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Online Professional Development Sessions
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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.
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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.
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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)
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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
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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.
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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:
- 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
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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.
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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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