Identity & Illusion

[Spoiler alert: This post is, in part, a reflection on the show “In & Of Itself“, written and performed by Derek DelGaudio. If you are near New York City, I strongly encourage you to see this show before it ends on 8/19/18 and before reading below.]

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.

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Reflections on Autism, Ethnicity, and Equity

Guest Post by Michael Ortiz
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.

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Posted in ableism, equity, graduate school, implicit bias, inclusive pedagogy, intersectionality, introduction, latinx in math | 3 Comments

Toward humanizing undergraduate mathematics education: A re-imagining through historical perspectives in mathematics

Photo from Dr. Sara Hottinger’s Coastal Carolina faculty profile webpage

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.

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Posted in culture, equity, feminist theory, history of mathematics, math education, teaching | Leave a comment

What’s the buzz? Tell me what’s happening: A conference on ethics in mathematics.

Guest Post by Catherine Buell

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 articleIs 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.

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Posted in ethics, public scholarship, social justice | 1 Comment

Trans Day of Visibility: a reading list

 Today, March 31st, is Transgender Day of Visibility. As seen on the left (taken from the banner on the community’s Facebook page), the day is more than just about visibility. Again, from their page, “March 31st is Transgender Day of Visibility, when we celebrate, empower, and raise awareness of issues facing the trans community.”

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Posted in gender research, inclusive pedagogy, intersectionality, LGBTQ+, math education, spectra, trans day of visibility | 3 Comments

Highlights from the Latinx in the Mathematical Sciences Conference

It is hard to know where to start when speaking about this conference, held this last weekend at the Institute for Pure and Applied Mathematics (IPAM) at UCLA, and organized by Federico Ardila, Ricardo Cortez, Tatiana Toro, and Mariel Vasquez. Maybe it’s because the snow storm on the East Coast prevented me from getting there for the first day, and once I got there I felt as if I was already in catch-up mode. Maybe I was overwhelmed by the joy, talent, and radical thinking surrounding every single interaction. But I think it was more the fact that, like with many amazing and busy conferences, I just have lots of memories that are more scenes and feelings than clear summaries of talks or a play-by-play of chronological events. So in this post, I walk you through some of the most memorable moments from the conference.

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Posted in conferences, immigrants in math, latinx in math, mentoring, minorities in math, social justice | Leave a comment

Workshop on Increasing Minority Participation in Mathematics: Reflections on A Park City Mathematics Institute program

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

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? Continue reading

Posted in equity, introduction, leadership, minorities in math, social justice, women in math | Leave a comment

Should I Stay or Should I Go?

Raise your hand if you were just rejected by the NSF! Fun times, right? I don’t know about you, but I like to celebrate such occasions with a full re-evaluation of all of my life choices. So of course, I am currently wondering whether I should stay in academic math. It’s a question I have been asked and I have asked myself way more often than my more successful or more white-male-type colleagues have (as far as I can tell). When you don’t fit in, whenever there is some sort of friction, suddenly you have to justify your continued presence.

I wasn’t always wondering if I should do math. In fact, I loved math and was comfortable being associated with math for my entire childhood. College was the first time I hit a set-back. I immediately quit math and moved on with my life. That is, until I un-quit and decided to go to graduate school. Ever since then, I have had two strong and conflicting feelings about being in math.

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Posted in mathematics experiences, minorities in math, participation, racism, sexism, women in math | 6 Comments

Here, There and Back Again: Developing Pre-Service Teachers’ Racial Consciousness Abroad

Guest post by Dr. Mike Egan of Augustana College.


“If the streets shackled my right leg, the schools shackled my left. Fail to comprehend the streets and you gave up your body now. But fail to comprehend the schools and you gave up your body later. I suffered at the hands of both, but I resent the schools more.”
Ta-Nehisi Coates, Between the World and Me

Ta-Nehisi Coates’ deservedly acclaimed Between the World and Me provides an honest and jarring window into his experience as a Black man in present-day America. His portrayal of his time in the K-12 school system is particularly unsettling: he describes monotonous rote instruction, a not-so-implicit curriculum that esteems conformity over creativity, civics lessons preaching social passivity over political action, and worse. “I came to see the streets and schools as arms of the same beast,” he writes. “[F]ear and violence were the weaponry of both.”

These messages can readily be taken as an affront to members of the predominantly white American teaching force that serve a majority non-white population of students. Speaking for myself as one member of this force, I must acknowledge a feeling of defensiveness come on as far as Coates’ words might be applied to my own practice. I accept my imperfections as a teacher, but surely I’m no agent of fear and violence, right? My defensive impulse subsides when I recognize that Coates is not pointing directly at my classroom, but rather at a collective system that effectively serves to maintain the privileges of some while limiting or outright damaging the humanity of others. I have come to take ownership of the painful and unfortunate fact that, as a (White) teacher in this system, I am a contributor to its unjust totality. I suspect that White readers of this blog have arrived at similar conclusions, and perhaps share my view that we must develop a critical mass of justice-minded White folks who will acknowledge the dehumanizing effects of institutional racism and collectively work at the side of all who seek justice to dismantle a system built on White privilege.

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Posted in inclusive pedagogy, international study, math education, racism, social justice, supporting students, teacher education | 2 Comments

We can be better

As many of us look forward to the sense of community at the Joint Meetings this week, we should remember that conferences include many situations that are fraught with the danger of harassment and alienation, especially for people in our community with less power or privilege. We can be better.

This short post was inspired by the attention that has recently publicized harassment and marginalization issues at Political Science, Psychology, and other disciplinary conferences. Below, you will find list of articles, ranging from first-person narratives to survey research to suggestions for code-of-conduct policies. Because the articles below are from other disciplines, I thought I would share three short anecdotes that I have observed at math conferences to help connect with these articles.

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Posted in ableism, bystander intervention, conferences, introduction | 1 Comment