Rooting Out Opportunity Hoarding and Perverse Incentives in the Math Classroom

tl;dr   The incentive structure of the math classroom is broken.

I live and teach in a community where opportunity hoarding is rampant. Students hoard points as if they were drops of water in the desert.

This leads to some perverse behaviors in the classroom. Students who have mastered a task or level want to take their attention to other parts of their lives. Their attitude is, I finished MY work; therefore MY obligations to math class are done. Students who have almost mastered a task or level of a topic become demanding of my attention in infantile ways. As soon as they run out of ideas, they tug on my sleeve, demanding that I re-teach them (or re-re-teach them) individually or in small groups. They value productive struggle only up to the point where they get stuck. The most challenged students feel so ashamed that they don't even know how to get started or even minimally unstuck that they try to hide in plain sight.

In a word, the incentive structure here is truly broken -- and perversely so.

I believe this is because the incentives here are all based on an assumption of individual attainment.

To allow a culture of individual attainment (what score /grade/mark did I get?) is to be complicit with the toxic culture of opportunity hoarding that pervades our whole society. I believe that the drive to hoard opportunity is one of the most powerful factors underlying the culture of systemic racism and oppression in schools.

Dylan Wiliam talks about how feedback needs to be more work for the recipient, yet every working classroom teacher I know knows that you can't force a kid to read or digest the comments. This is especially true when you have massive classes. With 37 kids per class, it's just not feasible. Kids look at the score and move on.

In my view, this is because the incentive structure of the math classroom is wrong. Not only is it wrong, it is sick and toxic. And we need to rethink these incentive structures if we truly want math class culture to heal.

If my grade means I personally have mastered or not mastered a topic, then once I get the score I want, my job is 100% done.

My problem with this is that, from the societal perspective, that is not my job as a classroom teacher.

My job as a classroom teacher is to get everybody over the finish line at the highest possible degree of mastery. For this reason,  my classroom's economy of achievement needs to become more collective, and less individual. I need to cultivate an incentive structure of positive interdependence -- "I" don't win unless others win too. Then we all win together.

There are times in my room when we're 37 individuals and there are other times when we are one classroom community. This is how things work on teams and in organizations throughout one's life in the U.S. So if we're one classroom community, then we need every individual to be as empowered as possible to achieve at the highest possible level.

For this reason, I've been expanding my whole-class skills quizzes. For a compound, complex skill such as solving a multi-step special right triangle problem (with interdependencies along the way), the quiz that I give is one that individuals take but each person's grade is an average of the scores of all the individuals in the class.

For two days leading up to the quiz, we do intensive collaborative work, including reciprocal doing-and-teaching practices such as speed dating. We also have unstructured time in which students identify as tutors or learners and then work to help each other improve the overall level of mastery in the room.

Our goal is a whole-class goal of mastery -- not an individual one. The goal is to raise the overall level of mastery in the room. Our goal as a class is to get everybody's level of understanding up. If you want to sit off to the side and work on your chemistry homework, then you're going to have to answer to your peers -- not to me. And if you don't like the grade that the whole class achieves, then too bad. Positive interdependence rules the day.

There are always one or two students who are so addicted to the toxic culture of individual attainment that they object, demanding, "If I understand it and they don't, then why should I be punished?"

And I have to explain to them over and over again. I tell them, "That's an infantile perspective. The better-prepared everyone around you is, the richer and more powerful your own learning experience is going to be -- both now and into the future. My job is to provide you with the richest possible learning experience so that you can go as far as you want to go. My job is to set the floor, not the ceiling. And this is how I, as the expert on learning, am empowering us to raise the floor of understanding."

Our school is unusual in that students get to choose their classes, their sections, and their teachers. My classes are very popular and are always among the earliest to fill up.

I choose to use this platform and my privilege to educate them. I'm blunt with the students who complain. "Listen," I tell them. "You chose this section. If you'd prefer a teacher who only gives individual scores on everything and lets you work on your chem homework when you're done, then we should talk to Counseling and get you into a course section where your desires are going to be met, because that's not going to happen in my class. There are plenty of other kids who'd be happy to switch with you."

