*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.]

]]>Welcome to Math Class, I am Professor I-Get-To-Have-A-Name. I will probably never learn your name, and that is okay. Who you are doesn’t matter. I may try to get you interested in math, but not actually you because I know nothing about you. I am basically never talking to you.

First we’ll go over the syllabus. In the syllabus you will find rules, policies, percentages, office hours. You will not find anything here that matters to you. You will not find a reason to care anywhere within these pages.

I will ask you if you have any questions on the syllabus, and then we will start the first lecture. You may not know it yet, but I’ve already lost you.

You have several other classes, and other work or family obligations, or maybe you’re struggling to manage your social life or your mental health. Either way, mine is not your only class. But it’s a new semester and you are totally going to put a lot of work in for all of your classes.

Things don’t play out the way you expect. You do the homework. You don’t get it all right, but this is how you learn, right? Your quiz scores aren’t what you’d hoped for; guess the class is hard. You don’t come to office hours, because you don’t know office hours are for you. At any rate, if you just study really hard for the midterm, it’ll be okay.

At any rate, if you just study really hard for the next midterm, it will be okay.

You send me an email, if you just do really well on the final will it be okay?

Now you reach out to me, you really really really need to pass the class and you’ve struggled all semester with personal issues and you’re certain you’re ready for the next class, because next semester your life will be settled and you can really study hard all semester long you just really really need to pass.

Welcome to Math Class, I am Professor Harron. I really want to learn all your names, but I probably won’t because I haven’t worked through my guilt and anxiety about the situation. I idly run through various “fun” ideas, but at the end of the day I have so many other things I have to get done. I want you to know that you matter, but I don’t know how to tell a class this size that everyone matters. I want to tell you that you can each email me anytime you want, but I couldn’t possibly reply if you all emailed me at once.

I want to talk to you about so much more than the bare minimum. I want to talk to you about so much more than just this class. Most of you are still caught in a punitive mentality from high school and you need help transitioning to college level responsibility. I want to empower you by saying you can make your own choices and you don’t have to give me excuses, but it probably sounds like I’m saying I don’t care what you do. I want you to be emotionally invested in this class, but if you decide I’m wasting your time, it’ll show up in the student evaluations.

I ask if there’s anything you want to discuss about the syllabus, and then I start the first lecture. I know I’ve already lost, but there’s nothing I can do.

Homeworks come in. In theory, this is my chance to see how you’re doing with the material. In practice, I don’t have time to read through the assignments. In theory, the data collected is my chance to see how you’re doing in the class. In practice, there are just too many numbers. Again I will think idly about all the ways a better person might reach out to her students, but after running through all possible scenarios (as my anxiety dictates) I can’t decide on any particular action. In class, I talk about how important the homework is and that you should aim to do *better* on the homework than you want to do in the class. I tell you you should come to office hours, but maybe I’d put more effort into getting you there, if I didn’t use that time to prep lectures, update the website, and answer the few student emails I do get.

I do not know what Calculus class is right for you. I have opinions on what the course “should” cover and what a student “should” be able to do. But those opinions are based on my own privileged experiences. Many of my colleagues have even higher standards, filling me with insecurity. If I make the course too hard, this does not help you, as you just learn that you “can’t do it.” But I’m afraid that if I make the course too easy, you won’t know what calculus is, and you’ll be moved on to a harder course you’re not ready for. And it will be my fault. And I will be the unserious professor who doesn’t value mathematics and is a pushover in the classroom.

High expectations require extra support. If we don’t have the resources to give you the attention you need, do we lower our expectations so that more of you have a positive experience? Or do we keep our expectations high so that the best prepared of you achieve your potential?

Exams are stressful for me because I try to prepare you, and it isn’t enough. I don’t know if your scores are low because of the system or because of me or because of all your experiences before you met me. I assure you that there will be a curve. I assure you I will give you the best grade I can morally justify looking at the work you’ve done.

