Daniel L. Reinholz, Robin Wilson, and Amelia Stone-Johnstone

**Introduction, by Daniel Reinholz**

As mathematicians, we think deeply about *what* mathematics we want to share with our students. We think about all of the beautiful aspects of the discipline that they might be interested in. As mathematics educators, we also think about *how* to help our students learn these ideas. We do our best to develop meaningful activities that can engage our students in the deep work of really doing mathematics. It takes considerable expertise to understand mathematics *and* to teach it well. At the same time, it can be easy to overlook *who* gets to participate in the activities we create. When we facilitate a discussion, how do we make sure all students are getting a chance to participate? How do we keep track of the students who do have access to opportunities to learn in our classrooms, and what do we do when we notice some students don’t seem to be getting a fair chance? This blog post focuses on one tool, EQUIP, that can help address these issues (see Reinholz & Shah, 2018; Reinholz, Bradfield, & Apkarian, in press).

Mathematics teaching and learning doesn’t happen in a vacuum. It happens in a complex, historical and evolving world. To teach equitably, and to make sure that all of our students are getting a fair chance to learn, we need to be aware of all of the ways that the world outside impacts what happens in our classrooms. There are many issues, such as — structural racism, toxic masculinity, homophobia and transphobia, ableism, stereotypes, and class-based discrimination — that marginalize some students directly (see Martin, Rousseau-Anderson, & Shah, 2017) and also can impact us subtly through implicit bias. Implicit biases are the unconscious attitudes and stereotypes that impact our actions in an unconscious manner (Staats, Capatosto, Tenney, & Mamo, 2017). Research shows that all people have biases of some sort; what is most important is that we acknowledge them and learn to address them.

EQUIP (Equity QUantified In Participation; https://www.equip.ninja) is a freely available web app for generating analytics about classroom participation. EQUIP is designed to help us gain insight into *who* is participating in our classrooms. Given the complexity of orchestrating a discussion with a group of mathematics students around complex mathematical ideas, it is very easy for bias to seep in our teaching in ways we are not aware of. It is in these moments that we may unconsciously favor some students over others, simply because we have been bombarded by problematic stereotypes and other messages throughout our life, or because we have preconceived notions about some students’ abilities. Research shows that this can impact even the most thoughtful teachers, for instance, who may have false perceptions that boys are more mathematically capable than girls in their classes, as early as elementary school (National Science Board, 2018).

What is needed are data that can help us understand when biases impact our teaching, so that we can become consciously aware of them and correct the issue. EQUIP provides such data that can be used after-the-fact to understand these patterns of participation. It allows us as instructors to slow down the automatic work that happens while we are teaching, so we can reflect on who is participating and how, and how this participation could relate to larger systemic factors and our own implicit biases. Since co-developing EQUIP, I know that I personally have become much more aware of my own biases and how they could impact my teaching. This awareness has pushed me even more to teach more equitably in every single class I run.

—

Here we reflect on our experiences running a professional learning community organized around EQUIP analytics. Daniel and Amelia served as facilitators in this community, and Robin was a participant looking at analytics in his own classroom. Daniel provides an overview of the EQUIP tool and the professional development process, Amelia reflects on her work as a facilitator, and Robin focuses on his experiences as a mathematics faculty member.

**The EQUIP Tool, by Daniel Reinholz
**

EQUIP was initially designed by Daniel Reinholz and Niral Shah as a research tool for understanding patterns of participation in mathematics classrooms (Reinholz & Shah, 2018). Building on this initial work, EQUIP has now been developed into a free, fully customizable web app for professional development (https://www.equip.ninja). By default, EQUIP describes seven dimensions of student participation, but for this study, we customized it to focus only on three: type of teacher question, quality of student talk, and length of student talk. By using just a few dimensions, it streamlined our process for analyzing teaching, and facilitated quick reflection on the analytics.

The EQUIP analytics take three forms: (1) a classroom-level summary of student participation, (2) an individual-level comparison of how much each student participated, and (3) group-level comparisons (e.g., by race, gender). At the group level, EQUIP compares the actual distribution of talk-based participation with the expected distribution, using classroom demographics as a baseline. Consider a class where 40% of the class is women, but they only participate 10% of the time. This would indicate an inequity, which could be driven by an implicit bias or some other sort of contextual factor. In either case, awareness of the issue allows an instructor to take intentional action to address it. For more on the equity ratio, see https://www.equip.ninja/faq.

To generate analytics, we first create a classroom profile for each instructor we are working with. To do this, each instructor provides us with a seating chart and demographic information for their students. To protect student identities, we only use first names, and the data are not shared with anyone outside our team. During the semester, instructors share video recordings of their teaching that our team analyzes with EQUIP to generate analytics. These analytics serve as the basis for debrief conversations and collective planning on how to improve equity in mathematics teaching.

We emphasize that EQUIP does not evaluate instructors. Instead, provides a starting place for deeper conversations about race, gender, and other social markers and how they play out in the classroom. Also, the analytics don’t tell someone how to teach. There is no “target distribution” for EQUIP analytics. In other words, EQUIP doesn’t set out a particular goal, such as equal participation for all students. It is up to instructors to make sense of the data and what they will do with them, based on how they conceptualize “equity.”

The reflections below describe our use of EQUIP in a semester-long learning community organized around EQUIP analytics. The learning community began with each participant sharing their goals for the semester individually with the developer team, and after that there was a series of four meetings during the semester that focused on EQUIP analytics and change over time. The basic format is that: (1) each instructor would set a goal for their teaching, (2) they would record their teaching and have it coded with EQUIP, and (3) they would discuss the results in a safe, group-based setting. During these discussions instructors made action plans for changes in their teaching, which will hopefully be observed in the next round of analytics. In this way, EQUIP makes it easier for instructors to see improvements to their teaching over time. We now turn to Amelia’s reflection as a facilitator of the community.

**Reflection as a Facilitator, by Amelia Stone-Johnstone**

I write from the perspective of a graduate student who has been working with EQUIP for the past year and a half. I have used EQUIP to observe and code almost 200 teachers, ranging from middle school to college-level mathematics. In a recent project, I also played the role of facilitator — after coding and analyzing the data, I worked with Daniel to help mathematics faculty members use the analytics to guide improvements to their teaching. What I describe here is my learning process as a facilitator, and how it brought new insights into my own teaching.

As a fly on the wall it is easy to identify what is present and not present in a classroom. Is the teacher only asking the boys to explain their answers? Are certain groups of students not participating at all? When I reflect on my prior experiences of being an instructor at a community college and at an undergraduate university, I realized that I have had some of the same struggles that many of the teachers that I observed experience. How do we engage everyone in the class, **and **probe student thinking using high-level questions, **and **still have enough time to cover all the material in the short period of time? These are the types of questions that I have considered while presenting teachers with analytics from their classes. It is one thing to tell an instructor what they are not doing but it is another to help guide them through the data analysis and help them reflect on their practice. It’s easy to know what *not* to do — it’s harder to know what *to* do.

My fondest experience so far while working on EQUIP-related projects has been interacting with instructors and learning about how their experiences have guided their practice. The most recent group of instructors that we have worked with were all very excited to participate and were open to getting some feedback about what was going on in their classes. These were very thoughtful instructors. It was interesting to see the different dimensions that each instructor chose to observe about their students. For instance, besides looking at student participation in their class by race and gender, Robin (see below) was interested in looking at differences based on the number of hours of non-academic work commitment. He was curious about the extent to which working part-time affected participation in his class. He seemed very eager to use the analytics to inform his pedagogy.

While I am not teaching right now, I know that I will eventually be back in the classroom and will need to confront the everyday equity-related issues that teachers may navigate. In our biweekly meetings as a cohort of instructors, we would discuss emergent topics like how to effectively engage students in a lecture-based course, whether rotating student seating will affect the amount (and quality) of participation by different groups of students, and how we can ensure that group work is productive. It was interesting to hear the different takes on how to approach some of these problems. It was also refreshing to see that regardless of someone’s teaching experience, they have at some point had to navigate some of these same problems. We’re all in this together. In my opinion, a person’s willingness to receive feedback and listen to constructive criticism tends to make them a better teacher. As I analyzed each instructor’s video, I could see in their teaching practices how they consciously transformed aspects their pedagogy to confront some of the areas that they were interested in changing.

** **

**Reflection as a Participant, by Robin Wilson**

As a mathematics teacher who has been committed to implementing equitable instructional practices for my entire career, I was surprised to find out how much I could learn from having access to data about student participation. I often hear talk about teaching and reaching “all” students in the classroom. I see this in research journals about math education, in curriculum guidelines, in blog posts about teaching, and in teaching statements from faculty job applications. This is, of course, is one of my own goals as well, to “include all students in rigorous mathematical learning and mathematical identity building” (Laursen & Rasmussen, 2019). Each day in the classroom I set out with the goal of teaching all students and getting all students to participate in meaningful mathematics activities, but without actual data about what is actually happening in my classes of 30-35 students I now realize how much in the dark I’ve been about what is actually happening in my classroom. Having access to the EQUIP data was like shining a bright light on my teaching, and it illuminated for me in a easily digestible way who was and was not participating, and in what ways the students were participating. Having the data broken down into gender and ethnicity provided an even clearer focus on what students I was and was not serving. After participating in EQUIP I’ve realized just how much that my positive feeling that I can have about how the class went, who participated, that I reached “all” students is riddled with my own biases.

My participation with EQUIP spanned the course of one semester, and at the outset I really didn’t know what to expect. What I got out of it was one of the most impactful and practical professional development experiences of my career. Here’s how it worked. At the beginning of the Fall 2018 semester I set things up so that four sessions in one of my Calculus I classes would be videotaped. (It’s always a bit nerve wracking to have a camera on me while I’m teaching, but this wasn’t my first time with a camera in the class, and I quickly forgot about it for the most part.) Before the term started I was asked to identify what demographic characteristics that I wanted to track. I didn’t have a good idea of sense of what features I wanted to identity, so I chose the categories of: 1) ethnicity; 2) gender; and 3) the number of hours each student worked each week outside of campus. I chose these categories since I was able to use the data I collected on index cards on the first day to determine how each student self-identified in terms of gender. I also collected information on hours worked the first day so I threw that in there as well. I tried my best to identify each students’ ethnic background, which certainly has its drawbacks but served its purpose, and I shared that information with the EQUIP leadership team so that they could use it to code the data. One thing I should point out is that the data was only collected during the time that I was lecturing or during whole group discussions, and student contributions were not tracked during small group or paired learning activities which was a significant portion of each class.

After each of the four videotaping sessions, I met via video conference with our Faculty Learning Community (FLC) consisting of the other two faculty that were using EQUIP in the college classrooms, the researcher that coded the data, Amelia Stone, and the lead researcher on the project, Daniel Reinholz. So, on the first day of videotaping the camera came and went, and the time came for our small group to meet via video conference to discuss the data from the meeting. When we met this first time, I received a pdf file summarizing the data from my course. I was presented with a “Classroom Summary” that tracked the number of students that contributed, and the total student contributions. During the group discussions we had a chance to reflect on the data for each instructor, and were able to all share suggestions for how to increase the number of students that participate, and for allowing them to participate in more meaningful ways.

Figure 1. Classroom Summary.

