It’s been a year, friends. 

 

Although the last 365 days have felt more like a lifetime than a single rotation around the sun, that is exactly what it has been: one year since many of us began doing a new, difficult thing, learning new, difficult skills, teaching in a new, difficult way. With doing difficult things, the heaviness of this season has been ever present, like a weight sitting on the chest, preventing a full inhale.
 
Since President Biden announced the positioning of teachers as essential and therefore eligible for vaccination before the general public in their same age bracket, I have seen many a picture grace my twitter feed filled with hope. And since almost all of the last 365 days have brought with them a sense of dread and despair, I am thankful for the remembrance of hope. Each of your masked smiles, band-aid covered arms,  and “I DIDN’T THROW AWAY MY SHOT!” stickers remind me that hope is eternal. No matter how long we sit with despair, hope will return. 

 

 

I encourage you, friends, that with every “Second Dose Done!” tweet you see, you pause and rest in hope. Let it fill you up. Let it bring you joy. May you be encouraged. Even if you haven’t been offered your vaccine yet, may you receive the joy in being connected to the hope fulfilled from others. 

Lauren
@LBmathemagician

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#Eventmath: a math educators community resource for lessons paired with news articles and social media posts

“But the next thought I had really stopped me cold. I thought, ‘That’s the thinking we need to do in order to understand our national dialogue.’ I had not once, in more than a decade, taught a single student to do that thinking. I taught over a thousand students mathematics. This was the math they needed to be responsible citizens. And it’s not in our college curriculum. It’s not in the K-12 curriculum.

Jefferson knew that we needed an informed electorate to sustain our democratic republic. And part of that is mathematical knowledge. Where are we giving our students the math that they need to be informed citizens?”

That’s a quote from the beginning of a TedX talk by Dave Kung, Professor of Mathematics at St. Mary’s College. As Director of the MAA’s Project NExT, Dr. Kung has advised early-career college teachers. He also won a 2006 Teaching Award from the MD/VA/DC Section of the MAA. And here he is in this presentation talking about how, for a long time, he was failing students. (My words, not his.)

I first watched this video in December 2020, at the end of a semester during which I taught a “math for liberal arts” course for college students majoring in humanities. It’s a course I’ve taught for several years now, and I’m always tinkering with the subject matter and course design to make it better. But this video made me really wonder about how effective I have been at giving students the mathematical knowledge – and, moreover, confidence in that knowledge – that they need to make informed decisions in the modern world.

I tweeted about that video and how it made me question my teaching practices and course design. And that tweet sparked a conversation and some questions, including:

• Does there exist a living resource of examples that map important real world topics and current events to the standard mathematics curriculum?
• Where are these kinds of examples found, and how can we make it easier for instructors to find and use them in their classes?

Link to relevant Twitter thread:

This was the genesis of #Eventmath, an online repository of mathematics lessons based on current events, news articles, and social media posts. There are a few guiding principles of this project:

1. Students of all ages need to practice mathematical thinking in context. They want examples that are relevant and important to their lives, not contrived “real world” exercises in a textbook.
2. Dedicated math educators are already finding and sharing interesting examples that require mathematical thinking. For instance:
   • Dave Kung’s Tweet above mentions #MathForSocialJustice.
   • In the January 26, 2021 issue of this newsletter, Sammie Marshall wrote about “A Few Lessons from Recent Research on Social Justice Mathematics” and mentioned #socialjusticemath and #sojustmath.
   • Readers may also be aware of #takebackmath.
3. However, it is challenging for instructors to do this on their own, to keep finding good examples to use in their classes. Even after finding a good example of a news article or social media post to use, it can be hard work to craft a lesson plan around that example and to create meaningful assignments for students.
4. Some textbooks aim to teach quantitative literacy, numeracy, and mathematical thinking. For instance:
   • My Tweet above quotes the “Calling Bullshit” account which also has a book.
   • Dave Kung mentions the Common Sense Mathematics text from the MAA Press.
5. Alas, those texts are inherently static resources. Furthermore, not all instructors have the resources and/or freedom to choose such texts, and not all students have the ability to pay for such texts.
6. Therefore, it would be wonderful to have a resource that accomplishes the follow things:
   • Has lesson plans and assignments based on current news articles and social media posts, as well as relevant math curriculum content.
   • Is open and freely available to all instructors: anyone can find, use, and contribute to such a resource.
   • Is open and freely available to all students: the news articles and posts on which the lessons are based are not behind paywalls.

