Recentering
 

In my geometry courses, I loved teaching triangle center points. (Thank goodness this is a group of self-defined nerds, or starting a post off with that might be a real problem). The idea that we can define center from multiple points at the same time defined by different constructions held deeper meaning. To me it signaled that when you measure from a particular perspective, you get a different result than other people who measure from a different point of view. The orthocenter, incenter, circumcenter, and centroid all result from measuring using different line segment constructions of triangles (altitudes, angle bisectors, perpendicular bisectors, and medians respectively). Each one of them has a different purpose within the triangle, and they each come with particular perspectives on defining “center”. Yet, some of them come with a rather peculiar placement within or even outside of the triangle body, like when you measure the orthocenter of a right triangle and it lands on the vertex. Calling these instances a “centerpoint” almost seems odd, and yet we know exactly what we’re measuring when we do so. 
 
I have been wondering. What are the different centerpoints in math education? I believe each of us is measuring from some centerpoint. How do you justify your reasoning for measuring by the centerpoint you choose? 
 
I believe that there are multiple centerpoints in mathematics education, just like within a triangle. I also believe that they *do not* nor ever will coincide in the same point. In my mind, each centerpoint of mathematics education, just like with triangles, measures something specific and different than the others. And, just like with the different centerpoints, there are benefits and consequences to measuring by the different points we choose. 
 
For many months, I have felt this recentering occurring in math education. It’s as if we are making a collective shift. For the past ten months, many have been asking, “What even is standardized testing measuring?”. For some, standardized testing is a centerpoint. To these people, it represents teaching to a “standard”, that they share no responsibility in defining, yet use as a marker for knowing whether or not their students are learning. As the consistent call that students are “behind” due to virtual learning echoes loudly, COVID-19 continues to erode that measuring by any sort of “standard” at this point is only measuring the difference in resources, funding, and access to internet, food, and health care. 
 
From a different angle, some might say that math education is centering the “be kind” movement, that as math teachers our ultimate job is to create kind citizens. This is important and inherently good. In the aftermath of the United States presidential inauguration and the events of January 6, we have to ask if centering kindness at the expense of justice measures the right thing. If, by trying to “be kind”, we become peacekeepers instead of peacemakers, we ultimately create “kind” citizens who are quiet when faced with overt acts of racism, sexism, ableism, and classism to maintain the status quo. For many, because they are at peace, kindness is an easy centerpoint to use, as they disregard the lack of peace and justice for others.
 
One last centerpoint I see in math education is learning/teaching math for social justice. Dr. William Tate wrote, “Until recently, embedding mathematics pedagogy within social and political contexts was not a serious consideration in mathematics education. The act of counting was viewed as a neutral exercise, unconnected to politics or society. Yet when do we ever count just for the sake of counting? Only in school do we count without a social purpose of some kind. Outside of school, mathematics is used to advance or block a particular agenda.” (Tate, 2013) This centerpoint, then, measures math education as students’ ability to use mathematics to change their world for the better, to act justly with mathematics. 
 
We know what the other centers have brought us. Centering on standardized testing has brought us a system focused on viewing every child as a number, using math to do more harm than good, all in the name of comparison. The centerpoint is nowhere near the center mass, and in fact measures the outer edge of learning. Why are we surprised when standardized testing reflects back to us that systems of injustice exist and can be quantified? 
 
Centering on the passivity of kindness allows more students to pass through our classrooms without being pushed to recognize the beauty that comes with diversity, that teaches students through the use of mathematics that “others” are whole beings worthy of respect and equal treatment. Why are we surprised then when “kindness’” is in reality a mask for whiteness, a mask quickly removed when moments of injustice occur? 
 
Why do we keep centering math education on centerpoints that produce outcomes that we know are not fair? Not equal? That do not promote justice or goodness? That maintain the status quo? With the decades of centering math education in these known spaces, what would it take to get the main body of educators to recenter to measure a new space? What would centering on math for social justice look like? How would you justify its centering? I think that the mainstream of math education has never taught math for social justice, and therefore we don’t know what our collective power could be if we measured from here. Maybe it’s time to recenter the purpose of math education to see if we can measure something new. 
 
