Age 64, born on January 31, 1939 in Buffalo, NY and raised in Depew, NY, died on July 5, 2003, in Charlottesville, Virginia. Gordon received his Ph.D. in Mathematics from California Institute of Technology in 1965. In 1970, he joined the Mathematics faculty of the University of Virginia where he taught, as Professor, until the time of his death. Gordon will be laid to rest in The University Columbarium at the University of Virginia Cemetery on Tuesday, July 8.
In August 2000, I quite literally ran into Mr. Keller the day after I received word that I passed the last of my comprehensive exams toward my PhD. The first day that I was ‘officially’ looking for a dissertation advisor. He said, “If you’d like to do a dissertation reading course with me, come see me. I like the way you work!”
Mr. Keller was a funny guy – king of math and dad jokes. He was a big guy who drove a red Chrysler Neon. He would generally be in his office late, only tearing himself away from work when his family called to ask if he was coming home for dinner. He was infamous for a lengthy and challenging set of optimization and related rates word problems he assigned in Calculus to his undergraduates. He was infamous for the group work proofs he made each class of graduate algebra students complete, especially the proof of why every group of order 168 was simple. He had the best recommendations on local restaurants, and especially barbecue – and you trusted every single one of them. He made the best five-ingredient chili in central Virginia (it involved cocoa powder and applesauce and was divine!) I treasure that recipe to this day.
He was a low-key advisor, not always prepared for our meetings. He preferred that I steered the conversation and the speed of my research work. We met weekly, and I always wanted to impress him. I gave my oral qualifying exam on several articles we were working through in 2000. That fall, Mr. Keller let me know that he had prostate cancer.
I hadn’t ever known anyone with cancer. I didn’t know what that meant. Did this mean he would die? How long would he have? I had a very professional relationship with Mr. Keller and his guidance meant my success in attaining a PhD in mathematics. So many questions. At least I had filed the paperwork with the university to grant my MS in Mathematics, my Plan B?
We didn’t speak much about his health. There was a surgery, some recovery, there was chemotherapy and he lost quite a bit of weight. We met throughout this time; his family brought a twin bed into his office so that he could take naps during his workday. I probably should have seen the writing on the wall.
In late June 2003, I served as a TA for the Carleton College Summer Mathematics Program for Women. I went to meet with Mr. Keller one final time before I drove to Minnesota for a month. I knocked at the door, there was snoring on the other side, but then he woke up and I heard him fall. I heard his shouts from beyond the locked door and ran to get help. Mr. Keller went to the hospital that afternoon. I left for Minnesota the following day. I got the call that he passed away on July 5, 2003.
When I returned for classes in the fall of 2003, I got an email from Mr. Faulkner. Mr. Faulkner and Mr. Keller were what appeared to be best friends. I always saw them at women’s basketball games together in their season-ticket seats. Mr. Faulkner let me know that he promised Mr. Keller that he would help me finish my dissertation. When I provided him the work I had completed, we realized it wasn’t much. Mr. Keller’s illness had affected us both. I had to start from scratch, in a tweaked area that Mr. Faulkner knew better. This was at the start of my sixth year, and graduate student funding technically ended in the fifth year. The mathematics department continued my funding until I finished my PhD on May 22, 2005.
Mr. Faulkner and I grieved together. I visited him each time I was at a women’s basketball game to say hello. We still exchange holiday cards to fill each other in on our adventures. I’m not much of a philanthropist, but I give annually back to the Mathematics Department in honor of the Gordon E. Keller Mathematics Majors Dinner. This brings me peace, but also sadness. Mr. Keller was a quirky university mathematics professor who cared deeply for undergraduates. I wish I could have have said goodbye.
 At The University of Virginia, University faculty are referred to as Mr. or Mrs. instead of Doctor, even if they have a Ph.D. Students and faculty historically addressed each other in this manner as well.
If we think of mathematics as science that is free of bias, it might be hard to comprehend how there is any other explanation for some groups’ lack of success in mathematics other than the fact that they are less capable. But when we investigate how privilege plays out over the course of history, over one’s lifetime, and over the course of one’s day, we can see how one can be placed in a position to either access or be denied access to an equal chance at participation in society. And societal participation includes participation in the mathematical community. In her article, “The Culture of Exclusion in Mathematics Education and its Persistence in Equity Oriented Teaching” [Louie, 2017], Nicole Louie describes what she calls the “culture of exclusion” in the mathematics classroom:
“The restrictive and hierarchical culture that has historically dominated American mathematics education limits all students’ access to rich and meaningful mathematics learning experiences and further limits many students’ opportunities to develop identities as mathematically capable learners and thinkers.”
One of my first memorable experiences with the culture of exclusion in the mathematical sciences happened in my transition from middle school to high school. My mother, as a teacher herself, was keenly aware of the denial of opportunities to Black students in STEM in our school system. She also knew that in many school systems, including mine, a student’s status in math at the end of the 5th grade determined a student’s ability at access the nation’s top universities. So, she engaged me early on in extracurricular activities around mathematics and science. She signed me up for a science-themed summer program in elementary school. Later, she got me involved in the Mathematics, Engineering, Science Achievement (MESA) Program at my middle school. The summer after I took pre-algebra in 8th grade, my mom placed me in a self-paced algebra class that was offered at a local college and taught by a college instructor. I struggled through the course the entire summer and suffered the experience of always being the slowest one, but I survived the long days in class and the long bus rides home on public transportation. When I went to my high school for the first time to meet my guidance counselor, who happened to be a middle-aged white person, he looked first at me, then at my record, and placed me into pre-algebra again. Despite my summer spent learning algebra, he convinced me it that it was in my own best interest to repeat the pre-algebra course. My mother, on the other hand, upon learning about my schedule, marched up to the school the next day to demand that I be placed in the appropriate mathematics class—algebra. She knew that if I did not have access to that algebra course, then I could not access Calculus, which was then and is still an unstated admission requirement at many elite universities.
It wasn’t until I was an adult that I was able to reflect on the significance of this experience. If I hadn’t been given the opportunity to take algebra as a freshman, I’m not sure where I would be today. I’m sure it’s possible that I would have still gone on to become a mathematician, but it would have been following a different path with more obstacles. What’s of much bigger concern to me, though, is the thought of how many students, like me, were placed in mathematics courses below their ability level by this same counselor or by other staff in similar positions of power. These gatekeepers were unintentionally (or perhaps intentionally) undermining the education of so many students. Multiply that number across all the high schools in my hometown of Sacramento, the state of California, and the country, and the impact is staggering.
My high school was a public one and was exposed to its share of violence; more than a few of my peers were victims of gun violence and the prison industrial complex. For these students, having greater access to mathematics early on could have made a very real difference in their lives. For many students today, the issue of access to a quality mathematics instruction can literally mean life or death.
I remember an incident I experienced in my junior year. I was at my school on a weekend, and when I walked past the cafeteria, I was surprised to find it full of people. I stopped to look through the window, trying to figure out what was going on inside. I didn’t recognize many of the people. I also noticed that the students didn’t really reflect the entire demographic of our school, which was very diverse. After asking someone what was going on, I found out that it was a math competition! So, there I was, literally on the outside looking in, first wondering why I hadn’t been invited, then feeling glad that I wasn’t invited because I didn’t think I’d fit in or perform well anyway. It’s interesting to look back on that experience from the perspective of a student who was capable and interested, but who was not invited into the math community in high school. In addition to being denied access to a mathematical enrichment activity, I was also denied the opportunity to network and build mathematical relationships with other students and teachers from the whole metro area. This perfectly illustrates an experience in which a student (in this case, me) may have been capable of performing well or excelling in a specific math community but was not invited into the room to even find out.
In high school, I never thought of myself as “good at math.” Calculus was a struggle, and I was even persuaded by my Calculus teacher not to take the AP exam for fear of harming her strong record of students succeeding on the exam. Despite my lack of success with AP Calculus the first time around, not to mention my mediocre SAT scores, I was accepted to UC Berkeley just before they pulled the plug on Affirmative Action in 1995. It wasn’t until later, after I graduated with a degree in mathematics with “honors,” that I realized what poor indicators of success those SAT scores really were for me, as they have been for many others.
