This post was written by my dear friend and former colleague, current Standford graduate student, Emma Gargroetzi. I’m glad she wrote it for me! ; )
There must be something deeply attractive about the idea that children’s math success can simply be forced upon them. On Aug 7, yet one more opinion piece promoting drill and memorization in children’s math education was published in the New York Times. By the morning of Aug 8th is was trending in the #1 spot. In “Make Your Daughter Practice Math, She’ll Thank You Later,” Barbara Oakley argues for the importance of math in the lives of children. Unfortunately, she does so in a way that is fundamentally misinformed about both the landscape of K-12 mathematics education in the United States and the research-based consensus on learning theory and cognitive development. Also unfortunately, when an opinion piece is written by a professor, even though it is an opinion piece, the assumption is that it is based in research. People take it as truth. The stakes of this misconception…
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Having had the opportunity to meet Tricia Ebarvia in person at a Teaching Tolerance workshop in June, I have been reading her #DisruptTexts tweets and posts with interest, admiration and a little envy. A former English major, a part of my heart has always stayed in the literature place, and I love the work that Tricia and others are doing to transform the teaching of ELA into a more equitable practice. I am not without envy, however, because this path – content-wise – does not seem as clear to me as a teacher of mathematics, even though this work has been the lion’s share of my professional development for the last five or six years, and has been on my radar even longer. When I was a second year teacher in 2007, I discovered Jonathan Osler’s Radical Math curriculum on line, and volunteered to teach an elective course at my school with the same name. I borrowed liberally from Osler’s curriculum, incorporated a unit of study around the Jena 6, and the class – populated with students in need of ‘just one more math credit’ – was marked with lively discussion and high engagement. Unfortunately, since that time, I have not had that degree of freedom in creating my own curriculum and refining my early efforts; I teach in New York, land of the Regents Exam.
When I saw Dylan Kane’s post, Disrupt Math, thus, my interest was naturally piqued; I have been thinking to myself the last few weeks “Why don’t we have a hashtag like that? Where is this conversation in the #MTBoS?” Like Dylan, I am aware of the MTBoS Book Club, but the reading schedule during the school year was more with which I could realistically keep pace. Many of us are talking about equity, posting about equity, tweeting about equity. And that is important. But the conversation, in my mind, needs to develop some focus, or foci, because it is all too easy for us (and by us, I am referring to the white teaching community) to raise the banner of equity, proclaim ourselves proponents of social justice, consider ourselves woke, and assume our awareness is where it needs to be.
I want to conversations that center the learning of mathematics, and how all of our students should and can learn math, and what changes we, as individuals, can make in our classrooms and math departments to create spaces that are more equitable than the ones that currently exist. I want to share strategies and practices that ensure that all students are given voice in the mathematics classroom – things like mathographies and name tents, visibly random groupings, and vertical non-permanent surfaces. I need ideas for allowing this space to exist inside a classroom and school and system which lives by standardized testing, a place where I may need or want to stay for a myriad of reasons, one of which is not abandoning the students of color who remain there.
But before we do that, or while we are doing that, we need to ‘take fearless inventory’ of ourselves (referring again to my white colleagues) and of the system by which we benefit, and of which we are inexorably a part – the white supremacist system that runs on deeply embedded structural racism. Until we do that, in my view, we are only giving lip service to the idea of equity.
We need to let go of our imagined exemptions from this despicable system when educating ourselves – I am female, I am gay/trans, I am Jewish (or Italian, or Irish…), I have chronic health conditions – whatever you think your passport out of this may be, forget it. If we are white, we benefit from racist structures, and have privilege in too many ways to enumerate, or maybe even perceive. We need to work on lifting the veil for ourselves in order to equitably serve all of our students, else we run the very real risk of becoming well-meaning white saviours – something many of us were taught to be in our alternative teacher training programs. Well-meaning white folk are not going to help, and may even make things worse in the ignorance with which they approach the work.
