cheesemonkey wonders

cheesemonkey wonders

Thursday, December 6, 2018

ASKING A DIFFERENT QUESTION: a manifesto on skills mastery & assessment

I am one of those urban public school math teachers with a truly absurd spread of abilities in my gigantic Algebra 1 classes, so don't even get me STARTED on the whole "the trouble with identifying student skill levels" thing. 

Through painful experience, I have learned what a cop-out it is to quote lines like, "You just need rich enough problems!" or "Proper use of roles will solve all of your difficulties!"

I say this because every experienced teacher knows that at some point, you are going to come face to face with the life-saving need to reteach (or remediate) some of the most fundamental skill and/or concept areas that some students missed and truly need to understand in order to get the maximum benefit out of their education.

This problem punched me squarely in the face this past month in Algebra 1. In spite of Common Core and district promises that all students would arrive in 9th grade with a deep and thorough understanding of slope, linear equations, intercepts, and slope-intercept form, my students — who are among the most capable students in my city and county —had at best a shallow familiarity with these skills and concepts.

The whole thing was just a hot mess — and it got dumped in my lap.

And so even though I am an experienced, equity-focused teacher with a lot of skills for accommodating diversity and differentiating to meet student needs, I was really struggling.

I did a lot of meditation on it, researching and soul-searching, until I decided that I had been asking a wrong question.

I started to wonder, what if, instead of focusing on individual mastery of these linear equation skills, what if I were to frame the challenge in a collective and collaborative way?

A class is a community, it is true, but it is also an economy. And in an economy, individuals respond unconsciously to the incentives they are conditioned to respond to.

This gave me an idea. What if our goal — our incentive — as a whole class were to get EVERYBODY in the room over the finish line at a high degree of mastery?

And if that were our collective goal, I started to wonder, how could I best restructure the system of incentives to support students to want to help other students to get over the hump in mastering these skills?

This line of questioning felt dangerous — a sure sign that I might be on the right track.

Things changed a lot when I thought about the problem this way. For one thing, it became clear to me that the incentive needed to be a whole-class, positively interdependent one — in other words, I needed to make each individual's incentives contingent upon every other individual's ability to perform the tasks at hand.

I announced that our skills quiz for this unit was going to be a whole-class skills quiz, in which everybody would earn the AVERAGE SCORE of all individual quiz scores taken together.

My 9th graders looked around at each other as if they had never really seen each other before.

Then I announce the structure of practice we would use for the next two days.

There would be three stations around the room, one for each of the skill areas were were focusing on — given the coordinates of two points:  (1) Find the slope; (2) Find the line (i.e., the equation in slope-intercept form; and (3) Convert the equation to standard form.

Each person would be responsible for self-assessing on their role: would they serve as a Tutor or as a Learner?

Tutors positioned themselves at the various stations.

Then Learners chose a station where they would work with a Tutor or Tutors on the practice problems that were available at that level.

I said, "Go" and the mood in the room was transformed.

The most noticeable change in the room was the transformation of status. There was no longer any shame in being a Learner and no special advantage to being a Tutor. The class became more like a hive of bees — everybody become focused on figuring out how they could do their part to raise the class' average level of understanding.

Some people paired up and started working in pairs. Others took to the whiteboards (VNPSs) and created their own teaching and learning structures. After a while, certain students would trade roles. "Now I'll  be the Tutor and you be the Learner."

We did this for two days. There were no slackers.

On Day 2, one of my most capable students circulated around the room, checking in of his own accord on different pairs and groups, offering a "free reference sheet" and assistance with any of the harder problems that might need clarification.

Instead of competing with one another, my students were truly collaborating — consistently and sincerely — in sustained and authentic ways that I have not seen before.

Changing our skill goals from "I" goals to "we" goals broke their conditioned habits of competition.

I gave the six-question quiz yesterday, and individuals could get instant feedback on their personal level of mastery without worrying too much about doom. Everybody knew that the class as a whole was more than the sum of its parts — and there would be plenty of time in the future for deeper practice.

I was shocked as I scored the papers. I had made the quiz HARD. Really hard. But the average individual score was hovering around 93.

I am buying every kid a donut. Seriously. :)

But I am also going to internalize as much of the social and emotional wisdom I have stumbled into as I can.

Harnessing the power of the collective to improve the learning of the collective is a powerful tool for situational motivation that disrupts status issues in the heterogeneous classroom.

It also centered compassion as a guiding motivation in ways that I truly value.


  1. That sounds like you're making the best of a poor situation. After the last school board election is there any chance that 8th grade algebra will come back?

  2. There's no way to know what will happen. But I've decided I want my students to have the most meaningful learning experience I can give them regardless of what policy is in vogue at any given moment.

    This is also good practice in collaboration for life.

    - Elizabeth (@cheesemonkeysf)

  3. I'm curious what "making the best of a poor situation" refers to (I teach in Berkeley Unified so I know may way around 8th grade algebra politics). We don't teach algebra in 8th grade to anyone anymore. We teach Math 8 to everyone. But it seems like what Elizabeth faces in terms of the vast spread of skills will exist no matter what. I teach an 8th grade intervention class and my kids' skills span 1st-5th grade level. The span is just as wide whether or not we have 2 different levels of classes in 8th grade.

    On another note...I LOVE this post. I have done very similar things from time to time in years past. This post reminded me of the power of this lens. Our district exam is at the end of next week and I'm going to think about how I could showcase the class with the highest average and create similar structures as you did for our review sessions. Thanks for this post. What a gift!

    1. Allison, Thanks for this response! I think what Benjamin is referring to is my district's insistence that students are NEVER permitted to be placed according to their skill level, interest, or readiness (a policy with which I disagree but commit). The skill level spread here at my school is beyond ridiculous, and so even though this serves no one well, this is the policy.

      And thank you for your thoughts about showcasing whole-class achievement! I love how this is shifting student perception and engagement.

  4. "Only dead mathematics can be taught where competition prevails: living mathematics must always be a communal possession." —Mary Everest Boole

    What a great example of living mathematics in the classroom!

  5. Hey, this post is terrific.

    My classes are much much smaller, but skill differences are a problem I worry about. (I think one thing about teaching at a shmancy private school with small classes is that there really is a difference between the spread in September vs. December. Or at least this year there is.)

    The thing I've been telling my students often this year is, OK, let's see if we can spread some understanding around. Right now a few people have ideas, strategies, solutions. Talk to the people you're sitting near and see if we can spread that around.

    I'm looking forward to hearing about where this goes next!

  6. One of the questions I've gotten on Twitter has been how I respond to parents of very capable (and sometimes competitive) students.

    Because this is Algebra 1, which is the foundation for, like EVERYTHING quantitative, I encourage these parents to look at this as an opportunity to improve the overall level of the education their child is going to receive.

    If every teacher here can count on a higher level of average preparation, then they will be able to teach at a more advanced and interesting level for everybody... and that is going to make their own child's educational experience much, much richer.

    I want to encourage students and their families not to squabble over crumbs. We want to emphasize an abundance mindset in our classroom economy by building something bigger, something better for our society.

    If we improve the overall educational experience of everybody, that is going to improve their own child's classroom experience immensely.

    - Elizabeth (@cheesemonkeysf)