Before I arrived at Berkeley, I was recruited through my high school MESA program to attend the Professional Development Program (PDP) program at Berkeley. This was the program that Uri Treisman started to help African American and Latinx students become successful in Calculus classes at the university. The program helped provide a safe space for me to learn where I could be myself and didn’t have to sacrifice my identity to participate. It was a place where I was welcomed, where there were lots of other young people that looked like me, dressed like me, listened to similar music, and shared an interest in STEM. I was entrusted with a key to the building, and even the custodian for the building became an advocate for our cause because of the long hours we would spend in that space. It was the program director, Lana Fukasawa, (who, by the way, did not have a math background)—and not one of my teachers—who was the first person that I recall expressing confidence in my mathematical abilities. It was because of her persistence that I eventually decided to give the math major a try.
One incident that affected me deeply while I was an undergraduate was something that happened to some friends that were in my PDP cohort. A small group of them were taking the same upper division math class together, and one day, they garnered up the courage to visit the department’s social hour where students and faculty mingle over tea and cookies. This group of students ran into their instructor at the event. They overheard him say to his colleague when he saw them that the department was going to need metal detectors for the group of “thugs” that were taking his course. These young math majors were frightened and outraged, and they rightfully decided to take the issue to the undergrad coordinator. To their dismay, after waiting outside of the coordinator’s office for some time, when he finally showed up, they realized he was the person that their instructor had been talking to. Undeterred, they took the issue to the department chair and the response that they received was: “Welcome to Berkeley.” This incident was a shock to all of us in our small community and was a rude awakening to what we already suspected: that we were not welcome in the math community at our university (which was all of the math community that we could see), and that we would have to fight for our right to be in our math classrooms each and every day.
It’s hard to describe the feeling of walking into my upper division math classes at Berkeley and having to confront head-on the negative stereotypes about who could and should do mathematics. It was one thing in the large, lower division classes, where it felt like it was possible to hide. However, the upper division classes were much more intimate. I still recall the almost transparent thoughts on my classmates’ faces on each first day of class. Their looks told me that they thought I was in the wrong room. And the thoughts were almost as transparent when I didn’t leave once the class started. And then again, the feeling of surprise when I showed up again the next day. It’s possible that some of this was in my head, but I’m convinced that much of it was real. My own response was to lean a little more into my cultural tropes—to wear my pants a little lower, to make sure to keep my skullcap on, and to keep my big headphones around my ears until class began to make the point that I was going to embrace my identity and that I also wasn’t going anywhere. These feelings also forced me to put on my mental armor to protect myself from the stereotypes and micro-aggressions and push to harder, to show up for help as often as I could, and to place some demand on my instructors for their support despite their lack of engagement or interest in my success.
As an undergraduate, I was not invited into the math community by any students or faculty in the math department at my own university, but I was included in the emerging scholars program community which operated in a different space. It was outside of the department but at the same time provided a “safe passage” that we could take to get in and out of the math department space. Almost no faculty in the math department ever expressed the slightest interest or confidence in me or my abilities until the last week of my senior year when I handed in my honors thesis project. Looking back, I find it puzzling that I had never even heard of the Putnam exam until my 4th year of graduate school and probably learned about the Math Olympiad around the same time. I didn’t even know colleges had math clubs for students until I became a faculty member. Instead, my “math club” was the peer group that I formed in the PDP program. It was the community of role models and mentors that I met through joining the National Association of Mathematicians, attending the NAM Undergraduate Mathfest conferences. It was the mathematicians that I discovered on my own by spending lots of time on the Mathematicians of the African Diaspora website. These experiences in racialized mathematical spaces also caused me to seek positive and safe spaces where I could learn mathematics. I spent time studying mathematics at Morehouse College and the University of Ghana, Legon as an undergraduate and Howard University as a graduate student.
I am confident that my experiences with racism in mathematics are just the tip of the iceberg of the culture of exclusion that exists in STEM spaces. This culture of exclusion extends beyond the classroom, and it serves as a gatekeeper of access to the mathematics community. It also provides a barrier for access to the formation of positive mathematics identities, for access to careers in the mathematical sciences, and for the discipline of mathematics to be of service in the fight for social justice for underserved communities. It is a culture that values theorems over people, a culture that can turn a blind eye to not just racism, but also sexual hostility, harassment, and assault.
Looking back on these experiences, I am reminded of the work of Dr. Ebony McGee whose research seeks to understand students’ racialized experiences in mathematics and engineering spaces. I have found that my experience mirrors much of her research findings. In her work, she shares the story of Tanisha, and Black engineering student who also felt a sense of exclusion from students and professors. She says that “I know I’m not crazy. And [I] see them looking at me, and they are saying, ‘You don’t really belong here.’” [McGee, 2015]. I see affirmation in McGee’s work. I find that as a faculty member working to teach and mentor other students, especially those who are likely to face similar challenges, her research provides a healthy and sustainable outlet for the racialized experiences that I still face. One thing that Dr. McGee’s research has made clear to me is that no matter how effective a teacher I am, no matter how good a mentor I am, and no matter how strong a researcher I am, I will not be able to teach, mentor, or research myself out of systematic racism in STEM. For this to occur, to quote Dr. McGee, “The culture of STEM departments must be indicted and completely revamped to accept the full humanity of URM people in STEM” [McGee, 2021].
Things turned out alright for me in the end, but I wonder how different things could have been if I had been exposed to the same opportunities that many of my peers and classmates in high school and college had access to. In some ways, it’s as if my experience in mathematics has taken place behind a “veil,” to borrow a phrase from W. E. B. Du Bois as it was articulated in his 1903 book, The Souls of Black Folk. For Du Bois, the veil is a reference to the experience of blacks in America in which there is a world that they can see—and are in many ways a part of—but cannot access in the same way as their white American counterparts. As Howard Winant explains in “The New Politics of Race: Globalism, Difference, Justice” [Winant, 2004]:
“For Dubois, the veil not only confined and excluded black people, but it also protected them from at least some forms of white violence and domination.”
He goes on to say that, because of this double consciousness that is imposed by the presence of the veil, “the veil not only divides the individual self; it also fissures the community, nation, and society as a whole.” This metaphor plays out in the mathematical sciences as a fissure in the mathematical community that also passes beyond the community into the discipline itself. At the same time, seeing the world through this veil has its advantages as it gives an extra perception of depth through which to see the world that others without similar experiences cannot access.
For me, the repercussions of these experiences have been profound. My identity as a mathematician, how I see my role as a faculty member, how I relate to students, and how I relate to and socialize with others in the field are all shaped by these experiences. Now, as a full professor with little left to prove, I still find myself wondering from time to time what it would be like to experience a bit more entitlement around mathematics. I question where I belong in relation to many of my peers. When the imposter syndrome rears its head, nowadays I am able to remind myself that there is no “syndrome” that I am suffering from. That feeling comes from the fact that I have been positioned as an imposter by the experiences with structural racism in mathematics that I’ve been forced to confront [McGee, 2021]. Yet I often still wonder what it might feel like to be able to participate fully in the mathematics discipline without it having to be so much of a struggle.
Du Bois, W. E. B. The Souls of Black Folk. New York: Bantam Classic. pp. 116-117, 1903.
Louie, Nicole. “The Culture of Exclusion in Mathematics Education and Its Persistence in Equity-Oriented Teaching.” Journal for Research in Mathematics Education 48 (5), 488-519, 2017.
McGee, Ebony. Robust and Fragile Mathematical Identities: A Framework for Exploring Racialized Experiences and High Achievement Among Black College Students. Journal for Research in Mathematics Education, Vol. 46, No. 5 (November 2015), pp. 599-625.
Winant, Howard. The New Politics of Race: Globalism, Difference, Justice. Minneapolis: University of Minnesota Press, 2004.
Robin Wilson is a Professor of Mathematics at California State Polytechnic University, Pomona. The product of the public school system in Sacramento, CA, he attended UC Berkeley where he developed a passion for teaching mathematics as a student in Berkeley’s Professional Development Program started by Uri Treisman. He joined the faculty at California State Polytechnic University, Pomona in 2007 after an appointment as a UC President’s Postdoctoral Scholar in the Department of Mathematics at UC Santa Barbara. Dr. Wilson was a Visiting Professor at Georgetown University in 2014 and a Visiting Professor at Pomona College for Fall 2017. His current research interests include both low-dimensional topology and math education.
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As a student graduating high school, I was convinced of one thing: I was going to be a high school mathematics teacher. Everything I had done in high school and the inspiration and encouragement I received from teachers, family, and friends helped me feel reassured that my decision was the right one. As a high school student, I excelled in every subject, but doing mathematics was a passion. My love for mathematics led me to tutoring both middle school and high school students in mathematics, participating in mathematics competitions, and learning about other areas of mathematics outside of the curriculum. I had even earned the highest achievement award every year for mathematics in my grade level, so being a high school mathematics teacher seemed like the perfect choice for me.
