By Sabrina Pawlak

While there are technical ways to approach the question of how Covid affected students via testing, performance reviews, surveys, etc., I opted for an anecdotal approach. While this may not satisfy the conditions for extrapolation, I find it relevant to share my perspective—from what I experienced to what I have seen as a resident advisor, tutor for high school mathematics, and a teaching assistant for Differential Equations—by reviewing my time, through all four years of my undergraduate experience through pre-, mid-, and post-pandemic life.

A classroom is a place of collaboration. Conversations constantly occur through verbal and visual cues—facial expressions, engagement levels, body language, etc. This interaction between the students and professors creates a comfortable classroom environment for learning. However, in 2020, this conversation was immediately stripped away as the classroom became virtual, and the visual cues became the thumbs-up react button on zoom. The beginning of 2020 to the present became a trip like no other, which forced an 'adapt or bust' mantra.

Spring 2020

During Spring Break 2020, I was living in the dorms, a first-year student, living away from home, finally having the freedom to create my own identity devoid of parental influence. It was freeing to step into my true self. Then, the Colorado School of Mines followed the state schools' lead in shutting down the residence halls and extending Spring Break to prepare for the transition to virtual teaching. A 24-hour notice was given to students in the residence halls to move out. There was no time to process this directive. I had a place to go home to and parents who readily had space and financial support for me, but I knew of quite a few others who did not have their familial support. As mentioned, college is a time for young adults to understand their identity. When these identities clash with parental beliefs, home no longer becomes a safe place to return to, but so often it was the only place.

During Spring Break, everyone got emails about their new accounts on Zoom, GradeScope, and Proctorio. There was a great rush to ensure all students had working computers with cameras and microphones, and if not, methods to access such technology. Then school resumed virtually, from my childhood bedroom, just me and my Harry Potter collection. At this point, the technical infrastructure was not understood by either faculty or students; most of us opted to use pen-and-paper instead of any digital medium. Office hours lacked this technical component for some time, as students would hold up their piece of backlit paper to a computer camera only for the resolution to make it unreadable. Explaining math only verbally is excellent if you are an auditory learner. Still, it becomes almost impossible to understand if you fall into the other three categories: visual, read/write, and kinesthetic. This prompted the speed at which many students and I modernized, renting or buying devices to use the whiteboard function on Zoom with a stylus and submit homework without having to take pictures and turn them into PDFs. In classes where we did not know people, collaboration would come about from an email to a random student, reading, "Hey, I know that you don't know me, but we were in a break-out room together, and I was hoping that we could compare homework solutions over zoom sometime!" Simply put, this semester felt like a catch-up to modernize, to get through all the content with the shift in teaching methods, and it was difficult to feel satisfied after finishing the course because it felt incomplete.

2020-21

At the start of the next academic school year, I was a Resident Advisor for a group of first-year students in a school that was still entirely virtual. The dormitories now had rules that made it very hard to meet new people, no visitors from other residence halls, masks had to be worn indoors unless one was in their own room, weekly Covid tests, and a positive Covid test meant a strict two-week quarantine with meals delivered and regulated outdoor time. This environment was highly isolating. When floors got quarantined, students had to question if they should go home and potentially be responsible for getting their family sick or be sick away from home for the first time, dealing with a novel illness alone while still trying to be a student. While many first-year students adapted and managed to remain social with the new regulation, not everyone did, and some students were experiencing their lowest of lows in an isolating place.

As the semester turned into a year and some change, my friends and I felt that we were not learning what we needed to get good jobs after we graduated, as our curriculum felt more and more like a certificate in Zoom. In particular, my skill set felt slim as critical thinking was quickly switched to google searches. The number of projects was reduced, so tangible products of my curriculum that I could speak to during interviews were gone. We had access to the internet twenty-four/seven, so using the web to aid our understanding did not feel like academic misconduct; it felt like another tool in our arsenal to combat the constant changes around us, one being reduced help hours. However, this tool became an inhibitor. Using WolframAlpha to check that you solved something correctly may give you the grade, but it fails to give you the self-confidence needed to feel competent in your given major. Searching for how to start a proof allows you to finish a homework assignment; still, it fails to help you  develop an analytical lens to understand mathematics. Always having access to the internet pushed me to become dependent on it and made me lack the desire to memorize these concepts. Justifying my actions with the argument, "If I work in industry, I could just look up this formula." When does this accessibility become an inhibitor? When a recruiter asks about an optimization problem, I stumble instead of feeling confident in my ability to apply logic and mathematical rigor, as I have always had access to online assistance.

