Online Professional Development Sessions

No Webinar this Week!

Next Tuesday 12/15

Wonder, Plan, Run, Reflect: Action Research in the Math Classroom

Presented by Theresa Hickey

Being a responsive educator means getting to know your learners, leveraging their strengths, and tailoring your approaches so that the highest level of learning can take place. To do this, you need to try new things. But how will you know if your adjustments are making a difference?…. Action research! Join us for some great tips on designing and running this research in your own classroom!
 

To register for this webinar, click here.

Check out past and upcoming Global Math Department webinars. Click here for the archives or get the webinars in podcast form!

You can also visit our new YouTube Channel to find videos of past sessions and related content.

#GMDWrites

Swimming in Water: Carceral Pedagogy in the Math Classroom 
 
By: Lauren Baucom and Sara Rezvi

Poetry has a way of cutting to truth, of separating waves from the shorelines all the while observing both simultaneously.  In his powerful poem, Guante notes that ‘white supremacy is not the shark, it is the water’. We swim in it, we are surrounded by it – these heady waters, this deep throbbing silence. Because of its constant presence, for many, it goes unnoticed, the water set as an unquestionable background. So, too, is the everpressing presence of carceral pedagogy in educational spaces. As writers of GMD, we refuse to participate in this silence. We mourn loudly. We bear witness deeply. We grieve. And we demand that these ideologies have no place within the mathematics classroom.
 
What is carceral pedagogy? How does it intersect with the mathematics classroom? What does it look, sound and feel like? Like the words of Guante, will we ever know it exists if we do not take time to recognize the waters in which we are constantly surrounded?
 
In a recent #Slowchat, Dr. Ilana Horn (@Ilana_horn) defined carcerality as “the physical domination and confinement of bodies in institutions, especially when they reinstate white supremacy.” Elsewhere, Dr. Bettina Love (@BLoveSoulPower), has discussed carcerality as systemic domination imposed by laws and enforced by incarceration. For the purpose of this piece, we define carceral pedagogy in the mathematics classroom to be the physical, mental, and social domination presented by the systems of white supremacy through laws, written and unwritten, that confine students’ bodies, minds, and spirits in the dehumanizing experiences  of their mathematics education. 
 
 In this moment of virtual teaching when teachers have a voyeuristic ability to track, watch, and mandate policies through their surveillance apparatus of choice (ClassDojo, Zoom, Google Meets, etc), we’ve experienced how EduTwitter has taken the purpose of education as a source of liberation and used this time and space to incarcerate students’ minds and bodies through a system of compliance and oppression. Children are subjected to the ever-present disciplinary gaze of the carceral teacher. Some examples include: (1) when they can’t visit the bathroom in their own homes, (2) being forced to turn on cameras to be counted as present, and (3) being told not to eat in class when their caregiver offers them a snack. We must name these efforts of carcerality as they have quickly seeped into this new world of online learning during a pandemic. Rather than offering grace, compassion, and boundless love, carceral teachers have led the charge in creating spaces that invade privacy and invalidate the need to attend to growing bodies.
 
Simultaneously, we must revisit the mathematics classroom space of face-to-face teaching to understand how carcerality has been used in the past to oppress the bodies and minds of students. 
 
In many classrooms, we have been sold the myth that students from low income areas require carceral style classroom pedagogy in order to succeed, and that without this type of oppression, they aren’t capable of doing the work. This kind of ideology is rooted in systems of white supremacy and dehumanization. We reject the narrative that the carceral teacher (who often is white) alone knows what is best for families and children of color. It is not the children that are lacking, but the carceral teacher. 
 
There has been much research to show how students of color, specifically Black girls, have been denied their right  to joyfully belong in math spaces. Using the ocrdata.ed.gov site, we can find countless examples of the literal barriers that imprison students to classes that are unworthy of their brilliance. How is it possible that in a district where almost 4 out of 10 of the students enrolled are Black, that less than half are allowed entry into Calculus classrooms? What unwritten laws govern the body language of students who appear “deep in mathematical thought” versus those who are “lazy, unproductive, and unmotivated”, physically barring them from mathematical spaces? We find it interesting that these narratives begin for students of color at young ages and continue onward into adolescence, almost as if these ideas are baked into our societal consciousness – as if we are all swimming in it.

Carceral pedagogy is often thought of to be discipline-based classroom practice, but it is also curricular. With the constant reminder from textbooks that mathematics was created in Europe by White males and no one else, the lack of representation confines students’ minds and social identities. Texts such as Francis Su’s (@mathyawp)  ‘Mathematics for Human Flourishing’ and Talithia Williams’ ‘Power in Numbers: The Rebel Women of Mathematics’ eloquently work to decenter this notion that mathematics has only ever been a Eurocentric endeavor rather than a Human one. Elsewhere, I (Sara) along with my co-authors, have argued that mathematics, just like literacy, needs to have its own set of windows, mirrors, and sliding glass doors.  
 
Another example of carcerality that appears in the mathematics curriculum occurs when a teacher requires a particular method of solving, rather than being open to the expansive, liberatory solving process that mathematics encourages. 
 
Carceral classrooms are about control; when we try to control students’ thinking we create a low/no-trust environment with students that entraps their minds and eliminates the need for creativity, ingenuity, and authentic, original thought. 

How is it that this meme can be so readily found when we describe math classrooms? That this concept of illegality in alternative thinking is synonymous with math classrooms, rather than the liberatory experience we know mathematics to be?
 
In closing, we reflect on the immediacy and urgency of Arundathi Roy’s quote. The pandemic is a portal. How we swim through it or whether we drown in it, is up to us. Where it leads to is up to us. We engage deliberately in the practice of freedom dreaming, of imagining a world beyond the violence enacted upon children in mathematics classrooms. 
 
We are swimming in rough waters these days, full of murky sediment, glimpsing blearily into the unknown void. We have named here the silence, the complicity of holding onto dysfunctional systems that dehumanize children in the name of carcerality, of disciplinary productivity that seeks to mandate how we engage in mathematics (and beyond) as human beings.  We ask the reader to consider the following – If we are more aware of the water, is that enough? Is our awareness enough? Do we keep swimming? Or do we change the scope of our navigations?

Online Professional Development Sessions

Webinar Tonight! — December 1st, 2020

Bringing the Math Back: Lessons in Educational Recovery from Around the World

We’ve been told repeatedly that we are teaching in unprecedented times, but in fact this is not the first round of education recovery post-natural disaster in modern times. We will look at lessons from around the world and how various nations reshaped their mathematics classrooms after interruptions due to disease, war, and weather-related phenomena. In these stories of resilience and innovation, we will imagine how our own classrooms may be reimagined in the wake of Covid-19.

Presented by: Brianna Kurtz

To register for this webinar, click here.

Check out past and upcoming Global Math Department webinars. Click here for the archives or get the webinars in podcast form!

You can also visit our new YouTube Channel to find videos of past sessions and related content.

#GMDWrites

I have been grappling with the idea of “smart” this year. Who do we consider “smart”? What fields of study do we consider the realm of “smart” people? (Mathematics is high on that list.) How are “smartness” and school success and fulfillment in life related?

I don’t have answers yet, but I came across a definition by Tressie McMillan Cottom (@tressiemcphd) that has shifted my thinking:
 

 
I love Tressie’s definition and until something better comes along, this is the definition I’m working with. Mostly, I appreciate the recognition of “smart” being relational, as opposed to some kind of Platonic ideal. Smart as a construct of correspondence also fits nicely in the constellation of ideas that have been helping me grow as a math educator: (1) rehumanizing mathematics (Dr. Rochelle Gutierrez, @RG1gal); (2) unlearning deficit frameworks, particularly “current conceptions” (Dr. Maria Zavala @mdrzavala); and (3) redefining who is a math person (Howie Hua, @howie_hua).

Behind all of these ideas is the understanding that we are constructing mathematics, and we are constructing our measures of success (smartness). And therein lies our power: In accepting that these are things we make, we can decide to make something different. If we value different abilities (persistence over speed), and create different environments (collaboration over competition), we will produce different definitions of smart. The power is in knowing that our current definitions of both smart and mathematics are the result of decisions made by humans, and that we can make new decisions.
 
Two last things about this sentence: “I am smart in the right way, in the right time, on the right end of globalization.”

1. I appreciate the humility in this definition. We could all use a bit of humility when thinking about our smarts.
2. Acknowledging our moment in history feels like a call to action. How many “smart” people are we losing to the wrong side of all manner of structural violences?

Big, challenging questions, but I believe in our ability to figure them out together – we are a smart bunch.

by Idil Abdulkadir (@idil_a_)

Editor’s Note: Special thanks to Idil for being this week’s guest writer! Have an interest in writing for the Global Math Department Newsletter? Check out the invitation at the end of this Newsletter.
 

Focusing on the Positive

“It’s human nature to focus on the negative, but often a lot more is going right in your classroom than is going wrong.”

2020 has been a tough year to say the least, but good things are happening in 2020—we just might need a shift in perspective to help us see them. Simply learning how to look at a situation from a different point of view can change our negative interpretations to more positive ones.

With this in mind, I want to share this 2018 article by Patricia Jennings and MindShift (@MindShiftKQED) called “Changing How Educators See Negative Experiences in the Classroom.”

I invite you to give a read. And then take a look around you. What are some good things that are happening this year? How can we look at 2020 with a positive perspective?

by Amber Thienel (@amberthienel)

Thorn, Rose, Rosebuds
 

For this week’s entry in the Global Math Department newsletter, I’m keeping it simple by adhering to the “thorn, rose, rosebud” framework: one thing that’s no good; one thing that’s good and happened; and two things that are good and on the horizon.

Thorn 
Ellie Murray (below), Dave Kung (tweet) and others (e.g.) drew attention to a print ad from AT&T in the NYTimes. It is nice that the response to “thorny” ads like these is swift, but there were surely numerous points from brainstorming to publishing during which this could have been interrupted. I’m all for the call out, and/but: If you find yourself somewhere in the pipeline with the opportunity to disrupt before materials like these appear, be the one who speaks up!