As an undergraduate student, I immediately declared that I wanted to be a mathematics education major. Although I would have to be accepted into the program, I was sure of my choice in major. Completing the requirements to get into the program were easy because I was eager to be a math teacher. For the first few years of undergrad, things were going well. I added the mathematics major to my degree program and became a double major in mathematics and mathematics education. I was accepted into the mathematics education program and was set on my goals; everything was going well.
Fast forward to the spring semester of junior year, something changed. While taking a math education course focused on technology in the classroom, I found myself in a situation that I could not explain and one that could not be explained to me at the time. One of the first assignments in the course was to write an argumentative essay on technology in the classroom and its benefits or hindrances. When I wrote my essay, I focused my attention on the hindrances and how too much technology could lead students to rely heavily on devices and not enough on understanding the concepts. In the end, I received a low score on this assignment and when I inquired about the low score, the teaching assistant responded, “It’s just wrong.” This was just the beginning of a long battle of receiving low grades because “it’s just wrong.” Those words haunted me, so I stopped inquiring and just accepted the grades. I received lower grades than my peers, even on assignments where we had the same answers. I really disliked going to that class, but I knew I needed to finish the course because it was a requirement for my mathematics education degree. The real test came during the group final project. The project consisted of a group paper and a class demonstration on teaching a math topic to students. For the group paper, my group scored near perfect, but on the class demonstration, I scored significantly lower than my classmates. My group members and I did not understand it since I had written over half of the group paper and the project idea was one that I had brought to the group. I spent countless hours working on this project only to get near perfect or perfect grades on the group graded portion of the project but a low grade on my individual portion.
After receiving the group project grade, I had had enough. I decided to meet with the instructor of the course about my grades and my displeasure with the course. During our meeting, I asked the instructor to explain to me why my grades were much lower than classmates, especially on assignments where we had the same answers. It was then that I learned that this was not about my work, but about who I am. The professor outright admitted that the teaching assistant had given me lower scores because I was Black. The professor was already aware of the situation and had been for semesters before I became a student in his course. It had happened to other Black students who had taken the course before me. I was given assurance that while my grades were low, my final grade would not be. When I left that meeting, I cried. I was angry. While I knew that the particular teaching assistant would not be a grader for any other courses I would take in the major, I felt that I no longer had a place of belonging in that major. Despite feeling like I didn’t belong, I still had a passion for teaching high school mathematics, so I was determined to complete the degree.
The determination to continue with my mathematics education degree would change while I was a participant in an 8-week summer REU mathematics program. When I arrived at the REU program, I had no knowledge of how to conduct mathematics research and I was also unsure of what exactly I would be researching. However, with good mentorship from my research mentor and a postdoctoral student (now a tenured faculty member), I found myself interested in mathematics beyond teaching it. I was interested in solving math problems and I found that sense of community during the REU program that was lacking in my home department. Within the first few weeks of the REU program, I had decided that I wanted to get a PhD in mathematics–a thought I had not had before. My research mentor gave me advice on preparing and applying to graduate school. I took the advice and applied for PhD mathematics programs.
When I returned to my university the fall after the REU program, I was still pursuing a double major in mathematics and mathematics education. I knew that I had only one semester of coursework before I would be student teaching, but there was some unrest in me in continuing my mathematics education degree. I had just come from spending an entire summer doing math research, and I had this motivation in me to pursue a PhD. A week before classes started, I dropped my remaining mathematics education courses. After dropping the courses, I found myself in the position of being able to graduate at the end of the semester since I needed only one mathematics course and one elective course in a certain area to graduate. However, I decided I wanted to stay the entire senior year, so I enrolled in two mathematics courses and other electives.
While I dropped my mathematics education courses, I did not immediately drop my mathematics education major because I was still a bit torn about the idea of perhaps not being able to teach high school mathematics. However, before the fall semester ended, I went for it. I dropped the major and pursued my newfound interest of getting a PhD in mathematics. I started on a research project with a faculty member in the mathematics department and began submitting applications for graduate school. I submitted a number of applications for PhD in mathematics programs before the Thanksgiving break, so everything was going well.
In the spring of my senior year, I had another incident that solidified my pursuit of a mathematics PhD. I attended a graduate school fair at my institution to learn about other graduate programs at other institutions. While doing so, I stumbled upon a master’s program in mathematics education and thought to myself: “Well, maybe I could get my teaching certification while in this program because after all, I still had a passion to teach high school mathematics.” The program was at an institution close to my hometown, so that also meant that I would be able to spend more time with my family. The deadline to apply to the master’s program had not yet passed, so I thought to myself I would give it a shot. I spoke with the program’s representative, and we discussed the program and my GRE scores. She told me that I would likely get into the program with probationary status due to my GRE composite score. When I told her I had already been accepted into PhD programs in mathematics, there was a bit of shock on her face (and I am sure on mine as well). What I knew to be true was that my GRE Verbal Reasoning score was not as high, but I had done well on the GRE Mathematics portion. The composite score missed the mark for their institution to be granted full admission, so with this information in mind, I did not apply to the program. I continued with my plan to get a PhD in mathematics and finally decided that teaching high school mathematics was not the best fit for me. The following fall, I went off to graduate school, pursuing a mathematics PhD program at the same institution I had done the REU. Six years later, I completed the program and earned a PhD in mathematics.
Now, as I write about this experience almost ten years later, for the first time I ask myself, “How can eight weeks change the whole course of your life?” This is exactly what the REU program did for me. It changed the course of my life. It gave me a mathematical experience that I had not encountered before. It provided me with the mentorship I needed to succeed and gave me a sense of belonging in the mathematics community that I had not felt before. It also provided me with motivation to pursue something different–a doctoral degree. For this, I am grateful.
Two years ago, I had an opportunity to fulfill my passion of teaching high school mathematics. I taught calculus to a group of underrepresented minority students at a STEM summer program for high school students. This experience was just as joyful as I thought it would be, and I will always cherish it.
Shanise Walker is an Assistant Professor of Mathematics at the University of Wisconsin-Eau Claire. She received her Ph.D. from Iowa State University under the guidance of Professor Ryan R. Martin. Her research interests lie in extremal combinatorics and graph theory. In particular, she has studied forbidden subposet problems, graph partitioning problems, and more recently the intersection of game theory and graphs. At UW-Eau Claire, Dr. Walker supervises undergraduate research projects. Dr. Walker is also active in service to the mathematical profession related to equity, diversity, and inclusion.
Teachers, mentors, guidance counselors, program directors, and admissions officers all have the ability to provide us with opportunities and guide us along our paths. These same people can also act as gatekeepers, offering a leg up to those fortunate enough to be allowed in, while either deliberately or thoughtlessly keeping certain others out. In Living Proof: Stories of Resilience Along the Mathematical Journey, there are numerous stories that demonstrate the damage that people in positions of power can inflict by communicating to a student that they don’t belong or denying them opportunities they have earned. One example comes to us from Robin Wilson, who shared an early memory of encountering a gatekeeper who nearly altered the trajectory of his life.
“The summer after I took pre-algebra in 8th grade, my mom placed me in a self-paced algebra class that was offered at a local college and taught by a college instructor. I struggled through the course the entire summer and suffered the experience of always being the slowest one, but I survived the long days in class and the long bus rides home. When I went to my high school for the first time to meet my guidance counselor, who happened to be a middle-aged white person, he looked first at me, then at my record, and placed me into pre-algebra again. Despite my summer spent learning algebra, he convinced me that it was in my own best interest to repeat the pre-algebra course. My mother, on the other hand, upon learning about my schedule, marched up to the school the next day to demand that I be placed in the appropriate mathematics class—algebra.”
Starting around middle school, students are typically sent down one path or another in their math education. One path leads to completing Calculus in high school, an accomplishment that is virtually required for admission into some elite universities and is certainly expected for most students who aspire to a career in a STEM field. The other path, often labeled “remedial,” is one that signals to students that they don’t have what it takes to do math at a high level. Students get sorted into these different paths based on course grades, standardized test scores, parental advocacy, or simply a counselor’s impression of them. At each step, there are opportunities for gatekeepers to make decisions for children that have potentially life-altering consequences. “You are allowed in!” “You don’t have what it takes.”