When I saw that 47% of the students in the class that day participated, I have to say, I felt pretty good! After discussing the data with the rest of the group however, I also became increasingly aware that this also meant that the glass was half empty, and that the evidence did not suggest that I reached all students that day. It bothered me that without giving all students the opportunity to participate, it was very possible that I was not providing all students with access to rigorous math learning and identity building opportunities. What was most surprising to me is that this wasn’t the story that I remembered about who participated, and in many ways the story that I told myself about how that class went wasn’t the same as the story told by the data. Confronting this reality was really frustrating, and brought out a range of emotions. Moreover, with this information I was face to face with the names of the exact students who didn’t get a chance to participate. Who were those students? What did I know about them? How could I do more to get them to participate?

Figure 2. Individual student contributions.

The next set of data that I was presented with was about *how *the students were participating. The software tracked how many “how”, “what”, and “why” questions I asked, as well as how many “how”, “what” and “why” question students answered. The software classified student responses, as long (21+ words), medium (5-20 words), and short (1-4 words). It was quite humbling to see that close to 50% of the student talk were responses to “what” questions (like “what is the derivative of x^2”) and there were only 3 students that answered “why” questions which provide a deeper level of cognitive engagement and a more effective informal assessment of student development. The worst part was that 75% of the student talk was in the form of a short answers, which showed that there was not much depth in the ways that my students were participating despite the fact that nearly 50% did contribute during the course. After the conversation with the group about this, I was motivated to do something to change this and also left with some concrete strategies. For the next class, I also took the time to dig up some resources on some simple “talk moves” (Hemingway, 2015; IOLA, 2013) that I could use to probe deeper into student thinking like “How do you see that idea?”, “Why is that true?”, and “Does your answer seem reasonable?”. This was a significant shift for me and it wasn’t an area that I would have noticed that I needed to grow in, if not for the EQUIP data.

The next set of data that we were presented with was a breakdown of the contribution ratios across the demographics that I had provided to the EQUIP team at the beginning of the study. I was given the data on teacher questions, student talk, and length of talk by ethnicity, gender, and hours worked. It wasn’t much of a surprise that there wasn’t much correlation between participation and who worked the most hours outside of class and if I could do it again I think I would track the students level of math anxiety on a 1-10 scale, and their comfort having dialogue in English on a 1-10 scale since those issues seem to be relevant for the student population that I teach and the data may have more of a correlation with those demographics. The information on race and gender however, was very revealing. It was a relief to see that the cis-women and transgender man in the class were participating in at least as high a rate as the cis-men, and that there were contributions from several different ethnicities in the course. The data did reveal from the first observation that the Latinx students in the course didn’t participate as much in proportion to their representation in the classroom as did students from other ethnic groups such as the white, Asian, and MENA (Middle Eastern and North African) students. It was also apparent that I didn’t have much participation from the Filipino students in the classroom. What was to do with this information and this new lens on my teaching? Not only did I have this data in front of me, starting me in my face, but I also had the data on exactly who the students were that did not get the chance to participate in a meaningful way that day. By ignoring that fact, I felt like I would be ignoring their very existence in my classroom, and that I had to try to make some changes that were measurable by the EQUIP study the next time the camera came into videotape my teaching.

Figure 3. Comparisons of participation by social markers.

When I’m in front of the classroom there are lots of things running through my mind, seemingly all at once: the content I’m delivering, the sequencing of the content, the clarity of my exposition, the length of my wait time, the choice of active learning activity, my use of the board, the timing of the group activities, the time left in the class, where I left the eraser, and the list goes on. At times I find myself so overwhelmed by all of these things it’s hard to decide what to focus on. The EQUIP data however, helped with this this decision making in that it cleared room for me to shift my focus to the students. How could I get more students to participate to push pass that 47% participation rate? How close could I conceivably get to 100%? How could I get more students into the “how” question and “long answer” categories of the data analysis? I could focus on getting more Latinx students involved. I could also remember to not leave out my Filipino students the next time. In addition, I could make a list of all of the students that didn’t participate in my last class, and have it in front of me the next time we met to hold myself accountable for including them. What a powerful tool!

My experience with EQUIP helped change the focus of my teaching from thinking about what I was going to do next mathematically, to focusing on who was going to participate next in the classroom. And beyond focusing on who was participating, it also helped my focus on how they were participating. In my classes these days, I try to keep things as active as possible and for quite some time I have felt fairly good about the number of students that I’ve been able to reach. The problem however, is that this feeling is based only on my gut and that “look in their eyes” and not on hard data. This reminds me of research by my colleague Stacy Brown (2018) about the *“illusion of participation”. *I have been wondering for the past couple of years about how much of my own sense of student participation is really an illusion, supported by this story that I tell myself that is subject to my own biases and blind spots. In a class of 30-40 students it’s easy to think that just because I had some positive interactions with a handful of them a bunch of times throughout the day that I’m reaching everyone. But it’s clearer to me now than ever that by harnessing the power of data in our classrooms there is a lot more that we can do to achieve that seemingly impossible goal of reaching all students and provide them all with equitable access to rigorous mathematical learning and mathematical identity building.

**References**

Brown, S. (2018). E-IBL, proof scripts, and identities: An exploration of theoretical relationships, Proceedings of the 21st Annual Conference on Research in Undergraduate Mathematics Education, San Diego, CA, 22-24 February (pp. 1- 15).

Hemingway, K. (2015, May 26). Talk moves create a culture of talk: Fostering student talk and classroom dialogue – Part 3 [Blog post]. Retrieved from https://www.inquirybydesign.com/talk-moves-create-a-culture-of-talk-fostering-student-talk-and-classroom-dialogue-part-3/

IOLA. (2013). A typical day. Retrieved from: http://iola.math.vt.edu/typicalday.php

Laursen, S. L., & Rasmussen, C. (2019). I on the Prize: Inquiry approaches in undergraduate mathematics. *International Journal of Research in Undergraduate Mathematics Education*. https://doi.org/10.1007/s40753-019-00085-6

Martin, D. B., Rousseau-Anderson, C., & Shah, N. (2017). Race and mathematics education. In J. Cai (Ed.), *Compendium for Research in Mathematics Education* (pp. 607-636). Reston, VA: National Council of Teachers of Mathematics.

National Science Board. (2018). Science and Engineering Indicators (NSB-2018-1). Alexandria, VA: National Science Foundation. Available at https://www.nsf.gov/statistics/2018/nsb20181/assets/nsb20181.pdf** **

Reinholz, D. L., Bradfield, N., & Apkarian, N. (in press). Using analytics to support instructor reflection on undergraduate mathematics instruction. International Journal of Research in Undergraduate Mathematics Education.

Reinholz, D. L., & Shah, N. (2018). Equity Analytics: A Methodological Approach for Quantifying Participation Patterns in Mathematics Classroom Discourse. Journal for Research in Mathematics Education, 49(2), 140–177.

Staats, C., Capatosto, K., Tenney, L., & Mamo, S. (2017). *State of the science: Implicit bias review 2017*. Columbus, OH: Ohio State University: Kirwan Institute. Retrieved from http://kirwaninstitute.osu.edu/wp-content/uploads/2017/11/2017-SOTS-final-draft-02.pdf

Erica Walker, Scott Williams, and Robin Wilson

*In Mathematics, more than any other field of study, have we heard proclamations and statements similar to, “**The Negro is incapable of succeeding**.” **Ancient** and **present achievements** contradict such statements. One of the **purposes** of this website is to exhibit the inaccuracy of those proclamations by exhibiting the accomplishments of the peoples of Africa and the African Diaspora within the Mathematical Sciences.[1]*

Over twenty years ago, SUNY Buffalo Professor Scott Williams took it upon himself to create a website in the early days of the internet that would provide African Americans with access to the many, little told stories of African Americans mathematicians. He called the website the Mathematicians of the African Diaspora. At the time, most images of African Americans in popular culture were of athletes, actors and musicians, and little information was available about African Americans in the Sciences, let along in Mathematics. This website is being updated and modernized and the new version is available at www.mathad.com. In this article we share reflections from three authors, including Scott Williams himself, on the importance that the Mathematicians of the African Diaspora Website has had on their lives and careers, and on the American mathematics community in general.

**Introduction, Robin Wilson
**

In 1792, Thomas Jefferson who was secretary of state at the time but would soon become the third President of the United States expressed his opinion about the potential for an entire race of people to contribute in a meaningful way to the mathematical sciences:

“Comparing them by their faculties of memory, reason, and imagination, it appears to me that in memory [the Negro] are equal to the whites; in reason much inferior, as I think one could scarcely be found capable of tracing and comprehending the investigations of Euclid; and that in imagination they are dull, tasteless, and anomalous.”[2]

Over 100 years later, in the 20^{th} century these attitudes were still prevalent in American society and were not only embraced by the academy in America and Europe; indeed, academics were the source of many of these racist attitudes and beliefs. In *The Measure of Intelligence, *Stanford Professor and former American Psychological Association President Lewis Terman stated in 1916 about “Mexican families of the southwest and American Negroes” that “They cannot master abstractions, but they can often be made efficient workers” and that “from a eugenic point of view they constitute a grave problem because of their unusually prolific breeding”[3]. The consequences of such attitudes still have widespread repercussions today as evidenced by Lisa Delpit’s book *Multiplication is for White People*, when she shares the story of a middle school math student telling his teacher “Black people don’t multiply; Black people just add and subtract. White people multiply”[4].

Growing up in Baltimore, Maryland in the 1940’s and 50’s Scott Williams was no stranger to these myths. Scott decided to earn his PhD at the age of 12 after his mother took him to visit MIT. He went on to study mathematics at Morgan State University under the late-great Clarence Stephens, and he earned his PhD in 1967 in General Topology from Lehigh University. Scott’s upbringing in the large Black community of Baltimore, as well as his experience at Morgan State University, provided him with a large amount of evidence of Black intellectual excellence, and left little room for doubt about his own potential. After earning his PhD he joined the faculty in the Department of Mathematics at SUNY Buffalo in 1971, and documented his own struggles with racism at the university in the 1970’s.

Much later in his career, Scott decided to experiment a bit with the relatively new thing called “the internet” by building his own website so that he could learn to code in html along the way. It was to become the latest of one of his many hobbies that also include art and poetry. The content of the site was to be motivated by one purpose: To dispose of the myths of the inability of people of African descent to excel in the mathematics classroom and to perform mathematics research at the highest levels. To do this he would focus on both the historical contributions of the continent of Africa to the early development of mathematics, as well as share profiles of as many mathematicians of African descent with PhD’s that he could find. He ended up with a list of profiles for over 500 mathematicians from around the African Diaspora, with most of them alive and working at the time his site first went live. Scott called the website the “Mathematicians of the African Diaspora” or the MAD pages for short. The acronym was not only catchy but it also represented the subtle sentiment of a large number of Blacks in the mathematics community that had to persist in the discipline despite experiences with overt racism and other forms of wide-ranging systematic attempts to exclude and discourage them from participating.