Rose
As mentioned in a past newsletter, the Fields Institute planned and held its LGBTQ+ Math Day!

You can read more about the event in the AMS Inclusion/Exclusion blog post or on the event page (site hosted by Anthony Bonato). Relatedly, check out the sequence of tweets from Laurie Rubel here.
 
Rosebuds
Marian Dingle is giving a talk this Friday! It is entitled “Opening the Mathematical Gates: Moving Toward Inclusivity and Belonging,” and if past talks are any indication, it will most surely be worth your time. You can visit the talk page or find it in the tweet below (note the timing: Friday, December 4th, at 8PM EST):

Finally, the United States is at an exciting turning point such that a weaponized Department of Education, headed by unqualified republican megadonor / “shoot the grizzly bears” betsy devos, is transitioning to an incoming administration that will have a First Lady, Dr. Jill Biden, who holds a doctorate in education! The new administration has a “Join Us” website, and so I am personally urging YOU as a reader of the Global Math Department newsletter, if eligible to work in the United States, to consider submitting your CV/resume for consideration. A government, like any organization, is only as strong as its people; perhaps nothing will come from it, but I believe that an influx of applications by GMD readers would be a step in the right direction:

by Benjamin Dickman [@benjamindickman]

The Global Math Department and researchers at North Carolina State University are undertaking a study to learn about teachers’ learning experiences from participation in the GMD. You can participate in this study if you have participated in the GMD as a presenter, attendee of a GMD conference, or reader of the GMD newsletter. 

We invite you to click the link to join the study as a participant and to learn more!

Click Here to participate in this study

Get Involved with the Newsletter

Our team of writers and curators is committed to produce content that is reflective of our Statement of Solidarity and with the goal of moving these words into action.

With this in mind we are calling for new volunteers to expand our perspectives and raise our collective voices to move this publication forward. If you are interested in becoming a regular contributor or would like the opportunity to contribute as a guest writer, please fill out this form.

Online Professional Development Sessions

No Session This Week.

Next Week, 12/1 at 9:00 PM ET.

Bringing the Math Back: Lessons in Educational Recovery from Around the World

We’ve been told repeatedly that we are teaching in unprecedented times, but in fact this is not the first round of education recovery post-natural disaster in modern times. We will look at lessons from around the world and how various nations reshaped their mathematics classrooms after interruptions due to disease, war, and weather-related phenomena. In these stories of resilience and innovation, we will imagine how our own classrooms may be reimagined in the wake of Covid-19.

Presented by: Brianna Kurtz

To register for this webinar, click here.

Check out past and upcoming Global Math Department webinars. Click here for the archives or get the webinars in podcast form!

You can also visit our new YouTube Channel to find videos of past sessions and related content.

#GMDWrites

Numbers and Sense
 

Last week in Washington, D.C., I overheard a conversation on the train between two strangers:
 
A: I just don’t believe COVID is real.
 
B: But the news is reporting that cases in the U.S. are rising. How could you ignore that?
 
A: Where are the infected people? The news is just reporting numbers. Numbers aren’t the facts! Numbers aren’t the infection. The people have the infection! Show me the people!
 
I’ve been thinking about that conversation. I’ve been thinking about numbers and about how we process and react to them. I’ve been thinking about tweets like these:

And about podcast episodes like Dispatch 1: Numbers from Radiolab, which talks about the numbers connected to COVID. 
 
With the pandemic came a national conversation largely spoken in the language of mathematics. Education scholar Bill Barton describes mathematics as any system for dealing with the quantitative, relational, and spatial aspects of human experience. How are people dealing with the quantities, relationships, and spatial life of COVID?  What are people doing or not doing with this knowledge?
 
We teach students how to do all kinds of things to quantities, relationships, and space. They learn how to represent them as objects, cut these objects up and piece them back together, and reconfigure them into increasingly abstract forms. But often, quantities, relationships, and space are not abstract. They point to things that touch our lives such as whether COVID cases are low enough that schools can remain open or how district borders affect racial segregation in schools.

How often are teachers helping students process the quantities, relationships, and spaces in their lives? In a literature class, students talk about their personal reactions to a Toni Morrison novel. In an art class, students talk about the meanings and intentions behind their work. But in a traditional math class, it’s like students learn how to cook without ever being asked what they think about the food. 
 
To be fair, not every mathematical concept needs to be tied to a “real-world” context. But numbers can matter, and numbers don’t speak for themselves. Numbers can make us feel. They can make us act. They can change how we see ourselves and one another. How this happens is not automatic. Like everything else, our relationship to numbers is a learned phenomena.
 
The Slow Reveal Graphs by Jenna Laib (@jennalaib) is one way we can promote quantitative and spatial literacy while also giving students space to talk about how certain numbers and graphs impact them and why. This instructional routine does a nice job promoting “number sense” by giving equal weight to “number” and “sense”. The slow reveal graphs take a rigorous approach to data analysis. But at the same time, there is nothing inherently objective about numbers. Numbers are always accompanied by a regime of perception that makes some things “make sense” and other things unrecognizable. For instance, consider how a “1% fatality rate” can make the world look a certain way depending on how you think about it while also hiding information about issues such as race and class. The slow reveal graph routine invites students to think deeply about this connection between numbers and perception.

Maybe the numbers aren’t the facts. But we can’t avoid our responsibility to engage with numbers and ask where they come from, how they make us feel, and when they lead us to act. Mathematical sense making is not a purely technical affair. Instead, it’s a practice also concerned with ethics and responsibility and a willingness to challenge what even constitutes “common sense”. This is the essence of mathematical sense making, which gives students the agency and hope to decide what is sensible beyond the boundaries of what society already tries to impose on them.

@melvinmperalta

Why Don’t You Care?
 

Please answer this question for yourself.

This will be evaluated on the Final Examination.

@HKhodai

Learning to be a Teacher in a Pandemic

 
Virtual teaching is tough → biggest understatement of the year. But what about learning to be a teacher amidst a pandemic?

My name is Jess Moses, and I am a senior at Vanderbilt University, in the elementary education program. My teacher education has been upheaved by the pandemic. My student teaching placement got cancelled. In the semester where I expected to have the opportunity to teach more than I ever have, I haven’t worked with a single group of students.,  The secondary students in our program have been able to work with mentor teachers, so I was curious about what they are learning. I spoke with Maria Aguilera, also a senior at Vanderbilt, in the secondary education math program. We work together as research assistants on Project SIGMa (Supporting Instructional Growth in Mathematics), and we wanted to unpack some of her learnings from a semester in the online classroom. We sat down for a chat, and these are some of the key things we noticed.

Maria shared her experience applying her learning thus far about teaching in these unexpected times. Across our conversation, a theme emerged of pedagogical shift— transformation of all of her abstract knowledge about what an engaging, caring, conceptually-oriented mathematical classroom looks like.

Her first instinct when faced with the question of virtual teaching was to think about the different pedagogies she had been learning through her program and how to translate them exactly into virtual teaching. However, she soon realized that, instead of attempting to fit in-person teaching into this virtual space, she could embrace virtual teaching as something new. This was the first pedagogical shift. There would be some overlap, but this was an opportunity for all teachers, whether new or veteran, to be learners and collaboratively experiment with different pedagogies to discover what is effective, and when, in a virtual classroom.

So far this semester, Maria has felt supported by her professors, undergraduate cohort, and mentor teacher. Her mentor teacher has been a thought partner as they learn to navigate virtual learning together. Maria says that creativity is her strongest asset right now, as there is a lack of information about effective technologies and pedagogies for the virtual math classroom. With the resources that do exist, the overarching question about efficacy still applies: “effective for whom?” It can be easy to forget about all the non-content elements that make up teaching when you stare into a black screen every day talking to students’ floating profile pictures.

Building classroom community when you have never heard students’ voices or seen their faces requires another fundamental pedagogical shift regarding what community is and how it may be constructed. Maria has been thinking about the fact that her students still don’t know much about their classmates; some of them haven’t even seen their school yet or walked the hallways. She wonders what the impact of this is for the overall classroom community and what the transition to in-person teaching will mean for the community of learners. Will the students know their classmates? Will they want to engage in non-content related activities such as clubs or sports? 

A third pedagogical shift is around our notion of student engagement, which is being pushed beyond previous conceptions and understandings. Previously, student engagement was often gauged through physical and verbal cues, which inform the teacher of a student’s understanding, or lack thereof. Maria expressed that, in her program, she had been taught to use these visual and behavioral cues for confirmation of student engagement. However, now, she’s had to think beyond what she can see to understand student engagement; a task that requires creativity and courage. To her, student engagement now looks like student responses in the chat or sharing random memes/gifs to convey how they are feeling. Student engagement can also mean logging into the school online portal or joining the class call at 7:05 a.m., when class starts.

Even though so much is uncertain, including when schools in Nashville will return to in-person teaching, there are many lessons that Maria, as a pre-service teacher, is learning from this experience. For example, she mentioned learning how to incorporate technology and using it fluidly during live class sessions. It has also been remarkable how students have adapted to the new technologies her mentor teacher introduced at the beginning of the year, such as Peardeck and Desmos, and how these specific technologies allow her to provide more students with immediate, intentional feedback to an extent that was impossible during in-person teaching.

She is hopeful that some of the things we are attending to now will continue to be foregrounded when we return to in-person teaching. Maria has noticed a higher emphasis on social emotional learning and is considering how best to bring this attentiveness back into her secondary  math classroom, which can tend to be more content-focused. Maria and her mentor teacher begin classes with a daily check in where students pick a “would you rather” or drag an icon to an emoji to let them know how they are feeling at the start of class. These check-ins happen at the beginning and end of class, which is new. Maria and her mentor teacher ask students to give them a “temperature check” about their confidence about their understanding of a given topic. Our students are human beings first, and we are all given the opportunity to attend to this humanity, especially as we reflect on our own needs as humans.
 