So how do we do this? There is no recipe, no list of steps one can take, because this is a process, and the work is – wait for it – endless. (Sorry.) But like any process of evolution, there are levels of awareness we will reach as we re-educate ourselves. And while the picture of American whiteness and its concomitant history may be difficult with which to live and imagine yourself a part, I have found that it is the only way to proceed honestly.
I am not any kind of an expert. I am a middle-aged, cisgendered, straight, lapsed-Jewish white woman with health issues, who, recognizing that it was not my job to ‘save’ my students but rather to educate them as best I could, has taken upon a course of self-study in order to honestly see myself and the system in which I operate. I am grateful for anyone who has (knowingly or not) pointed me in the direction of resources with which to educate myself, or who has shared themselves and their stories with me – on Twitter, through blogs, PLTs, workshops – so that I might further open my eyes, and hopefully, help others open theirs.
Here are some resources I have used/am using/recommend:
White Fragility by Robin Diangelo – I am only several chapters in to this book, but every paragraph holds some resounding truth.
Revisionist History – Season1, Episodes 4 and 5, and Season 2, Episode 3 – These episodes from Malcolm Gladwell’s podcast explore how our educational system systematically overlooks students of promise who are poor and frequently people of color, as well as a deep dive into Brown vs. Board of Education.
Learning to Be White: Money, Race and God in America by Thandeka – this book by a Unitarian Universalist Theologian and journalist, explores the politics of between white in America.
This is a very short list of a myriad of books that I have read over the last ten years which have contributed to my growing awareness of my whiteness and the structural racism of which I am unwittingly yet undeniably a part. However, these particular books and podcasts have given me the clearest mirror in which to look. (Additionally, I am writing this post from Lake Dunmore in Vermont, and don’t have access to my bookshelves.)
I started out writing in response to Dylan’s post, and I want to go back there. Dylan poses three questions he would like to further discuss in order to explore how to achieve greater equity in mathematics:
Who practices mathematics?
How is mathematical knowledge created?
What does it mean to practice mathematics?
I think these are worthy questions which can help us as a teaching community begin to disrupt mathematics teaching as it currently exists in the United States (to make a sweeping generalization). But I believe that until we understand how we are cogs in what has become a self-maintaining wheel, and how we might disrupt the operation of that wheel, we cannot fully grasp, and thus begin to correct, the inequities in math education.
As I open up this draft page, WordPress prompts me to “Share your story here…”, and I immediately ask myself how much I want to actually share. I haven’t been writing much this year because most of what I’ve been thinking about and dealing with has been deeply personal and not laundry I care to air publicly (though I realize that allusion might in fact be hypocritical by definition). But Jennifer Fairbanks’s exhortation to write is irresistible today – I contractually have to be at school until 2 pm, with my only responsibilities to distribute caps and gowns finished at 10:30 am. What else do I have to do?
Professionally, I believe I did in fact achieve one of my goals this year – to see my students more clearly and improve my relationships with them. This isn’t an easy goal to measure, but I will use as data the name tents on which I left one slot open the first week of the term. I received helpful feedback from the students at the outset, and used the name tents to say goodbye to them on the last day of classes. The comments the students returned to me were like treasures – good wishes for the summer, thanks for playing music, gratitude for a good semester, accolades FOR deltamath, diatribes AGAINST deltamath, and most importantly to me, an acknowledgement that I care about my students. They felt it, and my goal was met to some degree.
So what about new goals? I became highly dissatisfied this year with my Algebra 2 curriculum. I’m pretty good at teaching it the way my school wants it taught (student learning as measured by the NYS Regents exam…a dubious standard but that’s a whole SERIES of posts), and keeping kids engaged in the process. But I haven’t been teaching in a way that I’m wholly (or nearly satisfied with), and I’m working on some strategies for next year.
The first relates to classroom culture; because classes and student schedules are juggled considerably during the first two weeks of school, it behooves me to keep up with the breakneck pacing calendar until equalization. But I’ve decided that there’s nothing to stop me from taking a ‘curricular pause’ AFTER equalization for some culture-building – think 100 Game, or Broken Circles, and Marshmallow- Spaghetti towers. It will be a welcome respite from the initial dive into procedural content as we settle in to the school year.