Lauren Baucom
@LBmathemagician

• Focus on issues that students care about. One teacher in my (2020) study has learned through experience that some topics may be overwhelming for students, and can produce strong emotional reactions. Kokka (2017) also found that students who had faced similar challenges to what they were studying, such as struggling to pay rent, had “strong emotional reactions such as anger, sadness, worry, and frustration” (p. 73). Nasriah Morrison (@nasriahmorrison) told a similar story in a previous GMD post of being exhausted and retraumatized by a lesson on police brutality, highlighting the harm that can come from “the prospect of any students being made to complete a series of tedious calculations with the goal of assessing whether their lived experiences were truly ‘valid.’” Instead of using math to verify, for example, an issue of racism that students know very well is real, I recommend starting by asking students what problems they want to use math to explore. 
• Think about local, not just national, issues of injustice. You might ask what systems students see holding people in their community back, and what questions they have about them. This can open up opportunities to mathematize aspects of their world that students are curious about and ready to explore. Gutstein (2007) argues that members of a community “have a clear and critical understanding of the political forces allied against them” (p. 111), so problem-posing pedagogies that draw on local issues can help students work on issues they are already invested in, knowledgeable about, and want to get better at combating. 
• Ask students and families about their comfort level with challenging topics. The teacher in my study who realized that some students had a strong emotional reaction to her lesson decided in the future to give a survey to both parents and students previewing upcoming topics, and asking about their comfort level in discussing such topics. She also prepared alternatives for students who may have too close a personal experience with an issue of injustice.
• Try to leave your own agenda behind. A teacher in Kokka’s (2017) study emphasized that her goal was not to change students’ minds, but rather to elicit students’ opinions and give them the tools to come to their own, mathematically-based conclusions. The teacher in this study asked strategic questions and encouraged students to gather mathematical evidence, only stepping in to guide when she needed to combat stereotypes or other harmful statements. 
• Try to anticipate partial and problematic understandings that students may have. Another lesson that the teacher in my study said she had learned was that students may need scaffolding for not just the mathematical topic, but also the social injustice under study. In her first teaching of a lesson, she showed a brief video and then released students into groups to discuss a topic, only realizing later that students did not fully understand the topic and were discussing it in common but highly problematic ways. I recommend thinking about the worst narratives floating around society about that topic, and either preemptively providing information to combat those narratives, or at the very least developing a specific plan for how you’ll respond should they appear during your lesson. 
• Find community! One of the most important lessons the teacher in my study stressed was that you should not try to go it alone in integrating math and social justice. She runs her lessons by her co-teachers and colleagues, but also recommends connecting with folks on twitter and at conferences. Many people have been engaged in this work for decades, and have much wisdom to share. Check out the Creating Balance Conference and the hashtags #SoJustMath & #socialjusticemath for starters. 

• Dr. Kari Kokka’s compilation of Social Justice Math Curricular Resources
• Berry and colleagues’ book, High School Mathematics Lessons to Explore, Understand, and Respond to Social Injustice
• Rethinking Mathematics
• Jonathan Osler’s guide for integrating issues of social and economic justice into mathematics curriculum
• Radicalmath.org
• Creating Balance Conference Resource Site
• Math for a Change

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The Narcissism of Mathematics Education
 

In “The Narcissism of Mathematics Education”, Alexandre Pais says that “mathematics education research is narcissistic because, lacking a concrete object, it sees nothing but itself”.  Math education researchers who talk about “mathematics for all” turn a blind eye to the reality that many students are in math class for the school credit, and so mathematics is not actually “for all”. Instead, math education researchers—and by extension people interested in this research—create “an imaginary world where mathematics can be an adventure into knowledge, the ultimate problem solving technology or the most crucial component of critical citizenship”. 
 
The math education research community, as he claims, is sometimes so optimistic about the role of math in kids’ lives that we don’t stop to consider when kids may be in it for the grades and not the math. By subtracting from reality the economic role of school math, the research community flourishes under the illusion that math has inherent relevance while creating the very problems it seeks to address.
 