Written by Maria Aguilera (@aguileramf) and Jess Moses (@Jess_Moses1)

The Global Math Department and researchers at North Carolina State University are undertaking a study to learn about teachers’ learning experiences from participation in the GMD. You can participate in this study if you have participated in the GMD as a presenter, attendee of a GMD conference, or reader of the GMD newsletter. 

We invite you to click the link to join the study as a participant and to learn more!

Click Here to participate in this study

Online Professional Development Sessions

Tongiht!

PCMI in the Time of Pandemic

Presented by Monica Tienda and Barbara Lynch
 

The Park City Math Institute (PCMI) is an intensive 3-week residential conference that’s been around in some form or another for 30+ years. The Teacher Leadership Program of PCMI offers a phenomenal professional opportunity for classroom teachers unlike anything else around. The global pandemic may have interfered with 2020, but come see what’s up for PCMI 2021!
 

To register for this webinar, click here.

Check out past and upcoming Global Math Department webinars. Click here for the archives or get the webinars in podcast form!

You can also visit our new YouTube Channel to find videos of past sessions and related content.

#GMDWrites

Centering #BlackMathWeek
 
Highlighted By: Sara Rezvi (@arsinoepi)

This month’s contribution to GMD seeks to highlight the grace, vulnerability, brilliance, and joy of #BlackInMathWeek. 
 
With permission from the organizers, I write here on why it matters to highlight and uplift these stories (especially as a non-Black person of color), and the importance of centering and standing in solidarity with Black mathematicians, math educators, and math ed scholars. 
 
Dr. Noelle Sawyer shares the following about #BlackInMathWeek and why it was created: 
 
Black in Math Week was November 8th – 13th, 2020! It was a week on Twitter to celebrate community among and uplift Black mathematicians. Black in Math Week is a part of a series of “Black in X” Weeks. They started with Black Birders Week after a white woman called the police on a Black birdwatcher in Central Park. You can find the page at @BlackInMath on Twitter. Throughout the week, the twitter page highlighted profiles of Black mathematicians, Black Mathematicians in the media, advice to aspiring mathematicians, a focus on Black math educators, and all culminated on a movie night on Friday November 13th with the Netflix Movie: Jingle Jangle: A Christmas Journey. A few of the organizers for the week were Marissa Loving (@MarissaKawehi), Candice Price (@916ice), Noelle Sawyer (@blkmathmagic), and Dwight Anderson Williams II (@mathdwight). If you’re interested in checking out what happened during Black In Math Week, search the tag #BlackInMathWeek for general posts, #BlackInMathRollCall to find Black mathematicians on twitter, #BlackInMathMedia to find appearances of Black mathematicians in the media, and #MyBlackMathJourney to see the stories that Black mathematicians shared about how they’ve gotten to where they are today.
 

Here are some must-read threads to check out:
 

Anna Gifty’s (@itsafronomics) powerful thread on representation and the microaggressions that occur in schooling and childhood connects to how racism and exclusion in math is reproduced. 
 
This tweet from @BlackInMath highlighting Dr. Candice Price’s (@916ice) work in mathematics by meeting a mathematician virtually. In the vieo Dr. Price talks about protein folding, topology, and network theory in environmental studies along with her WHY for becoming a mathematician.  #BlackInMathMedia
 
LaShonda Mackey (@msmackeymath) writes here on the importance of being seen mathematically by teachers and the impact of being challenged above and beyond a standard curriculum.
 
This thread from Dr. Brook Alemayehu (@bta77) on challenges, pushing through, intellectual humility, and finding a passion for teaching mathematics. 

Some ways you can center #BlackInMathWeek: 
 

1. Have students read Dr. Candice Price’s Favorite Theorem Blog post on Scientific American and give students the opportunity to reflect on favorite theorems or math observations of their own! This can be done for any age. Alternatively, there is a podcast. Check out: My Favorite Theorem Podcast ft John Urschel! 
2. Read through #MyBlackMathJourney. The hashtag offers insights on the realities of learning mathematics as a Black person.
   1. What are some common themes reflected here? Why does that matter?
   2. How can non-Black people show solidarity and push back against Black peers, colleagues and classmates being silenced, belittled, or harmed in math spaces? 
   3. How should mathematicians openly discuss the realities of racism in mathematics (and beyond)? What internal work and self-interrogation needs to be done? 
3. Listen to Black Math Ed Scholars and check out #BlackInMathEd. Create a watch party with other teachers at your school and have a conversation about the insights brought forth here by the scholars linked below: 
   • Dr. Nicole Joseph and her research on Black girlhood and mathematics
   • Dr. Danny Martin on the brilliance of Black children
   • Dr. Gloria Ladson-Billings on Building Culturally Relevant Schools Post-Pandemic
   • Dr. Zaretta Hammond on Taking the Distance Out of The Learning

The election and its aftermath are a mirror – one in which white people in particular, and NBPOC need to look at our reflections. We live in a country that is built on stolen land and stolen people, on genocide, enslavement, and the torture of Black people and of this country’s continued inability to reckon with that truth. The erasure, fragility, and defensiveness that ensues from this fact is why there were alt-right, white supremacist parties marching in the nation’s capital this weekend. 
 
How do these realities impact how you are interacting with Black students? What do they see when you say nothing in your math spaces? Math is and always has been political in the United States. The right to study fully, to equal access to education, to qualified teachers that see the full humanity and brilliance of Black children has remained out of reach both historically and in the present day. 
 
What are some ways that you can do better for Black people? Today? Tomorrow? Daily? Without gain for self? Without centering you? Without co-optation or commodification? 
 
How can you approach this work with humility, grace, and a genuine desire to do better (even if you might mess up)? None of us can do this alone, but it is incumbent upon us to NOT leave our current realities alone either.  

One of our Own
 

Last Saturday, on November 7th, the majority of news outlets following the election polls called the 2020 election for Joe Biden as the 46th elected President of the United States of America. And while educators may have been divided over the outcome of the election, there seemed to be a common chorus coming from teacher groups across the nation.

Betsy Devos, who served as the Secretary of Education, was consistently ranked as President Trump’s most unpopular Cabinet Secretary. Unfortunately, she was also one of the few who never got fired, making her tenure as SoE one of the longest. Her goal of dismantling public education through the use of corporate capitalism was met with constant resistance from educators across the system.

One of the reasons Betsy came under constant scrutiny from the education field was because of her lack of experience in a school setting. Devos was never a teacher, never worked in a school position, and visited very few schools in her time as SoE. In the last year of the pandemic, Devos used her political agenda to pressure schools to open full time, and then used the resistance from that decision to push for school choice options that allow federal, public funds to be used in charter and private schools, without accountability.

On November 7th, for the first time in a long time, educators heard an encouraging message involving public schools. President-Elect Joe Biden said, “Jill’s a military mom, an educator. She’s dedicated her life to education, but teaching isn’t just what she does. It’s who she is. For American educators, this is a great day for you all. You are going to have one of your own in the White House.” [emphasis added]
 
Whether Dr. Biden will have as much influence on education policy as has been anticipated will remain in question. But I can’t help but think of the relationship I have with my own spouse, and hope. My husband works in another social sector of agriculture. Our jobs are very different, and yet, over the course of our marriage we have found many common threads. 
 
After long days of teaching, I would come home and share my heart with him for my students; sometimes joyful, sometimes in sorrow. He has laughed with me at the jokes my students have told, and held my hand as I cried for the students that I lost. He listened as I told him how frustrated I was with the systemic injustices found in education, and vowed to help me find a way to help. Through those many conversations, he noticed how his work changed, how he began to humanize the people he was working with, to open doors for more people, to disrupt injustices head on. 
 
I’ll never forget the time we were with some friends who were championing school choice being open to all students because of the positive experiences they had with their own children. We listened quietly as several people advocated for the lack of accountability in school funding. During that conversation, he caught my eye, gave me a side smirk, and a wink. He knew I was ready to dismantle that entire conversation. And when the pause in conversation came, I didn’t hear my voice first. I heard his. “Well, actually…”
 
And then, I listened to the spouse of an educator speak to the alternative side of school choice with facts, statistics, and known injustices as if he had spent years studying. And in fact, he had. He not only listened to me, watched series with me like “America To Me”, but he took to researching so he was knowledgeable on his own. 
 
I remember riding home that night and asking him how he knew all that stuff about education. His response was, “Well, I guess when you’re married to an educator, you realize how important education really is, and it moves you.” 
 
This is my prayer for President-Elect Joe Biden. I hope that Biden himself has been moved by Dr. Jill Biden, simply by listening to her stories about teaching, to her frustrations with the system, and to her heart as an educator. I hope he goes home after hard days to hear her stories, and to remember why he needs to fight hard for teachers, students, and public schools. I hope he remembers he has someone who has done the work in the White House with him. And I hope that Biden’s administration and work in education policy show a direct link back to his being married to an educator, that he would see just how important education really is. 
 
She doesn’t have to be the next Secretary of Education for that hope to exist. She can simply be Dr. Jill Biden, married to Joe Biden, President-Elect of the United States of America.

Lauren Baucom
@Lbmathemagician

Online Professional Development Sessions

No Webinar this Week.

Check out past and upcoming Global Math Department webinars. Click here for the archives or get the webinars in podcast form!

You can also visit our new YouTube Channel to find videos of past sessions and related content.

Coming Next Tuesday: November 17th, 2020!

Park City Math Institute in the Time of the Pandemic

The Park City Math Institute (PCMI) is an intensive 3-week residential conference that’s been around in some form or another for 30+ years. The Teacher Leadership Program of PCMI offers a phenomenal professional opportunity for classroom teachers unlike anything else around. The global pandemic may have interfered with 2020, but come see what’s up for PCMI 2021!

Presented by: Monica Tienda and Barbara Lynch

To register for this webinar, click here.

From the Writing Team

Not Doing Math When You Should Be

 
I love math memes. Here is one that I recently saw:
 

I was amused by this meme because I knew that the result of the US Election was decided without the Nevada count: The President-Elect is Joe Biden, the Vice President-Elect is Kamala Harris, and the people of the United States voted out a failed fascist and overt racist. COVID can be stopped with masks and distancing, yet the sitting president* encourages mask-less gatherings (some of which become super-spreader events). The People of the United States deserve to vote, and voting by mail during a pandemic should not be a concern due to interference in the United States Postal Service. Families in the United States, irrespective of their citizenship status, deserve to remain together; we should not be caging children or losing track of the kids and parents separated from one another. As hard as it may have been to Cast your vote, it should have been easy to Decide your vote.
 
