cheesemonkey wonders

cheesemonkey wonders

Sunday, January 19, 2020

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.


@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.


  1. So do you do group grades, like grading kids with their table mates, or you do a whole class grade? This all sounds really cool and inspiring.

    1. I used to give group grades on group projects or group tests, but I have always been dissatisfied by the variability in responsibility and contributions. There are a lot of unexplored reasons why this is the case -- but I find group projects and "participation quizzes" to be mostly ineffective. There's always some variability I find too frustrating.

      What I want is for EVERYBODY to really put their shoulder into it. I want everybody to make their utmost effort. The benefit of doing targeted practice and reciprocal teaching and learning activities leading to the whole-class skills quizzes is that the really make everybody accountable to everybody else. I tell students, Figure out what your best contribution to this process can be. If you need to be a leaner, be a really engaged learner. If you understand these skills, your job is to find people you can really help to get over the finish line on their own.

      When we do a unit test or the final exam, everybody rises or falls on their own individual understanding. But review activities continue to be centered on structures of positive interdependence.

      I am trying to balance whole-class and individual assessments, but I like the values that whole-class skills quizzes are establishing. Each student benefits when the general level of knowledge and skill in the room improves. Each student's learning experience is better when everybody around them is better.

      The general ethic in my classroom needs to be centered around the question, "How can I help?" In our school, there's a lot of confusion for students about how this ideal could best be lived.

      Cheating can be a huge problem for kids from high-pressure backgrounds, but as a symptom of social sickness, it reveals an emphasis on the after-the-fact aspect of learning. Adolescents believe they can "help" their friends by giving them answers. I wanted to find a way to make it make more palatable for them to pour these positive energies into helping each other out BEFORE anybody could get left behind.

      We are the adults, and the incentives are broken. In my view, we need to reorient the incentives around mentally, emotionally, and academically healthier options.

      Thanks for engaging in this conversation.

      - Elizabeth (@cheesemonkeysf)

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