**Reflection, Robin Wilson**

It was around my junior year in college when I decided to take on mathematics as a major. Despite my success with my mathematics

courses it was not an easy decision, especially since it meant I was going to be isolated as one of the only Black math majors at the institution. I was also putting my education in the hands of faculty who had not experienced many, if any, Black students in their classrooms and provided no mentorship. In fact, when I decided that I would go into mathematics at one point in time I thought for a moment that I could be the first Black mathematician because I didn’t know of anyone before me that had chosen this path. It was around this time that I discovered Scott William’s website Mathematicians of the African Diaspora. I was amazed to find the profiles of over 500 Black mathematicians. From Scott’s site I learned that the first Black PhD mathematician was Frank Elbert Cox, who earned his PhD in 1925 from Cornell University. This achievement is remarkable for the fact most institutions in the US frowned upon having Black students at any level, and in addition only 28 PhD’s in mathematics were given out that year.

From the MAD pages I also learned about people such as J. Ernest Wilkins who earned his PhD in mathematics at 19 in 1936, the same year that Jesse Owens sent his own blow to the Eugenics movement with his 4 gold medals in the 1936 Summer Olympics in Berlin. And about Euphemia Lofton Hayes, the first Black woman to earn a PhD in the US in 1943, four years before Jesse Owens joined the Brooklyn Dodgers and 13 years before Althea Gibson become the first woman of color to win a Grand Slam title in Tennis (the French Open). I also found it quite frustrating that as a young person I learned a lot about these athletic achievements that I was told I could aspire to, yet I learned nothing in school or at home about these great intellectual achievements.

I also spent time searching the site’s historical information on the contributions of the African continent to mathematics from the dawn of time to the present. Scott painted a picture of a continuous stream of contributions by people of the African Diaspora from pre-history to the present that started with some of the oldest mathematical artifacts ever found, the Lebomo and Ishango Bones, the Ahmes (or Rhind) Papyrus, and the Moscow Papyrus. The story continues through the trans-Atlantic slave trade and includes Thomas Fuller, the slave born in Africa who could perform extraordinary feats of mental arithmetic; as well as Benjamin Banneker, who was a contemporary of Thomas Jefferson and made contributions to both astronomy and mathematics. The story picks up

immediately after slavery with figures like Kelly Miller, who was the first Black mathematics graduate student at Johns Hopkins from 1887-1889. Miller went on to teach mathematics at Howard University, and hired Elbert F. Cox and many others. The MAD site takes us up to present day, and for several years the site was updated annually with profiles of the new Black mathematics PhD’s that graduated each year until Scott stopped maintaining the website around 2006.

The value of this resource should not be overlooked. This was a labor of love that Scott Williams took on as a hobby for almost years. He also did not anticipate the number of responses he would receive from students and teachers around the country, nor could he imagine the number of lives he would touch that he will never hear about. I can say almost with certainty that without having found Scott’s site I would not have had the persistence to continue in mathematics as a student, nor would I have the same foundation and perspective needed for me to find my place in the mathematics community as a professor.

Scott stopped maintaining the website when he retired from SUNY Buffalo. While the site is still up on the SUNY Buffalo servers (http://www.math.buffalo.edu/mad/) there has been a recent effort, led by the National Association of Mathematicians, to transfer the content of the MAD pages to a new server host and to modernize the website.

In what follows, you will find a reflection on the website and its impact from Scott Williams in his own words. Also included is an essay from Erica Walker, author of *Beyond Banneker: Black Mathematicians and Paths to Excellence*, where she shares the importance of the website to her own work as well as the larger mathematics education community.

**Reflection, Scott Williams
**

Over tweny years ago, in 1997, I began the website Mathematicians of the African Diaspora or MAD. As a child I was struck by the emphasis, within the general American culture, upon achievements in the Sports/Entertainment Industry as indications of success. Within the African American subculture, those indications are even stronger – just consider the winners of the NAACP Image Awards among other celebrations. On the rare occasion a scientist has won an award, there has been a limitation to the medical field. In addition, where it concerns successes in mathematics and the sciences, I discovered much incorrect or misconstrued information available in texts and especially on the web.

The impetus for creating MAD was a desire to suggest modern Mathematicians and Scientists as images of success to present to the African American community. My steadfast personal view over the years has been *thinking precisely has more class than looking good*. As mathematicians’ interest often vary, I added both Computer Science and Physics to the web site before those fields began their own projects of this nature. For some years I also provided a location for data on The African National Congress.

My qualifications include 7 years in the segregated Baltimore public schools (5 more as a guinea pig in ‘desegregated’ schools), 4 years of excellent undergraduate mathematics training with research orientation at a historically Black College, 4 years of graduate training with research orientation, numerous Master’s Degree students (at Pennsylvania State University, Ohio University, and the University of Buffalo). In addition, I have had four Ph.D. students, have spent four decades as a research mathematician with interests in Topology, Logic and Dynamics, am a member of the Council of the African American Researchers in the Mathematical Sciences, and I have a personal library of thousands of books by Africans and African Americans.

What problems did I encounter other than debts to my personal time?

- At a time when web space was measured in kilobytes and megabytes, my department (SUNY at Buffalo) opened gigabytes for my web space use in this project, yet I was unable to obtain financial resources, inside or outside the university, to aid my efforts. During the 2006 Black History Month, MAD received four hundred thousand visitors and nearly ten thousand emails.
- I am thankful that my department chairs agreed to provide legal help in the project. I received a number of legal threats from individuals who did not wish to be known as African American Mathematicians, and from individuals who deemed the project as racist.

Positive acknowledgements have been received from The Chronicle of Higher Education, The New York Times, USA Today and Science Magazine to name a few; however, I must thank the more than twenty million visitors to the website, it is they that have exhibited its worth.

Scott W. Williams

Mathematics Professor Emeritus of The University at Buffalo, SUNY

**Impact of the MAD Pages, Erica Walker**

I don’t recall how I first was introduced to the MAD website, but as a mathematics educator interested in history and historical developments in mathematics, it was crucial to expanding my knowledge base about Black mathematicians. MAD, quite wonderfully, had extensive citations and links to important archival documents, books, articles, and other texts that have been critical to my own work and research as a professor of mathematics education. It was here that one could easily find information about Black mathematicians in the United States and around the world, information that was unfortunately for many years missing from the broader discourse about mathematicians and their work. It was here that one could learn about the role of organizations and institutions in the development of initiatives that increased the participation of African Americans in mathematics. And it was here that I first learned of Thomas Fuller, an important historical figure who has become central to my own research exploring the formative, educational, and professional experiences of mathematicians in the United States. Fuller has served as a central metaphor for the work I do around equity in mathematics education – his life underscores that mathematics talent can often go unrecognized and unrewarded. But for a twist of fate, many more of us would know Thomas Fuller’s name in addition to, say, that of Benjamin Banneker. Because Banneker was born free and was literate, we know much of his mathematical experiences and contributions to US history. Fuller died as an enslaved person: indeed, as his obituary posted on the MAD website notes: “Had his opportunity been equal to those of thousands of his fellow men, even a Newton himself should have shamed to acknowledge him a brother in science”. In many speeches and talks, I have posed the question to mathematics teachers, administrators, and researchers alike—‘Are there Fullers among us?’ –and exhorted them to conduct policy, practice, and research that seeks to focus on excellence, rather than failure, and to work to ensure all students have the opportunity to learn rigorous and meaningful mathematics.

The existence of this website helped to reframe for me and many others the truth of Black excellence in mathematics. It made visible people that were in many ways invisible to the canon of mathematical thought and production in the United States and around the world.

MAD’s importance as an educational tool must also be acknowledged. It is here that someone can get pleasantly lost exploring intriguing historical developments, as well as learning about the range of areas of mathematics study. For many of the profiles, there were compelling stories told by mathematicians about their early lives, which for me spurred new ideas about how we develop as ‘mathematical persons’. It has spawned research on deeper understanding of the role of family members in mathematicians’ development, for example. (So many mathematicians tell stories about uncles and aunts exposing them to mathematics!). It is here where one can see the impact of particular institutions, which over generations demonstrate an admirable capacity to develop, hone, and support mathematicians’ talents. And it is here where one can trace the influence of influential mentors and teachers, who direct and affect the careers of their students and their students’ students.

Without MAD, it would have been much harder to engage in my major program of research that has emerged over the last decade. It, for many years until very recently, was the only place where one could look up the term “Black mathematician” and see that there were numerous people who fit that description. Although we don’t have empirical evidence about how many schoolchildren and other students used the website for research of this type, I suspect that it was a substantial number.

With the new MAD website it is my hope that the spirit of MAD lives on – as an important living and breathing space for the documentation of historical and contemporary events that captures the essence of the triumphs and travails of Black mathematicians in the US and around the world. And I hope we are able to capture impressions of who visits the website, and why. As a teaching tool about mathematics, history, the meanings of what it is to be a mathematician, and how to inspire others to participate in the world of mathematics MAD is unparalleled. It has significant interdisciplinary reach—addressing those with interests in history, sociology, policy as well as mathematics. Professor Scott Williams has done a great service for all of us in mathematics and mathematics education—and beyond—with this incredible resource.

Erica N Walker

Professor of Mathematics Education

Teachers College, Columbia University

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[1] Mathematicians of the African Diaspora Website [On-line]. Available: http://www.math.buffalo.edu/mad/myths_lies.html

[3] The Measure of Intelligence, Lewis Terman. The Riverside Press, 1916. Available: https://psychaanalyse.com/pdf/THE_MEASUREMENT_OF_INTELLIGENCE.pdf

[4] Multiplication is for White People: Raising Expectations for Other People’s Children, Lisa Delpit, The New Press, 2012.

[Editor’s note: Readers will also want to explore Mathematically Gifted & Black: http://mathematicallygiftedandblack.com/]

]]>I was recently told by someone that they were “eagerly awaiting” the inclusion/exclusion roundup of diversity and inclusion events, talks, panels, receptions, happening at the meetings, similar to what we did for the last JMM. Not ones to disappoint our readers, we are happy to comply.

Luckily, the AMS did their own roundup, available in this handy flier. We combed through the schedule, and found a few additions. Just like last year, we chose either events that were explicitly about equity, inclusion, diversity, and social justice, or events promoted by groups that primarily support underrepresented mathematicians (like the Association for Women in Mathematics and the National Association of Mathematicians). By “events” we mean invited addresses, special sessions, panels, and social events. We are also only including the events not in the AMS flier (so please check that out too!).

If you know of any events we may have missed, please share in the comments section below.

**Wednesday January 16**

- MAA Invited Paper Session on Building successful communities in Mathematics, 8am-10:50am. Room 323, BCC.
- MAA General Contributed Paper Session on Outreach, 9am-9:25am, Room 301, BCC.
- MAA-SIAM-AMS Hrabowski-Gates-Tapia-McBay Session: Lecture, 9am-9:45am,
*On the discrete Hilbert transform,*Rodrigo Banuelos, Purdue University. Room 307, BCC. - AWM Reception and Awards Presentation, 9:30pm, Room 327/328, BCC.

**Thursday, January 17**

- MAA Contributed Paper Session on The EDGE program: Pure and Applied talks by Women Math Warriors, 8:45am-10am (Session I), Room 322, BCC & 1-3:35pm (Session II), Room 323, BCC.
- AWM-AMS Noether Lecture, 10:05am-10:55am,
*Dynamics of systems with low complexity,*Bryna Kra, Northwestern University, Ballrooms I & II, 400 level, BCC. - NSA Women in Mathematics Society Networking Session, 6-8pm, Paca, Hilton.
- Spectra reception for LGBT Mathematicians and Allies, 6-8pm, Harbor Ballroom, Marriott.

