidence was at an all-time high.

I began to wonder if I would like to go to graduate school in mathematics. It sounded both terrifying and delightful at the same time. But would my B+ average in my major be enough to get me into graduate school? I wasn’t sure. I soon learned that the department offered the opportunity to write an honors thesis in mathematics. Surely, this was something that I should pursue, because it would help me to decide whether graduate school was for me. In order to write a thesis, I had to complete a qualifying exam in the spring of my junior year. The exam consisted of three parts. The first part tested one’s knowledge of the ‘core’ subjects: Calculus 1, 2, and 3, and Linear Algebra. Each student was then able to choose two additional subjects in which to be tested. I chose Real Analysis and Combinatorics, since I had recently completed those courses. This was the same exam that seniors faced in order to earn their degree in mathematics. Seniors were required to earn a ‘pass’ on all three parts of the exam. Juniors wanting to qualify to write a thesis would need to earn a ‘high pass’ on all parts of the exam. I would have two attempts at the exam.

Some of my friends pursuing other majors on campus did not have to ‘qualify’ in order to write a thesis. All they had to do was express an interest, and they could begin writing. To me, this was a further statement about the exclusivity of the field: mathematics is such a rigorous discipline that we must restrict access to the very top students. Students who undertook the challenge of a thesis would have a chance to graduate with Latin honors. I couldn’t care less about graduating with honors, but I very much wanted the experience of writing a thesis! So, I spent my winter break studying intensely in hopes of doing well on the exams.

Sadly, I was not able to earn the three scores of ‘high pass’ that were needed to qualify to write a thesis. I think I earned two grades of ‘high pass,’ and on one part of the exam I simply earned a ‘pass’. On my second attempt, it was the same thing, only a different part of the exam tripped me up. I was devastated. Couldn’t the faculty see my passion for mathematics? Didn’t that count for anything? At that point, I felt that I should abandon any hope of going to graduate school. I was not among the best and the brightest. I was not good enough. While the fall semester of my junior year had boosted my confidence, by the end of the year my confidence was gone.

I did my best to forget the exam experience and to just move forward and enjoy the rest of my mathematics major. My senior year, however, required that I spend some time thinking about what to do after college. I sought the advice of family, friends, and faculty. My family suggested that I pursue engineering because I could get a reliable and high-paying job, and a friend of mine suggested actuarial work because that was what he planned to do. All of these ideas sounded practical, but I knew deep inside that my passion was to continue studying theoretical mathematics. When I discussed the future with my Topology professor, he said that he thought that I would be a great teacher. Of course, he was suggesting that I teach high school. While this was intended as a compliment, it stung a little bit, because through his words I could hear that I was not good enough for teaching at the college level, which was my secret ambition. I didn’t share my secret ambition with anyone, for fear that someone would say the words directly to me: Graduate school in mathematics is for the best and the brightest. You haven’t proved yourself to be in this group.

I convinced myself that teaching high school would be fun, and I would still get to interact with mathematics. I entered a graduate program where I would be teaching at a public high school and earning an M.Ed. and teacher certification at the same time. While I enjoyed the teaching, I missed the challenging and fun math classes that had made me feel so invigorated in college. One day as I was lamenting this, I came to the realization that there was nothing stopping me from continuing my studies. Maybe I hadn’t been a straight ‘A’ student, and maybe I didn’t write an undergraduate thesis, but I was willing to work hard and I was passionate about mathematics. I mustered some confidence, sent in a few applications, and crossed my fingers. I was thrilled when I was admitted to graduate school with a teaching assistantship to help pay my way.

I was so happy to be back in the classroom—both as a student and as a teacher. Being able to teach all of the courses in the calculus sequence was awesome. It reinforced my knowledge of the subject and it gave me some useful experience which helped a lot when I was applying for jobs. In graduate school, I took my first and only course that was taught by a female professor, and it was wonderful. Who knows? I might have gone into abstract algebra if she had stayed around. Fortunately, there were other very supportive faculty around me, and I found a home working with a wonderful real analyst.

Of course, things got more challenging as I worked on a thesis and struggled to obtain results. I thought about quitting more than once, because it was so easy to get discouraged when the results weren’t coming quickly enough. It did not help to see three friends of mine—all women—leave the Ph.D. program before completing their degrees. By that point, however, I knew the exact career that I was after. I wanted to be a professor at a small college – I felt that I would be good at it, and that is what got me through the tough times in graduate school. I kept my eye on the prize.

The disappointment that I faced in my undergraduate years haunted me for way too long, but once I had a good job I was able to put it behind me and focus on my career. I can now say that not writing an undergraduate thesis was probably for the best. Perhaps I was not fully prepared for what it entailed. Perhaps I would have done a poor job and become even more discouraged. Or maybe I would have rocked it! I will never know. The experience definitely woke me up to the reality that there would be other challenges in the future—qualifying exams, a thesis defense, job interviews, a tenure decision. We are always being evaluated by others, and it is very difficult to get away from that. The key is to stay true to yourself and not worry too much about what others think of you. Unfortunately, most of us don’t come to this realization until we are more settled in our lives and careers.