After looking around online, we found that no website currently accomplishes all of those goals. So, we want to build one! It started as a shared Google Doc, where Greg (@HigherMathNotes) and I worked on fleshing out two lesson plans:

One lesson plan is based on an activity I’ve done in that “math for liberal arts course” where we read an article from the Huffington Post that makes a claim about “voting power” in the Electoral College. We gather census data in a spreadsheet, perform calculations to quantify “voting power”, and then discuss the main claims of the article. This is the kind of numeracy and mathematical thinking that Dave Kung described in his video as what we students need to be informed citizens. But it’s also something that I developed over several semesters, tweaking the lesson, creating assignments and resources. Now, all of that information is described in the Google Doc, including a link to a spreadsheet with all the necessary data, so that an instructor does not have to reinvent this wheel. There are also links to relevant websites and YouTube videos about the mathematical content (proportional reasoning) and the “real world” content (how the Electoral College works).

The other lesson plan is based on a recent semi-viral Tweet that purported to show that Germany’s COVID-19 deaths are somehow comparable to the USA’s. I encountered this Tweet in my feed when I saw several people commenting about Riemann sums and calculus. Greg made this into a lesson that could fit in a precalculus or calculus course. It asks students to grapple with what the original Tweet is implying, to question how one might confirm or refute that claim, and then to use calculus-based reasoning and graphing to investigate further.

Okay, at this point, I hope I’ve convinced you of the usefulness and importance of having such a resource. You might also be thinking: “Wouldn’t a Wiki site make the most sense here? That way, members of the math educators community can find the site, consult the resources there, use them in their classes, and then edit the resources and make suggestions, based on their classroom experiences.”  To which I would say: Exactly! Now, here’s you can help with that …

We want to build the infrastructure for such a Wiki site, and we’ve applied for grant funding from the Wikimedia Foundation to do exactly that. Our grant proposal describes the vision for this resource that I have shared here, as well as how we will work to initially build the portal and teach people how to contribute to it. Importantly, we are proposing to create the infrastructure, not the entire site. The whole point of using a Wiki is so that this will be a living resource, sustained and updated by the math educators community. We don’t claim to be the arbiters of what makes for good content, and we certainly won’t be creating all that content. Rather, we hope to start building a place that all math educators can use, support, and develop over time.

We need endorsements and feedback on the proposal. From now until March 4^th, grant proposals are in Community review. The goal is for members of the relevant community (that’s you, math educators!) to comment on the proposal (which is a Wiki site, of course) so that the grant reviewers understand how beneficial this project would be for the community and whether it could be a self-sustaining resource in the long term.

Please go to the proposal site and look for the endorse and join buttons below the main info box. Click “endorse” if you’d like to add a supportive comment for the grant reviewers to see. (You can scroll to the bottom of the page to see an ongoing list of such endorsements.) Click “join” if you’d also like to add your name as an interested volunteer who would contribute this resource during and after its creation. Both of these types of support are helpful at this stage!

If you are able and interested, we would also appreciate constructive feedback on the proposal so that we can make changes before the next stage of the process. You can click the “Discussion” tab to open the “Talk Page” for the site and add your comments there for us to see.

We appreciate any guidance, support, and suggestions you might have. Thanks for reading.

Brendan W. Sullivan [@professorbrenda]

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An AMC for the Mathematics Community

 So you’d never drop a problem?
If it’s a math problem, it’s hard to get something that would make me drop it, unless somehow something was proved that said that it is not possible. To me, “drop” is a really strong term. Because what if in 10 years a new technique developed? It’s a new weapon, you should try it.
– Coach for the International Math Olympiad US team, in Quanta Magazine
 
Making mathematics more inclusive? It’s a difficult problem but not an impossible one. As a community, we have not exhausted our arsenal of weapons to fight for diversity, equity, and inclusion; even if it takes decades of work, we cannot drop this problem! Inspired by the MAA’s American Mathematics Competition, we invite the mathematical community to participate in the following exercise. Share your answers (full or partial) on Twitter with #GMDWrites.
 
About the Authors: We three authors met on Twitter in a thread about the Quanta interview. We decided to get together (on Zoom! on a weekend!) to talk about some of the exercises below, and we’ll continue to meet to formalize some of these thoughts into a letter to the MAA and to Quanta. We hope others will join us to continue this discussion, as each of the three of us carries the privilege of being a tenured white woman mathematician, and thus our perspective is limited.