The bigger plan, and second strategy, I’ve been working on is entitled in my mind “Algebra 2 Going Rogue”. Even as I type that, it sounds way more dramatic than it may in actuality be. Going rogue, for me, means moving away from this (photo), and going BACK to teaching things the way I believe they should be taught – with inquiry, discovery, and with a deeply conceptual approach. I have a couple of BIG things I need to keep in mind while I am doing this – first of all, my school is not annualized, at least not for Algebra 2. This means my students will leave me at the end of the fall term, and I will get a mostly new crop of kiddies at the beginning of February. Second, they still need to take that darn Regents exam, and get a grade by which both of us will be evaluated – and that evaluation will stick with them (on their permanent transcript) longer than it will with me (I get re-evaluated each year, with every batch of scores). But here’s something else I know for sure – I can train people to do well on tests. Years of teaching AND tutoring have helped me hone some very fine test prep skills. If I am teaching for deep understanding, then test prep should be – well, maybe not a breeze, but it should follow the learning without too much trouble.
I need to re-examine and re-plan each unit as follows in order to meet this goal. I’m thinking I will structure the units as follows:
- Opening explorations for inquiry and question-posing
- Large exploratory task setting up need for content; discovery of content as applicable
- Instruction or rather ‘revelation’ of content
- Practice and application
- Assessment task
- Test prep and standardized assessment
I’m very excited by this model, and while it may not seem particularly revolutionary, it is for me, teaching in the traditional environment that I do. I’m confident enough in my knowledge of the curriculum that I can do this without doing my students a disservice on the state assessment. As far as my own evaluation – there are way worse things in life than disapproval for trying something new. I have the benefit of age and [sometimes unfortunate] experience to have shown me that. I’d rather be able to live with myself.
Speaking of living with myself, the elephant, for me, in this post, is my over-arching goal always- the Big One, the one that supersedes everything, and the objective that must be infused in everything I do, inside the classroom and out of it, and that is doing everything I can to disrupt systems of racism and white supremacy, particularly as they affect my students in my classroom. My summer plans include participating in (while facilitating!) a workshop on how these systems show up in my classroom and what actions I can take to undermine them in service of equity of opportunity for my students, past, present and future. Further, I hope to start a Critical Friends group at school in the fall, the goal of which would be to open up conversations about inequities at school, systemic changes which need to be made, and how to begin effecting those changes. I’m writing about it here to hold myself accountable.
In the meantime, I’ve got 4 days of Regents grading ahead of me, one more full day of classes (why, Governor, why???), and a homeroom day for distribution of report cards. Then summer, glorious summer.
I think I’ve got my work cut out for me.
This may be the most difficult post I have written, but I am committed to writing it, because, as Marian Dingle pointed out to me, the silence she noted after Danny Martin’s talk ‘Taking a Knee in the Mathematics Classroom: Moving from Equity and Discourse to Protest and Refusal” at NCTM Annual two weeks ago was disturbing.
I heard Dr. Martin speak on Friday, April 27, about 36 hours after the rousing keynote by Dr. Chris Emdin. I was mentally prepared for the keynote, because I watched his talk at SXSWedu last year, and I’ve read For White Folks Who Teach in the Hood..and the Rest of Y’All Too. I had read a brief article or two of Dr. Martin’s as well, but his articulate and academic writing, while powerful and moving, didn’t quite compare with the live
‘Pentecostal ‘preaching’ showmanship of Dr. Emdin. That all changed when I heard him speak. The subject of his talk – the mathematics education that Black children currently receive versus the mathematics education that they should receive – was both radical and logical. His language and examples were clear, compelling, and perhaps revolutionary.
I was deeply moved by everything Dr. Martin said, despite the fact that I may have no place in his vision. And I am not bothered by this (I think).