**Friday, January 18**

- AMS Special Session on If You Build It They Will Come: Presentations by Scholars in the National Alliance for Doctoral Studies in the Mathematical Sciences, 9-10:50am (Session I) and 1pm-5:50pm (Session II), Room 327, BCC.
- MAA Contributed Paper Session on Ethnomathematics: Ideas and Innovations in the Classroom, 8am-10:35am, Room 301, BCC.
- NAM Haynes-Granville-Browne Session of Presentations by Recent Doctoral Recipients, 1pm-4:30pm, Room 333, BCC.
- AWM Workshop: Poster Presentations by Women Graduate Students and Reception, 5pm-6:15pm, Pratt St. Lobby, adjacent to JMM registration, BCC.
- NAM Banquet, 6-8:40pm. (Tickets need to be purchased, Cox-Talbot Invited Address immediately after dinner). Holiday Ballroom 6, Hilton.

**Saturday, January 19**

- AWM Workshop: WinCompTop: Applied and computational topology, 8am-12:20pm (Session I) & 2-4:50pm (Session II), Room 307, BCC.
- MAA Invited Address,
*The Inclusion Principle: the importance of community in mathematics,*Deanna Haunsperger, Carleton College, 10am-10:50am, Ballrooms I & II, 400 Level, BCC. - NAM Claytor-Woodard Lecture,
*On Mathematics Problems in Geometric Optics,*Henok Mawi, Howard University, 1pm-1:50pm, Room 316, BCC. - MAA-AMS-SIAM Gerald and Judith Porter Public Lecture, 3-3:50pm,
*Big data, inequality, and democracy,*Cathy O’Neil, ORCAA, Ballrooms I & II, 400 Level, BCC.

Bonus features:

- Here is a recent interview of Edray Goins about his upcoming invited address, by Mike Breen. (This talk is a must-see if you’re interested in matters of inclusion and equity.)
- A group of people are organizing events related to the Women’s March happening in D.C. and Baltimore on Saturday, January 19. Email me (asalerno@bates.edu) for more information.

About a year ago, the American Mathematical Society (AMS) agreed to take part in the National Science Foundation-funded *STEM Inclusion Study. * The study’s goal is to identify potential mechanisms of disadvantage at the interpersonal, organizational, and professional levels in science, technology, engineering and math (STEM) fields. It is the first large-scale, national-level study to simultaneously examine the experiences of women, racial and ethnic minorities, persons with disabilities, and lesbian, gay, bisexual, transgender, and queer or questioning individuals working in the STEM workforce. The study has two phases: first a survey of large samples of the members of participating professional organizations, then in-depth interviews with selected survey participants. By participating in the study, professional organizations not only guaranteed that their members will be represented in the broad results of the survey, but they also received a summary of their member’s answers to a small subset of the survey questions. The summary provides some insights into the beliefs and experiences of our members, specifically concerning their places of work, but does not provide any of the details that researchers expect to glean from follow-up interviews with a smaller sample of the survey participants. (Note that for most of this analysis, only respondents who were employed at the time were included, with graduate students included only when comparing responses across employment sectors.) The goal of this post is to share the results in the summary received by the AMS.

**The survey results**

The (unfortunately unsurprising) findings include that women and respondents with disabilities report significantly less positive experiences than men and respondents without disabilities “on *nearly every measure *of marginalization and professional devaluation” examined in the study, and that there is “a pattern of negative experiences” for LGBTQ individuals. On various measures there were significant differences found when comparing responses of white participants with those of Asian participants and with those of Black participants. There were also significant differences found between Hispanic/Latinx responses and non-Hispanic/Latinx white responses. All of these results were analyzed controlling for employment sector, education level, and age.

In many ways, however, the survey responses paint a rather positive picture of mathematics as a profession. The researchers report that among the respondents, personal experiences of harassment are relatively low, and that across demographic groups, respondents generally feel that their work is respected by their colleagues and that their supervisors treat them with respect. Respondents on average believe their bosses give them the credit they deserve and that they do not have to work harder than others to be given the same professional recognition. Few respondents reported high levels of LGBTQ bias in their workplace (though this could be due to the lack of visibility of LGBTQ status), and the majority of respondents did not observe instances of workplace unfairness toward persons with disabilities (though this could result from low numbers of visibly disabled coworkers). While these general trends suggest that members of the AMS tend to have positive experiences in their workplaces, this was certainly not universal and, as described above and detailed in the following, significant differences were found when comparing responses between different demographic categories.

**Legitimate Professional**

On the question asking participants to rate their level of agreement (from strongly disagree to strongly agree) with the statement “I have to work harder than my colleagues to be perceived as a legitimate professional,” the average response for each demographic group falls between “disagree” and “neutral.” Yet, women are significantly more likely than men, Hispanic/Latinx respondents significantly more likely than non-Hispanic/Latinx white respondents, LGBTQ respondents significantly more likely than non-LGBTQ respondents, respondents with disabilities more likely than respondents without disabilities, and both Black and Asian respondents are more likely than white respondents, to agree that they have to work harder to be perceived as a legitimate professional. (In the figures throughout this blog, all of which were provided by the STEM Inclusion Study, significance is denoted as follows: ***p<.001, **p<.01, *p<.05, †p<.10, two-tailed test.)

**Standards for Promotion**

Survey takers were asked to rate their level of agreement with the statement “I am held to the same standard as others for promotion and advancement.” This is an important question, since there is a tradition of viewing academic mathematics as a meritocracy and 79% of these respondents work in colleges and universities. All comparison groups averaged between “neutral” and “agree,” yet, women, LGBTQ respondents, and respondents with disabilities agreed significantly less strongly than men, non-LGBTQ respondents, and respondents without disabilities, respectively. In particular, it should be noted that *none* of the groups averaged near “strongly agree,” all falling at most slightly less than “agree.”

**Harassment**

An important finding is that women, Hispanic/Latinx respondents, and respondents with disabilities reported significantly higher frequencies of being harassed verbally or in writing on the job in the last year, than men, non-Hispanic/Latinx white respondents, and respondents without disabilities reported. Further, in rating the frequency with which a co-worker “makes a negative comment or joke about women, racial/ethnic minorities, LGBTQ people, or people with disabilities,” significantly higher frequencies were reported by women, Hispanic/Latinx respondents, LGBTQ respondents, and respondents with disabilities. More generally, the researchers found that Hispanic/Latinx and Asian respondents “were significantly more likely than their white peers report that their competency and value was questioned in their workplace and experience professional devaluation and marginalization.”

**Workplace Fairness**

The researchers compared questions concerning what they call “workplace fairness” across the employment sectors: academic, for profit, and “other employment.” On questions asking whether or not women, racial/ethnic minorities, or LGBTQ individuals in their workplace must work harder to convince people of their competence there was no significant difference between these sectors. On the other hand, there was a significantly smaller proportion of respondents with “other employment” who reported witnessing person(s) being treated differently at work due to gender in the last three years. The same is true with “gender” replaced by “race/ethnicity.”

That said, the actual numbers in the workplace fairness section of the report should serve as a wake-up call to those of us who like to think that the inequities are few. The researchers found high proportions of respondents across the different employment sectors “reported systematic biases in their workplaces and reported witnessing differential treatment in their organizations in the last three years.” Specifically, 27.5% of respondents reported that women in their workplaces must work harder than men to be viewed as competent and 17.9% of respondents believe the same for people from racial/ethnic minorities. Further, 27.3% of respondents overall reported personally witnessing individuals’ being treated differently due to their gender, and 14.4% of reported individuals’ being treated differently because of their racial/ethnic minority status.

The responses from graduate students are even more striking. For example, 36.6% of graduate students reported witnessing individuals’ being treated differently due to gender in the last three years, 24.1% reported witnessing individuals’ being treated differently due to race or ethnicity, and the proportion of graduate students who reported witnessing individuals’ being treated differently due to LGBTQ status, though much smaller, was twice that of the non-student academic employees.

**Additional Questions**

At a request from the AMS Committee on Women in Mathematics, we asked the researchers to add some additional questions to the end of the survey given to the sample of AMS members. We learned that 29% of respondents have on-site childcare services at work and 63% are covered by a policy allowing parental leave. About 73% reported that they are aware of policies promoting diversity and inclusion at their place of work, and about 51% are at a workplace that offers training or mentoring in working effectively with a diversity of people.

**Final Thoughts**

Personally, I am both encouraged and saddened by these results. As I wrote above, the overall results paint quite a positive picture, yet when looking at the disaggregated data, it is clear that mathematics has a long way to go. Each of us needs to remain vigilant in the workplace and to work to find ways of stopping inappropriate behavior by our friends and colleagues. We also need to look at ourselves to see if we are unwittingly contributing to the problem.

Graduate programs need to acknowledge that inequitable treatment of students due to gender, race, ethnicity, or LGBTQ status is a problem and that they need to identify ways to address it. It is the responsibility of the department and institution to provide a safe, harassment-free environment for the students. I’d like to encourage departments with graduate students to do their own internal, anonymous surveys, preferably combined with some interviews, to obtain more details about their own situations.

I want to acknowledge the fact that the differential treatment found in this survey may well include behaviors and activities meant to address disparities that already exist in our system — what is sometimes referred to as “reverse discrimination.” Rather than ignoring such beliefs (and sometimes accusations), we need to explain and make clear that we are working towards equity, and how and why equity differs from equality. What may appear to be preferential treatment, is simply an attempt to “level the playing field” and to undo errors of the past (and, all too often, of the present). We should make clear that our final objective is for *all* of our students to achieve their mathematical goals, and that equity is an important step to this end. (This picture is from the Interaction Institute for Social Change; the artist is Angus Maguire. I prefer, but don’t have rights to the version at https://www.scc.losrios.edu/equity/f-a-q/ .)

Most important, though, is the fact that we now have some data. It is far from perfect: some of the questions seemed poorly worded and the lack of the input from the individual interviews is frustrating. Although the data don’t paint a detailed picture, they do provide us with information beyond the anecdotal. This snapshot of the AMS members’ workplace experiences, though far from complete, is enlightening and useful. I want to thank all of the AMS members who took part in this study.

I am looking forward to the researchers’ final report(s), drawing together the input from members of a wide range of STEM professional organizations. All too often, mathematics is left out of STEM-focused studies and programs. It’s good to know that members of both the AMS and the MAA (possibly along with other mathematics organizations) have made sure that mathematics is being well-represented in this national study.

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*Uniform Convergence **is a one-woman play, written and performed by mathematics graduate student Corrine Yap. It juxtaposes the stories of two women trying to find their place in a white-male-dominated academic world. The first is of historical Russian mathematician Sofia Kovalevskaya, who was lauded as a pioneer for women in science but only after years of struggle for recognition. Her life’s journey is told through music and movement, in both Russian and English. The second is of a fictional Asian-American woman, known only as “Professor,” trying to cope with the prejudice she faces in the present. As she teaches an introductory real analysis class, she uses mathematical concepts to draw parallels to the race and gender conflicts she encounters in society today.
*– synopsis that was included in the MAA MathFest 2018 program

In 2016, at a graduate school open house, I was told by a math professor that I would fit right in because they had “a large group of international students from China.” I responded, “Oh, I’m not international; I’m from Missouri.” He replied, “Well, yes, but it would be a good group for you.” Throughout my life, I’ve had many little exchanges like this. *Uniform Convergence *was not born out of these experiences but rather out of my struggle to discuss these experiences (and race in general) with other people.