But. Over 71 million people voted for the pro-COVID, anti-USPS, cager/separator of children. donald trump has always been a loser. He aimed to enrich himself by running for president in 2016 without the goal of actually winning; it has been to the detriment of the United States, and the world, that he Lost at Losing and emerged electorally victorious. In 2020 he ran for re-election, but this time he wanted to win; as we now know, he lost like the loser he will always be. We cannot, as a nation, simply cast off those who voted for him despite these four years of intentional harm directed primarily at marginalized peoples. 71 million is simply too large a number. We also cannot “meet them halfway” on questions of fascism versus anti-fascism, or racism versus anti-racism. I don’t have game-changing advice on these voters right now. Not yet. Sorry.
 
What does “not doing math when you should be” mean? I have been doing math, incidentally, but it hasn’t been strictly school math.
 
There are a lot of current joyful happenings in the world of mathematics:
 

• I hope that you are following BlackInMath during this #BlackInMath week
• I was excited to see my former classmate-then-coworker Dr. Brandie Waid publish an NCTM MTLT article called “Supporting LGBTQ+ Students in K-12 Mathematics”
• There is great work happening on mathematical gerrymandering that goes way beyond the “ChartThrob” casting of some white dudes on CNN and MSNBC whose math amounted (mostly) to arithmetic:

In the tweet above, I mention that the most impressive mathematical feat of this election, from my perspective, has been the voter organization of Stacey Abrams and others. With two competitive Senate races coming up in Georgia this January, I urge you to engage with the math that you should be doing.
 
To that end (who are the “others” besides Abrams, you may be wondering), here is a spreadsheet entitled “Georgia BIPOC-led voter outreach organizations (created by They See Blue Georgia)” via Cathery Yeh:

I want to go back to “doing math.” I want to dedicate more of my brain space to teaching and learning and shifting school mathematics (including a longstanding battle against Calculus, as Nas discusses below). I want to do types of math that go beyond Nevada’s slow counting—no disrespect to counting. And: Now that we have lodged a major victory in the presidential race, we need to do the math on how to keep pushing the United States forward. That starts with the Blue State of Georgia, and continues with, for example, understanding that so many of today’s 16/17 year olds can vote responsibly in the 2022 midterms.
 
We must engage in the types of math that ensure we live the words of John Lewis, as Vice President-elect Kamala Harris quoted in her acceptance speech, when both reminded us that “democracy is not a state—it is an act.”
 
What is the math that you should be doing?
 
Benjamin Dickman [@benjamindickman]

 
Since my first middle school viewing of “Stand and Deliver,” I dreamed of taking calculus in high school and, much later, instilling the same excitement for college-level mathematics in my own middle school algebra students. Beyond Hollywood fantasies of rising from arithmetic to perfect AP Calculus scores in under two years, the expectation of taking calculus in high school has become all but normalized over the last few decades. Significantly, high school calculus is often promoted as a mechanism for both engaging historically underrepresented students in STEM and in increasing access to STEM careers. To both these ends, and with no disrespect to Jaime Escalante or my own wonderful calculus teacher, I propose an alternative: all students should be required to take a full year of college-level discrete math as their terminating high school mathematics course.
 
Arguments against the push to take calculus in high school often cite the rapidly growing number of seniors enrolling in calculus out of a desire to bolster their college applications despite inadequate mathematical preparation or interest. Consequently, as reported by the Mathematical Association of America, a large percentage of students who successfully pass the AP Calculus Exam retake Calculus I in college because university math departments often claim that even students earning high AP scores are still poorly prepared for college-level mathematics. With significant research and discussion around the detriments of tracking students, I am less interested in these elitist pushes toward reserving calculus for only the most mathematically “gifted” high schoolers.

Having been lucky enough to teach both a conceptual calculus course last year as well as the start of a discrete math course to seniors within our wholly de-tracked high school, I argue that discrete math is both the more equitable as well as the more rigorous option for students regardless of their post-high school plans.
  
Case 1: For High Schoolers Interested in STEM Careers
 
The entryway into coding afforded by the typical discrete math course renders it an obvious selection for students pursuing a wide range of STEM careers. Its appeal to students of pure mathematics, however, has historically been a bit more varied. Only ten or so years ago, my undergraduate math department—troubled by low student retention in the subject—opted to make discrete mathematics a required course for mathematics majors, their stated goal being to more adequately prepare students for advanced study in mathematics through rigorous exposure to proofs.
 
Despite skipping multivariable calculus and lower-division linear algebra, I found that my familiarity with formal logic as a result of taking discrete math enabled me to successfully complete the core upper-division courses for the major. In this way, discrete math provided more extensive exposure to the types of problems and reasoning I would experience as an advanced math student than my AP Calculus class. By contrast, students at my university who had excelled in calculus but had not taken discrete math or other courses building formal logic skills frequently expressed frustration at their upper-division math courses’ unexpectedly heavy emphasis on proofs. Offering discrete math at the high school level will not only provide more students with the requisite skills for success in future math classes but also a more representative view of what the field entails.
 
Case 2: For High Schoolers Not (Yet) Interested in STEM Careers
 
With broad applications in economics and other social sciences, calculus is often marketed to high school students seeking careers outside of STEM as a “necessary evil” that will benefit them in future research endeavors. By including units on combinatorics, Bayesian probability, and formal logic, discrete math similarly provides students with essential tools for analyzing “real-world” phenomena through a mathematical lens. An intuitive understanding of conditional probability, for instance, might go so far as to help patients decide on the best course of treatment. The importance of teaching logical deduction to all students prior to their high school graduation is particularly uncontroversial. (For a fun read on the topic, Professor Eugenia Cheng makes a compelling case in The Art of Logic in an Illogical World). 
 
Unlike calculus, however, the comparatively minimal prior content knowledge required for even college-level discrete math courses provides new entry points for students who have experienced limited past success in the subject. While the most common arguments advocating against high school calculus take issue with students’ insufficient exposure to intermediate algebra and trigonometry, discrete math defines all core concepts within the scope of the course. This quality allows students to explore a range of low-floor, high-ceiling non-routine problems early on with minimal anxiety. 
 
In all these ways, discrete math presents a unique combination of accessible, rigorous, and transferable skills and concepts that will universally benefit students regardless of their future career interests. If you are convinced and interested in designing a discrete math course (and possibly collaborating), check out this open-source textbook as well as this cool graph theory resource. 
 
Nasriah Morrison [@nasriahmorrison]

Online Professional Development Sessions

Tomorrow Night at 9:00 PM EST

Breakout Rooms for Teaching Math

Teaching mathematics includes student to student collaboration. Learn how to create structures that keep students focused, positive, and talking in breakout rooms. The gradual release structures can be used in any grade level.

Presented by: Theresa Wills

To register for this webinar, click here.

Check out past and upcoming Global Math Department webinars. Click here for the archives or get the webinars in podcast form!

You can also visit our new YouTube Channel to find videos of past sessions and related content.

From the Writing Team

We Need Each Other More Than Ever
 

How are you doing?
 
This question has taken on new significance in these past months. What is ordinarily somewhat superficial demonstration of care has taken on new tones of concern.
 
Since March, my doctoral student Katherine Schneeberger McGugan and I have been following a group of secondary mathematics teachers who are all teaching remotely this fall. Katherine has been interviewing them as they manage their work in the strange new world of pandemic teaching, and we write each interview protocol to start with the sincere version of the question, how are you doing?
 
The title of our study comes from something a teacher told us in our first round of interviews last spring: we have a whole different job now.
 
And it’s true. We used to think of students as absent or present. With online teaching, students are now absent, logged in with camera off and not engaged, logged in with camera off but engaged, and logged in, camera on, and engaged. Remote lessons take two to three times as long to plan for, since it is so much harder to improvise discussions or the sharing of work –– oh, and you need slides for so many things that could have been communicated in other ways. Those informal interactions we had with students really shaped our relationships. The quick doorway talks helped us develop relationships with students more than we realized. How do you have those quick asides –– those little check ins –– as students enter or exit our space, when that space is virtual?
 
Teachers also report a few upsides. A lot of them tell us that they are learning and loving new technologies, especially Desmos. Some of them are finding meaningful collaboration with department colleagues as they share the extra burden of online lesson planning. Everyone is a first-year teacher now, one interviewee told us. People need each other more than ever.
 
Across the teachers in our study, it is clear that everyone is working twice as hard to feel half as effective at reaching their students and helping them make sense of the mathematics. If you find yourself in a similar situation, know that you are in excellent company. If you have wisdom to share, we invite you to please do so with the Twitter hashtag #zoommath and tag @GlobalMathDept so we can help get it out to the community.
 
We really do need each other more than ever, because everyone is a first-year teacher now.

Written by Ilana Horn (@ilana_horn) with contributions from Katherine Schneeberger McGugan (@kath_schnee)

Who Counts?
 

“Counting is hard”. This is a common quip among combinatorialists. It plays with the idea that counting is something we learn early on in life, and yet there exist counting problems that can challenge us to our core. 
 
I am writing this on the Sunday night before an uncertain and high stakes U.S. election. Counting is on my mind. Counting is hard. No better time than the present highlights the challenges inherent in counting.
 
But more difficult than the act of counting is the question of who counts. Having privilege means that one rarely has to think about this question. But this question has been and continues to be a source of violence and oppression, both in terms of who gets to do the counting and who gets counted. Let’s do some counting now: 
 
One: settler colonialism (who counts as human?)
   Two: slavery (who counts as property?)
      Three: ownership (who counts as a property owner?)
         Four: suffrage (who counts as having a voice?)
            Five: census (who counts as existing?)
               Six: coronavirus (who counts as worthy of care?)
 