I really really really want you to do well in the class, to learn, and to feel good about it. You see, teaching is very stressful and way more subjective than we like to talk about in math. How your grade compares or contrasts with your scores throughout the semester and with the grades of other students reflects on my skills or deficiencies as an instructor.

I receive your “I really want to pass” email and my thought is “same.”

Welcome to Math Class, I am a black femme and I sometimes have pink hair, and you probably haven’t had a math class taught by someone like me before. But I don’t talk about it in class. I have anxiety, I carry pill bottles, I go to therapy, but I’m led to believe I shouldn’t talk about it in class.

You may be a woman or femme or person of color, but we’re not supposed to talk about it. The white men in the class may be more comfortable speaking up in class than everyone else, but we’re not supposed to talk about it.

You may have a family member who is at risk under the current policies, but we’re not going to talk about it. You may know someone who had their passport revoked, or who is afraid of being deported, but that’s “politics” and this is “math,” so we’re not going to talk about it.

You may need help. You may be missing connections. You may be struggling with other things in your life. Your understanding (and your grade) is suffering, but your issues aren’t strictly related to the actual class. You’ve learned from me that we must only discuss things that are in the textbook, on the syllabus, related to the subject at hand. You may need help, but you think you don’t need your Calc prof. So you’re not going to talk about it.

I am still learning the subjects I teach. I learn from my students. I learn how they think about problems, how they learn. I still learn new connections from teaching, new ways of thinking. I learn from my students, but I need them to write “professor has mastered the material” on their student evaluations, so I don’t talk about it.

Welcome to your first day of Calculus, I am just a small part of a large, enduring system that says we cannot afford to discuss the most important aspects of our lives. This class will, at times, make you feel powerless. You will feel as though your only recourse is pleading and excuse-making, but they won’t work. You probably won’t blame me, as I come off as empathetic and enthusiastic, and to be honest, I care and I’m doing the best that I can. But the truth is, we are all guided by past experiences, external pressures, stress, and pre-existing hierarchies. It’s the first day of class, and we’ve already lost our chance to meet as human beings struggling together.

On the first day of this semester, I took what felt like a huge risk. It is too early to know what the results will be. After going over the syllabus I spent probably thirty full minutes telling my students things I thought they should know. To summarize:

- 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.

I got some extremely positive responses from some students, but I am still stressed about missing a lecture (and we ended up losing a second lecture due to the weather), and I have no idea whether this will actually help students do better. But at least I was honest, which is something I strive for in general.

]]>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.

In a time before Cambridge Analytica but after Snowden, there was a buzz in the maths hall at the University of Cambridge. Two Cambridge academics, Maurice Chiodo and Piers Bursill-Hall, together with many of their students began discussions addressing the ethical situations mathematicians find themselves, and often without much guidance or principles specific to a mathematician and the field. From these initial discussions, the Cambridge University Ethics in Mathematics Society (CUEiMS) grew into being on the campus. The mission statement and constitution of the society are on the website, but from my perspective, there are two simple threads to the mission: doing good and preventing bad.

“…[W]e see that the utility of mathematics is derived from the way that it empowers us to understand, change, direct and manipulate the world around us, and not the other way around. It does not change the world because it is useful; it is useful because it can change the world.”

“Mathematics is a tool wielded *by* people, and thus subject to the desires, objectives and will *of* people. As such, we as mathematicians need to be aware of this. We need to realise that mathematics can be, and sometimes is, used in a harmful way. We need to have the foresight to anticipate such events before they happen. And we need to be prepared to do something about it.”

The Society hosted speakers from mathematics and computer science including Bonnie Shulman, who the organizers assert was one of the only search results when seeking “Ethics in Mathematics.” Thanks to James Franklin, Mathematics and Ethics now has a Wikipedia page adding to the relevant search results. But it was Dr. Shulman’s article “*Is There Enough Poison Gas to Kill the City?: The Teaching of Ethics in Mathematics Classes*” and subsequent video-linked talk for the society that opened up the conversation of ethics beyond the profession of mathematics and into both the curriculum of mathematics and social ethics.