I am proud of my resilience throughout all of the challenging times—especially when I viewed those exam results as a sign that I was not good enough for graduate school. I had to put aside my past failures and my concerns about how others viewed me, and just go after what I wanted. I knew that if I didn’t try for the Ph.D., I would always wonder about what might have been. Once I realized this, I knew that I couldn’t move forward along any other path if I was always dreaming of being a mathematics professor. There was nothing to do but to continue on my mathematical journey.

Historically, the doors to the field of mathematics have not been wide open to all, but I have hope that this attitude is changing. My experiences have taught me the following: as a teacher, my words mean so much to a young, impressionable student. My encouragement, or lack thereof, is visible to others. Moreover, noticing someone’s interest is as important as recognizing their talent and hard work. I hope to do my best to welcome my students into mathematics so that they can enjoy it as much as I do. While it is tempting to be “realistic” when they struggle in my classes, I hope to remember to not give up too easily in nurturing their passion for the field.

For the past 25 years, Pamela Pierce has been teaching at The College of Wooster, where every student writes a senior thesis. She earned her bachelor’s degree from Amherst College, her M.Ed. from the University of Massachusetts, and her M.S. and Ph.D. degrees in mathematics from Syracuse University. She has been inspired by many of her mathematics professors, but especially by Dan Waterman, her thesis advisor at Syracuse. Pam works in the field of real analysis and is active in the Summer Symposium in Real Analysis, which she has hosted twice. In 2009, she won the Trevor Evans Award from the MAA, and she is currently serving on the editorial board of Math Horizons. In her spare time, Pam enjoys music, traveling, and swimming.

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Liverworts, Nuclear Waste, and Parenting: Unexpected Connections During Virtual Teaching, by Dominic Klyve

In March 2020, I received news that seemed at the time to be a once-in-a-lifetime jolt.  A jolt that, as I soon would recognize, struck almost every teacher on the planet.  My instruction, including my finely honed classroom management and my practiced camaraderie with my students, would be conducted only virtually for the foreseeable future.

Like many people reading this, I grieved, fumed, and then tried to begin adapting as quickly as possible.

Perhaps, I mused in my brighter moments, this new reality will come with new opportunities. For a brief second I let myself imagine the benefits technology could bring my classes. We could connect with experts across the country (or around the world!) about our topics. We could engage in lively asynchronous conversations in which no voice drowned out any other, and where all ideas could be heard.  The range of media from which we could draw in our studies might come to be worth more than the loss of in-person communication.

And then reality struck.

Teaching online was a lot of work, and I was prepared for none of it.  On top of that, my wife (also teaching online) and I joined the legion of parents trying to help our kids (ages 9 and 12) to complete their elementary and middle school curricula online. The visions of new opportunity faded, seemingly as quickly as they had appeared.

My university runs on a quarter system, and COVID-19 struck just before finals week of winter quarter, so by the time classes resumed, I had new groups of students (almost none of whom I had met in person) and new pressures seemingly daily. My classes weren’t as good, I knew, as they could have been, but they ran better than I feared in my darker moments. Nevertheless, the visions of new possibility stayed at bay, held back by the stresses of professional and parental reality.

But fate is an interesting thing, and connections are found in the most unexpected places.

One of my classes was a “History of Science” course for our Honors College. It’s a class I’ve taught many times, and I love it, in part for the large array of subjects we cover. The range means that however much I think I’ve prepared, at some points in the class I’ll come upon the limits of my knowledge.

So it was in week five of our quarter, during a class in which we were discussing the disposal of radioactive waste. The students, as always, had submitted questions and comments on reading online, and I answered the easier ones in our virtual class session before declaring that due to my own ignorance, I couldn’t answer the rest of their questions.

Then one of my students unmuted herself.

“Umm… that’s my mom’s job,” she said.  “I’m sure we could ask her if we had questions.”

I looked at her image, one small rectangle in a grid of student faces.  “Her job?”

“Yes.  She’s a project manager at <a local site dealing with nuclear waste>.”  (Details omitted for privacy reasons.)

I was fairly excited by this serendipitous turn of events, and asked my student to let her mom know that we’d be thrilled to hear about her experiences, should she ever want to share.

My student smiled in a helpful way.  “I’ll ask her.  I can’t ask her now, though.  She’s working from home, and she’s upstairs on a call.”

And then, less than 30 seconds later, she called out, “She just came into the kitchen….  Mom!!”

After a hurried consult, my student’s mother, very much in her kitchen, sat down at the screen, and led us on an impromptu and fascinating discussion about her work.  My other students chimed in with questions, and we all learned a lot.

After class, I was thrilled. Finally, after weeks of struggling with virtual teaching, we had had an experience better than that which would have been possible in a traditional class. A parent, no doubt struggling in many of the ways I was, had taken time to share her knowledge and wisdom, and she left us better for it.

I shared the interaction with anyone who would listen, and vowed to try to ensure this would not be our last such experience.