Dr. Martin’s talk addressed the brilliance of black children that goes unacknowledged, undermined, even attacked in our [mathematics] classrooms, and the violence and dehumanization on so many levels in [mathematics] education, which is rooted in both anti-Blackness and white supremacy. He asserted repeatedly (and correctly) that efforts at reform and discourses around equity in mathematics education manage to sustain themselves despite their failure to “respond to Black oppression and dehumanization” [quoting his slides] and ultimately preserve the status quo.
And he thus called for Protest and Refusal in the form of a Black Liberatory Mathematics education: ” the framing and practice of mathematics education that allows Black learners to flourish in their humanity and brilliance, unfettered by whiteness, white supremacy, and anti-blackness.” Dr. Martin outlined a Black Liberatory Mathematics education as follows:
“A Black Liberatory Mathematics education prioritizes liberation over integration and freedom. This form of mathematics education is skeptical of liberal notions of inclusion and equity, appeals to democracy and citizenship, neoliberal multiculturalism, and refuses all forms of systemic violence against Black learners. The freedom to participate, integrate, and be included into anti-Black spaces characterized by systemic violence is not freedom.
A Black Liberatory Mathematics education is designed and directed first and foremost by liberation-seeking Black people including parents, caregivers, community members, Black teachers and Black students.”
Dr. Martin pointed out that the fight for civil rights left behind a nation that remains segregated, with multitudes of black children living in poverty, and where life expectancy of African Americans has actually declined. He is committed thus, to a struggle not for civil rights, but for the “infinitely more important struggle for human rights”, and to an educational system that addresses the needs and brilliance of black children, as defined by their community.
I’m not going to paraphrase (or quote) more of his talk – I recommend you watch it yourself. It will be time well spent.
What he said resonated so powerfully with me – things I have seen in the schools in which I have worked, what I have read and observed in the media, what I hear people say – our system – the system of which I am a part, the system which gave my own [white] children a wonderful education – does not serve Black children equitably on so many levels. They are done ‘soft violence’ in terms of curricular tracking and reduced course offerings, and more overt violence in our discipline systems and routine treatment by deans and school security. So, yes, the answer may be Dr. Martin’s Black Liberatory Mathematics education. And the system he described – by and for Black people – does not include a role for me.
I knew this as I listened to him, and the inner [white] voice that kept asking, “but what about me? What can I do? How can I help?” needed to be silenced, and reminded, that this was not for me or about me. The first question from the audience at the conclusion of his talk was just that, “What can we do?” This question was not asked by a white person, interestingly enough.
Dr. Martin said, “Step 0: Hear me.”
So I am hearing, with, as he suggested, open ears and an open heart. I am reflecting on my piece in this complicated puzzle – an educational system which only serves some people well. To be honest, I’m not really concerned about my role in his vision, because I know it’s not about me, and I know that the way things are – well – it stinks for a lot of kids. I can’t be more articulate than that right now, but I know this to be true in my heart. Dr. Martin also said – and this continues to echo in my mind – “There is no road to justice. Justice is right here, right now.” (Again my apologies for poor paraphrasing)
I think that well-meaning white educators hearing this talk might feel bewildered, and at a loss with this vision that doesn’t necessarily include them or ‘need their help.’ But I think this is exactly the point. With a son about to enter school, Dr. Martin spoke about his decreasing level of trust with a system that provides neither democracy nor citizenship for all of its constituents. I have to honor this hugely intelligent man’s perspective and vision for Black children because he speaks things that I am sadly certain are accurate.
So, step 0: hear him. You can watch the video of his talk here.
…to be honest, I’m not completely sure. I love blogging, sharing my classroom and thoughts on education, participating in the online community that virtual though it may be also nourishes my professional soul.
But then again, I know the reasons. High drama at home, medical issues, making myself too busy for one more year, and a gnawing professional dissatisfaction for which I cannot envision a solution. Yet. (It’s the magic word in the classroom, isn’t it?)
I’m writing this post mostly for myself, to catalogue what is going well, and what isn’t, what I’m doing to help myself and my students, and what I could be doing as well (in those copious moments of free time between midnight and 5 a.m.).