When we get to college, who and what the gatekeepers are changes, but their impact can still be damaging. Jen Bowen had this experience.
“I attended a mid-size liberal arts university. Since I was in the Honors Program as a first-year student, my advisor was not in the Mathematics department. Late in my junior year, I finally was assigned an academic advisor in Mathematics. I was excited about my senior year, thinking about what was beyond college for me – I was considering a Ph.D. program. I read the catalog and noted every detail of my remaining requirements. The catalog indicated that I could substitute a graduate (800) level course for Abstract Algebra for the undergraduate (300) version. Eager to meet my new advisor and let him know my plans, he greeted me gruffly. No warm and fuzzy “Glad you’re my new advisee. Tell me about you and your goals!” When I carefully explained that I desired to register for a two-semester sequence of 800-level Abstract Algebra for my senior year, he responded, “Well every single undergraduate who has taken that route has either failed or withdrawn from the course.” Boom. Crushed. When I went to register, I realized that I could sign up for whatever course(s) I wanted for the next year. So, I registered for the 800-level algebra courses, I earned an A- and a B+. I didn’t go back to meet with the advisor again.”
Fortunately, Jen persisted in this story, knowing that she could tackle the challenge of taking graduate-level courses as an undergraduate. What doors did having these courses under her belt so early on open for her? Now, imagine a scenario in which Jen had followed her advisor’s advice. What opportunities might she have missed? How often does it happen that a few discouraging words from an advisor make a student feel unworthy to pursue their goals? Is Jen’s persistence exceptional, or are students routinely able to ignore bad advice from those who are supposed to guide them?
When on the path to earning her PhD, Chawne encountered someone in a position of power who made her feel small.
“I’d been in grad school a couple of years and earned a master’s before transferring to another school for my PhD. My grades were pretty good and admissions test scores were not too shabby. Which is all to say that signs were good that I had the preparation to succeed in a regular math doctoral program. Through a private fellowship I’d been awarded, I attended an annual doctoral mentoring program run by the foundation. The director of the program had us go around the room to introduce ourselves and mention our fields of research. He praised each new doctoral fellow, in turn, on details he recalled from their dossiers and offered encouraging words. However the word “math” seemed to trigger something in him. This man who I’d never met before had no kind words about my academic record and just declared to the room that I would surely fail. He said he had never seen a black person succeed in the math PhD program at my school. It was a gut-wrenching moment to say the least. In the years after that, I came to understand that he had spoken impulsively from the experiences of two grad students who had attempted the same program before. One finished the program with a few bumps along the way, and the other switched to a Math Ed graduate program (and has had an extraordinarily successful career ever since!). But I never returned to the mentoring program after that happened.”
Chawne successfully completed her PhD in math, but what opportunities did she miss out on as a result of being made to feel unwelcome in her mentoring program? What message did the program director send not only to Chawne, but the other fellows in her program about her ability to succeed? Chawne knew deep down that she was well-prepared to succeed, but how might the same message have undermined the confidence of someone else in her situation?
The three stories shared here demonstrate some important themes. First, gatekeeping is potentially damaging to students along their educational journeys. So, when we are in positions where we can either encourage and support our students or discourage them from taking the more challenging option, let’s choose to offer our support!
Second, one way people are able to overcome setbacks dealt by gatekeepers is by having advocates who counteract the messages or override the decisions of those in power. When we are in positions of power, let’s be those advocates for people! If someone comes to you to tell you about how someone else discouraged them from pursuing a goal, consider counteracting that discouragement with encouragement! Give a pep talk. Help your student/friend/child/colleague map out a plan for how they can achieve their goal!
Third, believing in yourself and having a growth mindset can help you be resilient in the face of a setback. It can be hard to follow a path that people tell you that you are not cut out for. But are you willing to learn? Can you put in the work? What if you put some energy into finding mentors, coaches, advocates, and friends to support you? What dreams could you fulfill?
Jen Bowen, Allison Henrich, and Chawne Kimber are members of the Editorial Board of the Living Proof blog.
I would assume that my math journey started much like everyone else in this country, learning to count in grade school and progressing from there. But that is probably where the majority of similarities end. By the time I was in second grade, my teachers were having “difficulties” with me and my ability to keep up in class. They were mostly perplexed by this since I tested extremely high for things like comprehension and reasoning, I was able to read and understand vocabulary far above my level and I was just a sponge for knowledge. My brother, one year older than me, and myself were administered an IQ test just before middle school. Mine was described as elevated, and his was described as “intimidating”. At the time, I didn’t really understand what that meant, and it was all for naught anyway because eventually my ability to do school work deteriorated. In 3rd grade, my teacher said that my inability to sit still and my inattentiveness was such a distraction to other students that I would need to be transferred to an “Alternative Learning Center” or medicated. My parents chose medication. So, at 9 years old, I was responsible for managing a prescription for psychological and neurologically altering pharmaceuticals. This was in 1995 when ADD was the most over-diagnosed mental disorder and was still vastly misunderstood. From 1st grade through high school, I went to five elementary schools, four middle schools and three high schools. I “passed” only two math classes in my entire K-12 education, and both of them were with D’s. One D was in Algebra and the other was Business Math. I took Algebra four times between middle school and graduating high school. I have since taken Algebra three more times in college, and I have never been able to pass it.
The irony of all of this was that I was able to do well on standardized tests. Once I realized I didn’t have to learn the information–just figure out how to score high enough on the test–I focused on that. I got decent enough SAT scores and was able to crush the ASVAB (Armed Forces Vocational Aptitude Battery), scoring in the 98th percentile. I had my choice of basically any job in the military. In 2004, after graduating high school, I started a career in the Navy as an Avionics Technician. Then, for the first time, I had to use real, applicable math. And these weren’t equations on a test; these were calculations that had real world consequences. Fortunately, there were also real world calculators. After avionics school, I learned about resistance, current, voltages and a wide array of electronic components and how they interacted. All of a sudden, math wasn’t a terror for me. It was a tool, just like a screwdriver or wrench, and using the right version of it for the proper application made my job a whole lot easier.
After serving in the military for four years, I left the service in 2008 and started college just in time for the economy to collapse. After a year and half of working full time and paying for college entirely out of pocket, I gave up. Having taken math twice back-to-back, I was on the verge of failing it the second time. Trying to pay rent while driving myself further into debt and paying for college classes that were never worth credit became ridiculous. Trying to learn how to solve for x for three hours a day didn’t have the same value as working for three hours a day, and I didn’t need algebra to figure that out.
I dropped out of school and continued to work full time. At this point, I was working for a manufacturing company that had a government contract. With no college education, I was doing electrical troubleshooting and quality control on units that cost hundreds of thousands of dollars. Somehow, this furthered my distaste for math. I felt robbed in the sense that I spent so much painful effort to learn this stuff only to realize that I could use prebuilt specific calculators to do the same work. The ironic echo of “you won’t have a calculator with you everywhere” was almost comical at the advent of smartphones that were rapidly taking over. This was a brief time of stability that did not last long. I was laid off by the company after only two years of working for them. I was lowest on the totem pole and they felt that because I was the youngest employee at the company, I had the highest chance of being able to “recover” from losing my job.
I was evicted from my home, and I lived on couches of friends until my welcome wore out. I was literally on the verge of becoming homeless. Sometimes, I would tell people I was “moving, but my new spot wasn’t going to be available for a week”. I would move my minimal pile of possessions into a garage or closet and then sleep on other people’s couches for a week until I found someone else who would hold my stuff.
A new liquor store was about to open up around the corner from where I was sleeping. The owner had a large amount of respect for veterans and offered me a part-time job. This store had a section that had a sign hanging on it that said “craft beer”. I had no idea what this meant, but I did recognize some of the words from when I was stationed in the Pacific Northwest. Things like “Stout,” “Porter,” and “IPA”. One of my weird friends in the Navy made beer in his garage, and I remembered Deschutes brewing from living there. The owner of the liquor store grabbed six random different beers from the cooler and handed me the six-pack. He said, “Try them out. They are going to be REALLY popular!” I did, and I fell in love with them. I was interested in how these came to be. How is it that most of the beer I had been drinking all tasted the same while all of these tasted so different? I began to research this to an obsessive extent. I worked at that liquor store and eventually moved in with several new roommates as I explored my interest in homebrewing. My roommates were excited about my new hobby and, as I was making more beer than I could drink, they had no problem helping to clear the fridge.