In response to the growing conversations, numerous incidents, and the calls from isolated mathematicians working on this issue, Maurice Chiodo, with the support and assistance of CUEiMS, organized the first Ethics in Mathematics conference at Cambridge University on April 20^{th} -21^{st} of this year. The conference was live-streamed and included both present and video-linked participants. Those participants included mathematicians, legal scholars, computer scientists, and philosophers. And in their ranks were Turing Award winners, whistle blowers, scholars and leaders in their field from the UK and Australia, and a few, fantastic, friendly faces from Fitchburg State and Ferris State in the US. It might seem odd to have to have professors from small, public universities in the US at this conference, but this invitation came through the organizers’ relationship with Bonnie Shulman. I have worked and continue to work with Bonnie on the mission of mathematics, social responsibility, and social justice. The organizers asked me if I knew others who might be a good fit and I thought of my mathematician-lawyer peer at Ferris State University, Victor Piercey. True to their mission, the organizers realized there needed to be speakers from other disciplines to address what ethics may mean and how to design ethical standards in mathematics, but they also included mathematicians coming from experiences and math cultures very different from their own (see me and Victor).

This varied perspective built a more inclusive dialogue about what it means to be a mathematician (the profession at Cambridge and the profession at Fitchburg State University look different), but ultimately there is an ethical education we wish to instill in the students that pass through our buildings no matter the building. You know, whether you are studying here:

or here,

you should be part of the conversation. This is a different type of inclusion in mathematics and an important one.

Having said that, as with a majority of math conferences, there were voices missing from the room. There was one person of color and only a handful of women at the conference. Again, this is unfortunately the status quo of most conferences in the US and aboard. Nevertheless, the organizers worked through their growing yet limited ethics network to increase representation. As Maurice pointed out, we can look at a place like Silicon Valley were most people are middle-upper class, young, white men, and working on projects that are shaping the world. Without a diverse mix people in the room, groupthink is more likely to happen, as people struggle to see that their view of the world is not the only view. He said, “Diversity is not merely a token gesture; it genuinely adds value to any decision-making process.”

My talk focused on integrating social justice issues into a mathematics curriculum in order to build an ethical foundation. The premise was that if we have discussions of power, ethics, justice, and equity in the mathematics classroom, we are informing the larger community that these are values of the discipline. They are necessary to show value to our students and respect their desire to see their community and selves reflected in their studies. By leaving them out, we are, perhaps inadvertently suggesting, that people with these values are not “in the club.” While some at the conference spoke to the fact that the powerful and the privileged have established our rules of ethics (or lack thereof) and we require mathematicians to act as democratic citizens, few participants went so far as to suggest the necessary social justice incorporation. For example, many spoke about how working on algorithms for predictive policing might be unethical; however, if you do not talk about the issues of race and ethnicity, then this lesson can fall flat. It was not lost on me that after my talk nearly all the women in the room and the only person of color came over to talk to me about the lack of inclusion of the social side of ethics. The impression they had received was that the social side of the ethics conversation was less valued. However, conversations about social ethics and issues of race and gender in the field are happening between the organizers and the participants, and both Victor and I were hopeful that the conversations would continue to engage and incorporate more voices.

While most of the conversation surrounded training mathematicians to be ethical and mindful as to how they conduct their research and professional lives, as well as the future consequences and roles a mathematician plays in the use of that research, it was generally understood that an ethical education would not magically occur. Among the suggestions where ethics courses with case studies or ethical dilemmas to educate mathematics students. In addition, several speakers pointed out that integration of these lessons across the curriculum is necessary. It could be seen as an ‘add-on’ unless the values for an ethical mathematician, and dare we say ‘one doing good’, are intertwined with the curriculum from early on. How do you recognize different ways to solve problems if you haven’t been first exposed to many problems and their solutions? We teach methods of proofs and encourage leaps in creativity after building a solid foundation. Should not ethics be the same why? If these discussions seem important to you or if you want to learn more and add your voice, you can see the videos from the conference on the society’s youtube channel.