I’ll confess that no floodgates opened, and after this fortunate encounter many parts of our class stayed the same, but I did find myself more open to new possibilities.  I was still looking for my opening when a few weeks later we read about modern museums in Bill Bryson’s A Short History of Nearly Everything, in a chapter in which the author highlighted scientists who studied bryophytes (mosses, liverworts, and other non-vascular plants to the rest of us).  The students were, on the whole, a bit surprised that a person could devote their professional life to the study of moss. In an attempt to demonstrate the range of ongoing research on the subject, I pulled up the websites of several journals devoted to bryology, and tried to summarize the work for my students.

When looking at the webpage of the Journal of Bryology, I noticed that two of the most recent articles were by the same person, a pleasant-seeming fellow (based on his webpage) named Des Callaghan, who works as a “consulting bryologist”.  I wondered idly aloud whether the students would like to meet this person with the most unlikely of professions, if it would be possible, and I received an immediate and enthusiastic affirmative.

Thus, buoyed by our impromptu discussion with the nuclear waste expert, I emailed Dr. Callaghan and explained that my students and I would love to meet him and to pick his brain. It turned out that he had been cut off from his fieldwork for the same reason that our class was meeting remotely and that he had time to spare – he may even have been pleased that strangers took an interest in his work – and he happily agreed to be our guest.

So it was that on June 1, 2020, the CWU History of Science class hosted Dr. Des Callaghan, consulting bryologist, as our guest. To my great pleasure (and relief), he was every bit as fascinating and interesting as his website led me to believe. He told us stories of discovering a new species in Madagascar and shared some of the pitfalls of his work. (To work in the field, it turns out, you have to accept that other people will think you’re crazy as you crawl around the ground with a magnifying glass. We also learned that dogs find this behavior exciting, thinking it an invitation to play, while horses are quite disquieted by humans moving in such a way!)

At least one student later described this day in class as the highlight of the term.  Certainly, I couldn’t have been more pleased. I’d like to think that whatever the future of teaching looks like, I’ve learned and started to embrace a new tool for my future classes.  And it wouldn’t have happened without a student’s mother being willing to step into a new role, and to start to bring the world a little closer together.

Dominic Klyve (KLEE-vee) is a Professor of Mathematics at Central Washington University. He is the author of more than 40 papers in number theory, the history of mathematics and science, and applied statistics. His interdisciplinary works have appeared in journals ranging from Gastrointestinal Endoscopy to Shakespeare Quarterly. Klyve has been nationally recognized for promoting the use of primary sources in the teaching of mathematics, and currently serves as a co-PI on a $1.5 Million grant from the National Science Foundation to develop classroom materials for this purpose.  He was a 2014 winner of the Mathematical Association of America’s Alder Award.

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The Takeaways, by Rachel Vale

One of my earliest memories of mathematics is the struggle I faced in second grade learning subtraction.  I understood the concept and what I was supposed to do but I continually struggled with speed tests and doing computations in front of my peers.  My parents had high expectations for me and would make me practice in the evenings, however, by no fault of their own, this practice quickly began to feel like punishment.  I even began having nightmares that kidnappers called “the Takeaways” were after me.

My struggles with math peaked again in fourth grade with long division.  I remember lying to my parents that I couldn’t see the board because I was not sure how to explain my inability to do well on division tests.  Around this time, my mother and several other adults in my life began to console me by sharing that they also were not good at math.  This was comforting to me because it validated my struggles and gave me an excuse to ignore this daunting subject.

For the next few years, I excelled in school, especially in science where I was deeply interested in biology.  I did fine in math classes, but my arithmetic skills were still quite weak, and I continued to rely on my self-identity as “not good at math.”

In my sophomore year of high school, I wanted to take honors science but, in order to do so, the schedule would require that I take honors math as well.  The honors math teacher, Mr. Burrill, was notoriously challenging and had high expectations for his students.  My first quarter in his course, I earned a C.  While I was ready to drop the course and go back to relying on my excuse of not having a “math brain”, Mr. Burrill would not let me quit.  In fact, he doubled down on helping me succeed.  He connected me with a tutor who worked with me on arithmetic and algebra facts.  He made explicit his requirements that every step be shown neatly and in detail and, as much as it felt like a chore to do, it helped me understand what I was doing.  In addition, he started giving me different homework problems from what he was giving the rest of the class.  Recognizing my strengths with logic, he would let me skip the traditional textbook problems if I could write a convincing proof of the quadratic formula, for example.  I began to enjoy math for the first time in my life and, better yet, I began to see myself as talented in math.  By the end of that course, I was earning high marks and I was excited by what I was learning.

For the rest of high school, I continued to enjoy studying mathematics and I even passed AP Calculus my senior year.  I remember reading Simon Singh’s book on Fermat’s Last Theorem that year and feeling awed that people do mathematics for a living.  Still, I harbored deep seated beliefs that my abilities in math were somehow weaker than that of my peers.  I decided that the only way I would know if I was good enough was to major in math in college.