*Uniform Convergence* began as an end-of-term project in my first playwriting class. The assignment was to write a history play: something about a historical person or event. As a math and theater “double major” at Sarah Lawrence College (we didn’t actually have majors), I jumped at the chance to be interdisciplinary. I had initially chosen Sophie Germain, but my analysis professor/mentor suggested Kovalevskaya. “Her life was full of drama. And Sophie Germain has already been done.” My professor wasn’t wrong.

At the same time, certain news stories began cropping up: stories of students of color calling out college administrators for their lack of progress in catering to a non-white student demographic. Yale, Oberlin, Claremont McKenna, and eventually Sarah Lawrence, to name a few. In the years that followed, incidents of hate and intolerance seemed to be on the rise.

In response, I wrote. Not for anyone but myself, at first. I wrote monologues given by characters who were facsimiles of myself on stage, ranting about injustice and emotions and the lack of diversity in my theater department’s play choices and casting choices (this was a source of heated debate and discussion until the end of my time at Sarah Lawrence, and probably still is).

I was frustrated. I was also taking real analysis. So I wrote a monologue for a professor who was teaching analysis but who was also angry and tired and fed up. I put it in my Sofia play, between a scene of her with Karl Weierstrass and an argument at the train station between her and her husband before they part for the last time. I didn’t know what this professor had to do with Sofia, but I knew that they shared a feeling of powerlessness in a world that was not built for them. I didn’t want my history play to live in the past. It had to give the audience something to take with them when the play was over. I presented this mish-mash of scenes in class, and the feedback was unanimous: this is going somewhere; keep working on it.

In the following year, I studied abroad – theater in Moscow and math in Budapest. Slowly the play morphed from a cast of 10 to a cast of 2; from pages and pages of dialogue between Sofia and her sister, Sofia and her husband, Sofia and Weierstrass, to “etudes”: wordless physical scenes that are the building blocks of much of Russian theater; from a jumble of monologues relating math and my personal life to the slow progression of a professor reacting to rising tensions on a college campus.

Its first performance was on April 27, 2016 at Sarah Lawrence College. At the time, it was a “solo show with two people”; a second actor played Sofia’s husband Vladimir. I think of this draft as the one with the most frills and the most self-indulgence. Because I had the resources of a school theater department known for being “experimental,” I could pull out all the stops: walls made of math papers taped together from floor to ceiling, a character called “Figure at the Piano” whose hands were live-feed projected onto the chalkboard, a semi-dance sequence to the song “Start Wearing Purple.” Looking back, I can see why the Professor character has remained mostly unchanged since Draft 7 while Sofia’s story looks almost nothing like it did before. From the beginning, the Professor has represented what I wanted to say, the things that I wanted the audience to know, and that hasn’t changed. But I had to figure out how to fit Sofia’s story into that.

After I started grad school at Rutgers University (I had decided that it would be easier to have a career in math and do theater on the side than to have a career in theater and do math on the side), the play was accepted to the NuWorks Festival at the Pan-Asian Repertory Theater in NYC. This time, I performed on my own – no director, no second actor, no designers. There were no chalkboards available in the space, so I taped sheets of butcher paper to the walls and danced with a coat rack that played the part of Vladimir.

Again, you can see why I continued to edit the Sofia storyline.

This brief off-Broadway run brought two questions to my mind: (1) What is the purpose of this play? and (2) Who is this play for?

I thought I had always known the answer to (1): the point is to share my experiences with prejudice, stereotyping, and discrimination, as a woman and an Asian American in a STEM field. It has taken a while, but I have finally accepted that my story is one worth telling. A worry that I (and I think a lot of other artists) have is about self-indulgence: why should my story matter? Who cares? Offering up something so personal for public viewing always raises these questions for me. Even writing this blog post, I am asking these questions of myself. Over time, I’ve had enough people come up to me and thank me, or tell me a personal story, or ask me to perform at their school that I don’t agonize over the play’s existence anymore. But what is the message of the play? I don’t know that there is one. My hope is that the play starts a conversation, or makes people think about issues that they might not have considered before.

This answer to (1) doesn’t address approximately half of the play: why Sofia? NuWorks made it clear to me that Sofia’s presence in that version of the play was more of a hindrance, an extraneous plotline, than a necessity. I wanted the play to be about Sofia’s struggle just as much as it detailed my own. In Drafts 1 through 15, however, Sofia’s story was centered around her conflict with her husband. This was supposed to be a play about two women fighting for a place in a male-dominated field, and here I was making half of the play rely on a male character! So that summer, I killed my favorite scene – the first scene I had written, a scene at a train station where Sofia leaves Vladimir for good, the scene that I had continued to include in every draft only because everyone in my playwriting class said it was their favorite scene. I killed the coat rack and rewrote Sofia’s story to be about her. This was Draft 16.

That brings me to question (2): who is this for? Before NuWorks, I didn’t think it was for math people. I was worried that my classmates and professors in grad school would think I was weird for having a one-woman show, or feel uncomfortable with the subject matter. Regarding the former, I was flat-out wrong. Each of my performances in the past year has resulted from someone seeing a previous performance and asking, “Can you come to my school?” Even my most recent show at the MAA MathFest was a result of Pat Devlin (former Rutgers grad student, now postdoc at Yale and probably *Uniform Convergence*’s greatest champion – he has seen the show four times) pointing me in the right direction.

Regarding the latter, I’ve come to realize that the discomfort of dealing with subjects like race cannot and should not be avoided. Conversations about stereotyping and diversity and inclusion need to happen. As I mentioned, this play resulted from my struggle to have such conversations: it’s easy to talk to people who agree with me but hard to bring up such topics with people who don’t – or worse, people whose opinions I don’t know. If I tell them that story about the professor who believed I have more in common with Chinese-born-and-raised students than with fellow Americans, will their response be “Wow, that’s awful!” or “Well, he’s got a point…”? I’m horrible with confrontation, and I was scared of receiving a response I wasn’t prepared for.

So *Uniform Convergence *became my conversation-starter, my jumping-off point, my way of telling people, “Here’s what I want us to be talking about.” I found allies in my classmates and colleagues with whom I had chatted about tensor products and graph embeddings but never dared to broach the topics of politics or race. I still don’t dare, sometimes. But I am using this post to challenge you – and thereby hold myself accountable – to have these conversations, to talk about these things that we “aren’t supposed to talk about” in math.

Ask a colleague if they knew that in 2015, women made up almost 1/3 of math doctoral recipients but only 22% of doctoral hires.[1] Ask if they have any female undergraduate students. Ask if they’ve asked any of those female students about attending graduate school. Ask if they know that the number of non-white Americans who earn math Ph.D’s each year has remained at 6 to 7.5% of all math Ph.D.’s granted that year in the U.S., for the past 15 years.[2] And yes, that includes Asian Americans. Ask if they know the names of their students. Now ask if they know the names of their east Asian international students. Now ask if they know which Asian students are not international students. (Perhaps they will say none, to which you may respond “Are you sure?”) Ask if they care about representation of women and minorities in mathematics. Ask what they think they can do to effect change. Perhaps they will say nothing. Perhaps it’s because they’re a graduate student with a million things to do and no real power. Perhaps it’s because they’re just a small part of a large and largely unjust system, and it’s hard to figure out what to do, what to say, how to say what to which people to make it matter. That’s okay. You had a conversation about it, and that’s already a step forward.

*Corrine Yap is a math Ph.D student at Rutgers University in New Brunswick, NJ. For photos, videos, and reviews of the show, visit **www.corrineyap.com/uniformconvergence**. If you’d like to invite Corrine for a performance, please send her a message at **www.corrineyap.com/contact**.*

[1] according to the AMS Annual Survey http://www.ams.org/profession/data/annual-survey/demographics

[2] Ibid.

]]>Francesca Bernardi & Katrina Morgan

girlstalkmath@unc.edu

http://girlstalkmath.web.unc.edu/

Programs supporting girls in STEM are becoming more and more common. But we believe there is a gap in these offerings: General STEM programs tend to leave out the M, at least in the way that a mathematician would define Mathematics. Most of the math centered programs for girls focus on students at the undergraduate level or higher. The math programs for high school girls that are out there tend to be designed for the top students who are competitive enough to win a spot.

These programs are important as they offer much needed support for talented young girls, but what about the girls who think they’re not good at math? We know they’re out there. Research has shown that girls as young as 3^{rd} grade start to believe they struggle with math even though they perform as well as their male peers who see themselves as capable. If we want to address the low number of female mathematicians, we can’t limit outreach to high schoolers who managed to make it past the first hurdle.

The reason that more girls don’t enter mathematics is not simply that they didn’t have the opportunity to study it. Women and minorities do not see themselves represented among mathematicians and therefore do not see the field as one that is available to them. Underrepresented groups also often report feelings of social isolation that contribute to decisions to leave mathematics. When we dreamt up the Girls Talk Math summer camp, our goal was to create a program that not only introduced high school girls to fun and exciting mathematics, but also addressed the issues that we know would prevent these girls from continuing in mathematics. No one program can address every barrier girls face in entering mathematics or engage every under-confident student, but we wanted to reach some of the young women who underestimate their mathematical abilities to increase their confidence. We developed a non-traditional math camp with the goal of attracting non-traditional math students from a variety of backgrounds. We hope our approach, the lessons we have learned from implementing it, and our camp curriculum (now freely available online) will be useful to others engaged in similar outreach initiatives.

Over the summer, one group of campers comes to the University of North Carolina at Chapel Hill (UNC-CH) Mathematics Department every weekday for two weeks from 9:00am to 4:00pm to attend *Girls Talk Math*. 26 girls participated in 2016, 35 in 2017, and 39 in 2018. During camp, participants are divided into groups of four or five, and each group is assigned a problem set focused on a challenging mathematics topic outside the high school curriculum. Together with the problem set, campers are also given the name of a female mathematician or physicist who has worked on related problems. During the first day of activities and icebreakers, we give a 2-minute description to the campers about each of the available mathematics topics with some highlights of what is involved in each problem set (i.e. pen-and-paper math, coding, physical experiments, etc.). The groups are made based on their preferences and mathematics background.

By the end of the two weeks, campers are expected to work together on their problem set and report their mathematics experiences in a blog post. Additionally, they write and record a podcast about the life and work of their assigned mathematicians after researching their story. Blog posts are available through the Girls Talk Math website, while podcasts are available on the website, on SoundCloud, and on iTunes.

Our problem sets were created by UNC Mathematics graduate student volunteers. Our colleagues came up with ideas of topics they wanted to work on and thought suitable for high school students. We now have a total of 10 problem sets covering a variety of undergraduate and graduate level topics:

- elliptic curve cryptography,
- RSA encryption cryptography,
- classification of surfaces,
- knot theory,
- special relativity,
- quantum mechanics,
- mathematical epidemiology,
- fluid dynamics,
- number systems,
- network science.