What’s been going well in my classes this semester:
- better questioning, by both me and the students
- more use of whiteboards, vertical and otherwise
- more open-ended classwork
- stand and talks
- Beyond White Dudes bulletin board
- Introduction to Python
- student connections – I do enjoy those kiddies; they make it okay to get up at 5:20 a.m.
What’s not so great:
- I haven’t figured out how to effectively engage teenagers with Algebra 2 at 7:15 a.m. (As I type this, I’m thinking, seriously? Who thought that was a good idea?)
- I’ve got low participation in some classes despite my efforts to randomize questioning, intrigue and engage.
- On exams and homework, I have come across some pretty nasty cheating and copying (curse you, Photomath!).
- I feel increasingly constricted by the all-hallowed Pacing Calendar which prevents inquiry-based activities and by which I am continually judged.
- I also feel increasingly frustrated with administrative shunting aside of students and refusal to increase advanced offerings to all programs.
- As a result of #4 and#5, I am feeling ineffectual in the work for equity, especially locally (at school).
What I’ve been doing to keep my spirits afloat:
- I have been co-facilitating a book group at Math for America; we are doing a close and slow reading of Tracy Zager’s Becoming the Math Teacher You Wish You Had.
- I am the process of cooking up a great idea for a workshop this summer with a new online friend!
- I have been taking Geometry-oriented workshops at Math for America which involve paper-folding and needlecraft – they have been super fun and inspiring mathematically.
- I am working on my NCTM presentation with a wonderful colleague and dear friend – best way to stay in touch long distance!
- I play with my cats frequently.
- I lurk on Twitter, and when I dip my toe in the water, I am always invited in for a swim. It helps to know the community is there when I ready to join, even in my funk.
I don’t really like this post, and if you have read this far, I thank you profusely for listening to me whine. I kept looking at the date of my last post and feeling the pressure to write, even without anything concrete to say. Is this a mid-career slump? Am I getting too tired? Worn out by awful news day after day (answer: yes, but me and everyone else I know)? I never want to be that teacher (or person) who is complacent, and I know there are always new and exciting things to do (I’ve still got to try my Clothesline #1TMCthing). I’m hoping that writing all this down, and looking at what has happened in the last three months that is positive will help me finish the year with hope and energy for 2018. If I’ve learned anything, it’s that life is good and meant to be lived as well as we can, and for me, part of that is teaching – math and all the rest of it.
I’ve been tweeting about various highlights of the start of the school year – wonderful comments on name tents, successful ‘stand and talks’, the launching of “Mathematicians Beyond White Dudes”, and the “What is Math?” lesson. The last two in this list, I am convinced, has won me some engagement for which I might have otherwise needed to fight, if indeed those students were willing to become involved at all in my math madness. And I owe debts to Rachel Rosales, Sara Vanderwerf, Annie Perkins, and Brian Palacios for sharing their hard work so that I might improve my practice, and the educational experience of my students, hereinafter occasionally referred to as “the kiddies,” with great affection. I have hesitated to blog about all this, because I am standing on a lot of shoulders, and don’t want to claim someone else’s genius as my own (that, and the fact that my body is screaming from the enforced transition from an 8 am wake-up time, to 5:15 am, or, as appropriately dubbed by my daughter, ass o’clock.
But today I had a success that I am pleased to own. This is a lesson that flopped dismally last year which I was able, with reflection, to fix. In our department, we have debated the value of teaching systems of equations in three variables; we don’t do 3D graphing, or cover the equation of a plane, and opportunities for context are thus lacking. But the Math Overlords in Albany (aka the Board of Regents) have included it in the standards, which by the way, have been recently revised and renamed the Next Generation Learning Standards- but I digress and will only inflict THAT rant on close family and friends.