As you may expect, discussions about the culture of mathematics came up frequently. The culture, norms, and behaviors of mathematicians harm our ability to reach out and work with others and can close the door to diverse voices. Who should be a mathematician? What does a mathematician look like? When we close our doors to the diversity of ideas and backgrounds, we are doomed perpetually to continue the culture that has allowed mathematicians to remain distant, revered, aloof, or excluded from broader conversations of ethics. I have faith, given the openness of the CUEiMS team and the value they associated to our presence, that there is desire to grow the community as the issue of ethics in mathematics and we will need everyone onboard. The players who benefit from the lack of ethical discussions among mathematicians (NSA, GCHQ, and others) have power, money, and prestige. This Society and this movement should and continue to challenge the status quo as more mathematicians enter the global discussion of what is good, what is ethical, and what is necessary for a democratic society.

]]>

In this spirit of empowerment and raising awareness, in particular in the context of the mathematical community, together with my co-editor Luis Leyva, we have compiled a short reading list for you to do today.

**Mathematical Inqueery, by Kai Rands.**Rands has been doing a lot of scholarship related to “queering” mathematics. In this article, published in the Springer volume on “Critical Concepts in Queer Studies and Education”, Rands summarizes many of his areas of research. I found this to be a particularly helpful guide to the current research, which goes from the “add-queers-and-stir” approach (a term I adore, and which basically means add queer issues, characters, etc., to the existing mathematical curriculum, in the way many people have been doing with math for social justice approaches), to the other definition of “queer” as used in queer theory, where “[r]ather than inclusion and representation,” Rands says, “queer theory emphasizes questioning and inquiry.” I found the latter more difficult to understand, but it makes sense as a way of pushing back against this notion that mathematics is devoid of social context and identity. “Mathematical inqueery challenges normativity and questions the boundaries of social, identity, and mathematical categories.” He also talks about these two definitions of “queer” as being in tension, but not in opposition to each other. Throughout the article Rands also offers many examples of what this would look like in the classroom, which is particularly useful to newbies like myself. For a publicly available text, if you don’t have access to Springer, you can look at a description for a working group Rands wrote with James Richard Sheldon called “Queering, Trans-forming, and En-gendering Mathematics and Mathematics Education,” which covers much of the framing for the current work, and thoughts on future research projects and pedagogical approaches. Another article by Rands which is more directly related to the topic for the day is “Supporting Transgender and Gender-Nonconforming Youth through Teaching Mathematics for Social Justice,” published in the Journal of LGBT Youth.**Speaking Up and Speaking Out about Gender in Mathematics****, by Laurie Rubel.**This short article appeared in the February 2016 issue of “Mathematics Teacher”, and takes us through a few examples of how assuming gender binaries and heteronormativity in math problems. All of her examples were purportedly used to help the students “connect” with the material, but they can actually detract from engagement for LGBT students. I liked the specific examples used, as someone who still regrets using a gender binary as an example of complements of sets (you can see this post for a longer description.)**Trans* Resilience Blog, by Z Nicolazzo.**Nicolazzo’s research is at the intersection of gender and sexuality studies and education (not focused on math, but still a lot here for us educators). From Nicolazzo’s webpage, “My research agenda focuses on mapping gender across college contexts, with particular attention paid to trans* collegians. My work is also focused on affirmative- and resilience-based approaches to working alongside trans* collegians as well as promoting the (un)learning of normative gender constructs in higher education.” The blog in particular includes posts ranging from collaboration, summaries of other interesting articles, and book reviews, to larger reflections like “What the heck am I trying to do?”, which I found particularly grabbing. Nicolazzo describes the blog as “a space where I engage with ideas, concepts, and research that seeks to increase life chances for trans* people. ” I can’t wait to read some more!