Most of the problem sets are pen and paper based, others include coding, while a few incorporate hands-on experiments. They are all written from an Inquiry Based Learning (IBL) approach. Campers are handed a problem set packet on the second day of camp that includes all the instructions and information they will need to work on their assigned topic. Each group has a volunteer team leader, typically an undergraduate or graduate student, that can guide them throughout their work, answering questions and checking their answers.

The female mathematicians are chosen by camp organizers and in some cases work on topics only relatively connected to the problem sets. From the Chapel Hill camp alone, students have now produced podcasts focusing on 22 female mathematicians. Campers are invited to focus on whatever aspect of the mathematician’s life and career most interests them. Some of the female mathematicians our attendees have researched are Grace Hopper, Katherine Johnson, Maryam Mirzakhani, Moon Duchin, Fan Chung, and Jennifer Tour Chayes.

The main goal of the podcasts is to highlight the many talented women doing mathematics and provide role models the girls could see themselves in. We purposefully choose a diverse group of women with respect to age, race, nationality, and mathematical interests as well as a blend of current and historical mathematicians. Our campers come from a variety of backgrounds, so we want the women they learn about to be diverse as well. Less than 50% of our campers are Caucasian. We have students enrolled in public, private, charter, and magnet schools as well as homeschooled students. For some of the students, English is not their first language. While we have a large representation of students whose parents have at least an undergraduate degree, we also have soon-to-be first generation college students. Additionally, the podcasts the campers make are available for other girls to listen to and discover the wide range of women doing advanced mathematics.

Making the podcasts a core part of the curriculum also helps in our goal of reaching the girls who don’t see themselves as math people. A high schooler who is curious about math or knows the value in it but doesn’t enjoy math class is more likely to attend a math focused camp if they have the chance to participate in other activities. Several of our campers have indicated on their applications that they aren’t math people but know math is important. Some campers have even told us directly they don’t generally like math. While a significant part of the program involves grappling with difficult math concepts, this is not the only activity campers are expected to engage in. Our advertising clearly indicates the role of the problem sets in camp but also emphasizes the podcast creation. Many girls who are capable but lack confidence in their abilities are likely to be intimidated by a traditional academic math camp. By incorporating and advertising the podcasts we are able to reach a broader range of students.

Recruiting campers who don’t see themselves as math people is one challenge, but changing their minds is another. We took an IBL approach to designing the camp curriculum because we believe it aligns well with the program goals and philosophy. Through active learning, campers take ownership of their work and learn to see mathematics as creative problem solving. Many high schoolers are taught an algorithmic version of math that understandably fails to get them excited. The IBL problem sets engage the campers in answering challenging questions through their own reasoning. The collaborative group work structure helped to create a sense of belonging to a small mathematical community. For girls who find themselves in math classrooms full of mostly boys, this provides a unique chance to connect with other girls interested in math. One of the campers who attended the 2017 camp wrote an article for her high school paper about her experience at Girls Talk Math which captures this community culture beautifully. She says that she came to camp despite not liking math and cites the relationships she built and people that she met at camp as the primary reasons she left the program with a different view of mathematics.

We chose to develop an IBL curriculum because we believed it would be effective in increasing confidence and getting students excited about the material. (Visit http://sigmaa.maa.org/ibl/ for more information about IBL.) An average camp day includes two 1hr 15min time slots for group work. Each group indicates whether they will be working through the problem set or researching and planning their podcast. Team Leaders check in with each group to help them plan and prioritize, but campers choose how to spend their time, giving them ownership over their work. The problem sets are challenging, but everything the students need to know to complete them is provided in the packet. 30-minute interactive lectures on each of the problem set topics are presented throughout the two weeks so that campers can see what other groups are working on, but these are not prerequisites. Campers are encouraged to talk with each other to get through problems they are struggling with. Team Leaders regularly check in with each group to assure campers are not getting stuck and simply not speaking out. In our volunteer training we emphasize to the Team Leaders that their role is to ask probing questions and guide students through challenges rather than give them the solutions. In many of the podcasts, campers mention the problem sets and struggling through them. They talk about the process of going from being totally confused and a little overwhelmed to being able to make sense of things and how this made the idea of tackling new problems a little less scary. The girls’ reports of their experience support the idea that the IBL philosophy fits well into the framework of addressing the barriers girls face that prevent them from entering mathematics.

The camp has evolved from the first run in 2016. In the last two years we have included a variety of activities that relate to our camp goals without necessarily being directly connected to the covered mathematics topics.

One of the highlights of the first day of camp is our *Barbie Bungee Jump*. Campers are divided into groups and each group is given a Barbie and a bag of rubber bands. They need to create a bungee cord for the Barbie to jump off of a 28 ft high walkway in the mathematics building. Students are allowed to practice on staircases around the building, but they only have one shot at the final jump. We then have an informal mini-tournament. Two teams at a time drop Barbie off the walkway; if she touches the ground, the group is eliminated. If both Barbies *survive* the jump, the team that gets her closer to the ground without touching wins the match. After the first round, all the winning teams compete in the final. The game is always a favorite of our attendees and volunteers.

In 2017, we created a camp library full of books, comic books, activity books, and games that is at our campers’ disposal throughout the two weeks. Students can browse through the books during the camp breaks and check out the titles that most interest them. We have chosen books on a variety of topics: mathematics-focused titles, novels, nonfiction books reporting the stories of scientists from underrepresented minorities, and many more. Our goal is to give our campers free access to materials they wouldn’t otherwise see. We want to increase the visibility of scientists, activists, educators, and historical figures who have worked towards breaking barriers and achieved the unexpected.

This year we have invited local professionals in the mathematical sciences for a *Mentor Lunch*. We organized the camp room so that each professional was assigned a table with a name tag. Campers were given short bios for the mentors in advance to decide who they were most interested in meeting; students were invited to move around and chat with as many mentors as they wished. Campers asked questions and all tables seemed to be having lively conversations for the entire duration of the event. Our mentors came from numerous professions; for example, we had a statistician for a government agency, a science librarian, a mathematics online curriculum developer, and a chemical engineer from a pharmaceutical company.

Last fall we organized a follow-up event for the 2017 campers. Thanks to the help of two UNC librarians, we organized a *Women in Mathematics Wikipedia Edit-a-thon*. Campers returned to campus for one day in September and learned how to edit Wikipedia to update or create pages for the female mathematicians they had researched during camp. The event was a success, so we decided to include the edit-a-thon in the camp activities for 2018.

The elements we added contribute to the culture of creativity, exploration, community, and empowerment that we hope to provide for our campers. We want the girls who come to camp to feel inspired to explore more mathematics and believe they are up to the challenge. By consciously choosing camp activities that support these goals and acknowledge the barriers and challenges young girls face, we believe we have created a program that is effective at reaching young people who might not otherwise have seen themselves as potential mathematicians.

Girls Talk Math is expanding. This summer a *sister camp* ran for the first time at the University of Maryland at College Park, thanks to Sarah Burnett and Cara Peters, camp directors and Ph.D. candidates at UMD. They used our curriculum and resources for activities, structure, etc., but recruited their own volunteers and campers, as well as secured their own funding.

We have been contacted by other students and faculty at various Universities in the United States interested in learning more about our program and potentially starting their own Girls Talk Math camp. One of the main obstacles for a program such as this is having original curriculum to choose from and a structure that has already been setup. We are excited at the opportunity of helping anyone interested in expanding our program to other locations, offering support in planning, organizing, and maintaining the camp. For more information on how to start your own Girls Talk Math camp, visit our website.

We are planning to publish online with open access on GitHub and our website the curriculum that has been developed for our program. We will periodically upload more problem sets for people to download, use, and make their own. We are hoping that not only folks wanting to start their own camp will take advantage of the publication, but also high school teachers, tutors, educators, middle and high school students, math circles, math clubs, etc.

We will continue improving our existing problem sets based on the feedback we receive from campers and general users. We would love for anyone who is interested in developing a new curriculum topic to contact us at girlstalkmath@unc.edu. The more topics are available, the more likely it is to capture the interest of a variety of students.

As the program expands, we hope to expand our community, connecting with the many mathematicians and educators who are passionate about making Mathematics inclusive. Changing the culture surrounding math is no small task, but with our combined resources and efforts we can create more opportunities for young girls.

[Editor’s Note: Readers may also enjoy a previous inclusion/exclusion post about Girls Get Math.]

]]>- This system works against most students. Everyone needs individualized support, and we are not offering that in the slightest. The way we talk about math makes people feel bad for needing support; that is false and harmfully unfair.

- Math is not just one linear set of classes or ideas, nor is there just one way of thinking about any particular math. The way we do math, what we call math, creates an artificial sense of who should do math. This is wrong and unfair.

- Every student matters. Every question matters. Confusion is part of the journey, something we all benefit from. It is rational to worry about derailing class with an “unnecessary” question, but it’s a counterproductive concern for a student to have. It is the instructor’s job to determine how to stay on track while also addressing student needs. I am still on the journey of learning the math that I teach, all the ways to think about a given problem or set of ideas. I learn from my students; they matter. Not only that but feeling that they matter, being emotionally invested, will be key to them making the sort of decisions throughout the semester that will keep them on track.

- My name is Piper Harron and I am openly and comfortably political. I do not mean partisan debates, though I can participate in those when I feel like suffering. I mean that when people live together in large groups, decisions get made, and this is politics. We are affected by national politics and local politics and university politics and I am comfortably and openly aware of how various decisions affect my life and the lives of people I feel obligated to watch out for (including students). I am openly and comfortably political on the internet and because of this I was harassed and bullied and threatened on the internet and it destroyed me. I have anxiety and panic attacks and that makes my life harder. I have mental illness, but that doesn’t make me unqualified for my job. It means I sometimes need help. Anxiety is just like my body’s on fire for no reason but anyway about that to-do list. I encourage anyone who needs accommodations for any disability including test anxiety to please contact the appropriate people and set that up.

- I conclude by saying that I want everyone to have a positive experience. I want the classroom to be a safe environment, but there’s only so much I can do. We will have to figure it out together. In my smaller class I had everyone say their names and saying anything more was optional because I didn’t want to stress anyone out. In my larger class I asked if anyone wanted to say anything, but nobody did.

This summer, I have helped lead a professional development workshop for mathematics educators on student-centered pedagogy. One session of the workshop [1] is organized around a paper by María Trigueros and Sally Jacobs entitled “On Developing a Rich Conception of Variable”. Trigueros and Jacobs argue that the concept of “variable”, which seems unified from an expert perspective, is multifaceted. Moreover, they point out the ways that this multiplicity is challenging for students and that there are structural issues with our curricula that fail to support the development of a rich conception of variables in most students. Faculty can easily take a deficit perspective on students whose conceptions are unlike our expert perspectives, and this concept in particular is at the root of a lot of the blame we lay on students when they think differently than we expected.

At the workshop, we use this image of an old parable about scholars and an elephant. The elephant represents the concept of variable, and the scholars each describe an important facet of the concept: as unknowns, general numbers, parameters, co-varying quantities, or something else. The point is that student conceptions of variables are reasonable attempts to make sense of the contexts in which we have placed them and judging them for not having integrated those contexts into a unifying concept feeds into some of the structural issues with our educational system.