I did well in my math courses in college and even engaged in summer enrichment programs in math as well as some math research.  Around this time, I became aware that I suffered from “imposter syndrome”, a psychological phenomenon where one believes, contrary to evidence, that they are not good enough to belong. I truly fell in love with mathematics in college, but I felt so sure that my classmates were all doing better than me, especially when I was often the only student coming to office hours or asking questions in class.  My senior year of college, I felt that I had barely scratched the surface of what mathematics was, and I envisioned graduate school as an opportunity to finally understand every aspect of mathematics thoroughly.  I also believed that earning a graduate degree in mathematics would give me the external validation to finally convince myself that I was good at math.

It turns out that my idea of graduate school was terribly naïve.  In place of deeply understanding all of mathematics, I began to deeply understand myself and my motivations.  Graduate school forced me to face my fears about not being smart enough.  The process of preparing for and taking qualifying exams is humbling for most students.  It was in this process that I was able to refine my ability to organize deep ideas in my mind and to recognize when and how to ask for help.  There were many times when imposter syndrome almost convinced me to give up, but I was blessed with a tight-knit community of faculty and classmates who supported me and encouraged me to keep going.  We would give each other practice qualifying exams and one of my classmates re-taught me Abstract Algebra from the ground up.  My program was extremely small and so there were no classes offered for certain topics such as Recursion Theory which would appear on my 4th area qualifying exam.  In these cases, I taught myself the material, making visual aids to remember proofs and find connections between topics.  I felt almost euphoric every time I was able to answer a question confidently and correctly in a qualifying exam.  I learned that I, just like my classmates, would sometimes struggle with a concept but that, in the end, it was just a matter of time, patience, and finding the right angle to look at the material.  I failed my Topology qualifying exam multiple times but, eventually, I was able to pass it. As I began working on my thesis research, certain topics and questions in math were intriguing enough that I didn’t mind admitting that I didn’t understand, and I was able to engage with the discomfort of uncertainty.  I continued to hone my ability to be brave in asking for help and, through conversations with my advisor and peers, I was able to solve an original problem in mathematics.  In the end, I completed my Ph.D. in mathematics and landed a tenure track job as a mathematics professor.

I still struggle at times with imposter syndrome, but I have learned to dampen my desire to compare myself to others or worry so much about making mistakes.  My fear of mathematics as a young child drives my love for teaching mathematics today.  I love working with students who identify as “not good at math” and helping all my students work through the discomfort of not immediately knowing how to solve a problem.  Mathematics is not about having the answer the fastest or always being right the first time; rather, it is the art of finding patterns and using logic and problem solving to discover why things work.  The biggest takeaway I try to impart to anyone who will listen is that there is no litmus test for determining who gets to be a mathematician.  A mathematician is anyone who does mathematics.

Rachel Vale obtained her bachelor’s degree in Mathematics from University of California San Diego and her master’s degree and Ph.D., also in Mathematics, from Dartmouth College. Currently, she is teaching mathematics at Portland State University.  She LOVES teaching math, especially to students who are uncertain about their own capabilities in math classes.  Rachel sees mathematics education and quantitative literacy as crucial aspects in improving racial, gender, and socio-economic equality in the U.S. As such, her recent focus is on empowering minority voices in student-centered classrooms.

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Uncertainty, Exhaustion, and Disbelief, by Jennifer Quinn

Teaching in spring 2020 was like nothing I have ever experienced in my twenty-seven years in higher education. A coronavirus unknown prior to December 2019 swept the globe, spreading the infectious disease COVID-19 in its wake. First detected in the United States in February 2020, by mid-March it had spread to all fifty states.

On March 9, the University of Washington’s three campuses transitioned to emergency remote teaching to close out the winter quarter: a final week of remote classes; a week for remote finals; and a week of “break” to grade everything, assign final grades and prepare for a remote start to spring quarter.  As more data was collected and the impact of the global health crisis was exposed, the remote teaching expectation for spring was extended through the end of the academic year. My ten-week quarter was divided into three distinct parts, each governed by different emotions.

Part I. Uncertainty and Anxiety

With no time for training or intentional curriculum redevelopment as an online course, I tried my best to recreate what I do in the classroom in a virtual environment. My goal was to build mathematical community and maintain active engagement.  I had lots of ideas on how this goal could be achieved but had no clue whether the ideas would be successful until I got to try them with my students. The uncertainty about what would work made it hard to plan. The inability to plan increased my anxiety. And anxiety spiraled to create more uncertainty. I spent too much time reading infographics from the Institute for Health Metrics and Evaluations and Financial Times looking for trends, trying to understand the risks to my family and students, and praying for signs of hope. I spent even more time in online discussion groups trying to sort out the teaching transition and learn new skills.

I approached the situation with a growth mindset. I learned from my mistakes, I asked for help, and I kept trying until I made things better. I was vulnerable and allowed my students to see that I was not always an expert. Each day felt like a mad race to prepare for class—not because of the content but because of the novel method of delivery.