I realize this may sound harsh, but they usually come around. And the fact is that my job is not to give them everything they think they want but to teach them and help them get aligned with the reality of things as they are.

The results bear this out. The lowest average on this first whole-class score of all my Geometry sections was an 87. The highest was 93.7.

The number of "free points" I provide in other parts of my class (through professionalism, home enjoyment packet completion, etc) makes this a wash. Nobody's grade goes down because of anybody else, but most people's grade do go up because their understanding improves. And as I tell them over and over and over again, what they need to do to raise their grades is to improve their understanding. The structure of the whole-class skills quiz empowers them to do so.

There's also less cheating and more cooperation because the incentive structures are aligned with our better, saner values.

There is still a place for individual attainment. Unit tests are individually graded as is the final exam. But individual attainment is demoted in my classroom and is put into better balance within our classroom community.

Individual attainment and opportunity hoarding are symptoms of our society's sickness. If we want to heal our learning environments and improve outcomes, we need to be open to revising the unconscious, unspoken incentive structures that keep reinforcing the systemic oppression we need to heal from.

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FOLLOW-UPS:

@KarenCampe asks:
Wow this is amazing. Kudos to you for implementing something that really changes the game.
Do you have parent pushback?
— Karen Campe (@KarenCampe) January 19, 2020

I'm fortunate to have a lot of support from both site and district administration. In my view, this is a moral choice. My job is to create an equitable learning environment. If a parent were to insist on an inequitable learning environment for their child, I'm not sure what there is that we could do to satisfy them, given that this is public education.

Thanks for the question.

@timteachesmath asks:
Thank you for sharing! 
You've detailed your conversations with those 'done early'; 
what do those still learning think? Is there pressure to catch up, or a super supportive community?
— Tim (@timteachesmath) January 20, 2020

They appreciate that there is time and support being made for them to master what they find challenging. They want to learn the skills, but they get to do so in a way that does not punish them for needing more time or practice. They appreciate being part of the solution rather than part of the problem. And they are better able to participate and achieve their ends -- which is the goal. We are trying to normalize high achievement for everybody -- not sort out who "got it" first and who didn't.

Thanks for the question.

More on katamari and speed demons #MTBoSBlaugust

Gotta squeak this one in under the #MTBoSBlaugust wire. :)

In the world of meditation retreats, what I've come to think of as "Emotional Breakdown Day" of a five-to-seven-day sesshin is pretty much always on a Wednesday (or Day 3, if the retreat doesn't start on a Sunday). You can set your watch by this. There is something about getting psychologically and emotionally heated up that happens after you've been simmering for three days. I think this is true at all spiritual retreats around the world. At a three-day retreat like Twitter Math Camp, it comes at Day 1.5. All of a sudden, Twitter and blogs are flooded with snippets or full-on geysers of despair at how great everybody else seems to be doing and how totally crappy you [INSERT YOUR OWN NAME HERE] are as a teacher.

I have tried to learn not to take this seasonality personally, but it's hard not to. When you go deep, you get invested.

This cycle seems equally true for me during the school year. Week 3 is inevitably my emotional breakdown week. I can no longer keep up the pace (or the illusion of the pace) and the kids can no longer keep it up either. So things start to break. Students act out. Norms fall apart. I lose my shit.

This is just the nature of the cycle of practice. Like winter, or hurricane season, or the World Series, It. Happens. So the real test is how I am going to deal with it.

I changed the seating chart in 7th block and rolled out my best rethinking of katamari and speed demon problem-based learning practice (see "Lessons from 'Lessons from Bowen and Darryl'"). I put the speed demons with other speed demons so they would leave my katamari alone already. I want the katamari to learn how to trust their own minds, their own guts, their own hearts. They lack confidence. But put a bunch of them together, and they have no choice but to trust themselves and each other. Without the speed demons to carry them along, they have to think.

And I tell you, my friends, it was magical.

