PCMI in the Time of Pandemic – 11/17/20

PCMI in the Time of Pandemic 

Presenters: Monica Tienda and Barbara Lynch

Date: November 17, 2020

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!

Recommended Grade Level: 3 – 12

Hosted by: Rana Hafiz

Watch the full presentation at https://www.bigmarker.com/GlobalMathDept/PCMI-in-the-Time-of-Pandemic

This Week at Global Math – 11/24/20







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Curated By Nate Goza @thegozaway

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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)

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This Week at Global Math – 11/17/20







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Curated By Nate Goza @thegozaway

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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: 

 

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

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This Week at Global Math – 11/10/20







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Curated By Chase Orton @mathgeek76

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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]

The Cases for Discrete Math

 
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]

 

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Breakout Rooms for Teaching Math – 11/3/20

Breakout Rooms for Teaching Math

Presenter: Theresa Wills

Date: November 3, 2020

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.

Recommended Grade Level: K – 12

Hosted by: Sheila Orr

Watch the full presentation at https://www.bigmarker.com/GlobalMathDept/Breakout-Rooms-for-Teaching-Math

This Week at Global Math – 11/2/20







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Curated By Nate Goza @thegozaway

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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 mathematicsethnic studies, and social justice math, among many others. Here’s a collection of things to look out for or look more deeply into:

  • 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.

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

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