Part II. Exhaustion and Power Drain

After three full weeks of spring teaching, the urgency and uncertainty abated. All the decisions that needed to be made about “how” to transition to remote teaching had been made and new information only made me doubt my choices. I heard a lot of certainty about the “right way” to approach remote teaching during the crisis. Opinions were being presented as facts, and I started to worry that I was doing it all wrong. The recommendations, guidelines, and best practices reached the level of information overload, and there was no more space in my brain to engage.

Every day, as I took a seat in front of my computer, I would feel a huge weight descend and my energy immediately waned. Remote teaching was draining both physically and emotionally. In a face-to-face classroom, I am recharged by the interactions with the students. Virtually, the energy that I invested dissipated into the ether and I felt little return. In addition, with no physical distinction between work and the rest of life, there were no cues to say, “you can turn off now.” So my batteries continued to slowly discharge all day.

In our all-remote-all-the-time isolation, nothing felt different. Special events, the ones that feed your soul, were hours in front of a computer screen. Rather than providing a change of pace, these events became additions to the standard day and just led to feeling exhausted even faster.

It wasn’t until Memorial Day weekend that I could see the light at the end of the tunnel and felt like I could breathe.

Part III. Disbelief

As we were entering the homestretch of the spring pandemic quarter, there arose another crisis to confront. On Memorial Day, May 25, 2020, the murder of George Floyd by a Minneapolis police officer, catalyzed a nationwide call for justice and dismantling of the racist practices embedded in our systems and society. And just as with the pandemic, I heard a lot of certainty about the “right way” to proceed, this time to promote antiracist practices and reaffirm #BlackLivesMatter.

Supporting my black and brown students to successfully complete this unprecedented quarter came first. My initial attempts were clumsy and not sufficient. But like my transition to remote teaching, I asked for help and I kept trying until I made things better.

When the final grades were officially submitted for spring 2020, my emotions were all over the place. I felt elated. I was in denial. I felt numb. There is more uncertainty heading towards fall, but I can approach it with less anxiety and greater purpose. What practical lessons will I bring forward to make the next quarter less extreme?

  1. Know that setting up and facilitating virtual interaction takes more time than in a face-to-face classroom. To prioritize student engagement, begin by pre-emptively reducing content to what is absolutely required.
  2. Reduce the grading burden. This might mean requiring less teacher-graded assessments or assigning more self- and peer-assessment.
  3. Take time to introduce important features of every tool that you expect your students to use whether in your course management system, your conferencing platform, or a downloaded app. Low stakes “getting to know you assignments” are a great way to build community and technological competencies. If it is not worth your time to ensure every student can access and use the technology, then it is not worth using in the first place.
  4. Do not ignore self-care. (As I told a student, “Remember a time when you helped someone in this class. Now be that person for yourself.”)

During this time of isolation, much was learned and much was lost. Still much remains to be accomplished.

Jennifer Quinn is a professor of mathematics at the University of Washington Tacoma. She earned her BA, MS, and PhD from Williams College, the University of Illinois at Chicago, and the University of Wisconsin, respectively. She has held many positions of national leadership in mathematics including Executive Director of the Association for Women in Mathematics, co-editor of Math Horizons, and currently President-Elect of the MAA.   Jenny will serve as MAA President in 2021 and 2022. She has been “staying home and staying safe”  in Tacoma, WA with her husband Mark Martin and two sons, a rising St. Olaf junior and rising high school senior. She chronicled her experiences with emergency remote teaching in her blog Math in the Time of Corona. Relive it from the beginning starting with the first post on March 7, 2020  (Day -1).

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My Living Proof Story, by Michael Dorff

In 1987, I was married with two children and was teaching math at a U.S. military high school in Germany. Two years later, in November 1989, the Berlin Wall fell, and with all the political changes, I expected that the U.S. might cut back on their military bases in Europe and that would mean fewer jobs for teachers at U.S. military high schools. So, my wife and I decided to return to the U.S., and I would start a PhD program in mathematics education. This was before the Internet, and I only knew one university that had a PhD program in mathematics education. I applied by sending in a hard copy application though the mail (no email at the time). I got accepted, but was told that they did not know if there would be funding for me until after the application deadline. So, I waited until after the deadline and called the director of the graduate program. He told me that he still wasn’t sure because there were two really good students who were thinking of applying but hadn’t yet. He said that I should come, and something would work out. My questions were, “Isn’t the deadline passed?” and “I guess I am not considered a good student?” but I did not ask them. I was naïve. We decided to do what he said and come.

When the high school year was over and I was done teaching in the spring of 1990, my wife Sarah and I moved our family of four with a third child on the way to that university, which was in a part of the U.S. where we had no family. I arrived at the mathematics department and met the director of the graduate program. He informed me that the good students he was waiting on did finally apply and there was not a TA position for me. In fact, they did not even have a scholarship for me, and, since I had moved from Germany, I would have to pay out-of-state tuition. I thought it would have been helpful if he had told me these things earlier. Also, he let me know that during the first two years of the PhD program in math education, I would have to take standard mathematics courses to earn an M.S. degree in mathematics. It had been several years since I had taken a math course and for my undergraduate degree the math classes I took consisted of calculus 1, 2, and 3, linear algebra, abstract algebra 1, and number theory. In a casual way he mentioned that I was probably not good enough to earn an M.S. in mathematics. I wasn’t feeling very confident in myself.