So, dear readers, take this short reading list, engage with the material, read it with a friends, and let’s all start actively thinking about how to incorporate some of this into our teaching, and in how we can use this to become a more welcoming and inclusive community for all. Finally, I will say that I am by no means an expert, and I am continuously learning and looking for ways to grow, and I invite you to join me in this wonderful process, as co-learners and as teachers.

And to all of our trans readers, we see you, and we welcome you. I leave you with this song by Laura Jane Grace (released in 2014).

]]>

**The community agreement.**It is starting to become more common (this is a good thing) to have some sort of inclusion or accessibility statement (these are not the same, but related), and in particular a way to establish a shared code of conduct so the experience is as fruitful as possible. Conferences like the SACNAS National Conference have been doing something like this for years, but it’s more of a set of policies than an invitation (the word “policy” itself is not very inviting.) I loved the one for LatMath, especially because it is more inclusive in its language, while still setting expectations in a clear way. Under the heading, “A welcoming experience for all”:”Latinx in Math is committed to creating a professional and welcoming environment that benefits from the diversity of experiences of all its participants. We aim to offer the same respect, opportunity and value to the contributions of every participant regardless of their mathematical experience, identities and orientations. We ask you to contribute to this positive environment, and to use extra care to ensure that your words and actions communicate respect for others. Discriminatory or harassing behavior will not be tolerated.”In particular, they also give email addresses that people can contact (in strict confidentiality) if there is something that makes them uncomfortable, unsafe, or concerned. Having this front and center sets the tone, and also signals what kind of conference we are at. I wish more conferences did this.-
**Inspiring Latinx immigrants.**Rodrigo Banuelos’s life as a series of unlikely events: from farm worker to working in a car wash where he met a mathematician who encouraged him to go to community college, then to Santa Cruz, then UCLA, and now full professor at Purdue; Edgar Lobaton and his research on biobots (cockroach cyborgs) and the ways in which we could use them for search and rescue missions in disaster areas (which by the way, raise your hand if you think this could be a good Part 3 of the Blade Runner series?); and Jesus De Loera constructing a beautiful bridge between pure and applied mathematics through integer optimization problems: “There’s no difference between pure and applied mathematics, the only difference is on the emphasis we put on certain approaches.” **My session!**I co-organized the scientific session on Algebra and Number Theory with the awesome Dagan Karp, and I couldn’t be happier with the results. We had a group of speakers with high energy, really cool (and important) research, a room full of friendly people willing to ask good questions, and a great sense of humor and community. Did I mention I was happy with our group?**Social Justice!**Just as there was a clear commitment to inclusivity in the organization and messaging for the conference, there was also a clear effort to highlight important work in the areas of intersection between mathematics and social justice.Lily Khadjavi took us on a mathematical exploration of racial profiling in Los Angeles. I particularly liked the careful approach Khadjavi took to speak of all these issues. Sometimes these ideas get dismissed as not being “rigorous”, but I think Khadjavi showed that there are good ways of thinking of these issues, from finding good definitions to really exploring the existing data. This information and its analysis leads to better and more humane policing practices as a result.

The panel on STEM disciplines and Higher Ed. highlighted the different paths we can take to mathematics, the different ways we can improve the culture, and Dagan Karp reminded us that all of this is an ongoing process: “We should be constantly engaged in self-examination”.

And of course, I cannot talk about this conference without mentioning the incredible Rochelle Gutierrez. From the pop-up session about how to support mathematicians who are doing public scholarship (and who are increasingly under attack by organized social media harassment campaigns), to her beautiful reflection on how to rehumanize mathematics, to her clearly generous nature (she was constantly talking to faculty and students, all of us very eager to get to know her better). The idea of rehumanizing mathematics was particularly powerful: the goal being to allow identity and self in mathematics and as a result to achieve better inclusion. In a recent conversation, a colleague mentioned that diversity on its own is never the goal. The goal should be equal access to everyone, diversity is just going to be a result of a successful inclusive practice. This used to be the idea of equity, but Gutierrez challenged us to go further: equity is also not the goal (and also very difficult to define) but rather re-humanization of our discipline, and then equity and diversity will follow. In the picture above, she mentions that we should think of mathematics as a way to help humans. By this she does not mean we should all do applied math, in fact math that brings us joy, that fosters creativity, also enhances our humanity (Francis Su made a similar point in this wonderful speech). You also have to hand it to someone who gets a huge room full of people to chant “Whose Math? Our Math!” at the end of a talk.