Who counts? This has always been an open question. From the civil rights movement and the courts, to the voter with a ballot and the voter with an open carry firearm, people have always wrestled with questions of counting because for many people, counting is a matter of survival. Counting is often the difference between oppression and liberation. Today, counting is the context through which people are enculturated into our neoliberal traditions, but counting is also a potential tool for protest, accountability, and collective action.
 
Counting is political. Can one escape this? I do not think so. Always, counting is haunted by implicit choices about who gets to do the counting and what is worthy of being counted. We cannot escape the question of who counts. Instead, we are forced to confront the act of counting not only as a technical challenge but also as an ethical one. Counting, ethics, justice, power. At first, one of these words does not seem to belong. I believe that part of our work as educators is to convince people otherwise.
 
@melvinmperalta

On the eve of Election Day in the United States we know that the good people of this community don’t need to be reminded to get out and vote.  However, we thought this might be a good time to take a look back and remind ourselves that math is political, teaching is political, and, now more than ever, rest and self-care are essential.  What follows are three articles from early this year that are on our minds as the election approaches.

From Melvin Peralta on 8/11
 

Math is Political

That’s it. That’s the article.
 
Sometimes, when people see the statement ‘math is political’ they either scratch their heads or run for the hills. What on earth does 2+2=4 have to do with politics?
 
Well, it turns out a lot. As an ongoing Twitter debacle about 2+2=4 makes evident, math has a lot to do with politics. I won’t link any threads or articles about the 2+2=4 issue because many of them appear to miss a significant point: a widespread philosophical argument about mathematical foundations and objective truth has been built on a foundation of harassment aimed at educators of color, many who are women. 
 
Prominent articles and Twitter threads, while helping people become more receptive to a more “playful mathematics” and understand mathematics’ cultural dimensions, are also contributing to an erasure of women of color by prioritizing mathematics over them and the ideas they are actually trying to promote. These ideas include promoting critical mathematics education, anti-racism, ethnomathematics, rehumanizing mathematics, ethnic studies, and social justice math, among many others. Here’s a collection of things to look out for or look more deeply into:

• Last Saturday, Dr. Nicole Joseph (@projnicolej) and Dr. Luis Leyva (@LuisLeyvaEdu) led the Math & Anti-Racism session of the National Educators for Anti-Racism Conference. Summaries of the conference can be found through the Educators for Anti-Racism Twitter account (@EdAntiRacism). Rachel Ernest (@rachelernst) has a thread about it. Conference attendees were asked to read Dr. Rochelle Gutiérrez’s (@RG1gal) article entitled Risky Business: Mathematics Teachers Using Creative Insubordination.

• Today (August 11) is the TODOS live session with Dr. Rochelle Gutiérrez where participants will reflect on ways to rehumanize mathematics. The live session will take place at 4pm PST / 7pm EST. Registration can be found through this tweet from TODOS.

• Benjamin Dickman (@benjamindickman) is looking for collaborators for an Algebra 2 social justice curriculum.

• Dr. Kari Kokka (@karikokka) has compiled a Social Justice Mathematics and Science Resources google doc.

• Dr. Tia Madkins (@ProfTiaMadkins) has compiled a list of Resources for Understanding and Supporting #BlackLivesMatter

If you want to support these efforts and the people who stand behind them, consider deeply engaging with the scholarship on critical math education, anti-racism, and ethnomathematics, encouraging others to do the same, and supporting school teachers who want to apply these ideas in the classroom. Recent events have taught me an important lesson, one that I have recently felt a visceral level: silence is complicity. Math educators are part of the same community, and while we may not necessarily agree on everything (which I believe actually makes us stronger), it is important that we step in and speak up for one another.
 
What’s one thing that the coronavirus and racism, homophobia, patriarchy, ableism, and postcolonialism have in common? Too many people still think they don’t exist. How will we as educators of math–the supposed last bastion of ‘rationality’ and ‘truth’–respond?
 

@melvinmperalta

From Hema Khodai on 8/11
 

Rest as Self Care
By: Hema Khodai (@HKhodai)
 

I constantly and continually fail at disrupting grind culture. It is a new practice to me, who glorified it not too long ago, measured my worth by it, and judged others by their inability to excel within it. Some label it as ascribing to the model minority myth, the desire to mitigate racial violence by leaning into whiteness. Some identify it as an immigrant mindset, an inheritance from those who traveled over distant lands and seas for a chance at survival. Some name it as a remnant of indentured servitude, memory that lives in bloodlines of survival inextricably linked to productivity. Some say I exemplify grit and resilience and have overcome so much adversity in my personal life. These romanticized notions of self-liberation through determination and hard work enmesh us deeper in capitalism, they lack a precision of language I attend to: grind culture is rooted in white supremacy.

Here are some ways complicity in grind culture appears in our lives with prompts to disrupt them:

• Upholding individual disruptors as paragons of antiracism and/or mathematics education.
  • Grassroots movements grow to a tipping point at which they become profitable. 
    • How might we show our appreciation and support in non-monetary ways or ways that sustain improvements in the living and working conditions for the communities we live and work in?
  • We are the sum of all of our interactions with the planet and its inhabitants. 
    • How do we meaningfully honour the communities and collectives that these individuals learned from?
    • How do we meaningfully honour the collective work of folx without coopting or profiting off their support and brilliance?
  • Classrooms (be they virtual or physical) are microcosms of larger society. 
    • Who do you uphold as a mathematician in your classes? Who remains invisible?
  • Indigenous, Black, and racialized folx often are not compensated for their labour in racial justice work. 
    • How might we measure our worth outside of capitalism?
• Uncritical consumption of self-directed learning. 
  • FOMO is real. 
    • How do we disengage from compulsive engagement with social media? How do we disrupt our performance of wokeness?
  • Greed is real. 
    • How do we selectively and collectively learn without signing up for every webinar? How do we share opportunities for coalition building?
  • Gatekeeping is real. 
    • Who do you invite to greater learning in your mathematics classes? Who remains barred at the gates?
• Constant striving to amass antiracist knowledge. 
  • Book Club Hopping is trendy. 
    • How do we intentionally plan time to develop our understanding of new knowledge and transfer it into our daily living?
  • Cultivating Genius is trendy. 
    • How do you uphold students and their lived realities as funds of knowledge over the mathematical canon?
• Lack of intentionality in the ways we move and live. 
  • Overscheduling is a thing. 
    • How do we hold healthy boundaries that promote collective well-being?
  • Controlling kids is a thing. 
    • How do you hold time and space for students to learn mathematics and identify as doers of mathematics?
• Endorsing the supremacy of mathematics.
  • Math is not neutral. 
    • How does your district use/misuse/abuse data to justify the back to school plan?
  • Math is not objective. 
    • How do you promote criticality in mathematical thinking over efficiency and accuracy?

 
What is the Plan?
 

 
What is your plan to start or continue discussions to illuminate for our families, friends, and colleagues the ways Black and Brown lives are regulated, directed, misinterpreted, and controlled and taken?
 
As we prepare for and start the new school year, knowing that in many districts Brown and Black lives continue to be placed at risk, considered to be expendable as we “hope for the best”, what is your plan for return to school?
 
What is your plan to contribute your labour and energy to the collective efforts of educators to abolish carceral pedagogy and imagine humanizing ways to teach and learn mathematics?
 
What is your plan to support the self-care efforts of Indigenous educators, Black educators, and racialized educators?
 
What is your plan to promote rest as self-care for yourself and your students? 
 
What is your plan to be a part of a collective that strives for liberation?
 

I humbly cite and uplift the work of Tricia Hersey (The Nap Ministry) and Awo Okaikor Aryee-Price (The Edu-Sage’s Companion) whose words and wisdom I learn from.

From Lauren Baucom on 10/27
 

Mathematics is political. 

Adolphe Quetelet was a Belgian statistician who was obsessed with collecting data about physical and social human characteristics. His preoccupation with understanding human growth led to what is now known as the Body Mass Index, but formerly known as the Quetelet Index. Yet, his main purpose was not to understand height and weight distributions among adults, but rather to define “The Average Man”. Setting distributions against the normal curve, Quetelet became hyper-focused on identifying what “The Normal Man” looked like in physical traits, and acted like social characteristics. But, in defining what is “normal”, one also defines what is “abnormal”. A quick google search for “the average man” quickly demonstrates how exclusionary it is to be deemed “normal” mathematically. Average according to these images means White, with brown hair, and approximately 5’10. Under this definition, the majority of the world is deemed abnormal. 

By placing human beings on a binary scale, Quetelet introduced a new tactic for humans to assure that being White and male meant being the dominant human species, a tactic that could be measured precisely. Since then, the normal curve has been used to measure many physical and social attributes that were never intended to be placed on a binary scale, a scale that erases our diversity as a human race and creates a system of hierarchy. 

Occuring in the 1830’s, Quetelet’s work was not the first to use mathematics for political purposes and it certainly hasn’t been the last. In more recent times, the mathematics behind algorithms has been used for many political purposes, including policing systems that disproportionately target communities of color. In the last 6 months, the politicizing of mathematics has been increasingly evident with the various ways of counting COVID-19 cases, or even the lack of reporting the data at all. Many of the decisions of how to count and what to report have been tied to who was in power of the state government, rather than what mathematics to use. 

In many ways, understanding that mathematics is political can be turned into an advantage or a position of power. Yes, Quetelet had a particular motive for using the Normal curve to define normality among humans; but in doing so, he also provided a way to prove the existence of massive inequalities along the socially constructed variables of race, gender, and class. As teachers of mathematics, we must reconcile the above cases where mathematics was used to help some gain and to oppress others, and we do so through this second reminder: 
 

Teaching mathematics is political. 

As teachers, we make hundreds of decisions each day on how and what to teach our students. Each one of those decisions is viewed through our lens, perspective, and past experiences. If we were taught in a room where raising hands was required to speak, we may use some of those same practices in our classroom. If we were taught privileging procedures and speed over conceptual development, this may show up in how we teach our own students. Failure to recognize the many, many decisions that we make each day in our teaching practice is a dangerous path, one of which begins to “normalize” what we do, and abnormalize the work of other teachers. 