2021-22

By my junior year, Covid tests started to become less frequent, quarantine spaces on campus decreased, and lessons were no longer automatically recorded on Zoom for people who were sick. Covid seemed over; three years of change, and we finally returned to normal, but what was 'normal' at this point? It is naïve to think we could even return to the previous baseline. As a student, I felt that I lacked fundamental skills. I had a minimal recollection of the calculus series, which made other more advanced classes challenging, failing to recall techniques such as the method of undetermined coefficients or partial fraction decomposition. Looking back on the semester of being forced out of the dorms, it felt marked by all the changes that had to be made, the anxiety of what the future held, and the constant reports of the disease: death counts, the number of people infected, the constantly updating maps of outbreak zones. The most memorable part of that time was reading about SIR models, how complex these models can become, and how finally, from my perspective, I understood how scary COVID was. But now, despite going into the end of Junior year, I knew very few of the professors and staff that made up my school's Applied Mathematics and Statistics department. The pandemic seemed much less pressing, but now my once large aspirations of wanting to go to graduate school waned, as I didn't have the support from professors at this time encouraging me, getting to know me more personally because there was no face-to-face interaction.

During my junior year, I also was a grader in Calc II and Linear Algebra and tutored for high school mathematics through Golden Tutoring. It was clear that there was a problem. Students lacked the fundamentals in mathematics; in college, students were getting confused in algebra, notation was unclear, and general mathematical proficiency and communication were lacking. In high school, students came from two years of online school, using online resources to solve most algebraic problems, and struggled with solving systems of linear equations and graphing functions without technological aid. I experienced the effect virtual learning had on my general mathematical foundation; first- and second-year college students felt this, and high schoolers were also in this battle. Despite this change, as students, we were expected to perform as if we weren't put through such a monumental event. We were not meeting the prescribed benchmark.

As a student, this posed one overarching question: is it our fault for not measuring up?

What can we learn from COVID?

We should avoid blaming the institution, the student, the teaching faculty, etc.; the blame is on COVID. COVID forced us to change our lives and adapt, and as mathematicians fond of the scientific method, we know that the first iteration does not always go as planned, especially when going in blind. While we did our best and should be proud, there is much room to improve. There are things we should take away from this event and things I'd rather not see or hear again, e.g., 'Can you all see my screen?'  For in-person learning, why not keep online and in-person office hours and record lectures and help hours so students can use them while studying? With zoom, we can now make courses more accessible by adding live captions, so why not do that? We now have tools that allow people to stop coming to class sick, so why have we stopped utilizing them? However, during the shift to the digital world, i.e., Zoom lectures, most professors switched to PowerPoint presentations to relay the content. Personally, this has never been effective. While it may be convenient now since these tools are created, deriving equations live, going through content by writing lecture notes on the board, forces a slower class speed, which I think is necessary for digesting content in class. I can read a slide and take it to be true, but actually working through the math connects the process with concepts and shows the validity of these claims. However, since every professor and teacher has now invested their time into making such Powerpoints, let students still have access to this resource.

As previously mentioned, I have qualms about the ease of access to the internet juxtaposed with an educational setting. It is no longer possible to have these be independent, nor do I think they need to be, but having solutions at your fingertips fails to get us students comfortable sitting in the unknown, working through the confusion. It inhibits the typical learning process, which requires some struggle. This topic is highly disputed among students; some make claims that Chegg and other similar online resources are the greatest teachers, but the reasoning most often given for why is simply that students can get a problem that is very similar to what they are solving, and have a defined algorithm that can be applied to their own set. However, some of my best professors have a classroom setup where we learn the content, practice the skill a couple of times, and then practice by ourselves on the homework. Practice, practice, practice.

Khan Academy took the classroom and made it virtual. They have provided multiple mediums to relay content: auditory, visual, and actual practice problems with worked-out step-by-step solutions. Chegg and any homework helper is simply a collection of problems that are worked out without the  understanding of why such solution methods exist or work. So why not have an online database similar to Khan academy but for college mathematics full of problems that professors have worked out solutions for. Make this source entirely fact-checked, safe, and something that is specifically developed to help solidify concepts. It not only helps students in college, but it makes the field of mathematics more accessible, especially for underrepresented groups and underfunded schools, giving students resources that they may not have had in their household. Not only could it help push students to a higher level of proficiency, but it can be the change needed to increase the diversity of this field.

Throughout my undergraduate education, I have read textbooks that leave me stumped and require a level of mathematical proficiency that I do not have in that niche area of mathematics. It shows how mathematics is a subject area where foundations need to be strong to understand harder concepts. That foundation needs to be built up but, most importantly, maintained. So, adding to this idea of an online source, have concepts linked, i.e., if the image of Fourier transforms is dependent on understanding orthogonality, link it to a lecture, a video, or practice problems that the concept applies to. We can create a graph of interweaving concepts that can link further and further back to foundational skills that may have been skipped or forgotten amid this global pandemic.

I want to end this narrative with a call to action. Our campus community, our city, our state, and our nation came together to work through COVID, and I believe we need to call on our community, once again at every level, to guide the youth and young adults back to the educational/mathematical proficiency that we once had before COVID.

Sabrina Pawlak is currently a senior at Colorado School of Mines studying computational and applied mathematics. On campus she is involved with the Society for Women in Mathematics and Society of Women Engineers. She hopes to continue her academic pursuit with graduate school after spending time abroad.