**People.**The best thing about this conference was the people. I had enough time to catch up with friends, colleagues, former students, future colleagues, collaborators, co-conspirators, and yet there were still many I missed or didn’t get to see as much as I would have liked. But I could see it the most in the students, many of them were just so happy to be part of a safe and welcoming community. In fact, I heard a couple of people warn them that not all conferences are this welcoming, positive, and happy. To which I say, maybe it’s time to commit to always being those kinds of conferences.

So, dear readers, what was your favorite moment from the LatMath conference? Please share any thoughts or comments below.

]]>Guest Post by Martha Shott

Assistant Professor of Mathematics and Statistics

Sonoma State University

*Question: What are you hoping to get out of the Workshop on Increasing Minority Participation in Mathematics?*

This prompt in my application to last year’s Park City Mathematics Institute gave me pause. Leading up to this question, the online form had asked for information that I am able to give on autopilot (*name, title, institution, email address*) as well as information that is relatively easy to speak to (e.g., *how did you hear about this program*?). But in considering my motivation for attending, my hopes for how I would benefit from the week-long program was a little bit harder to verbalize.

It wasn’t the case that I was unsure of what I wanted to achieve through my participation – on the contrary, I had specific concerns in mind from my home institution that had incited me to apply to the PCMI workshop. Our department was just beginning to develop four new “stretch” courses that were to replace our developmental courses in elementary and intermediate algebra – two places that we most often interacted with students typically underrepresented in math before they disappeared from our program. I was also thinking of the interdisciplinary science course that I teach for first-year students. That program was initially funded through an NSF grant which, in part, was aimed at closing the achievement gap in STEM – yet the student cohorts we have been able to recruit into that class have been dominated by white males, a trend that is not observed in other comparable general education courses.

Given that I had good reasons to apply to the Workshop on Increasing Minority Participation (WMP), why did I hesitate in my application? Well, the other side of the story is this: my summer was already pretty full of commitments. I was working as an academic advisor for our freshman orientation programs; I was on the instructional team for our university’s Early Start program in math; I had at least two manuscripts in desperate need of attention as I move toward tenure and promotion. To put it simply: I was already heavily committed that summer, and if I were going to carve out another week towards this workshop, I needed to walk away with actionable strategies that I could immediately begin to implement on my home campus.

But…could I really say as much in the application? My southern upbringing told me not to be so forward, to tone my request down to something more along the lines of, “I’m eager to learn more about supporting minority students, and I’m sure anything I gain from the workshop will help me in that regard.” (As it turns out, my hesitancy to ask for what would most benefit me was one of many themes that emerged in the workshop – some of our URM students do not feel that they are entitled to the same time and attention as their peers, and thus do not take advantage of services like free tutoring or office hours.)

I sat back for a moment and recalled meeting Bill Velez, one of the facilitators of the PCMI workshop. Bill had visited our institution a few months prior to complete an external evaluation of the mathematics program. During his short stay at Sonoma State, he made a huge impression on all of us by giving straightforward, candid advice – all of which was incredibly helpful, and much of which offered a refreshing change of perspective. Many of his recommendations were easy for us to act upon because he had so carefully weighed the needs of our students and faculty in order to make his assessments. I reassured myself that, with Bill at the helm of the PCMI workshop, I could certainly vocalize my intent to gain specific practices that would help my department and our students, and that the request would likely be realized.

I finalized and submitted my application, and in a few short months I was on my way to Park City, Utah. My colleague, Elaine Newman, had also been accepted into the program. After checking in at the PCMI headquarters and the conference hotel, we headed to the program catering tent to meet the other workshop participants at an informal dinner.