Topics for this year’s exercises were retrieved from the Mathematical Association of America.

1. Community. Should we believe that “the best pre-college math students in the world” are represented in the International Math Olympiad (IMO)?

• What efforts are being made to create math competition teams for high school learners, especially those in underserved communities? About 6,000 secondary schools in the US have teams, but there are approximately 35,000 high schools in the US.
• Does there exist professional development with the explicit mission to build a network of coaches in a broader range of high schools?
• How can math competitions (including the AMC) promote more collaborative problem solving? How would this affect the community of participant.

• The MAA allows users to create a report to study the breakdown of AMC participation in terms of the gender binary. What could we learn if we could create reports along other axes of diversity (race, ethnicity, ability/disability, gender identity, socioeconomic status, geographical location…)?
• Since we do have limited data about gender… where are the girls? Why are they competing in the European Girls’ Math Olympiad?
• How could math competitions (including but not limited to the AMC) broaden access to mathematics?

• Who gets to represent mathematics in venues like Quanta? What does that mean for how mathematics is represented? Whose achievements are highlighted?
• How could the structure of, and participation in, the decades-old AMC to IMO competition pipeline reflect our changing society?
• Why does the MAA promote this competition instead of others? What does the participation and format of the AMC competition (multiple choice test where students work independently) communicate to K12 students and teachers about mathematics?
• How could the MAA celebrate and advance creative mathematical achievements of high schoolers beyond the six students celebrated at the end of the IMO?

• How could the AMC to IMO competition pipeline align better with MAA’s vision to use mathematics to “promote human flourishing”?
• Why does it cost so much to prepare? How could the MAA provide high quality, free resources for the broader community? What role could the US team’s coach have in providing these resources?
• What are the research-based instructional methods and resources that are being used in IMO coaching?

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The Profession of Education
 

This last week, Christie Nold (@ChristieNold) posted a tweet that went viral. In the tweet she responded to the idea of educators working over the summer, noting that we are all exhausted. Being asked to do additional work, which most of us already are in these days of hybrid learning, only raises our own awareness of the fatigue we all feel as we try to simultaneously survive a pandemic and educate children. 

 

The idea of students attending summer school is related to the new trend of discussing “learning loss”. For an excellent article on how the concept of “learning loss” is problematic, read this one by Julia Matthews. In it she states,

One thread that ties the exhaustion of teachers now and the made-up take on “learning loss” from the general public together is the deprofessionalization of educators. I wonder: 
 

     What would it take for education to be taken seriously as a profession? 
 
In March, April, & May, teachers were heralded as heroes. In August, when they asked for safe working conditions and guidelines during a pandemic, we were told we were lazy and didn’t want what was best for kids. And now, in February, a year from when pandemic teaching began, we are exhausted and asked to make up gains for children in an imaginary standard in order to appease the general public. How can the professionalism of a career that many claim is so noble and consequential for society constantly be the target for others to denigrate? 
 

• Is it because we don’t have a standardized process for measuring teaching professionally? Nope, we have that. (see National Boards for Professional Teaching)
• Is it because we need research that shows that teaching mathematics, knowing mathematics, and doing mathematics are inherently different sets of knowledge? Nope. We have that. (see Math Knowledge for Teaching from Ball, Thames & Phelps, 2008)
• Is it because we need a large social catastrophe that demonstrates the weight of the profession in general society? (See the ongoing global pandemic)

 
If we have all the receipts for our work, how come others readily choose to ignore it as such? 
 
Sometimes, when I have more questions than answers, I go back and look at the receipts, especially the ones that come from the students. Fawn Ngyuen (@fawnpnguyen) posted yesterday asking teachers to share a comment that a student said that still makes you smile. The post brought me laughs, smiles, and a few tears. Thanks, Fawn. 
 
Pandemically Pondering,
 
Lauren Baucom
@LBmathemgician
 

The Critical Ninth-grade Year: Learning and Grades in a Pandemic
 

I hated teaching 9^th grade math until I loved teaching 9^th grade math. Ninth graders have a lot of energy and innocence but most of all, they have curiosity about the world, about themselves and their peers, about growing up and becoming a part of the world, and some (few) were even curious about math. Ninth grade is a critical transition year for young people and more so if you’re Black, Indigenous, or a person of color (BIPOC); research backs this up even if it’s not surprising for any high school teacher who has worked for even one year in a working-poor public school.
 