I revised the day's problem set to put the Important Stuff at the top (though I never label it as Important Stuff — that gives it too much weight for teenagers, plus too little weight for everything else), instructed them to get one table whiteboards, two markers, and a washcloth and I yelled, "GO!" I think the yelling is a particularly artful piece of instructional practice.

The room began to hum and glow in the late afternoon fog. This freed me to question and support the groups that felt particularly stuck — to help them get just unstuck enough to keep going.

They didn't even care when they worked beyond the time limit I had set for this work.

I especially loved the spontaneous alliances that formed across difference. After the first really juicy problem, two young men who hadn't said 'boo' to each other in the first two and a half weeks — a young black student and a Chinese-American student — gave each other a particularly complicated, multi-part handshake than made my heart smile. A table of girls cheered when they finished the same problem.

This is why I believe that getting students into a state of flow when they are doing mathematics is the most important thing. If you align yourself with everything we know is good and healthy and whole about doing math, then everything else will proceed smoothly.

#MTBoSBlaugust 3 - The Bumper Car Theory of Anti-Racist Training for Teachers and Staff

This one is challenging to write because I want to honor all appropriate boundaries while inquiring into my own personal experience of the process.

This next week, during our whole-school PD on Wednesday, we are embarking on our first year of a multi-year program of anti-racist training for teachers and staff. Earlier this summer, I was one of 25 teachers and staff from our school who attended the initial training, and naturally, nothing went as planned. Does it ever? Heavy Sigh. So this morning, we did our reset and met about our plan to do this training with our whole school.

The enterprise of confronting privilege to teach and learn about privilege is daunting, and it is unavoidable that many people who encounter this work will quickly get rubbed raw. In some ways, that is by design. You can't remain comfortable while digging into uncomfortable territory. But at the same time, conceiving the work merely as a project of "disruption" dishonors the good will and long-term focus of individuals who have come together on their own out of their own deep-rooted belief that we need to do better, both for our students and for ourselves.

So you can see how it's a complicated and messy process to get started.

Your face here

What I am coming to understand about it all is this: in order to have courageous conversations about race, we need to learn how to see our own personal invisible beliefs. These are hard to see because they are by nature invisible. They are blind spots. For example, as a high-status, highly educated white teacher, I tend to feel confident in sharing my views publicly; but at the same time, I struggle to keep my passion and confidence from appearing as arrogance to those with different patterns of privilege. And I'm just one individual teacher in a very large faculty. I'm sure that other teachers struggle to notice their own patterns of privilege. Plus the nature of the dominant culture in our school is unusual and complex. So all in all, learning to see the individual and collective belief systems and blind spots is going to be a real challenge. We are going to need to spend a lot of time in a space of collective and individual not-knowing, together. And I fully expect that process to be uncomfortable.

What strikes me most is that this whole process is like being in racial identity bumper cars. Like at a carnival. We need to expect to be disturbed and surprised and confused as we discover how other drivers in their own identity bumper cars interpret and experience life from their own points of view, because everybody is so certain that their own personal bumper car point of view is clear-seeing and constructive and intentional. But every time the ride starts up, whenever you try to steer your own bumper car, you cannot help but crash into other people's bumper cars. So the process of investigation is complicated because there is no way to step outside of the bumper car bumping arena while the inquiry is ongoing.

From the 30,000-foot perspective, I can see that the bumper car system is designed to thwart objectivity. In their own bumper car ride, nobody is 100% in control of their own bumper car. We all have our own projections and privilege and beliefs that we project onto every other driver who crashes into us. If you consider how the bumper cars are designed, you may understand logically that the bumping is unavoidable. But after you've been in the arena for a little while, trying to steer your own car for a bit, it becomes hard not to take things personally. It becomes impossible to avoid lapsing into the belief that other drivers are intentionally crashing into you to push you off course.

I think this model is especially true when you've got a large room full of public school educators — smart, highly educated, open-hearted people who do what they do out of dedication to learning and to contributing to the common good. The moment you start to prod individual teachers into seeing how they benefit from various networks of privilege, things get painful. People shut down or break down. And I've never yet seen it handled well. In our culture, teaching is already pre-constructed as a "Wretched of the Earth"-level of profession. Poorly paid, micro-managed, and bullied by corporate reformers and unelected politicians. What could possibly go wrong when you try to confront public school teachers about privilege?