For many of us, the curriculum that we use is decided for us. Many curriculums have a particularly political perspective that is viewed through the lens of what I am calling, “Mathematical exceptionalism”. Mathematical exceptionalism seeks to normalize the learning of mathematics as a sterile, benign learning process based in objectivity. Mathematical exceptionalism completely denies the privileging of White, Eurocentric, male mathematicians in curriculum, pedagogy, and access to upper level mathematics courses. Similar to the work of Quetelet, by using the Mathematical Exceptionalism lens for teaching mathematics, as teachers, we simultaneously define and counter-define who math is for and who it isn’t, to the detriment to the majority of the world who do not fit this definition of “normal”. 

The same is true not only for who we show can do mathematics, but also for the context we use to teach with. We must be careful not to repeat the mistakes of former mathematicians: to define some of mathematics as “normal” and some of mathematics as “socially just”. Teaching students to understand and act on the mathematics of known injustices is just as much mathematics as teaching students the quadratic formula. By ab-normalizing mathematics centered on justice, we place it among the outliers and define those who teach this way as “different”. Recognizing the diversity of mathematics brings beauty and awe. As math teachers, it is just as much our job to celebrate the diversity of mathematics itself as it is to celebrate the ways and contexts with which mathematics can be taught. 

It’s time to remember that math in the math classroom has always been political. Let’s honor the diversity of mathematics by teaching in a way that celebrates “the beauty of the people around you”.  
 
And if you live in the US, don’t forget to vote. 
 
Lauren Baucom
@Lbmathemagician

Online Professional Development Sessions

Tongiht!

Promoting Mathematical Literacy:
What our students need to know, why they struggle, how we can help!
 

Learning math is complex and challenging. Participants will have the opportunity to consider what our students really need to know, why math is difficult for many students, from social, emotional, and environmental elements, to the learning profiles for dysgraphia and dyscalculia, and how we can best support our math teachers and diverse learners.

Presented by: Mindy Adair, PhD

To register for this webinar, click here.

Check out past and upcoming Global Math Department webinars. Click here for the archives or get the webinars in podcast form!

You can also visit our new YouTube Channel to find videos of past sessions and related content.

From the Writing Team

This is the last newsletter you will read before the Presidential election of the United States of America begins on November 3rd. I take the timing of this newsletter as a huge responsibility to invoke thought in readers of the Global Math Department Newsletter, as we continue to make sense of how mathematics intersects with the world around us. And so, I’d like to start off with a reminder: 
 

Mathematics is political. 

Adolphe Quetelet was a Belgian statistician who was obsessed with collecting data about physical and social human characteristics. His preoccupation with understanding human growth led to what is now known as the Body Mass Index, but formerly known as the Quetelet Index. Yet, his main purpose was not to understand height and weight distributions among adults, but rather to define “The Average Man”. Setting distributions against the normal curve, Quetelet became hyper-focused on identifying what “The Normal Man” looked like in physical traits, and acted like social characteristics. But, in defining what is “normal”, one also defines what is “abnormal”. A quick google search for “the average man” quickly demonstrates how exclusionary it is to be deemed “normal” mathematically. Average according to these images means White, with brown hair, and approximately 5’10. Under this definition, the majority of the world is deemed abnormal. 

By placing human beings on a binary scale, Quetelet introduced a new tactic for humans to assure that being White and male meant being the dominant human species, a tactic that could be measured precisely. Since then, the normal curve has been used to measure many physical and social attributes that were never intended to be placed on a binary scale, a scale that erases our diversity as a human race and creates a system of hierarchy. 

Occuring in the 1830’s, Quetelet’s work was not the first to use mathematics for political purposes and it certainly hasn’t been the last. In more recent times, the mathematics behind algorithms has been used for many political purposes, including policing systems that disproportionately target communities of color. In the last 6 months, the politicizing of mathematics has been increasingly evident with the various ways of counting COVID-19 cases, or even the lack of reporting the data at all. Many of the decisions of how to count and what to report have been tied to who was in power of the state government, rather than what mathematics to use. 

In many ways, understanding that mathematics is political can be turned into an advantage or a position of power. Yes, Quetelet had a particular motive for using the Normal curve to define normality among humans; but in doing so, he also provided a way to prove the existence of massive inequalities along the socially constructed variables of race, gender, and class. As teachers of mathematics, we must reconcile the above cases where mathematics was used to help some gain and to oppress others, and we do so through this second reminder: 
 

Teaching mathematics is political. 

As teachers, we make hundreds of decisions each day on how and what to teach our students. Each one of those decisions is viewed through our lens, perspective, and past experiences. If we were taught in a room where raising hands was required to speak, we may use some of those same practices in our classroom. If we were taught privileging procedures and speed over conceptual development, this may show up in how we teach our own students. Failure to recognize the many, many decisions that we make each day in our teaching practice is a dangerous path, one of which begins to “normalize” what we do, and abnormalize the work of other teachers. 

For many of us, the curriculum that we use is decided for us. Many curriculums have a particularly political perspective that is viewed through the lens of what I am calling, “Mathematical exceptionalism”. Mathematical exceptionalism seeks to normalize the learning of mathematics as a sterile, benign learning process based in objectivity. Mathematical exceptionalism completely denies the privileging of White, Eurocentric, male mathematicians in curriculum, pedagogy, and access to upper level mathematics courses. Similar to the work of Quetelet, by using the Mathematical Exceptionalism lens for teaching mathematics, as teachers, we simultaneously define and counter-define who math is for and who it isn’t, to the detriment to the majority of the world who do not fit this definition of “normal”. 

The same is true not only for who we show can do mathematics, but also for the context we use to teach with. We must be careful not to repeat the mistakes of former mathematicians: to define some of mathematics as “normal” and some of mathematics as “socially just”. Teaching students to understand and act on the mathematics of known injustices is just as much mathematics as teaching students the quadratic formula. By ab-normalizing mathematics centered on justice, we place it among the outliers and define those who teach this way as “different”. Recognizing the diversity of mathematics brings beauty and awe. As math teachers, it is just as much our job to celebrate the diversity of mathematics itself as it is to celebrate the ways and contexts with which mathematics can be taught. 

It’s time to remember that math in the math classroom has always been political. Let’s honor the diversity of mathematics by teaching in a way that celebrates “the beauty of the people around you”.  
 
And if you live in the US, don’t forget to vote. 
 
Lauren Baucom
@Lbmathemagician

Online Professional Development Sessions

No Webinar this Week.

Check out past and upcoming Global Math Department webinars. Click here for the archives or get the webinars in podcast form!

You can also visit our new YouTube Channel to find videos of past sessions and related content.

Coming Next Tuesday: October 27th, 2020!

Promoting Mathematical Literacy:
What our students need to know, why they struggle, how we can help!
 

Learning math is complex and challenging. Participants will have the opportunity to consider what our students really need to know, why math is difficult for many students, from social, emotional, and environmental elements, to the learning profiles for dysgraphia and dyscalculia, and how we can best support our math teachers and diverse learners.

Presented by: Mindy Adair, PhD

To register for this webinar, click here.

From the Writing Team

Editor’s Note: This piece is submitted by a guest writer, Paige, who is a second year graduate student studying mathematics.
 

The Choice to Stay

This piece is inspired by Benjamin Dickman, who reminded me that I am a normal person, and to whom I said the phrase “I have to prioritize my safety and sanity over my learning.” My call to action: If we want to teach and learn math with humanity, we need to recognize the humanity in others, and act with humility ourselves.
 
When I was in undergrad, I read Judd Apatow’s “Sick in the Head”, and I was inspired. I identified a lot with his situation: he was a nobody in the comedy world, and he was staring up at the faces of giants. He could see people where he wanted to be, and getting the chance to talk to them, one-on-one, was like permanently moving to Disneyland. I used to dream about a project where I would go meet mathematicians at conferences and I would interview them. I held on to that dream for a long time. I used to imagine people would know my name as the author of that book, the person who interviewed the greats before they were great, more like an assistant than a fellow mathematician.
 
This book pretty much exists now, in the form of Living Proof, a wonderful book freely available through the AMS and MAA here. It has the stories of so many incredible mathematicians. But there’s something I couldn’t escape in reading it, and that was pain.
 
In the book I envisioned writing, there was mostly joy. The interviewees spoke only of a passion for the purest maths, lives well-lived, dreams fulfilled or nearly so. There was recollection, reflection. There were mostly older, white men. I didn’t realize this until much after the inception of my daydream, and this realization spoiled it for me. I’m still very proud of and impressed by those fictitious mathematicians I crafted life stories for in my head, but this picture I wanted to paint was woefully incomplete. It did what Instagram and other platforms now do to many of us, forcing us to compare ourselves to other people’s highlight reels, and upon the very natural conclusion of our own insufficiency, painting us into a very ugly corner of ‘not good enough’. There’s a reason I always imagined myself as the author of a book about mathematicians and not one of those interviewed – even in my own head, I didn’t – and don’t –  belong here.
 
It’s not that I don’t deserve to be here – I do. It isn’t that I don’t want to be here – I do! But it is undeniable that in most rooms, in most math spaces, I stick out like a sore thumb. And I’m white! I’m a domestic student. I have a supportive family, even if they all don’t know what I do and some of them hate math pretty vehemently. There are so many challenges I don’t ever have to face, and yet in each class I take I feel like there is a target on my back. I can feel eyes when I move or make noise; god forbid I have to leave lecture for any reason. This constant awareness, this hypervigilance, it’s pretty exhausting. Actually, it’s extremely exhausting.
 
You might ask yourself at this point, “Why is she here then? What is the point of this piece? Will she end with a heartwarming message about hope and perseverance?”
 