That’s quite the claim, and in response I say, cool, then let’s be narcissists. I don’t entirely agree with his argument. But even to the extent that he’s correct, it’s still an open question where this thinking takes us. The recent events at the Capitol and everything else kicking off 2021 make clear that taking a critical approach to mathematical, quantitative, statistical, scientific, and data literacy is now more important than ever. 
 
I think about a thread by Aristotle Ou, in which he, Jenna Laib, and Marian Dingle talk about asking students to feel and act in response to U.S. poverty rates and economic justice.
 
I think about the mathematics of machine learning algorithms, which have been used in AI technologies to perpetuate gender and racial bias. The Algorithmic Justice League has a new film, Coded Bias, which is screening in virtual theaters beginning this week.
 
I think about Kendra Pierre-Louis’s open question about how often the media covers white supremacists versus people who have experienced white supremacist violence.
 
I think about how many executions are happening now and how much racial bias continues to exist in a school-to-prison pipeline that can ultimately end in death.
 
I think about how $1400 is not enough and the mathematical models that have supported fiscal conservatism for the past four years.
 
I think about the minimum wage, teacher salaries, experiments around UBI, and the economic and mathematical “common sense” that drives repeated arguments against wage increases.
 
I think about the overwhelming whiteness of mathematics that results in this.
 
I think about this analysis of Paycheck Protection Program funding given to charter schools, religious schools, and private schools across the U.S.
 
I think about the spatial relationship between COVID fatalities and vaccinations in the U.S.
 
I think about pharmaceutical price hikes, bonus formulas, and what we let people do with math when we’re too preoccupied by whether the math is technically correct.
 
These mathematical questions matter. They touch students’ lives in ways that are sometimes hard to see and other times grievously easy. They are as real as grades and should be among the driving forces behind everything that goes on in math education. Sadly, this is not always the case.
 
@melvinmperalta

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Gratitude
by Amber Thienel (@amberthienel)
 

Dwayne Reed’s (@TeachMrReed) pinned tweet on his Twitter page reads, “Even if you weren’t the best teacher today, chances are, you were still someone’s favorite. Keep at it.”

 

 

Humans in general are not the best at expressing gratitude. Sometimes we just assume that others know how we feel about them. Or at least we hope that they do perhaps based on what we do and how we act.

 

Angela Duckworth (@angeladuckw) shared some advice in an opinion article from Education Week (@EdWeekTeacher) called “What Your Students Will Remember About You.” She said:

          

Don’t assume that people who have changed your life know how much you appreciate them. What is obvious to you may be invisible to them.

 

Do start a tradition of writing gratitude letters to people you haven’t properly thanked. If you can, muster the courage to read your letter aloud. Perhaps your kids will see you wipe a tear from your eye. Perhaps you will have to explain why. I can’t think of a better way to kick off the new year.

 

Originally, I was drawn to the article because of the tag line, “The best teachers care about students unconditionally but, at the same time, ask them to do things they can’t yet do.” And I do think this article is a good reminder that pushing students out of their comfort zone is important. And even if at first they resist they will thank you for it because they know you care about them. But I think this article is also a good reminder of how important gratitude is. This gratitude should extend to yourself as well.

 

Minaa B. (@MinaaBe) is a writer and licensed therapist whose mission is to “help people cultivate healthy relationships with themselves and others by being intentional about practicing self-care through the lens of boundaries and community-care.” This is an image from her Instagram page.

 
 

It’s important to remember, especially after a week like last week, that our students need us. And in order to show up for them, sometimes we need to take care of ourselves. Show gratitude to yourself. “Even if you weren’t the best teacher today, chances are, you were still someone’s favorite. Keep at it.” (@TeachMrReed)