After a few months of this, I was starting to realize something. My beer wasn’t getting better, and I didn’t know why. I was following all of the instructions for the kits I was buying, but things didn’t seem to improve. I finally had the opportunity to talk to a brewmaster, who handed me two books for free after talking with me for two hours about brewing techniques. As soon as I got home, I flipped through them, eager to discover the secrets to making good beer. Unfortunately, they were all full of numbers… ABV calculations, yeast cell counts, enzymatic conversion ratios—even the basic statistics of beer are made using calculations. A red beer isn’t just red, it has a number called the SRM (standard reference method) that uses the density of a solution and how much light it refracts to determine a numeric value that would translate to one particular shade of red. I believe I was about 24 years old at this time, and the subsequent three batches of beer I made got better and better. The fourth won an award. The fifth got recognition from professional brewers. All of a sudden, I loved math! Over the next two years, I went from working at a liquor store counter to teaching college classes as an adjunct professor at AB Tech in Asheville, North Carolina, with no college degree. I was able to memorize conversions of mL to Oz and calculate them in my head, I could convert bbls to gallons or liters on the fly. I eventually got into distillation and had to learn dilution calculations (actual algebra). I started off staring at 700 gallons of 127.4 proof whiskey that needed to be 86 proof. I googled a dilution formula, wrote it in my notebook, and within three months, I no longer needed to write it down. I could use the formula in my head. I built a ten-year career that took me all over the country, professionally judging beer competitions and consulting for breweries. I even designed and fabricated custom equipment that involved thermal load calculations, pump curves, and vacuum and pressure ratings of vessels.
After years of this, I started to realize my problem isn’t the idea of math, it’s the anxiety I associated with it. It’s making the same mistakes over and over because I can’t read numbers correctly. It’s swearing that the homework said problems 42-45 when they actually said 24-54. It’s paying for those mistakes with hours of mentally challenging effort that isn’t worth anything in the end. You can only do that so many times before it becomes overwhelmingly defeating. In my quantitative reasoning class this spring, we were taught about financial math. But I’ve already learned about financial math the hard way. I’ve learned about payday loan traps by paying $30,000 in a single year into them. I’ve learned about mortgage rates by buying houses, and I’ve learned about asset appreciation and depreciation while getting divorced. Most importantly, I’ve learned that math is unmeasurably useful. It’s our best tool for even attempting to understand the universe, and it’s the only universal language we are aware of, even if we as humans still don’t exactly understand it. Now, as a photography major, I want to use math to better estimate distances and scale. I want to use it in graphic design and in rock climbing. But one thing is for sure. I won’t ever stop learning it.
Matthew Fields is a student at Seattle University pursuing a Bachelors of Fine Arts in Photography. He served in the United States Navy prior to exploring a 10-year career in the craft brewing industry. He has traveled to every US state and lived in Italy for a year. Matthew now works in the outdoor industry and collaborates with outdoor-oriented non-profits. He also rock climbs and mountain bikes in the beautiful Pacific Northwest while creating captivating photography.
At the time of writing this, my first vaccine appointment is mere hours away. I’ve spent a lot of time thinking about this moment, slowly waiting for it to arrive. The end of the pandemic is just beyond the horizon for me. I haven’t spent the entire quarantine twiddling my thumbs waiting for the future. I have, however, spent a considerable amount of time reflecting on my past and on my future.
For a long time, I struggled with my handwriting. While other kids’ handwriting got continually better in school, mine quickly stagnated, remaining at the level of a younger child. Nothing I did would help fix this quickly developing problem, regardless of what I tried. Finally, it became clear that I had dysgraphia. My handwriting was never going to be on par with other students. While it has improved over the years (I’ve learned lots of techniques to help make it more legible), it can still be difficult for other people, and sometimes even myself, to be able to read my notes. At the time, no one really knew what I said in my writing; no one could communicate with me effectively outside of verbal conversations, and schoolwork became an intense exercise in what should have otherwise been a mundane activity.
This problem followed me to college. I’d miss points on my homework due to the illegible writing. While I’d go to office hours to fight back for full credit, making my dysgraphic thoughts understandable, it was very clear that my handwriting was going to be a detriment to my immediate success in collegiate mathematics.
Group projects were difficult. I’d need to draw diagrams, write equations, and do mathematics by hand in such a way that I could pass it off to my group partners without needing to always be able to explain every detail. Sometimes, this was easier said than done. Any of my friends will tell you that my ‘a’ and ‘9’ look identical, likewise with my ’s’ and ‘5’.
Normally, I didn’t worry about my handwriting—it was just another obstacle to overcome—but even after just a semester of mathematics, I could see that many difficulties lie ahead. My usual techniques for fixing my shortcomings in translating my dysgraphic thoughts were no longer sufficient to keep me at pace with my classmates.
I attended a college that emphasized writing and research. For the four years to come, I would dive headfirst into paper after paper, culminating in a seventy-page thesis full of original research, supported by a junior-year thesis, consultant work, and sophomore research–all supported by my helpful advisors in the math department. In short, when I chose Wooster, I knew I had a lot of writing ahead of me. It seemed that I was going to quickly run out of options for being able to communicate mathematics the way the other students are able to. Luckily, if you’ve made it through a math education in recent years, you know that all hope is not lost.
In my second semester of college, I took a class that required the use of LaTeX. Finally, a solution to the greatest barrier in my education was right at my fingertips. I could paint the beautiful pictures that mathematics requires, without the brushstrokes becoming unintelligible. The only solution I saw was to write every single homework assignment in LaTeX from here on out.
While that doesn’t seem like a groundbreaking conclusion, I could finally do homework and share the beauty of mathematics without worrying about losing points over my professors’ inability to read past the indiscernible markings on my homework. Nearly all of my peers continued to write their homework on lined paper, regardless of their new ability to type it out. This, once again, differentiated me from others. I didn’t mind; I was content with how things were turning out. It was only once in a while where other students would ask me, “Why are you typing out your homework?” followed nearly immediately by them peering at my notes and remarking, “never mind” or an equally annoying quip.
I’ve tried my best to ignore the strange consternations of those around me who observe my handwriting in passing, but the ability to write and illustrate beautiful mathematical statements is a staple of mathematicians. Would I always be constrained to putting these illustrations on printed-paper? How would I be able to teach mathematics in an effective manner if I am unable to get past my inability to paint the beautiful pictures that were given to me as a student?
I’ll never be able to fully solve the issues with my handwriting. But what is to become of my future as a mathematician should I fail to find a permanent solution to this conundrum? Mathematics is a beautiful discipline that oftentimes relies on illustrations or paragraphs of magnificent equations. Teaching mathematics, likewise, also relies on these same illustrations and equations.
The chalkboard is the mathematician’s preferred canvas. A great instructor can imprint the beautiful world of math onto their students through their simple strokes of chalk. That’s something I’ve seen with my own eyes.
But the chalkboard will never be my canvas. The sooner I accepted this, the more content I was. When I first started as a TA, I found myself constantly rewriting, restructuring, and reviewing everything I would write for my students. Every lesson was filled with my insistence that students interrupt me if they couldn’t read what I had written; every lesson was filled with students interrupting me with questions about whether or not “that’s an ‘o’ or a zero” or if that’s a “five or an ‘s’”.
Dysgraphia is more than just bad handwriting. It’s the way that I move my hands. The way I communicate with others. The way that I think–in my proofs, in my lectures, in my social interactions day-to-day. The fine-motor issues prevent me from ever holding chalk correctly, the words I think fail to come out the way I want them to, and the mathematical beauty I see in my textbooks I struggle to translate–to my students, my professors, sometimes even myself. Dysgraphia is not just bad handwriting; it vastly affects the way I interact with the world every single day.
How can I, as a professor, communicate the beauty of our discipline to students when I struggle to find the words with seasoned mathematical prose? The chalkboard is the mathematician’s preferred canvas. How do I use it as a medium without emphasizing the struggles that I endure? I could stick to the fields of math that limit the need for illustration, putting easily copied numbers and symbols at the forefront. I could avoid the chalkboard in favor of the PowerPoint. But these quick fixes do not erase my dysgraphia. Rather, they continue to push the narrative that issues like mine should inhibit my access to any particular field of mathematics.
Instead, I’ll plant my feet and fight through my students’ annoyance that I can’t draw straight lines or make a simple diagram without copious apologies for its illegible structure. I’ve learned to be okay with my dysgraphia, despite its implications for my experience as a mathematician, an academic, a person. The world is not what it once was, and it will not always be as it is.