At the dinner table that night, our WMP group exchanged names, information about our home universities, and chatted a bit about the short readings we had been sent a few weeks prior. The group consisted of mathematicians at various points in their careers – for example, Angelynn was gearing up to begin a tenure-track position at SUNY Potsdam; Rebecca is associate chair of the statistics and data science department at Carnegie Mellon; Jenny is associate dean of her college at the University of Montana; Alice is faculty in both the mathematics department and the learning skills center at Rutgers. Each of us was attending PCMI in a different capacity, but our conversations that night revealed a common goal – *what are we here to accomplish? What are our expectations for the week? *Not surprisingly, the others were as hopeful as I was for actionable strategies to increase access to mathematics for all of our students.

Thankfully we didn’t have to wait long to see what the workshop would bring. Early the next morning we got right to work under the skillful guidance of the group facilitators, Bill Velez and Erica Walker. Bill and Erica had developed a full agenda for our first three days, with the understanding that the remainder of our time would be spent on topics that the group identified as being most relevant to its goals. While I can’t even begin to scratch the surface of the many discussions we had over the course of the week, some of the highlights of the program included:

- A review of program requirements at several institutions, which led to a discussion about the math major – has it changed to reflect the diverse needs of our current student population? Should it?
- A discussion on how our programs are represented in an official web presence, on social media, etc.
- A brainstorming session on recruitment strategies, as well as the purpose of recruitment.
- A survey of common characteristics of mathematics programs that have been successful at attracting, retaining, and graduating historically underrepresented students.
- A Skype session with Leticia Williams and Talitha Washington about effective communication styles and advising practices to support all students.
- A breakout session for developing intervention programs that address students at critical points in their academic careers.
- A panel of current undergraduate students, all of whom provided anecdotes to speak to the influence that their faculty advisors and mentors had on their success through the major.
- A workshopping session to write and revise recruitment letters to incoming students.
- A half-day breakout session to develop action plans that we would take back to our home institutions.

As I had hoped, the WMP program expanded my understanding of the issues that face students from backgrounds that are typically underrepresented at math, and provided me with multiple strategies that can help me to support these students and foster their success in math. As I mentioned previously, I was fortunate to attend the workshop with another Sonoma State faculty member. While it may be unrealistic for most departments to find two or more faculty to attend the workshop in tandem, I would highly suggest considering it at least – Elaine and I have continued the momentum we gained from the workshop much more effectively than I believe I could have done on my own. Together, and (thankfully) with the enthusiasm of our other colleagues, our department has implemented several of the ideas we brought back from the conference.

Immediately before fall semester began, Elaine and I led our department’s pedagogy workshop with a focus on what we learned through the WMP as well as the action plan we developed for SSU. We divvied up the action items so that each of our department members had ownership of one or more tasks to set in motion. We have since held several informational sessions for our students: one was dedicated to options for careers or graduate school upon receiving their degree; one advertised activities that students should consider to help prepare them for their post-graduation plans, such as attending seminars, working with faculty, applying to REUs, presenting posters at regional meetings, etc.; another was specifically intended to demystify graduate school so that all students felt like it was a realistic option for them. Our department formed a “public relations task force” to consider how our program is advertised, and the images of mathematicians that our students see in our classrooms and hallways. We are also in the process of rewriting our mission statement so that it emphasizes our belief that ALL students are capable of doing math and should have access to resources to help them to learn math at a high level.

My week-long stay at the Park City Math Institute was a full and robust experience, but it was by no means the end to a conversation. For every potential solution that we discussed in the WMP, at least three other issues arose that need weeks, months, years of work to address. Our 2017 workshop participants are ambassadors for change in their home departments, are organizers of sessions on similar topics at national conferences, and are penning articles to increase awareness and action on behalf of our URM students – I am optimistic that participants in this year’s workshop will be enthused to continue in kind.

[Applications for “Shape of the River: Workshop on Equity in Mathematics Education” are open until March 7, 2018.]

]]>