1. Donations. I made a few small adjustments last year: When others have offered to compensate me in some way, I have shifted from outright refusal to asking that they donate the amount that they believe is appropriate; the most recent three times that I have done this, I have pointed others to Found in Translation, which I hope the reader will check out. When this last occurred, it was after assisting a former colleague’s child with their non-routine Calculus homework; that is to say, I successfully converted assistance on an antiderivative to money that can help sustain a program designed for low-income women. Similarly, when I was asked to give a talk on justice in mathematics education during the stressful month of October 2020, I asked whether there was an honorarium; transparently, the NSF sponsored conference offered 1100 USD for a Zoom hour. So, I agreed to write and deliver the talk, and I gave the honorarium to six different Senate races. In other words, I successfully converted NSF math education funds into money that helped Democrats compete in the Senate. Lastly, I am of the belief that restrictions on stimulus checks (“stimmies”) should err on the side of Too Generous, and that those who receive these extra moneys while in the privileged position of not seeing a significant interruption in income should consider giving the money away. I gave my first stimulus check to a double-matching campaign organized around cash bail; I gave my second stimulus check to a local food bank. This is not to guilt the reader or flex on anybody; and, I think that if you are at a real loss for how you can engage in direct action, then donating money to trusted organizations is a good choice.

2. Math Education. I have been contributing to the Global Math Department newsletters while also managing the GMD twitter account; this involves a fair amount of highlighting others’ powerful work, and has also – for those paying attention – involved a lot of proactive posts about elections (POTUS/VP in Nov 2020 and then Georgia in Jan 2021). Sometimes this means amplifying calls for action (e.g. from MoMath, which has yet to respond) and other times it means proactively thinking about boycotting ICM 2022 in Russia, or asking questions about ICME 2020 (now hybrid in 2021) in China as relates to ongoing human rights abuses in Xinjiang (thread). It also means that I am actively trying to incorporate Teaching Tolerance anti-bias standards into an Algebra 2 course, and that I am preparing to shift a junior/senior elective math course towards projects on, among other topics, Social Justice Math Trails. (Here are a subset of references compiled by a student who worked with me on a senior project last May around this topic; pull-quotes are in blue and her writing is in red.) There is plenty more to say here; off top, a shout out to the three people who reached out to me proactively over the winter break to Zoom around contemporary happenings (e.g. antiracist pushes in math education), as well as a separate shout out to Winger and Harris for their excellent book.

3. School-based Organization. This is the one area in which I will avoid detailing specifics; suffice to say that Rochelle Gutiérrez’s paper Strategies for Creative Insubordination in Mathematics Teaching is a must-read. Other than that, I have continued in my capacity as one of the two faculty members taking part in our high school’s social justice club, and I volunteered my time during Fall 2020 to participate in an Anti-Racist Committee that consisted of various stakeholders (faculty; staff; admin; students; alums; families; trustees). This was at a time in which the outgoing prez* was using BDV to weaponize her position as EdSec in policing language (like “white privilege” or talking about race, gender) used by private universities; I have no doubt that, were the racist-in-chief to have been reelected, we would have seen this tactic pushed out further (e.g. targeting public schools directly and threatening non-profit status for independent schools). I plan to push our collective AR recommendations hard in this calendar year, and one of my 2021 goals is to stop recreating mission statements and guidelines.

4. Political Candidates. The four areas here are not mutually disjoint, and/but I have grown tired of the superhuman rhetoric around Stacey Abrams. To be clear, Abrams’ work is transformative and extraordinary; yet, she is fully human – not “super”human – and, as she would tell you, there are many whose collective work went into “Georgia’s evolution.” Therefore, to those of you who are looking at organizing and potential political candidates for 2022, I strongly urge you to learn more about Danielle Allen as she looks into running for Governor of Massachusetts. Watch this video (2m18s) and check out her site. There is a republican gov in MA now, and here we have a Democrat Black woman with two doctorates (Cambridge University, Harvard University) who worked with a transdisciplinary team on a Roadmap to Pandemic Resilience produced through the Safra Center for Ethics of which she is the director. I have read through two of Allen’s books: one containing original research on the Declaration of Independence and another about her firsthand experiences with the criminal in/justice system and her incarcerated cousin (Adichie calls it “unbearably moving”). A supporter of RCV and MacArthur Fellow; an organized thinker who can govern based on institutional experience as well as lived experience; I hope that you will learn more and consider signing up under the site’s Take Action tab.

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