In his show “In & Of Itself”, Derek DelGaudio also engages the parable of the elephant and the scholars. But in his search to read every version of this story, he noticed that none of the stories ever tell the experience of the elephant. What would it be like to have scholars prod at pieces of you and then have a creepy argument in which they try to define you? And what if you really were a magical creature with a snake, spears, and fans on your front, a rope on you back, walls on your sides, and four tree trunks below? How long would it take for you to start feeling like an elephant rather than a magical creature if scholars always insisted you were an elephant?

DelGaudio suggests that this might be why we don’t see magical creatures in the world anymore. His larger point is that identity is an illusion, both internally and externally; in his framing this illusion becomes true identity when the external and internal illusions agree. But these illusions are built on partial and incomplete observations; we are defined more by what isn’t seen than what is seen. And the illusions have the power to influence the observations and the truth. In the context of our students, we never see all of their conceptions, and we certainly don’t see their whole humanity or identity. Any interaction can modify the illusion; in fact any interaction does contribute to the illusions, internal and external, especially given the power we have as educators. No interaction is neutral, so we need to be better and see the violence we are doing when we impose on students external identity-illusions. **Perhaps this is why we see so few mathematicians in the wild, among our students.**

On an even more personal level, the last decade has been very hard for me. People see parts of me, and they get to impose a narrative. Perhaps I was a sphinx, but the world got to set the narrative that I had to be a lion because sphinxes don’t exist, a snake because chimera don’t exist, a crow because I can’t be a phoenix. I’m not sure I remember. But I do remember the pain and the anger that bleeds and persists through the illusions. Over the years, I’ve used every tool at my disposal, including some attempts at therapy; I’ve gotten stronger in resisting the unwanted illusions, slowing down the violence, and I’ve made some big changes recently, including taking a leave to learn from and with students at a high school in Manhattan next year. But I was starting to give up hope about actually healing. DelGaudio’s Elephant gave me hope again.* I am a multitude, both seen and unseen. I can be what I seem in the world without being defined by or beholden to that seeming. I don’t have to forgive or forget to move on; I can simply rewrite the story to allow for magical creatures again, including me.*

PS: DelGaudio’s framing of identity is interesting and fruitful for me, but I haven’t had the time to sit with it and discover any implicit issues. Please forgive me if this framing of identity is flawed or oversimplified in ways that could hurt you.

[1] This workshop is funded by the NSF grant PRODUCT, and this session was designed collaboratively by Jess Ellis Hagman, Jane Cushman, Amy Ksir, Elizabeth Thoren, Nina White, and myself.

]]>Sul Ross State University

Rio Grande College

I’m an associate professor of mathematics at Rio Grande College, a branch campus of Sul Ross State University consisting of three geographically separated units in the middle Rio Grande border region of Texas. I teach four or five (or six) courses each semester, all different, all at the junior, senior, or graduate level, and all through distance-learning equipment. Students transfer from the local community college. Roughly speaking, the student body is about 70 to 90 percent Hispanic, female, first-generation, and low-income, with an average age around 30.

I received my doctorate in 2009 and began work at Rio Grande College immediately thereafter. I’m of Puerto Rican descent, and my graduate work was supported partly by the Ford Foundation Predoctoral Fellowship for Minorities. I grew up on the south side of San Antonio, Texas, and, later, in a small town to the west, within the service region of my current institution.

I drafted these reflections while attending the recent National Inquiry-Based Learning Conference in Austin, Texas, much of which focused on inclusion and equity. I’m a member of an ethnic minority underrepresented in STEM fields; I also have an autism disorder, which went undiagnosed until I was midway through graduate school. Actually, it was grad school that prompted me to seek a clinical evaluation. I’m hoping that my account might be helpful to someone. It’s impossible to tell whether a given effect might have been related to my ethnicity, my disorder, or my own shortcomings, so I’ll leave it to the reader to connect the dots as they will.

I’ll begin with my autism disorder, which has had the greater impact.

First off, I have a hard time interacting with people. I hardly ever talk. That’s not because I’m a misanthropist! I just have difficulty following what other people are saying and formulating my own responses. I’m worst at small talk, which requires a mental agility I don’t have. I rely on memorized formulas, expressions, and anecdotes, but when these fail me, as they often do, I lapse into silence. If someone changes the subject rapidly or gives multiple directions, it sounds like gibberish, especially if there’s background noise or movement. Under stress, I speak haltingly and with my eyes closed; sometimes I simply freeze, like a browser window with too many tabs open.

Like many people with autism, I don’t make eye contact. It overloads my senses and makes me unable to think. Faces refuse to resolve themselves into recognizable composites: they remain mere assortments of features. Given two people of roughly the same appearance, I have as hard a time distinguishing between them as another person might have in telling apart two sheep. Sometimes I fail to recognize acquaintances, and sometimes I mistake strangers for friends. I once recognized my wife’s nose from a distance in a crowded public place, well before I realized that my wife was attached to it.

This *prosopagnosia*, or face-blindness, is related to other impairments. Facial expressions and body language can carry as much content as words. That content is lost on me. I easily get confused in casual conversations. On the other hand, I convey my meaning in words alone, as though I were texting. My speech tends to be formal and pedantic, and my lack of expressiveness is interpreted as apathy or coldness.

Most of my life has been made up of intense, narrowly focused interests. For instance, I became an expert in entomology when I was about nine, memorizing taxonomic tables and scientific names, collecting specimens, reading field guides cover to cover. I even received a personal tour of the entomology department at a research university. I later became interested in mythical genealogy, herpetology, medieval philosophy, Icelandic sagas, Greek history, and other things. Despite my poor conversational skills, I can easily launch into a monologue about my interests.

I seem to inhabit a parallel plane peculiar to myself, a maze with invisible walls. I live in a glass box, looking out through the wrong end of a telescope. I operate my body like a skill crane, and when I speak, it’s like hearing someone else speak. I do still try to reach out to people: I study their mannerisms and speech, each new person being a new object of research. Some people are easy for me to “learn,” but with most I can make no progress, and to them I’m a silent robot. I seem always to miss the end by taking the means to a literal and ridiculous extreme, saying and doing things that are eccentric or inappropriate.

As a child I spoke and acted like Mr. Spock; I ate my Froot Loops one color at a time in spectral order; I obsessively stacked and arranged things; I was hypersensitive to certain lights, colors, noises, music, and food textures. But I was happy. Things went downhill as I got older. I was eccentric, naïve, awkward, uncoordinated, eager to talk about my interests but unable to relate to others in any other way. This resulted in frequent bullying, verbal, physical, and sexual, to which I reacted with silence, though sometimes I secretly injured myself as a way of coping with the agitation I felt. It’s humiliating to admit it, being as old as I am, but those experiences left a permanent mark that doubtless affected my grad school career.

With one exception, none of my grade school math teachers were particularly impressed with me. I got in trouble for things that other students seemed to do with impunity. Teachers would call me out and embarrass me in front of the class for fiddling with my pencil or doodling during math lessons. (I still draw during lectures: it’s how I pay attention.) I became a solid C student in math. That began to turn around when my high school algebra teacher, an eccentric person himself, had me help him perform an experiment with satellite dishes. I initially went to college as an art student, but in a design class I was shown a film on geometry, and promptly switched to math.

It was in college that I lived outside of south Texas for the first time. I’d spent the first part of my life in San Antonio, in a neighborhood that was a fairly even mix of black and white and Hispanic. My best friend, who lived across the alley, was bilingual, and his mother spoke only Spanish; I grew up with a mere smattering of Spanish myself, but my dad was fluent, and I often heard it at my grandparents’ house nearby. After we moved to a small town, I experienced life in a place where things were still very segregated, where the white population lived on one side, the Mexican population on the other (the side with unpaved streets). The kids at my school would say things like, “We forget you’re Hispanic because you’re smart.” No longer was I the star pupil. Teachers had little patience for my quirks.

It was in college, however, that I became conscious of the fact that I had to prove myself before people in authority would treat me as though I were on the level. Interactions with police officers devolved into frightening ordeals; once, for instance, during a routine traffic stop, my (white) future wife was taken aside and questioned as to whether I was kidnapping her or transporting knives, guns, or drugs. That sort of thing occurred on campus as well, but in less obvious ways, beginning with the time I was accused of cheating in my freshman history class. (For the record, I have never cheated, smuggled, dealt drugs, or committed violent crimes. On the contrary, I’m an Eagle Scout, and was named Junior Citizen of the Year by the Chamber of Commerce during high school.)

I was accepted to a graduate program at a large university. My awareness of my social deficits made me apprehensive of getting lost in all those numbers. At my campus visit, I committed the *faux pas* of expressing this to my faculty host, who responded by contemptuously asking how old I was. When I went to a conference for Ford fellows that fall, I asked an elder mathematician what advice he might have about my situation. He thought for a moment, then asked if I played a musical instrument or knew any magic tricks. (I didn’t.) I was surprised at the conference by how many fellows were in fields directly related to their own race, ethnicity, or gender, and how few in STEM fields. I assume that’s why I was selected, despite my less-than-stellar academic record.

My thesis advisor, a brilliant researcher and expositor who devoted an unusual amount of time to his students, was also known for being intimidating. I would spend half of every week preparing for our hour-long meeting by forming mental tree diagrams and flowcharts intended to cover every possible route our “informal” discussion might take. Of course we would be in uncharted territory within the first two minutes, and I would be reduced to a stuttering wreck. That, or my mind would go blank. I’d be up at his board, presenting something I’d been working on, and he’d tell me I should have used alpha as a variable instead of beta, and my brain would reboot.

These experiences were painful, but I got used to them, and they ceased to make me nervous. The funny thing was that that didn’t change anything. As to my faculty relations in general, it seemed that I was continually speaking to the wrong person at the wrong time or asking the wrong kind of question.

My peer interactions were worse. I would sit in my office like a desk-troll, working on math all day, not talking to anyone. I wanted to talk, to interact, to work with people, to join in the camaraderie that makes up so much of grad school. I just wasn’t able to. I was a fish, looking out of my fish bowl at the two-legs walking about. Some officemates told me I reminded them of robot; others told me they often forgot I was in the room. One of the latter actually made a snide remark about me to a student of his when he didn’t realize I was sitting a few feet away. I never blamed anyone for these incidents. I was used to the discomfort I caused. I didn’t like it, but I understood it.

One good friend I had in the department happened to be of Mexican descent. Actually, we’re both of mixed ethnicity, and perhaps that liminality is part of what drew us to one another. Notwithstanding the large size of our program, I can’t remember many other Hispanic students. I mean Hispanic students educated in the United States, subject to conditions here. There were many students from Latin American countries, but their position seemed somewhat different. My friend and I were both very isolated. Most every day we ate lunch and went for a walk together.

My social problems had become so acute that I began wondering if there was something seriously wrong with me. All this time my disorder had gone undiagnosed, or misdiagnosed, treated with prescription medicine I didn’t need. It had caused me trouble all my life, but for the first time I’d reached a point where my intelligence couldn’t find a way around my limitations. Schizophrenia has occurred in my near family, and I wondered if I might be schizophrenic. The symptoms didn’t seem to apply, however. Then, one day, I read in *Notices of the American Mathematical Society* about a professor who exhibited behavior similar to mine. A professor who had an autism disorder. It took time to get the insurance straightened out and the copay scraped together, but eventually I was able to go to an assessment center to be evaluated by a licensed psychologist. The result was my diagnosis.