The answer to the last question is no. I don’t plan to pretend that things are going to get better for me. Statistically they won’t, and the world is (literally) on fire, so my optimism is actually at an historic low. But the answer to the first question I think is the most important: I’m here because I choose, actively and every day, that I want to be. I am not here because I didn’t know what else to do; the truth is to the contrary. I now spend a lot of my daydreaming hours thinking about all of the other easier paths available to me. I talk with my friends about backup plans. If you know me, you know that being a goat farmer somewhere near a National Forest where I bake bread and sell grilled-goat-cheese-sandwiches and coffee to tourists is #1 on the list. But I choose to be here! In this environment so filled with toxicity I often find myself choking on the fumes. WHY?
 
In part, it is my own stubbornness that keeps me here. I have started this degree, so I would like to finish it. But more than this, I love math. I cannot overstate this. It’s gorgeous! It is fun, and complicated, and silly, and technical, and hard! I adore all of those things. I love how deceptively truthful math can be. How obvious, how convoluted, how multifaceted. “Math” to me looks like a Monet, simultaneously chaotic and perfectly concordant. It’s a mess! But it’s *my* mess.
 
This passion, and to a degree loyalty, to math still is not the most important factor in my choice to stay. The biggest reason, the only one I can think of that really matters, is how much I love the people here. This is harder to describe for me. I could name some names, but it would just be a terribly long list of people you could easily find on Twitter. When I think of these people, how they have carried me, helped me, buoyed me, gratitude for them and for those who have laid the foundation on which I stand almost obscures my faculties to describe how much they mean to me. I also feel a very real and ardent responsibility to those who will come after me. How can I help them? How can I make pathways for them to walk, to smooth the cobblestones into cement for a more accessible road? What can I do that will open a window and clear the stale air that permeates our hallways; how can I keep them safe so that they can use all of the space in their hearts for loving the math and the people, instead of having to fill so many chambers with grief and despair?
 
The message in this piece you are looking for is here: we are struggling. Struggling to breathe, to be architects of our fields, to belong, to feel safe. If you take anything away from this, let it be compassion for those around you, and let it be an understanding. When you see the only (blank) in the room, understand that they are brave. They are courageous, and every moment in that room is costing them a great deal. Understand that their daydreams have been subject to so many revisions by an inescapable reality that they are actively dealing with grief. Give deference to all that, and be generous. Be warm. Follow @annegalloway’s poignant advice: “We’re all smart. Distinguish yourself by being kind.”
 
I still want to do that book someday. You can DM me if you want to share a story, or have a vision for how to peel back the Insta filter.

Paige [@paaiiigeee]

 
Several years ago I completed a superintendent-mandated PD series for a curriculum claimed to re-engage students with limited prior success in mathematics through real-world, “social justice-oriented” applications. The first model lesson – an exploration of police brutality incidence using measures of central tendency – was anchored by a video of a handcuffed man, facing a wall, being shoved to the floor and beaten by a police officer.  In the ensuing discussion among the mostly-white group, one teacher posited that the handcuffed man might have “deserved” to be beaten (“we don’t know what he said to the cop”), while another expressed her enthusiasm for the lesson (“I think students of color would feel their negative experiences with police brutality are being validated.”)  I was exhausted: by the video, the conversation, and 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.”
 
While recognizing that there are much better curricula (and, frankly, teachers) aiming to dissect issues of social justice and equity through a mathematical lens, I have since become much more ambivalent about the tradeoffs of doing so.  As an undergraduate I gravitated toward math classes and formal logic classes in particular because of the opportunities they provided for temporarily disconnecting from the “real world”; and, through teaching math in summer programs throughout college, I delighted in seeing my own students echo my thrill and frustration of puzzling through new concepts.  It was in seeing my students build critical thinking skills and newfound confidence through these tasks, though, that I first internalized Bob Moses’s views of how math education could also serve as a mechanism for social change – not necessarily through diving into questions of police brutality and disproportionate minority contact with the justice system (although there is, of course, a time and place for this), but through equipping students with reasoning skills, tools, and language for making sense of their experiences. I wonder, now, which students we are potentially losing as we increasingly prioritize math’s practical applications – even purposeful ones – over the creativity and freedom that the field affords.
 
– Nasriah Morrison [@nasriahmorrison]

On Saturday, October 17, I gave a talk at Elmhurst University with the same title as this GMD entry. You can find a link to the talk here or in the tweets below. (Note: I caution against interpreting the slides too literally; without the words that were spoken, it will be easy to read them out of context. I am looking into the possibility of securing a copy of the recording.)
 

 
Rather than personally expatiating at length, I am using the rest of my entry this week to paste an email, verbatim, that a conference participant sent me. It contains a request around potential collaboration, which I am hopeful that a GMD reader will take up! (The email address is included at the request of the writer.) When I asked this person around permissions for sharing the email, she responded with:
 
“You have my permission to use any and all of my email – feel free to edit it down as needed or keep it in its entirety. I might add to it that I had only just begun to wonder if anti-racist/social justice math was even possible while a colleague in my PhD cohort shared about the Elmhurst NOYCE conference. It was surprising and then… I’m not sure of the right feeling, maybe a relief, to find that it is indeed ‘a thing’ and there are already people working on it.”
 
Here is the email.
 
—
Hi Benjamin,
Let me start by thanking you for your presentation yesterday. It was so inspiring and useful. I am a (n informal) STEM teacher but I honestly tend more towards Science Education. I tell people I am infinitely creative when it comes to science and zero creative when it comes to math. I’ve been working to change that.
 
I just started my PhD in Diversity and Metropolitan studies at the University of Alabama at Birmingham. I tell people it is essentially social justice through education. I am White and grew up in a liberal family; in the past year or so I’ve finally learned the depth of my privilege and how ignorant I was – thinking that because I am a BIPOC ally, I was not part of the problem. I’m working to fix that too ? My 4-month old son is bi-racial, bi-national, and multicultural. I don’t do this work for him, but he is certainly always on my mind as I think about the world I want him to join. It is also because of him that I have to ask you to excuse grammar, spelling, and concision errors here – as a new mom, PhD student, and full-time worker, I have very little free time or mental bandwidth for anything outside of survival mode.
 
I have a project I keep trying to get someone to do and I haven’t found a good setting for it yet. I thought it might appeal to you and I’m sure you could refine it to make it much better. If you’re interested, maybe we could partner, you pilot, I might be able to help fund materials, we co-author a freely available lesson plan and/or paper.
 
The basic idea is students create a 3D soundwave. This can be done with 3D printing, paper, washers, beads, or even these vulcanite discs from Ghana (https://www.etsy.com/listing/486931111/14-mm-african-vulcanite-vinyl-disc-beads?ref=user_profile)
 
There are instructions both for building the wave as a series of discs and as a whole 3D unit – I like the discs because of the opportunity for circle math, ratios, etc.
 
The sound could be anything – a loved one saying “I love you,” a clip of an inspirational speech, their best friend’s laughter. You could go for an environmental justice route and capture the sound of endangered animals, like a whale’s song, or the sound of a mother polar bear humming to her cub to nurse. For social justice you might ask a question like: ‘What does it mean to be powerful?’
 
The waves can be bracelets, necklaces, keychains, or art. Here’s an example of it as jewelry: https://www.instructables.com/Waveform-Necklace-Bracelet/ and here is an art instillation of Obama giving a State of the Union address: https://3dprintingindustry.com/news/obamas-3d-printed-voice-unveiled-3d-printshow-20013/
 
I think it has the potential to be very powerful and meaningful. I think about cultures with traditions of oral histories, how music and speech move us, and stories of people saving voice messages from deceased loved ones. I realized one night while talking to my grandmother that I didn’t have a recording of her voice. I was too shy to just ask her if I could record her saying things, so I took out my phone and secretly recorded our conversation. In the background is the staccato interruption of her oxygen machine, but I treasure it because it is one of the only recordings of her voice. Why didn’t I do it sooner, or more frequently? My dad read me the same stories over and over when I was a kid. One night I woke up crying because I had dreamt he was dead. I wrote him a letter the next day and asked him to record himself reading one or two of the stories so that I could always have it. He wrote back a lovely letter about how he doesn’t expect to die soon, but told me how much he loves being my dad. A couple of years later at Christmas he presented me with a CD of him reading the entire book. As a parent, I will leave my son many things like that to help him deal with the day I go; I don’t know why more people don’t do things like that for their children. Not that this project has to be about adults in your students’ lives considering their own mortality, but I wonder what kinds of treasures like my CD and Nana recording could come out of a project like this.
 
If you’re into it, I’d love to talk/brainstorm more. If not, no worries. Thank you again for sharing your lessons, wisdom, and experience with us. You have no idea of the value and inspiration.
 
Katie Busch [kabusch AT uab DOT edu]
University of Alabama at Birmingham
 
—
 
It is a wonderful feeling to receive a message like the one that Katie sent above. My thanks to Elmhurst University; conference organizers Dr. Robinson, Dr. Brown, and Dr. Cosgrove; the keynote speaker, Dr. Joseph; and all of the participants who have reached out to me through various channels before, during, and after my talk.
 
Closing remark: By the next time that I am up to contribute to the Global Math Department newsletter, the United States election will have already been held. As you can: Register to vote; plan to vote; cast your vote; and demand the votes be counted.
 
– Benjamin Dickman [@benjamindickman]

Online Professional Development Sessions

No Webinar this Week.

Check out past and upcoming Global Math Department webinars. Click here for the archives or get the webinars in podcast form!

You can also visit our new YouTube Channel to find videos of past sessions and related content.

From the Writing Team

Between pandemic life and a (perhaps consequent) twelve-second attention span, I haven’t been on Twitter much these days. But two threads last month did catch my attention.

1.  This tweet from Marian Dingle (@DingleTeach) directed me to Dr. Robert Berry’s (@robertqberry) talk entitled “Do Mathematical Practices Put Black Learners At Risk?” which continued a “conversation,” if I could be so bold as to call it that, with Lauren Baucom’s (@LBmathemagician) GMD post from February. They raise powerful examples of how mathematical practices can be used to analyze antiBlack racism but also, how mathematical practices can perpetuate antiBlack racism.