Even just twenty years ago, my dysgraphia would have hindered my ability to be a fully active member of academia. Now, LaTeX allows me to engage with the world around me without fear of being misunderstood or failing to properly write beautiful mathematics. Perhaps there will be a better solution to my conundrum by the time I finish my education and fully enter the world of academia. For now, I must be content with what I have at my fingertips.
Isaac Weiss is currently working on his MA degree in Mathematics at Bowling Green State University. He graduated from The College of Wooster in 2020, where he double majored in Mathematics and Political Science. His 70-page thesis, written in LaTeX, explored compactness measures for legislative districts and was mentored by Dr. John Ramsay and Dr. Bas van Doorn. He fell in love with math as a middle schooler when he was given misleading information about exponents, leading him to explore the rules of mathematics in depth with his father, an algebraic topologist. He was diagnosed with dysgraphia in the second grade and has spent every day since working on finding ways to work on his written communication skills.
Posted inDisability|Comments Off on Bad Handwriting in an Artist’s World by Isaac Weiss
I share with my students that I was homeless at the time I started the general exam for my PhD candidacy. That item comes in a list of several bits of personal trivia, some of them bizarre, none of them with any context. The homelessness mention seems to be one that makes the deepest impression, I think because many students feel substantially at risk of becoming homeless themselves, they recognize the stigma that homelessness carries, and they dread that situation. That saddens me deeply.
Here, I’d like to recount the comedy of errors that found me sleeping on unfamiliar floors during one of the most important exams of my life.
Frankly, although “homeless” is literally correct as a description of my situation, it was devoid of most of the connotations that accompany that term here in the 2020s. At no time during this episode did I ever feel that I was being persecuted; it simply was the confluence of several independent, impersonal mechanisms occurring at a most inconvenient time for me personally, with some of those independent events having developed quite suddenly, and I never had any thought that the situation was other than temporary. Nonetheless, it made an already challenging situation preposterously difficult. So, how did I find myself homeless at one of the most consequential moments in my life? Well, we’ll get to that.
I had lived very happily in dorms all four years as an undergrad, and when I went off to grad school, I signed up for my first year in the dorm there as well. However, the dorms at my graduate school had a different social atmosphere. They operated from much more of an in loco parentis attitude, with evening (human) monitors checking IDs of those coming in after hours, inspections of the rooms to make sure unapproved items weren’t present, etc., none of which had been in effect in my undergrad days. Even though I lived on a floor exclusively for graduate students (on whom enforcement of some of the rules were not as strict), it was an environment I nevertheless found stifling. Unhappy as it was for those nine months, in the long run that did work in my favor: I rapidly adopted my academic department and especially my fellow astronomy grad students as my social reference group, and this became the community I exclusively identified with.
During that first year, I resolved to abandon the dorm once the contract was up, and when a classmate indicated he wanted out of the shared house in which he’d spent his first year, I agreed readily to go in with him on a new shared student house. That meant I’d have to live by myself for that summer (his lease was for a calendar year, not an academic year), but that wasn’t a serious issue. I signed a three-month summer lease for a furnished apartment about five blocks from campus. I did own a car (an eight-year-old Ford gifted by its previous owner – my grandmother – to me after my college graduation), and I already knew it was not the most reliable vehicle. But the price had been right, it had gotten me from Washington to Texas, and I did not intend to commute daily with it, merely use it as shopping transport. I had very little in the way of possessions (I had, after all, been living in a dorm with summers at my parents’ house for four years). My books and notes fit easily in my portion of the shared-with-three-others grad student office, with some space to spare. And with my books and notes in my office, literally everything else I owned could fit in the car.
At the time, the General Exam in our doctoral program was given during the intersession just before the start of the second year of study. It ran four consecutive half-days, a single three-hour session each morning. As was customary, I took a single course during that summer term. Also that summer, I had some research duties that I embraced happily, and I spent much of the rest of my time in preparations for the General. I knew that the end of my summer lease came about a week before the exam, but I did not worry about lodging arrangements most of that summer. My roommate-to-be and I hunted around for both a house to rent and a couple more roommates to share it with. We found a decent deal on a house in what seemed like an acceptable location that was being renovated after long disuse, so we paid our damage deposit and first month’s rent, made deposits on utilities, got a semi-commitment from another grad student to go in with us, and hunted around for a fourth roommate. These deposits drained my modest savings, but with my student stipend, there was not yet a critical cash flow issue. I gave notice that I would not renew my apartment lease.
The problem that hadn’t been fully set out to us was that the renovations of the house weren’t complete, and once they were complete, a city inspection was required before it could be occupied. As it developed, multiple inspections failed. At the same time, my car’s electrical system went kazoo a couple of days before my apartment lease expired, and it did so on the far side of campus from my apartment. It was parked legally, and I could leave it where it was for a time, but it was unavailable as transportation and not at all convenient as storage; the cost of a timely tow and auto repair was beyond my depleted reserves during those crucial couple of weeks (and short-term credit was not available to 23-year-old students at that time). Considering where the car was, trying to use the car as a place to sleep did not cross my mind.
The night before I had to vacate the apartment, I carried my possessions by hand from apartment to office, which was about a ten-block walk each way, a process I began about 11 PM. Campus police stopped me twice as I carried bags and boxes of stuff through the night. I got everything ferried in three or four trips, and I got to sleep in the apartment starting about 3 AM. I was up at 9 AM, the apartment passed inspection, and I was out before the noon deadline.
I slept in the department’s common space the next two nights — which was of course against the rules — but it being the end-of-summer intersession, very few people were on campus working at all, let alone after hours. During the days, I tried catching up on the prep time I’d missed for the General Exam. I can’t say this made for particularly effective preparations.
Another grad student learned of my situation and invited me to stay at his place until my living arrangements sorted out. (Like me, he also came from not-quite-middle-class circumstances.) I slept on his floor in my sleeping bag for another two nights before the General, and then for the first two days of the exam. At that point, word came that the inspections of the house had finally passed, we got our keys, and I moved my suitcase of clothes and sleeping bag into the house. I was still sleeping on the floor, but at least I did not feel like I was in willful violation of rules or imposing on anyone else.
I finished the exam. Once the next month’s stipend check came, I had my car repaired and the rest of the move-in was accomplished in a day. Later in the month I learned I’d passed the General, in the middle of the pack of six who took it. I was a little disappointed, honestly; I like to think I’d have done better if I’d had stable living arrangements at the time, but all in all, it really didn’t matter. It remains the only exam I remember taking where all that mattered was passing.
And thus concluded that particular episode. As I’d felt certain of for its entire duration, it was an accidental coincidence of inconveniences that went away as quickly as they’d arrived, leaving no real long-term effect. Frankly, the deepest insight I took away from the experience was to notice that the one piece of significant personal charity I received came from the comrade who’d offered me his living room floor, and whose upbringing was, like mine, from a poor socioeconomic state.
As a postscript, the house arrangement failed after another few weeks. We still lacked a fourth roommate after the first month (and the third was about bail out on us to move in with a new girlfriend), and then on a Sunday evening, literally as we waited for the ten o’clock news to start, a car drove up slowly, halted, and fired three shotgun blasts into the house across the street before speeding away. The others rushed out to check on victims; I called 911. That event put an end to the interest anyone had in joining us in that house. We broke our lease, got a two-bedroom apartment, and stayed in that complex until my roommate graduated. It took me most of another year after that to finish my PhD, during which time I lived by myself in a studio apartment.
Dr. Jeffery Brown is a Senior Instructor in the Department of Physics at Seattle University. Born in San Jose, California, he grew up in transient, “army brat”-like circumstances, never living anywhere longer than three years at a stretch until he went off to college. He was pursued by good fortune all his life, though it only caught up with him when he paused before a serious obstacle. He got his BS from the University of Washington in 1978 and a MA and PhD from the University of Texas in Austin in 1986. After a postdoc at Indiana and a postdoc-research faculty appointment again at the University of Washington, he was an assistant professor in the Program in Astronomy (then part of the Mathematics Department) at Washington State University from 1996 to 2000. He was made program director in his last year, at the end of which he felt obliged to resign, move back to Seattle, and take a software position in private industry. Laid off at the end of 2003, he reflected that he was much happier in an academic environment despite the lower pay, and in late 2004 took two jobs, one as a scientific programmer at Fred Hutchinson Cancer Research Center developing an epidemiological population simulation for evaluating cancer screening strategies, and the other teaching physics and astronomy at Seattle University. In 2008 the grant at FHCRC ran out, and he transitioned to being a full-time lecturer at Seattle U, where he has remained and was promoted to Senior Instructor in 2017.