Whether or not I feel content is appropriately placed in the curriculum, I owe it to my students to prepare them for the gatekeeping exam they will take at the end of my course, and it behooves me to find some way to make the topic intriguing without having the time to address graphing in three dimensions, providing adequate context and background. Last year I came up with the idea of having the kiddies make up number puzzles. I opened the lesson with Task Cards; when students entered the room, each table had a different set of requirements of their card. I made sure my instructions were clear and easy to follow (famous last words, right?). Total flop- the kids had no idea what to do, and looked at me like I was speaking a language that none of them knew. I guess I was. After a little flailing about on my part, we abandoned the activity, and I launched into the very dry task of demonstrating how to solve a system in 3 variables.
Fast forward to Fall 2017. One year more experience, one more year of sharing online, participating in the #DITL (Day in the Life) blogging challenge, and attending high quality professional development at Math for America and being a part of that community. Another attendance at wonderful, inspiring Twitter Math Camp – probably most important of all – surrounded by friends, progressive teaching, and a group of educators dedicated to continual growth for both themselves and their students. A booster shot for my teacher soul, which I was terribly afraid was burning out.
Today, the 6th full day of school, I introduced Visibly Random Groupings in this class. I waited a week because this class is not in my regular classroom with its lovely tables, and we have to put the desks into groups when we enter. I’m still trying to work out the logistics in my mind of moving in and out of a classroom for one period, moving the desks, giving out cards for seating…I know there’s a smooth solution that I just haven’t envisioned yet (feel free to make suggestions!).
I began the lesson with a number puzzle above – it involved three numbers, didn’t necessarily require a system with three variables to solve. The kiddies got busy as soon as they entered the room. Several did write systems with three variables, and quickly substituted into them. Jonathan, my super-eager, super bright 9th grader in Algebra 2, asked if he ‘was allowed’ to solve it with just one variable. Pretty quickly, students arrived at solutions, and wanted to share them. We put some work on the board, discussed all the different strategies involved – guess and check, elimination, substitution – everything we had used when reviewing systems with 2 variables for the last two days.
Then I put this task on the board. I read the directions to them, giving them examples of what the result of each step might result be. I learned last year that it was crucial to the success of this task to be explicit – despite my faith in my students’ abilities, they needed some translation of what I was looking for; this leg up and the experience of the warm-up gave them enough support to begin to play without me telling them exactly what to do. The room was BUZZING. The kids debated which numbers to choose. They debated which variables to use. They wrote the systems and then tested them. Twice. And then I gave each group a small whiteboard on which to write their system. The groups swapped boards, and tried to find solutions. There were heads together, signaling across the room. Not a phone in sight. And I heard lots of great talk – students justifying to one another, arguing with each other. No one needed my help, so I walked around eavesdropping, and grinning. There was frustration and struggle, but the kiddies were so motivated to figure things out, that they took that frustration and used it to fuel another attempt. They took pictures of the whiteboards so they could continue working on them later. And I could see that the class NOW was truly primed for solving the more difficult systems that they will encounter on the state assessment. As the end of the period drew near, I presented an example of the type of system we would be working on next week, just to get them thinking. When the bell rang, several students stayed behind, continuing to work/argue/get excited about solving the systems they had traded with one another.
I’ve been working hard to incorporate engagement strategies and keep the kiddies talking about math to each other. I’ve seen enough positive action thus far to keep moving forward. I love the feeling of being so intentional and witnessing the results. Okay – I know the school year is only six full days old, but I’m on the right path.
A postscript that I’m trying not to dwell on: As of this fall, there are two tracks for Algebra 2 in my school: one for students who passed the Geometry Regents, and one for those who did not. (Students who retake the Geometry Regents and pass it in January can move from one track to the other). There are reasons for this that make sense and others with which I disagree. But the issue at hand is that many students were erroneously programmed in Algebra 2, and this is allegedly going to be fixed early next week – which means A LOT of students are going to be reprogrammed. I am currently teaching 2 sections of Regents Algebra 2 and 2 sections of non-Regents Algebra 2, and all this good work I’ve been doing of introducing my classroom culture and connecting with my students – well, we’re all in for some disruption. Wish me luck in weathering it all.