So I think it is going to take a certain gentleness, determination, and persistence to help a whole faculty to see how we as individuals benefit from different forms and degrees of privilege, both in our school culture and in our society. It is also going to take chocolate and a whole lot of radically appropriate self-care. I am hopeful in the long term that we will make progress, but I suspect that in the near term, things could get messy. Still, I remain optimistic and curious to see how things unfold.

On using privilege to combat racism: a love letter to #educolor, from an aspiring ally

It has been inspiring this past week to watch my young fellow Princetonians confront the legacy of institutional racism that is quite literally etched into stone at my well-intentioned, sometimes clueless, but deeply beloved-and-worth-improving Princeton (link).  Cornel West captured my feelings well with his support.  It is possible to love an institution and, because we love it, want it to grow and improve our society and our world.

It has also been quite moving to watch my Princeton classmate, University President Chris Eisgruber, as he wrestles with these issues in the public eye, working through layer upon layer of unconscious white privilege and commitment to anti-racist education. It has been impressive to see him come through it with open-mindedness, wholeheartedness, and a willingness to listen deeply, responding with integrity, and widening our commitment to inclusiveness at an institution that has not always supported inclusion. This is what I consider to be "Princeton in the Nation's Service."

So it was utterly disheartening to wake up this morning to a hate-filled screed on our Princeton Class of 1983 Facebook page from a different classmate of ours — a white woman who is a hedge fund manager on Wall Street. She was a leader at one of the hedge funds that nearly destroyed our country's economy. She and those she worked with have never been called to account for their crimes.

But first, a warning. Please note in advance that I strongly condemn this kind of hate speech. But I believe that hate speech needs to be called out because I believe it has no place in the power structure, much less in civil discourse. I also believe hate speech deserves no shielding or privacy. I wanted to capture these publicly-expressed pieces of hate speech before she could think better of it and delete them.

She wrote, "Churchill: 'You were given the choice between war and dishonor. You chose dishonor, and you will have war.'"

The she linked to the following truly reprehensible article (WARNING: this article contains contemptuous and morally disgusting attitudes that are blind to their own privilege. You may be as sickened as I was when you read it. I strongly condemn this hate speech): hate speech article link

Another classmate pushed back against this right away, writing,

as Eisgruber said “we should be aiming for a campus in which all students feel equally welcomed.” Commentary like the above and related blog posts are unwelcoming and also inaccurate (for instance saying all the students protesting at PU were black). There are many students, and people, of diverse colors and backgrounds, who support taking a hard look at campus life and assumptions. At PU there is a high value for tradition and a high value for making changes that make the educational experience the best that it can be.

But this woman kept on going with her racist rants. She lashed back.

I am quite prepared to believe that the BLM hysterics come in all colors. Their insistence on Maoist reeducation of their peers is a uniform pink.

And further:

Nothing says "welcome" like a mandatory Maoist reeducation program. Unless it's a building that you cannot access due to the color of your skin. Not to mention the black students who may not want to self-segregate -- if there is a component of pure evil to this profoundly racist and anti-educational movement, it is the pressure it will put on sane black kids to conform to the madness of the Maoists.

I could not believe my eyes, except that I spent four years with this woman and her entitled, privileged bullshit, so this was not the first of her objectionable ravings that I have been subjected to. Still, we are supposed to be older and wise. But apparently not everybody is actually committed to growing up.

The classmate who pushed back against her ravings wrote back:

That's your view and I am unlikely to influence it. However, I am quite prepared to think that the outcome will be orange and black, and not pink. And that there are apparently "hysterics" in various quarters. Just sayin.

This racist with a Princeton education could not stop herself, so she went on:

Except that if you're orange you can't get into the new "cultural" Affinity building.

And on:

Maybe Princeton should be renamed "Wilson University" to honor the new segregationism.

I couldn't take it any more, so I posted a reply objecting to her hate speech. But predictably, she screeched right back at me:

I hope that nobody would be surprised to find me pro-First Amendment and anti-Maoist. But you are welcome to a participation trophy anyway.