This pandemic has me thinking a lot about 9^th graders whose only experience in high school has been online, not having opportunities to connect with their peers, explore extra-curriculars and sports and all the other rites of passages that come with transitioning from elementary to secondary. And not to romanticize high school in any way because a part of going to high school at least in places like Chicago also involves not being academically prepared for the demands of high school, challenges involved with navigating a new bureaucracy with its own set of norms and regulations, increased freedom, and not the least of it all, class content that quite honestly feels largely irrelevant for teenagers.
 
While most high schoolers may not drop out during their 9^th grade, students grades and GPA in that first year are consequential for graduating high school, college enrollment, and even college retention through the 1^st year. In their research report, The Predictive Power of Ninth-Grade GPA, the Chicago Consortium on School Research (CCSR) lays out their methodology and key findings that show the impact of a ninth grader’s GPA on the aforementioned outcomes. In their study that draws on data from over 180,000+ students across 8 cohort of students in Chicago from 2008 to 2013, ninth-grade GPA is a strong signal of what’s to come years later. The short of it is that the more we can help ninth graders experience success in their courses and freshmen grades, the more likely they are to stay in school and do well. The research base largely done by CCSR over decades now in Chicago Public Schools, has led to a key metric labelled the Freshman-on-Track metric that measures the number of students in a given school who have accumulated at least 5 full-year course credits and no more than one F in a core class. This metric has catalyzed freshmen teachers, administrators, and support staff to hone in on the 9^th grade year ramping up efforts to provide students with the necessary supports to meet the metric. Schools have created such things as Freshman seminars dedicated to making the tools and steps for success explicit for students, summer bridge courses for struggling incoming ninth graders, additional academic supports at the ninth grade, among others. A system-wide focus on improving the Freshman On-Track metric with coaching and professional development resources has resulted in sustained, system-wide improvement in graduation rates, college access, and college retention rates. The documentary The Second Window: How a Focus on Freshman Transformed a System details the research base for its success.
 
Given what I know anecdotally from having taught 9^th grade math for over a decade, in light of the amassing research underscoring ninth grade as a consequential year for academic success has me thinking a lot lately about ninth graders’ remote experiences with even stronger anguish. And while the above research tells us that ninth-year grades are key, remote learning has presented us with a unique opportunity to rethink the purpose and ways of education. I’m not interested in ‘learning loss’ as much as making a call to all ninth grade teachers to take stock of our classrooms, our students and their families, and even our own families and communities in the current moment. Although I recognize that we, as teachers, hold ourselves to high standards for teaching content, we must remember that we teach children and then we teach content. Although I truly believe that teachers of all subjects are making space for students to make connections and are attempting, in their own creative ways, to address students’ social emotional needs, I want to offer two ideas from my experiences having taught ninth grade for others to (re)consider:
 

• Humanizing through Relationships: While not a new or unique idea, it is worth saying it again here: we have to find a way to humanize remote and hybrid spaces by placing relationships and students’ voices at the center. Whereas before we may have dangled grades and rules to try to get students to comply, it is clear that relationships and responsiveness could not hold a stronger imperative. This means that we may have to (if we have not already) let go of our press to teach as much content. We might even resurrect the Coalition of Essential Schools principle of ‘less is more’ here. If students are not engaged authentically, they are not really absorbing our lessons in any meaningful or enduring way. In order to engage students and meet them where they are at requires courage and vulnerability to put the textbook down and, yes, talk to our kids. Engage them in the current problem of teaching and learning, however you and your students co-construct it. By opening a mutual dialogue with students, you are offering them a space to co-author a solution that has more potential to actually be a solution, even if only temporarily, because the students created it. But know that students’ disengagement is not solely tied to remote learning as the pandemic has overwhelmed the kinds of supports that young people, families, and communities used to rely on in the past. This dialogue may raise issues that feel (and largely are) beyond our control. That is okay but sometimes just giving students the space to air their feelings and grief is an important step moving forward, building a community of connection. We must also find ways to celebrate our students, for their resilience, for their commitment to show up every day, and for simply being who they are.