Posted inQualifying Exams|Comments Off on Homeless for the General, by Jeff Brown
Back in the day, Berkeley had more graduate students than it could keep track of. It certainly had more than it could support financially. Oddly, if you didn’t have some financial support from the University, it wasn’t even necessary to formally enroll, and many didn’t enroll to save on tuition. As a result, there were over 400 mailboxes for graduate students and no one had any idea exactly which boxes corresponded to active students. The one exception was if you were supported—and hence had a TA-ship or other monetary support. Naturally, we were all keen to get and/or stay supported. To accomplish this, you had to do well on your qualifying exams. These were one-hour oral exams given at the end of each term. You had to take and do well on three of these selected from a short list of subjects. If you signed up for a “qual,” then about a week or two prior to “Qual Saturday,” a list was posted assigning you to an office and listing who your examiners would be. You got no choice in the matter other than signing up for whatever subject you picked for that term.
In my first year, I was unsupported and had decided that if I couldn’t get support, it was time to leave mathematics and get a job and perhaps a life. So, in my second term, I signed up for the algebra qualifying exam. It was my weakest subject, so I wanted to tackle it first.
At the time, the Mathematics Department was housed in the upper floors of Evans Hall. Evans was a hideous cement structure of ten stories with an additional two basement floors underground for classrooms. Hence, our crowded classes were held in the basement and at the end of each period, we would all crowd into elevators to go back up to the upper floors to find some light and our study spaces. Normally, almost everyone would first get off on the ninth floor where the mailroom was. Before email, checking your mailbox was one of the key activities of the day. Many of us were a bit obsessive about it. After seeing that no one had sent you anything, non-teaching students such as myself would slink off to a windowless cubicle to continue studying for our quals.
The elevators were large, and on the day this story starts, I was packed into the middle of one with twenty to twenty-five other students and faculty all waiting to emerge on the ninth floor. I happened to be crushed against the TA for the analysis course I was taking. He wanted to be nice to the nervous first-year student, so he started a conversation. Of course, he led off with “Are you taking a qual this term?” (This is what graduate students primarily talked about.) I said that I was taking algebra. He asked who my examiners were. I answered, “Professor Smith and Jones.” (The names have been changed for reasons that will become obvious.) To my horror—and I am not exaggerating—everyone in the elevator laughed. You may be sure that I was somewhat curious as to why announcing Smith and Jones’s names lead to universal laughter. Just at this moment, the elevator doors opened to the ninth floor and everyone filed out. I was very shy back then and rarely even spoke to my professors let alone a random professor. But there was one faculty member who was a little slower than the rest. I almost grabbed him physically and asked, “Why did everyone laugh?” Of course, I now know there was no way I was going to get any real information about his colleagues in a public place like the mailroom. Nevertheless, he did admit, “They are a couple of characters,” before quickly running away.
If I had been stressed about my qualifying exam before, you can be sure that I was over the top now.
I now know that Professor Smith was just a pompous twit fond of asking trick questions that would lead a student into making a fool of themselves. In my experience, one doesn’t have to trick nervous students into making missteps. They can handle that on their own. On the other hand, if the rumors were correct, Professor Jones was an alcoholic and tended to be a little out of it on Qual Saturdays. Nevertheless, it will be the presumably hung-over Professor Jones who will emerge as the hero of this story.
As is the way of these things, my obsessive worrying did not prevent Qual Saturday from arriving. At the appointed time, I presented myself at Professor Jones’s office. Professor Smith was already there and the blackboard was ready. I had studied the syllabus to the best of my ability and awaited the first question. Unfortunately, Professor Smith started with something that I was not prepared for. While some might say I should have been—and I am not going to embarrass myself by revealing the actual question—it was clear from the onset that I was at sea. You have to keep in mind that I needed to do well on my quals, and the situation is that you only have 60 minutes to prove yourself. However, Professor Smith was not about to switch ships until he had guided me to drive said ship well and truly upon the rocks.
Meanwhile the good Professor Jones had laid his besotted head on his desk and apparently gone to sleep.
After 15 minutes of sheer agony trying to construct something over the complex field of which I did not know the definition, it seemed that we had finally come to some conclusion. I was pretty relieved and excited to get back to the syllabus that I had mastered. But Professor Smith was not satisfied. “What if we work over the reals instead of the complexes?” What I thought was: “What if pigs could fly?” (Well, what I actually thought need not be quoted here.) Instead, what I said was, “Well, I guess we could try the same sort of approach.” The ever helpful Professor Smith was only too happy to point out, “Oh, but the reals are not algebraically closed, you know.” Of course, I knew that. As any idiot watching my qual whould have known by now, the problem was that I didn’t know what I was supposed to construct. But Professor Smith was not just any idiot.
However, our hero, Professor Jones, had not been completely asleep after all. I am now, some forty-five years later, still grateful that Professor Jones lifted his doubtless throbbing head from desk, turned to Professor Smith, and shouted in way that expressed his irritation at being disturbed, “Can’t you see he doesn’t know any of this?!”
Now, that may not have been the most flattering thing ever said about my mathematics. (There have been a lot of referee reports over the years.) But at the time, I could have kissed him. Somewhat grumpily, Professor Smith returned to what I considered to be the actual syllabus. Despite his trying, unsuccessfully, to lead me astray here and there, I must have done reasonably well. Professor Jones even rousted himself to ask a question or two.
Suffice it to say that in addition to passing the qual, I did manage to get some financial support my second year, and in the end, I managed to write a thesis and go on to have a successful career in mathematics.
I am still in Mathematics. Instead of taking quals, I now give them. They are still almost as unpleasant to give as to take—causing anxiety is just as bad as having it—but I don’t expect anyone to believe that until they get to give a few. When I give a qual, I keep the good Professor Smith in mind. He managed to teach me what not to do, which I think has been valuable lesson. My goal is to lead the student to the answer and not away from it. Even then, the road can be bumpy.
Dana Williams is the Benjamin P. Cheney Professor of Mathematics at Dartmouth College. He graduated from Cornell University in 1974 and got his Ph.D. under Marc Rieffel from the University of California at Berkeley in 1979. After six years at Texas A&M University, he moved to Dartmouth College in 1985 and has been there ever since. His webpage is math.dartmouth.edu/~dana/.
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Two roads diverged in a wood, and I took the one less traveled. And then it got dark and scary, and I ran back and went down the other one.
I never had to work too hard at my math classes in undergrad, and I took more than I needed for my degree. I enjoyed the people I was with and decided that teaching college math was the thing for me (having already transferred from the School of Education, where I decided teaching high school math was not). When I graduated from undergrad, I was admitted to a graduate program in mathematics at a well-respected school. The program was small, but very warm and welcoming. I made friends and enjoyed the environment. The faculty were friendly, and while I was the only female in my class, there were a handful of others ahead of me that I could look up to.
Fast forward several months, and I was taking my first oral qualifying exam. Leading up to it, classes were more challenging than undergrad, but still mostly fun. My exam, though, was a disaster. Despite having practiced successfully with other graduate students, I froze on the first question, which was really a gimme, a warm-up. It was so bad that I asked to be excused and ran outside to cry to a friend on the phone. I now know that it was anxiety, but after that, I started to really question whether I was cut out for a PhD in math. I was never really motivated by the research aspect of being a professor at the college level. I just wanted to teach something more exciting (for me) than Algebra II to a bunch of high schoolers who didn’t want to be there, and in my mind at the time, this was the way to do it.
Our school had an option where you could take a year of leave and return to the program if you wanted to, all financial aid staying intact. So, I did some exploring, looking into alternative career paths, and I stumbled upon actuarial science as an option. I ended up getting an internship as an actuary over the summer and enrolled in a master’s program in actuarial science while technically still on leave from my math PhD program. I figured I could leave the actuarial master’s and go back to math if I wanted, but if it worked out, I would be fine. It worked out great! I finished my program in a year and secured a job at a start-up Medicare plan.
Actuarial science was a great fit for me because the environment was dynamic and challenging but also combined some softer, business skills with the analytical ones. And there were no oral exams. Lots of written exams, yes. Presentations, yes, but no oral exams. And I was in an environment where I was the only actuary, so I was respected and looked to as an advisor. The best part was that I could still teach, which is what I wanted all along. After I earned my Fellowship in the Society of Actuaries, I taught actuarial students in the graduate program where I earned my degree on the weekends.