I went back home and talked with Sarah about the situation. I looked for a local high school math teaching position, but the K-12 schools were starting soon, and I couldn’t find an open position. So, by default I started the graduate program. The first semester I took graduate classes in real analysis, abstract algebra, and topology. I also sat in a class in calculus 2 since I had forgotten much of that while I taught high school. Because we needed money, I got some part-time jobs doing construction and grading free-response questions on standardized high school math exams in the evening.

One day after class I learned that there was a room in the math department where graduate students and the professors could go to talk and get snacks.  No one had told me about the room, but I decided to go. When I entered another graduate student told me I wasn’t allowed in the room. Later, I realize that she did not know that I was a graduate student. But with all that had happened during the past few months, I did not have a lot of confidence in my math worth and I silently left the room. During that first semester, I had little assurance that I could pass my math classes let alone do well in them, and there were times I was ready to drop out of the program.

At the end of the first semester, I ended up earning A’s in my three graduate math courses. The graduate director told me that a scholarship was available for me for next semester so that I wouldn’t have to pay tuition, but there was not a TA position for me. During the second semester I also received A’s in the next three graduate math courses, and I was offered a TA position for my second year in the PhD program. At this point I met some professors in the department who were very supportive. By the end of the second year, my confidence had grown and I transferred to another university where I earned my PhD in mathematics. In thinking back on this experience, I know that I could have easily stopped studying math. There were a lot of reasons for me to stop.

My story is not the only one like this. Too many others have gone through worse than I, and unfortunately there are some who are still experiencing dispiriting and demeaning situations, including those who want to studying math education instead of mathematics, work in industry instead of academia, those who are female or from underrepresented ethnic groups, and those who are LGBTQ. The book Living Proof: Stories of Resilience Along the Mathematical Journey (edited by Allison Henrich, Emille Lawrence, Matthew Pons, and David Taylor) shares a collection of such experiences and helps bring these elephant-in-the-room stories out in the open. We need to do a better job of supporting students and colleagues through their challenges, enabling everyone to flourish in mathematics. Let’s work to be more encouraging and empowering of all people in their mathematical journey.

I would happy if you sent me an email at mdorff@math.byu.edu telling me your thoughts on this article or sharing your own personal struggles.

© Mathematical Association of America, 2020. All rights reserved.  This piece first appeared as the President’s Message for April/May 2020 issue of the MAA FOCUS magazine. We would like to thank Michael and the editor of the FOCUS, Jacqueline Jensen-Vallin, for allowing us to republish it here.

Michael Dorff is the current President of the Mathematical Association of America (MAA). He earned his PhD in complex analysis at the University of Kentucky and is currently a professor at Brigham Young University. He has five daughters, the oldest of whom has three children and is working on her PhD in mathematics. In the picture to the left, Michael is with Sarah and their three daughters (Becca, Lizi, and Hannah) while Michael was in his first year of graduate school.

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Teaching Using Living Proof, by Allison Henrich & Matthew Pons

Since Living Proof: Stories of Resilience Along the Mathematical Journey was released by the AMS and MAA last summer, we’ve heard from colleagues all over the country that they are using the book in their courses. By using the book, faculty members aim to achieve a variety of goals. For instance, some want to foster a growth mindset in students where productive failure is acknowledged as a helpful learning tool. Faculty who work with future teachers report that they use the book to help their students learn what types of teacher behaviors can limit a student’s development, and which mentoring practices can enable students to flourish. Many among us are focused on creating an inclusive environment for math students of all types by showcasing successful mathematicians from a wide variety of backgrounds. And some professors aim to highlight the unequal treatment of mathematicians from different backgrounds in order to encourage our students to help us create a more just and equitable math community. Whatever the goals of a professor may be, Living Proof has provided another tool to help them achieve these goals.

So, in which classes have our colleagues used the book, exactly how have they incorporated the book into their classes, and what has the response from students been? To find out, we’ve gathered information from seven faculty members.

First, we were surprised at the variety of classes represented in this small sample. Living Proof has been used in a quantitative reasoning course for non-STEM majors called “Multicultural Mathematics” (Jim Humphreys, Seattle University). It has been used in a “Math for Elementary Teachers” course (Scott Zinzer, Aurora University) and a course called “Methods for Teaching Secondary School Mathematics” (Angie Hodge, Northern Arizona University). Christine von Renesse (Westfield State University) has used Living Proof in a Linear Algebra course, while Dana Ernst (Northern Arizona University) and Allison Henrich (me!) have used the book in an Introduction to Proofs course. The book was also used in a senior capstone course for math majors (Brian Birgen, Wartburg College).

Several of us used versions of the following prompt for the assignment.

Read the foreword, the preface, and two stories in Living Proof. For each story, write a short reflection. For instance, you might respond to one or more of the following questions. 