It reminded me of this experiment—a math education equivalent to the classic job applicant resumé studies—where teacher educators gave pre-service teachers a vignette describing a student who is “above grade level” but “disruptive;” when the student was identified as an African American boy, teachers were more likely to suggest that he be removed from the classroom, that he might have a learning disability, that he might need a positive role model, compared to when the student was identified as an African American girl, a White boy, or a White girl. (Aside: in the same book that published that study, Dan Battey (@DanBattey) and Luis Leyva (@LuisLeyvaEdu) have a chapter questioning whether teachers’ implicit racial attitudes might account for students’ mathematics learning as much as, or perhaps even more than, their mathematics instruction).

But more importantly, the question that Dr. Berry’s talk has lodged in my brain is: what else do we take for granted as being “good” in mathematics education—the way we (as teachers, as researchers, as a field) often assume that the Standards for Mathematical Practice can support student learning and also be helpful for teachers in making deliberate instructional choices—that can have consequences that reinforce racism or other systems of oppression?

2.  Christina Torres (@biblio_phile) provides a beautiful example of how to respond to someone who is offended by the idea of “politicizing” the classroom (Dan Meyer’s (@ddmeyer) latest blog post offers yet another entry in the lengthy “here’s why all teaching is political” column). I hope that someday I can be as gracious yet unwavering as she is.

Finally, if you’re experiencing the October doldrums, I’ve recently been thinking with some teachers about pedagogical responsibility and what matters most to them (as mathematics teachers) in this incredibly trying time. I’ve heard so many amazing teachers struggle with feeling like this year, for all the 2020 reasons, they’re not being the teachers they used to be or are capable of being, and worrying about burnout. First, if you’re feeling this way, you are enough, even though I don’t know how much doubt/frustration an anonymous person on the internet can really alleviate. But second, some of the teachers I’ve worked with have found it meaningful to name their feelings of burnout as actually being demoralization instead, using Dr. Doris Santoro’s (@DorisASantoro) study of veteran teachers (the introduction to her book is available for free here): burnout is an individual problem of individual teachers feeling overwhelmed and like they don’t have the capacity to continue teaching. Demoralization, however, is caused by systems, policies, and constraints that make it impossible for teachers to live up to their values at work. In this blog post, Dr. Santoro points out that demoralization is not a problem that can be solved by self-care, but offers some strategies that teachers in her study have used for re-moralization instead. That said, self-care matters too, so I hope you can find some moments this week for what matters to you, both personally and professionally.

Written by Grace Chen (@graceachen)

Online Professional Development Sessions

Tonight at 9:00 EST

What Works in Math Intervention

Presented by Sarah Powell

Many students experience difficulty with math and require targeted math support. In this presentation, we’ll focus on the design and delivery of math intervention. We’ll review how to select critical content to teach in intervention. Then, we’ll highlight five practices (explicit instruction, precise language, multiple representations, fluency building, and problem-solving instruction) with a strong evidence base for improving math outcomes for students who experience math difficulty. By the end of this presentation, you’ll know what works in math intervention!

Join us at 9:00 PM EST.  Click here to register!

You can always check out past and upcoming Global Math Department webinars. Click here for the archives or get the webinars in podcast form!

You can also visit our new YouTube Channel to find videos of past sessions and related content.

From the Writing Team

Hope is a discipline – a reflection by two math educators in Chicago
 
Sara Rezvi (@arsinoepi) and Joseph Ochiltree

Hope is a discipline. 
 

When I think of the word ‘discipline’, two meanings come to mind. The first – a practice, a commitment, a promise to keep at it even in spite of precarity and austerity. Not the gimmicky kind, the one that has a veneer of something more but turns out to be disappointingly superficial. No. That is not the discipline I think of, but I ascribe to a definition of practice, a promise that I make daily. To myself, to the students I serve, to the world I envision. 
 
The second definition – a function of control, a formatting power, a hegemonic violence –  what Foucault would call the ‘multiple forms of domination’. The kind that breaks people into particles and retrofits them into harm. 
 
It is the first definition that I choose to ascribe to as we unpack what this feels, sounds, and looks like in our daily teaching practices with our students. We pause and reflect about the importance of hope in our classroom spaces. 
 
Hope is a discipline. These words from Mariame Kabe, an organizer and prison abolitionist in Chicago, resonate with both Joe and I fiercely. Dr. Bettina Love, talks about hope as freedom dreaming, a radical act of imagination to extend beyond the violence of now into liberatory possibilities. These ‘dreams are not whimsical, unattainable daydreams, they are critical and imaginative dreams of critical resistance”, she writes (p. 101, We Want to Do More than Survive: Abolitionist Teaching and the Practice of Freedom).

Joe is a long-time high school math teacher in Chicago, and I am the program director of Math Circles of Chicago, a former high school teacher,  and a current doctoral student at UIC. We have been married for 12 years and counting. =) 
 
In this post, we try to make sense of what it means to practice hope as a discipline in a world that feels so precarious, and so lost. How do we practice this meaningfully, with grace and love for our students? Our communities? Ourselves? When we are splintering? Below are some snippets of our conversation that we recorded and transcribed to share with the GMD community below:
 
Sara: As a white, male educator, what does it mean for you to call yourself an anti-racist educator? What does that look and sound and feel like for you? Why are you choosing to do this? What are spaces in which you are continuously reflecting upon? 
 
Joe: Because I believe in it. I believe that I have to challenge myself to be explicit about it, to name it, to call out white supremacy for what it is, and how whiteness is perpetuated in math. As a teacher, I have to give my students the tools to combat this. At the same time, I have to be really careful and think about how I even make conversations like this possible in the remote setting. How do I make it so that there’s balance and purpose? Where there are moments and opportunities for hard conversations but that we have the ability to have fun and enjoy the beauty of mathematics as well? The number one thing I’m trying to be explicit about is that I value students’ backgrounds and cultures, that their identities and where they’re coming from matter, and that who they are and how they see the world is part of their family and part of the framework for their intellectual identity. 
 
Sara: So, what does that look like in practice? What are some moves you’ve made in class? How might that be hindered in the pandemic teaching we’re experiencing? 
 
Joe: The first thing that is coming to mind is a quote or paraphrase of Dr. King – ‘whatever the problem, the solution is community’. I want my 9th and 10th grade students to feel a sense of community, a sense of belonging, and hope with each other. At the same time, I am thinking about their academic identity development. So, for the last four weeks of school, my focus and emphasis has been on making it clear through the activities and norms we’re establishing that students’ ideas are valued, that their thoughts, even if they’re still forming, are important for the mathematical discussions we’re having. This is harder now that there are 20-35 rectangles that I try to keep track of for 6 hours each day – that I can’t put these norms up on the wall that students can see out of the corner of their eyes, but this has been my focus just the same. 
 
Sara: I know you used the website Mathematically Gifted and Black in your teaching. Can you say more about this? 
 
Joe: One of my students said the following this year, and it’s stuck with me. I’m paraphrasing here, but he said that as a Black teenager, that he has felt repeatedly that there is this lack of expectation for Black families to be intellectuals, to be thinkers. That he is really proud of all the learning and accomplishments that he’s made over his schooling, but that people seem to make assumptions that this is just not possible or true for kids like him. 
 
To address this, I can’t be performative. I can’t just say “Black Lives Matter” and be done with it. I have to practice that as well, everyday. I have to be in a space of learning with my students. 
 
 So, I had students go to this website,  Mathematically Gifted and Black, and asked students to find a biography of someone that resonated with them, to write a short summary about it, and then to present it to their peers. I did this because I am deliberately trying to combat the notion that mathematics only acknowledges the contributions of white men, and gives the message over and over again that this is the product of the minds of white men. Secondly, I want students to recognize and learn that every culture has mathematics that they’ve used for solving both practical and theoretical problems. That these contributions were critical to developing the mathematics we’re learning about today. 
 
Sara: And I would add that the storytelling that you are engaging in is a counterstory to the dominant perspectives in this country about what it means to be American, what it means to be in power, what it means to be in community with and with whom. Last question, what are three unique and distinct ways that you are showing up for and with your students in your classroom this year? 
 
Joe: Three things that immediately come to mind: 
 

1. People Over Math
2. Deliberate Focus on Cultivating Math Discussion
3. ‘Warm-Calling’ vs Cold-Calling

 
Sara: Sounds interesting! Can you explain briefly what each of these mean?
 
Joe: Sure, so, when I say People Over Math, I mean focus on developing the people side of my classroom before worrying about the curriculum, especially in this moment of great anxiety, grief, and frustration for my students. It’s a balance – I’m not forgetting about the curriculum or disregarding its importance, but if I have to choose between taking time in my class to address students’ needs regarding the Breonna Taylor hearing for example, I choose to do that instead.  I choose to center my students’ needs instead.
 
For the second and third one, I try to be deliberate when giving students a chance to respond. I say “I’m gonna give you three minutes to process”. I try not to talk a lot to respect that time. In pandemic teaching, I don’t know if they’ve heard me say I’m giving them 3 minutes to process – maybe the student stepped away to help a younger sibling, maybe the internet is fuzzy, whatever, so I’ll reiterate this in the chat as well. After the time is up, I use the responses I’ve gotten in Peardeck to ‘stack the deck’ in terms of sequencing a classroom conversation. I’ll ask students to share some of their brilliance with the class by ‘warm-calling’ on students. I think of warm-calling as a way for invitation rather than putting someone on the spot. So, I’ll say things like “I can see what you wrote, (student), would you be willing to read it or share it in the chat? You can say no and that’s OK” and what I’ve found more often than not, by respecting student agency and choice, students are more willing to share their thinking when they know it’s low-stakes and collaborative. 
 

Sara: Thank you for agreeing to co-write this with me, Joe. It means a lot to me to hear you reflecting about this intense school year, and how you are engaging in creating a space for students that is attempting to be warm, loving, and truthful from an anti-racist lens. I’m including what you wrote to your students on the day of the Breonna Taylor hearing, along with a link to the song you shared with them here: Anderson .Paak – Lockdown. I am hoping that we all continue engaging in active freedom dreaming, of collective liberation, of ensuring that mathematics spaces and beyond, as my professor Dr. Danny Martin would say, are worthy of Black & Brown children’s brilliance. 

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