This is the voice of someone who benefited from a world-class education, as well as from our open, inclusive, and welcoming immigration policy. It causes me a deep and lasting sadness that these are the values she took away from these uniquely American opportunities and institutions I hold so dear. 

When people reveal their true values in public, it is important to document and witness their doing so. It is also important not to let this kind of evil go unanswered. The witnessing function is one of the most important roles of an ally. So I am doing my best to do so here, however imperfectly and stupidly I may be doing it. I continue to grow and learn from my #educolor colleagues on Twitter and on blogs. And I am training my students for their roles as the leaders of the rebel forces.

As the Buddha said, "Hatred never ceases through hatred but by love alone is healed. This is an ancient and eternal law."

And as Michelangelo wrote on a scrap of paper left behind in his studio in the wobbly handwriting of his old age, "Ancora imparo" — "I am still learning."

Writing apologies for racist classroom actions

About a month before the end of school, I wrote my first apology note for colluding with racism in the classroom. I know this note will not be my last.

I used what I have learned from restorative practices over the years: Speak from the heart. Listen from the heart. Say just enough. Respect the talking piece.

The first thing I did was to listen from the heart. My student had yelled very loudly, "You're being racist!" I had been sure, even in that moment, that there was a level at which he'd been right. I needed to inquire into his perspective and into my own to understand as much as I could about how and why this had been true.

After meditating and reflecting and journaling about what had happened, I wrote him a letter.

Dear ___,

I owe you an apology.

I have been treating you unfairly. I have been calling you out for being disruptive in class more than I have called out others, and I agree with you that that is wrong. I need to not do that, and I pledge to be mindful of that from now on. 

I also realized that I have been pushing you harder than I push some of the other students in our class, and I realize that that is wrong too. My intentions were good ones: I see your brilliance and, as a citizen, I want to recruit people like you into leadership. Our leaders are lost, and my generation has really messed things up. I came back to teaching because teachers are the talent scouts of the future, and our country needs people like you in leadership.

But that is my stuff — not necessarily yours.

After you pointed out my biased treatment of you, I realized that you are right. I have been treating you differently, and that is wrong. It was wrong of me to try to impose my agenda onto you. It is also inconsistent with my own values because it is important to me that you be empowered and respected to choose your own goals and make your own decisions about how to lead your life.

So this letter is my attempt to clean up my own side of the street. From now on, I am going to do a better job of respecting your boundaries and keeping my personal agenda on my own side of the street.

I hope you can accept my apology.

With great respect and affection,

Dr. X

I asked his favorite teacher to give him the letter, knowing that, if I had tried to give it to him myself, he would have simply torn it up without reading it. I am a little ashamed about this part.

But if I am going to be an impeccable warrior in this fight, I need to accept that part too and be ruthlessly honest about moving beyond my own personal likes and dislikes. Everything I do needs to reflect the values I am trying to convey into this world.

My student and I never discussed the letter, but afterwards, I noticed a change in our relationship. For my part, I stayed focused on being as mindful as I could in my efforts to treat him and all students equitably. But I noticed a change in him too. He seemed to start showing up — really showing up —every single day in class after that. He left his earphones and his cell phone in his pocket and he was much more fully present in class than he had been all year. He advocated for his own learning and persevered in ways I had not seen before.

He was not perfect and neither was I. But we became a lot more relaxed around each other, and I got a felt sense that we understood each other a little better. We were both less defended and more porous and receptive to life. We could receive each other's humor better and learn from each other. All in all, we seemed to be moving together more harmoniously toward the goal of learning together. And that was what I truly wanted.

This is the compelling thing about restorative practices for me. They give us a way to continue forward together. I am pretty sure this is why Archbishop Desmond Tutu's memoir is titled, No Future Without Forgiveness. Rage won't heal the world. And an overly defended student cannot adopt an optimal learning posture. Since that is my deepest hope for all students in my classroom, I need to do everything in my power to make it an equitable place for every student so that can happen as often as possible.