• Learning and Grades: I would be remiss to not return to the Consortium research cited above that strongly correlates grades with future academic outcomes. While there have been recent calls to radically transform our grading practices now more than ever, there has been growing evidence for some time now to support the ways in which our current system is antiquated, inequitable and even mathematically inaccurate (Feldman, 2019). Undoubtedly, schools have probably seen more F’s on students’ report grades at every level forcing administrators and instructional leaders to rethink their pandemic grading practices and, in some cases, even hold back students’ grades due to lack of assessment evidence as students turn in less and less completed work. I’ll offer here an alternative and fluent grade that we created at the Young Women’s Leadership Charter School (YWLCS) in 2000 called the Not Yet which incidentally Carol Dweck mentioned in her Ted Talk on Growth Mindset in 2014. Each course at YWLCS was tied to 8-10 outcomes (majority content-based with few behavioral outcomes) for which each student was given a grade among Highly Proficient, Proficient, or Not Yet. The girls (it was an all-girls public charter school) had essentially up until their Senior year to make up their Not Yet grades which required them to work with the discipline-specific teacher to make a plan to work on the content and make it up. There were benchmarks put in place to ensure we were not setting them up to make it too far along without any Proficient grades, but, for example, I could be approached by a student in Algebra 2 wanting to demonstrate proficiency in an Algebra 1 concept or skill. I might quiz her right there on the spot or ask her to do an assignment to demonstrate her competency. If she demonstrated proficiency, I could and would go into the system and change the grade. While this might appear overwhelming (and it was), we learned to be assessment heavy changing our instructional practices and shifting our conversations with students from completing work to demonstrating proficiency. This was significant and should not go understated. Not only were students talking about and demonstrating content, they internalized the notion that learning is ongoing and is based on effort not ‘smartness’. This assessment system, or at least the concept of a Not Yet, could offer our current students (9^th grade and otherwise) acknowledgement that we are going through a pandemic together and that we hold their social, emotional, and physical needs with the utmost regard. It is not that learning is not happening: we might even take stock of what we are learning and reassure ourselves that academic competencies will be learned, in due time.

Written by Patty Buenrostro

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February
By: Hema Khodai (@HKhodai)
 

• Whose stories do we continually leave out of policy in education? 
• Whose stories are routinely whitewashed in spaces of mathematics advocacy?
• Do we accept that we are pattern makers? 

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“Are you sure you’re in the right class?” My new complex analysis classmate had waited until I was seated, smiling gently as he asked. In each retelling of this now all-but-cliché micro-aggression (among others), I emerge victorious – armed with a savage comeback and the resolve to dismantle stereotypes about women of color in mathematics through my own achievements. In truth, I wasn’t sure that I did belong in that class; I had enrolled in the “honors” section only because the others were either full or conflicted with my work schedule. I remember little of my actual response beyond its awkward, muted rage, and the lingering self-doubts that my various forms of privilege and past successes in mathematics could not buffer against.
 
In the decade since, I sought to support my students, and particularly my female students of color, in cultivating the types of positive mathematics identities that I had struggled to maintain throughout my own schooling. Drawing from Dr. Erica Walker’s (@EricaNWalker) research on mathematics identity, I designed student reflections around their experiences with and perceptions of mathematics, hoping that routinely integrating stories of diverse mathematicians and mathematics origins would gradually shift their own narratives. I implemented further lessons, developed in collaboration with my Math for America colleagues, around Imposter Syndrome – seeking to address the self-doubts that continued to haunt our less confident students even after they had experienced success in our classes. It was disheartening to realize this year that, once again, our most disengaged and struggling students were disproportionately young women of color. Even successfully completing the most challenging problems and communicating their strategies to peers yielded only fleeting improvements.
 
I had assumed until lately that my own mathematics identity had finally solidified, equipping me with sufficient tools to support my students along their own math journeys. It was just this semester, however – upon enrolling in my first mathematics course as a doctoral student – that I recalled how stubbornly and insidiously one’s mathematics anxieties endure. I chose to take a mathematical foundations course with a favorite professor, having loved and enrolled in nearly every available formal logic course and set theory course as an undergraduate. Even so, I found myself paralyzed with self-doubt over our first assignment before so much as looking at the problems. Only at my friend and classmate’s commitment to attend office hours together did I work up the courage to go – again, despite already knowing and liking our professor. It is doubtful that any praise of my mathematics skills or recounts of past successes would have reassured me.