After a decade or so of that, I have “retired” to stay home with my family and volunteer in my community, though I taught a little preschool for fun. I can think of a lot worse jobs than being an actuary, but focusing on my children is what’s right for me at this point. (Also, it’s ok to stay home with your kids, if you can, but that’s another topic.) Looking to my next phase of life, I am still figuring out “what I want to be when I grow up”, and I still haven’t ruled out a PhD in something else.
Looking forward has also made me think back more on my decision to leave academia in the first place. I used to feel like a failure and still sometimes wish I could throw that PhD behind my name, but mostly I know that I did what was right for me, and I now have seven letters behind my name (FSA, MAAA).
I could have stayed and struggled and probably ultimately graduated, but I suspect I would have ended up in a place where I constantly faced doubt and inadequacy. Instead, I took the skills and way of thinking that led me to academia in the first place and applied them in a totally different environment where my efforts directly contributed to improving lives and were rewarded handsomely without me having to constantly question if I was in the right place. Even though I definitely doubted myself for a while (see also: anxiety), I eventually came to be respected as an expert in what I did and was sought after for my skills and opinions.
My journey has taught me a few other things, too. Career exploration is hard and not addressed adequately anywhere, in my opinion. Mental health is important, and even recognizing when you need help is hard. I encourage anyone with doubts about whether they’re on the right path to first make sure their mental health is addressed and then explore a bit more. It’s definitely possible that there are careers out there that you have never even heard of, particularly if you’ve been headed in one direction for a long time.
Tiffany Eaton is a stay-at-home mom. In her past life, she was a health actuary for a small Medicare Advantage Special Needs Plan. As the plan’s sole actuary, she worked across cross-functional teams to communicate technical ideas to senior management and oversaw forecasting, reserving and analytics. Having traded Excel models for Lego models, she now spends her time volunteering in her community, sewing, and planning science experiments as well as outlandish birthday parties for her two kids.
During our research retreats, my research group, Creativity Research Group (CRG), uses our lunch/dinner breaks to get personal. To facilitate our discussions in a fun relaxed way, we have often used the New York Times article “The 36 Questions That Lead to Love” and similar questionnaires. During our most recent retreat we asked each other: “What’s your biggest academic or professional achievement/moment?”
As I did not go first, I had a minute or so to run through my academic career to quickly reflect on which moment “sparked the most joy” in my life. Was it achieving one of the highest ranks in the high school exit exam in Lebanon? Was it achieving the highest GPA in my cohort for four consecutive years in my undergraduate studies that got me a full scholarship as a result? Was it being accepted and fully funded to the master’s program at the American University of Beirut, one of the most prestigious universities in the Middle East? Was it being accepted and fully funded to two Ph.D. programs in the US? Was it passing my qualifying exams, then general exams? Was it my first publication with my advisor? Was it defending my dissertation successfully?
It was none of the above. It might sound snobbish, but I don’t think I have struggled in the formal setting of schooling. I always had the motivation to study, do homework, put in the hours, and most importantly ask questions when I did not understand something. As a student, I asked my peers and faculty questions in the classroom, hallways, office hours, etc. I did not mind spending time to problem solve and prove mathematical statements. These study habits made testing less of a struggle for me, but I still believe that forming a full understanding coming out of a class was my number one study habit.
I tried to never leave a class not understanding the big picture, even if it meant hijacking the class at times. As I come from an underprivileged, big farming family, I had made a promise (to myself) to always advocate for myself. Now, as I stand on the other side, I wonder if I was that obnoxious, selfish student who only cared about his own learning. Maybe at times I was, but I was also a peer instructor, at least informally.
Many of my peers used to copy my notes from class, my solutions to exam reviews, and ask me various questions on content. These instances and many similar situations have helped me to come to peace with my advocacy for myself. I do not view it as a selfish act anymore. In a way, I think advocating for myself was also advocating for others!
I sometimes wonder if my advocacy for myself has defined me as “rebellious.” For example, I would not tolerate “bad teaching” during my undergraduate studies. If you’re teaching Real Analysis by just reading theorems and proofs from the book, you got some heated commentary from me as your student. In Real Analysis, this actually developed into a protest activity where I led the whole class, except two students (Traitors!), to boycott the lecture and instead go to the chairperson. If your style of teaching is that problems can be done “MY way or NO way”, I probably protested by pointing out a different way of solving a problem. If your style of teaching was dismissive to questions, I stood up in class and demanded, “I’d like you to answer my question before moving on.”
I was fortunate to have only a few of those “bad teaching” experiences in my life. I am very grateful for having some of the most inspirational instructors, starting from elementary school up to my PhD. I am very grateful to have had an amazing Ph.D. advisor, Professor Jonathan Kujawa. I will always cherish his encouragement and support. Most importantly, I am indebted to Professor Nazih Nahlus who taught me during my time at the American University of Beirut. His advice and mentoring paved a path for me to pursue a Ph.D. program in Mathematics. Before chatting with him, I had never heard of a place called Oklahoma, but as he had done a postdoc there, he recommended it to me. I must say I am glad I followed his recommendation because my six years in Norman, OK were an absolutely a wonderful part of my life. I should mention that his deep interest and experience in Algebra has had a profound impact on my interest in the subject. Without his guidance, I would not have been where I am right now.
My experiences as a student have carried over to my current professional career. As a faculty member, I am now on the other side of mentoring students who have a keen interest in mathematics, and I try to emulate Professor Nahlus and be the voice that pushes my students to follow their dreams and aspirations. Additionally, as a program coordinator, I have gotten the chance to observe the teaching of my fellow faculty members. I still can’t tolerate the above teaching styles.
I have finally come to the conclusion that my advocacy for myself as a student has extended to an advocacy for ALL students. For instance, I now advocate for active-learning equitable practices in my classes and during department, college, and university meetings. I wonder sometimes if this advocacy gets me stamped with: “Houssein seems to be a difficult person to work/deal with.”
Maybe it does! Sometimes, I have struggled to communicate my ideas in the “best” (possibly Euro-centric) way. Recent encounters have pushed me to reflect on the way I communicate. Am I phrasing my thoughts in a strong demanding voice? Do I use “I” too much (I’ve been told)? Am I too direct? Does my advocacy for my ideas come across as “rude”?
Maybe it does to some people! Reflecting on my struggle with the academic job market in 2014 gives me this impression. I had many phone, Skype, and even on-campus interviews. On paper, I still think I was highly qualified, but nothing panned out. In April, I was still searching for a job, and self-doubt had started to sink in. “What’s wrong with me?” is an inevitable response to rejection letters/emails. They have found someone else who was a better fit. A “better fit”? But I excelled at schooling, teaching, and research; that can’t be it. What is it? Now looking back at that time, I think my lack of success on the job market might have been more about communicating in a “certain” way, a skill that was not part of my training at that time.
It does take a few people to believe in your abilities to keep moving forward! On a Saturday, in late April of 2014, I was at a Lebanese festival in Norman, OK. My friends and I were about to perform our traditional line dance “Dabke” after having some delicious Falafel and Taboule. My phone rang with Area Code 203. I took the call; I could not hear properly, so I ran to a nearby parking lot. That was the day that I became a University of New Haven Charger!
Dr. Houssein El Turkey is currently an associate professor of Mathematics at the University of New Haven. He is the Mathematics Coordinator at the University, a University Research Scholar, and a Faculty Fellow at their Center of Teaching Excellence. Before that, he completed his Ph.D. in Mathematics from the University of Oklahoma in 2014, where he studied Representation Theory of Lie Superalgebras.
After graduation, he developed a keen interest in qualitative and quantitative Research in Undergraduate Mathematics Education (RUME). One of his main interests in this area is studying ways of fostering mathematical creativity in the undergraduate classroom. Since 2014, he has been a part of the multi-institutional Creativity Research Group studying mathematical creativity, which has secured an NSF-IUSE grant to explore connections between mathematical creativity and mathematical identity in the Calculus classroom. He co-authored several publications and presentations in RUME.
Outside of academics, he enjoys cooking Lebanese food and being on the tennis court.
This short piece is dedicated to Professor Nazih Nahlus. His belief in me and mentorship have encouraged me to pursue a Ph.D. in Mathematics. His passing in 2018 was one of the saddest moments I have experienced, but he will always be remembered as my favorite mentor.
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