  • Did you identify with the author of the story? If so, in what way?
  • How does the author’s experience differ from your own?
  • What surprised you about the author’s story?
  • Did this story make you think differently about mathematics?
  • What about the story inspires you?
  • What about the story bothers you?

Some of us only assigned this once, and others of us required several similar assignments, each time having students choose two stories to read. Sometimes, which stories students could choose would be restricted to a certain part of the book. Other professors made recommendations about which stories might particularly interest students. For the most part, however, assignments involved student choice and open-ended reflection.

Christine von Renesse gave even more structure to her Living Proof assignment by incorporating videos into a more substantial reflection assignment in Linear Algebra. Here is her assignment.

Please watch one of the following video clips:

 1) https://youtu.be/0tqq66zwa7g (Mindset – Alia Crum)

2) https://www.youtube.com/watch?v=7XFLTDQ4JMk (Getting stuck in the negatives – Alison Ledgerwood)

 Then choose 3 stories to read from the book Living Proof. They are all written by different current mathematicians in the US. Write a 2-page paper (double spaced) addressing at least the following questions:

  • How does the video clip relate to your learning experience in this class? What does it imply about learning mathematics in general?
  • Describe at least one new idea from the video that you believe has great impact on how you learn and what you need to work on as a student of mathematics.
  • How have the stories you read influenced your thinking or believes about “becoming a mathematician?”
  • How do the stories support the idea that you could be a mathematician if you wanted to?
  • What are you curious about after watching the video and reading the stories?

So, what has the response to these assignments been? All of the professors we gathered data from felt like most students got something meaningful out of the assignments. Jim Humphreys had this to say about student responses in several sections of his “Multicultural Mathematics” class:

“It was highly successful in engaging the students. Students eagerly found articles by writers they could identify with: students of color read articles by mathematicians of color; queer students read articles by queer mathematicians; students interested in art or in athletics read articles by artist/mathematicians or athlete/mathematicians. One very common theme in the student essays was surprise over the emotional pull of mathematics for the authors; it had never occurred to the students that mathematics could have an emotional appeal. Another common theme was surprise at the fact that many of these professional mathematicians had had to struggle to understand some of the mathematics — many students assumed that mathematics just came easily to everyone who would pursue it as a career.”

Allison recognized this last theme as being a common one in student reflections from her proofs course, while Brian Bergen’s capstone students came away from the assignment thinking that every mathematician has to overcome feeling stupid and having someone tell them they couldn’t be successful. His students learned that their thoughts and feelings were normal. Christine Von Renesse’s students (particularly the future teachers) indicated this as an important theme as well.  One of Scott Zinzer’s students reflected, “Sharing stories like these helps others relate to mathematicians. Seeing and hearing about others’ struggles may inspire you to fight through yours.” A student in Allison’s course wrote, “Reading this story inspired me to keep pushing for what I want, even if there are others who expect me to fail.”

In addition, several students responded to themes in the book related to inclusion/exclusion. One of Dana Ernst’s students wrote:

“This story made me think differently about mathematics. Sometimes I forget that academia was not built by people of color or by immigrants, and I have to remind myself that there may be more obstacles for people who belong to those groups. Not only this, but reading this story reminded me that math and science fields contain disparities among minorities, and that being successful in mathematics is not only the consequence of hard work, but also of privilege.”

Christine Von Renesse noted that her non-STEM majors all commented that they could see a place for themselves in the mathematical community. A student of Allison’s wrote:

“I know that most of the successful people in my prospective field look like me, but there’s a clear divide between the success of Caucasians and people of color that should continue to be addressed until it no longer exists. This story makes me think differently about my place in mathematics and the place of others around me.”

Several of the students in Scott Zinzer’s Math for Elementary Teachers course also spoke about the inclusion/exclusion theme.

“This story showed me that the people behind math can be anybody.  It shows me that we probably do not even know who the most powerful mathematicians are because of the people that did not get the opportunity. It shows me to never give up on any kid that does not understand.”

“A lot of times students see their teachers as experts.  If they do not see a teacher who looks like them teaching in a specific field, they will often internally decide that they must be unable to succeed in that field.”

When we began the Living Proof project, our goal was to share stories from all corners of the mathematical community.  We believe that sharing our experiences with each other is crucial to making our community more diverse and inclusive.  A diverse and inclusive community will enable us to tap into far more sources of creativity and innovation to take mathematics so much further than we have been able to take it in the past.  However, if we cannot reach the next generation and assure them, regardless of their background, that there is a place for them here, our capacity for innovation will be limited. The evidence given in this post is hopeful. In the ten months since Living Proof was published, instructors have found innovative ways, across course levels, to use the collection as a resource to help students understand some of the highs and lows inherent in the mathematical journey.