With new insights into our students’ experiences, and in coming to understand one’s mathematics identity construction as an ongoing (perhaps lifelong) process, I am left wondering how to shift beyond merely positive math identities and toward what Dr. Ebony McGee (@RelationshipGAP) terms “robust” mathematics identities: ones grounded in authentic enjoyment of mathematics and internal motivations to succeed as opposed to, for instance, disproving stereotypes or making one’s family members proud (see Figure 1 below for a summary of McGee’s (2015) Fragile and Robust Mathematics Identity Framework). Perhaps one step toward this goal lies simply in supporting our students in building and maintaining mathematics learning communities of peers they can relate to, as Walker has articulated. I can attest to the benefits of not only talking through problems with one’s friends, but also of rallying together to attend office hours and laugh at the occasional micro-aggression.

 
– Nasriah Morrison [@nasriahmorrison]

1. name a justice-oriented context to which their item connects, or in which they are interested;
2. look up who their House Representative is, and check Congress dotgov to see what connects to their item/context.

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Recentering
 

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

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

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

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The Narcissism of Mathematics Education
 

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

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Gratitude
by Amber Thienel (@amberthienel)
 

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

 

 

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

 

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

          

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

 

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

 

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

 

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

 
 

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

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

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

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

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

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We Who Believe
By: Hema Khodai (@HKhodai)
 

We who believe in freedom cannot rest.
(Lyrics)

Lessons for the After Times
 

These last nine months have been…not normal. We’ve changed and adapted almost every aspect of our personal and professional lives and dealt with immeasurable loss and grief. At times, it seems like everything is awful (and truly, many things are awful).
 
But throughout these Corona Times, I’ve wondered: Are there things that we’re doing now that we can hold onto, even after the pandemic is over? Things that will serve us well in the After Times?
 
An obvious answer is that we’re learning to use technology to capture students’ thinking. I teach pre-service math teachers, and my students have been learning how to use all sorts of new technology in their student-teaching placements. They’re using video tools like SeeSaw and FlipGrid to capture students’ mathematical thinking. This has given them more thorough explanations than when students were working with just pencil and paper, especially for early elementary students who can say a lot more than they tend to write. They’re also planning interactive and exploratory lessons with PearDeck and Desmos, especially in secondary placements. Tools like these show us what students are thinking about during the lesson, and they give students multiple ways of engaging (even with their videos off). 
 
We’re turning to these technologies out of necessity — because it’s so much harder to know what students are thinking when we only see them in a little Zoom box. But even when we can see each other face-to-face, what insights into student thinking can tech tools offer? What new learning opportunities can we foster?
 
But even beyond the tech, I think (I hope?) we’re learning to cut each other (and ourselves!) some slack. Everyone is experiencing the pandemic differently — and struggling in different ways — but it’s been a hard year for everyone. As a result, I’ve noticed that, when assignments are missing or emails go unread, folks are starting to ask “What’s wrong? Is everything okay?” We’re checking in with empathy, instead of assuming that others are being negligent or lazy. Perhaps because we’re going through a collective trauma, we’re more likely to give others the benefit of the doubt. 
 
I hope that we can continue doing that, even when there’s not a global pandemic. Even in “normal” times, students and colleagues are dealing with death and loss, racism and other systems of oppression, food and housing insecurity, physical and mental health crises, and existential dread. What would the world look like if our default was to reach out with kindness and concern?
 
We’re also learning to connect in new ways — and to disconnect when we need to. Personally and professionally, we’ve been able to connect with folks from afar. We can join webinars and conferences without worrying about the cost or time of travel. We’ve been celebrating birthdays and graduations and weddings (and funerals) with loved ones that we don’t usually get to see. And the flip side of spending so much time online is that we have to disconnect, too. It’s become even more important than ever before to take breaks from the screen and to get some fresh air. 
 
Some of these have come out of sheer necessity — singing “Happy Birthday” on Zoom because it’s too dangerous to gather together or taking a tech break because we simply can’t bear to look at a screen for another moment. But what if we can continue having joyful moments with far-flung friends and family? What if we can maintain boundaries for our work-life balance?
 
Of course, none of this negates what we’ve been through, what we’re going through, or what is yet to come before the pandemic is over.
 
But I’m holding onto hope: Hope that we can let go of practices that weren’t really serving us in the Before Times. Hope that we will make it through these Corona Times. Hope that we can re-imagine and build a more humane After Times.

Written by Brette Garner (@brettegarner) 

Encountering Boundaries of Human and STEM: 
Some Wonderings as Told Through Six Panels

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