Autism can express itself in many ways. The causes and effects are far from clear. One person may be able to live and function on their own, with a few quirks, perhaps, but more or less like anyone else; another may need to live under constant supervision; yet another may be highly successful and independent in some areas while possessing severe deficits in others. Intelligence varies just as in the general population, but the intelligence of a person with autism may express itself in unexpected ways. When my own intelligence was tested during my evaluation, some measures indicated that I was above average, others below average. This “spiky” IQ is common in persons with autism.

My advisor, after I told him about my diagnosis, modified his approach somewhat. I noticed and appreciated this, and it helped a lot. But that was during my last year of school, too late to make much difference. And it wasn’t as though I could go around telling my peers. I had for some time abandoned my dream of being a research mathematician. I knew I couldn’t handle the ladder of postdocs and all the transitions and interactions it would entail. I decided to pursue a career focused on teaching, which was something I enjoyed.

Soon after I defended, one of my committee members, a person I respected, told me that she understood my desire to get out of research, as she was doing the same thing. She said it was a shame that, in this day and age, the math community couldn’t do better by people like me. I didn’t know what she meant. She told me, in some surprise, that she was referring to Hispanics. She thought I would be a good role model, which I hope is true.

I’d like to pretend that I went to work at Rio Grande College like Mother Teresa going to serve the poorest of the poor. The truth is that I wanted to go far, far away. I applied all over the country, but, despite multiple interviews, some on site, I wasn’t successful. When I interviewed at Rio Grande College, my message was simple and direct: this is where I’m from, I know the people here, I’ll stay here to raise my family, and I’ll take care of your students. They hired me on the spot. I confess that I was disappointed at first. Upon reflection, I knew I was where I belonged. Home again.

Now I divide my time between teaching evening and night classes and driving around south Texas brush country. I go through Border Patrol checkpoints on a weekly basis, where I sometimes get questioned and accused of smuggling contraband and ushered over to the station while my vehicle is searched; if my wife is with me, she still gets asked if I’m kidnapping her. Late one night a while back, I asked an agent who’d questioned me why I had provoked his suspicion. He told me that my halting speech and lack of eye contact were “red flags.” I have a rehearsed act now, and it gets me through every time.

My college rents its buildings; it is, truly, a *colegio sin paredes*. The faculty often work out of their vehicles, traveling from site to site. It’s a region with a long and little-known history of civil rights issues in education; one federal case, which began with the south Texas school walk-outs and integration movements of the sixties and seventies, was finally resolved only a year or two ago. Right now, legislative cutbacks and other factors are starting to undo the advances made by my college’s forty-year history. My students, who work full time, have children, and often support their parents as well, face adversity like I never did, but to them it isn’t adversity. It’s just life. It’s amazing how grateful they are to me just for treating them like they’re worth my time. They all think I’m a genius. I hope they don’t ever discover what a failure I am. Then again, I doubt they would care.

I’ll finish by saying that, while some approaches to inquiry-based teaching would have helped me, others would have (and did) cause me hardship. I hope it’s obvious why. The cavalier attitude with which some professors grade students without formal assessments and disregard their own syllabi (which are contracts) is especially problematic. Some students need explicit guidance and consistent feedback. A professor may argue that a student in their course needs to have the “maturity” to know what progress they’re making; that’s fair, perhaps, but also highly exclusive. Academia is a culture with its own standards, and students who belong to underrepresented groups or come from disadvantaged communities may lack the background their professors tacitly assume.

What I personally care about more than anything else is the integrity of mathematics as a field of human endeavor. But I also care about the humans themselves. I believe that varying practices so as to make the field accessible to more groups and communities can only make the world a better place. I may not have been anyone’s dream student, but I’m conscious of the debt I owe to my professors. The intellectual ethic I received from my thesis advisor informs everything I do to help my students improve their lives. And those students go out and affect other people. The trickle-down never ends.

I don’t think it’s possible to come up with an approach that’s fully just to all people all of the time. But I hope at the very least that every teacher can learn that there are many forms of privilege, and that many of them are invisible, even to the most enlightened or progressive of minds.

[Editorial: The art is also by the author.]

]]>This blog post was inspired from my reading of Sara Hottinger’s book, *Inventing the Mathematician: Gender, Race, and Our Cultural Understanding of Mathematics *(2016). Hottinger’s book advanced my thinking about how cultural contexts of mathematics perpetuate gendered, racialized, and other systemic forms of exclusion. She adopts a cultural studies approach to examine how four sources of mathematical representations – textbooks, histories of mathematics, portraits of mathematicians, and ethnomathematics – limit opportunities for building “individual and cultural relationship[s] to the field” (p. 7). Hottinger (2016) uses the term *mathematical subjectivity *to refer to how individuals make sense of themselves in relation to mathematics across these four sources. Her analysis highlights how exclusionary representations of mathematics result in the “construction of normative Western subjectivity and in the construction of the West itself” (p. 6) that limit possibilities of positive mathematical subjectivities among members of historically marginalized populations.

Considering the *inclusion/exclusion* blog’s focus on issues of social marginalization in mathematics and my research interest in increasing inclusive educational opportunities in undergraduate mathematics, I focus on Hottinger’s analysis about the history of mathematics – an area of inquiry associated with a special interest group of the Mathematical Association of America and incorporated in courses of study for mathematics majors in the United States. I begin with summarizing Hottinger’s distinction between *internalist *and *externalist *historical accounts and their respective influences on the construction of mathematical subjectivities. This is followed by a discussion of how Hottinger’s insights can be applied to re-thinking pedagogical practices in undergraduate education that challenge traditional representations of mathematics as void of sociohistorical contexts and personhood.

** Internalist and externalist accounts of mathematical history. **Hottinger distinguishes internalist and externalist traditions of writing histories of mathematics. The internalist approach is most widely used with representations of mathematics as universal and discovered, resulting in the de-centering of individuals and social contexts associated with mathematical knowledge production. Texts presenting internalist historical accounts, for example, often reserve insights about biographies and cultures on side margins or at the end of chapters. Thus, Hottinger argues that the prioritization of ideas over individuals in internalist histories of mathematics result in the disappearance of mathematical subjectivities.

Externalist histories are written with representations of mathematics as a human activity situated in cultural and historical contexts. With such foregrounding of individuals and their progress in mathematical knowledge production, texts presenting externalist accounts of history are often organized chronologically and incorporate relevant biographical insights in discussions about the development of mathematical ideas. Hottinger draws on David Burton’s *The History of Mathematics: An Introduction* (2010) as an illustrative example of an externalist text. While Burton’s text “humanize[s] the history of mathematics” (p. 63) through the centering of individuals and social contexts, Hottinger argues that this externalist account also limits constructions of mathematical subjectivity through portrayals of mathematicians as heroic figures. Burton’s (2010) representation of Isaac Newton, for example, illustrates how a mathematician’s subjectivity is constructed in alignment with discourses of mathematics in Western culture – namely, “difficult, cold, abstract, ultra-rational, important and largely masculine” (Ernest, 1992, n.p.). Thus, Newton is represented as an “ideal mathematician” (Hottinger, 2016, p. 76) and thus perpetuates gendered, racialized, and other socially restrictive opportunities for identifications with mathematics.

** Historically humanizing undergraduate mathematics education. **With recent calls for (re)humanizing mathematics education (e.g., Goffney & Gutiérrez, 2018; Mukhopadhyay & Greer, 2015), Hottinger’s analysis of mathematical subjectivity across internalist and externalist accounts brought me to consider how undergraduate mathematics educators can leverage her insights to (re)humanize mathematics, including students’ mathematical learning experiences. Narrow conceptions of mathematics and mathematicians through written histories can frame institutional practices in undergraduate mathematics education that produce inequitable opportunities to learn and identify with the discipline. Thus, I encourage undergraduate mathematics faculty to critically reflect on pedagogical possibilities for more humanistic presentations of mathematics and its history that motivate what Hottinger (2016) calls “feminist ‘aha’ moments” (p. 5) among students. Such moments provide undergraduate students a new lens for making sense of themselves, including their mathematical subjectivities and positions in the world.

Below I pose several questions for undergraduate mathematics course instructors to consider on how they pedagogically engage the history of mathematics for more inclusive opportunities of developing positive mathematical subjectivities across their classrooms. What cuts across these questions of practice is a re-imagining of undergraduate mathematics education toward “liv[ing] *mathematx*” (Gutiérrez, 2017, p. 18) by centering the voices, experiences, and practices often deemed non-mathematical in historical accounts. (*Mathematx*, inclusive of Western and Aboriginal forms of mathematizing, refers to “a way of seeking, acknowledging, and creating patterns for the purpose of solving problems (e.g., survival) and experiencing joy” (Gutiérrez, 2017, p. 15).)

- For courses about the history of mathematics, to what extent do adopted texts and your pedagogical use of them overcome limiting constructions of mathematical subjectivities across internalist and externalist accounts? Which Indigenous, non-Western figures and their contributions to mathematical knowledge production are represented in biographies explored throughout the course? How might the positioning of individuals or groups as mathematicians in the course reify the exclusionary image of the “ideal mathematician” and “trope of the great hero” (Hottinger, 2016, p. 76) by Western standards?
- For instructors of undergraduate courses not exclusively focused on the history of mathematics, what opportunities do your students have to explore the history of learned content in order to challenge representations of mathematics as ahistorical? How are students supported in critically engaging with primary sources alongside required textbooks for an analysis of Eurocentric bias that marginalize Indigenous, non-European forms of mathematical knowledge production? (For more about the use of primary historical sources in undergraduate mathematics education, check out project work from the TRansforming Instruction in Undergraduate Mathematics via Primary Historical Sources (TRIUMPHS) initiative.)
- In what ways do classroom participation structures promote hands-on, collaborative learning that challenge racialized, gendered norms of abstract thinking, individualism, and competition in mathematics toward broadening opportunities for building positive mathematical subjectivities (Battey & Leyva, 2016; Leyva, 2017)?

References

Battey, D., & Leyva, L. A. (2016). A framework for understanding whiteness in mathematics education. *Journal of **Urban Mathematics Education, 9*(2), 49-80.

Burton, D. (2010). *The history of mathematics: An introduction (7th ed.). *New York, NY: The McGraw-Hill Companies, Inc.

Ernest, P. (1992). The popular image of mathematics. *Philosophy of Mathematics Education Newsletter 4/5*.

Goffney, I., & Gutiérrez, R. (2018). *Annual perspectives in mathematics education: Rehumanizing mathematics for Black, Indigenous, and Latinx students. *Reston, VA: National Council of Teachers of Mathematics.

Gutiérrez, R. (2017). Living mathematix: Toward a vision for the future. *Philosophy of Mathematics Education Journal,* *32*(1).

Hottinger, S. N. (2016). *Inventing the mathematician: Gender, race, and our cultural understanding of mathematics*. Albany, NY: State University of New York Press.

Leyva, L. A. (2017). Unpacking the male superiority myth and masculinization of mathematics at the intersections: A review of research on gender in mathematics education. *Journal for Research in Mathematics Education*, *48*(4), 397-452.

Mukhopadhyay, S., & Greer, B. (2015). Cultural responsiveness and its role in humanizing mathematics education. In K. Krainer & N. Vondrová (Eds.), *Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education* (pp. 1624-1629). Prague, Czech Republic.