We acknowledge that this is just a small sample of faculty and student experiences with Living Proof, so we would like to think of this writing as a catalyst for generating more conversation about how these stories have been and might be used. We suspect that many of you have either used the book or have colleagues who have, or perhaps you’re thinking about using it in the upcoming academic year. To contribute to the continued sharing of ideas related to teaching and mentoring with Living Proof, we invite you and your colleagues to fill out the following survey:

https://forms.gle/6biLihXy7GdQcyoq8

Let’s keep the conversation going!

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Remember Why You Started, by Allyson Hahn and Vien Ho

With the rapid spread of COVID 19, our junior year of college went from collaborating with our friends, in-person, on a daily basis, filling up whiteboards in the Math Resource Center, and stopping by our professor’s office to gain clarity, to sitting at our desks and attending class from our respective homes. As students, we’ve been faced with many challenges over the past semester while acclimating to the remote learning environment. The learning curve was steep, but over time we developed strategies to become successful and overcome these obstacles.

We were eager to start the remote learning journey with Abstract Algebra II, but we encountered technical issues right away. Our first class period was difficult, as we struggled to hear our professor through the digital platform. This left us discouraged and we wondered whether we would meet the learning expectations we set for ourselves. But this just meant that we had to work harder. We spent hours reading the textbook and trying to understand concepts from notes and PowerPoints. Office hours were available virtually and via email, but it was challenging to communicate the mathematics. Thankfully, the audio was better after the first class, and we began to adapt to this way of learning even though other technical difficulties, such as suddenly getting disconnected from the digital platform or being unable to view the screen the professor shared, had become commonplace. Despite the challenges we faced, what motivated us to meet the expectations we set was our interest in the content, our belief in ourselves, and the reminder of why we fell in love with math in the first place.

This semester, we were also both in a small independent study course. In the first half of the semester, during class meetings we presented the proofs to theorems and lemmas; this helped our understanding of the material, as we explained it to our classmates and received feedback and further explanation from our professor. Outside of class, we would collaborate in the Math Resource Center to work on problems and ask our professor for guidance. However, we lost these opportunities when we switched to remote learning, which made it even more difficult to comprehend the material and tackle the practice problems. We felt that the first homework assignment due during remote learning was impossible, and we would never be able to finish it. After panicky texts back and forth, we decided to use Skype to discuss the homework and content. In the coming weeks, our calls would last for hours as we poured over the material and completed the problems. Math is incredibly visual, so we had to change how we collaborated. Since we couldn’t see each other’s work in front of us, we had to hold our solutions to the camera or send them via text. We didn’t have the luxury of working side-by-side to point out theorems and errors in each other’s work. However, this “video collaborating” experience made us better mathematicians because it forced us to be clear and concise in our work and discussion. This experience taught us not to be afraid to reach out to our friends and peers for assistance and guidance even if it might expose our weaknesses. But we wouldn’t have been as successful without our professor’s support during the remote learning journey.

As juniors at a small liberal arts college, upper-level mathematics courses are typically quite small, which can make remote learning difficult. With only 6-10 students in a class, we tend to foster a more informal environment when it comes to participation. This natural flow of learning and discourse, which we thrive on, was broken in remote learning. When a professor asks a question during remote learning, it is hard to jump in and answer. Not because we don’t have an idea of what the answer may be, but because when “in person”, the fear of being wrong was so diminished. In the remote setting, there is a new set of fears, that we would say something wrong or talk over someone. In addition, a student’s body language is telling, but without video, it is impossible for someone to pick up on those cues.  This is what causes the “Does this part make sense?” question to have an awkward silence, which we’re sure a lot of professors can relate to. In-person, a head nod would usually suffice, but in this new setting, it was somehow uncomfortable for us to say “yes.”

Since remote classes started, our learning process has been hindered by the numerous distractions in our homes. It is hard to admit, but there were days where we did not feel motivated to work on homework or try to understand new concepts. We learned that we had to structure our days with allotted times for classes, homework, and breaks in order to create a healthy mindset and a productive environment. Even little things like putting on jeans every day, turning off news notifications, or listening to music lightened the mood and helped increase our focus. Not only did we gain skills from learning how to navigate our classes and collaborate with peers and faculty during quarantine, but we also learned how to help ourselves mentally, by reminding ourselves of why we started.

This journey through remote learning was unexpected and left students and faculty to face numerous challenges as we all worked through the remaining weeks of the semester. However, it brought us an experience we will never forget and taught us many lessons. It taught us to be more independent but unafraid to lean on each other. It taught us how to adapt to a new environment and to find ways to work things out. It taught us to not take anything for granted and appreciate the time we had before the remote learning period. More importantly, it taught us to remind ourselves (and always remember) why we started our journey during difficult times. Remote learning ultimately was not a bad thing as it brought many lessons, and time to reflect and be grateful for every day that we get to spend with the people that we love. We are thankful to be safe at home and able to remain connected with our family, professors, and friends, while others are fighting on the frontlines to save lives and restore the world.

Allyson Hahn and Vien Ho are Pure Mathematics majors whose continued passion for mathematics was shaped by their dedicated and encouraging professors at North Central College. They share a similar goal of pursuing a Ph.D. in Pure Mathematics and eventually teaching at an institution. 

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