Growing Pains

The TMC leadership team just did a very useful blog post clarifying how they processed proposals for TMC19.

I found it extremely helpful in sorting through my own understanding of the confused and confusing messages in the response notices this year. I appreciate the leadership team's commitment to being accountable for its own stuff.

We are all on this journey together. We need to hold hands and stick together. #OtterNation

 I do think there was some inartful language in the acceptance letters — and I believe it caused more distress than was necessary. Communication matters, and sometimes we just get it wrong.

But this is why we need to be — and remain — in dialogue in this work. Alliances across difference are hard. They are impossible without receptivity on both sides of the dialogue.

Everyone in this community knows what to do when a lesson bombs. You analyze what happened, reflect, and try again. This is how we develop resilience.  This is how we improve our knowing.

We will all do better next time because all human beings are better than our greatest or our least. And this particular group of human beings is committed to doing things better, and to doing this work together.

Our community is rare because it is willing to accept feedback, to adapt, and to grow. Let's agree to do that now. It is natural — and necessary — to experience discomfort as we learn and grow. This is what our students experience. It is inevitable that we will experience it too.

This is one of those moments when we have to make a decision about how to love this community and our world.  My hope is that we can take what we know about powerful teaching and learning and use it to make TMC the kind of reflective, resilient, transformational community we envisioned right from the start.

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.

REFRAMING THE GOAL
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.

THREE STATIONS WITH TUTORS & LEARNERS
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.

COLLECTIVE PROBLEMS ARE MORE INTERESTING & FUN TO ADDRESS
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.

THE ACID TEST
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.

NEXT STEPS
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.

Proof Portfolios: Revenge of the Immersive Project

Some years ago, in a town about 11 miles south of here, I taught both math and English (I'm credentialed in both — shhh... don't tell anybody). Our English department was the single most functional academic department I have ever been a part of. When you came right down to it, what we did wasn't rocket science. We had a method, we used the method, and we assessed together by grade level. The 8th grade team consisted of Alec MacKenzie, Kelly Starnes, Linda Grady, and me. We are all still in the classroom, which strikes me as a minor miracle.

The writing method we used was a combination of the Jane Shaffer method and Six Traits. Every teacher in the district had been trained on the method, and collaborative rubrics and projects had been developed over the years. The method was flexible, but we all agreed on certain basic components. We used Jane Shaffer's method of color-coding, from elementary through middle school. This meant that every student in the district developed a common understanding of what a topic sentence is, what a claim is, how we use evidence to support our claims, and how we use reasoning to tie things together. I believe it is still one of the highest-performing writing districts in California.

One of our signature practices was that we gave a fall writing assessment and a spring writing assessment. In middle school it was a two-day affair, tied to the literature curriculum. Time was allocated for pre-writing and writing.

And then we teachers were given an on-campus release day so we could read and score holistically — together. We double-scored each sample, using a rubric and highlighters.

It drove us crazy, but it also enabled us to see patterns. And because we could see patterns, we could adapt instruction to address the gaps or needs we identified.

Shouldn't this be the norm for instruction?


I have long wanted to use this approach with my teaching of proof in high school, but this was the first year I got my act together to run my own personal pilot program. I don't have a colleague with whom to work on this, so I went it alone. I created a four-day project that and gave them one day's worth of stuff to work on each day.

Here is the zip file with all four days' worth of assignments: https://drive.google.com/open?id=1Zz3KlZ5zVO9K_0S4dW822hNJ9X4VtUdV

The secret of doing an assignment like this is radical: you have to relinquish control. You cannot be the only one giving students feedback. In fact, there is so much practice here, it is completely impossible. That is good. One thing I have learned as a writer and as a teacher of writing is that you learn how to write by writing a lot. The same is true with proof and proving. Students need space to immerse themselves and not worry about whether every mark they make is "right" or "wrong."

So each day had its "stuff." Four small proofs a day, plus reflection and peer review. Then more the next day.

The complaints and lamentations were filled with drama. "OH MY GOD, DR. S — THAT ASSIGNMENT WAS HARD." But they could tell that they had accomplished something.

My assessment strategy was to be rigorous about completion but merciful with points. It was only worth a quiz grade (100 points), and my default score for students who completed every section was a 95. There are rewards for following instructions. Missing sections or components left blank cost more points.

But none of that matters. My goal was to get students doing a LOT of proof -- writing shitty first drafts, comparing notes with each other, and using a rubric to assess each other's work. Dogen Zenji said, "When you walk in the mist, you get wet."

And it seems to have made a difference.

I am excited to see what happens on the next major test that includes a proof. Photos of student work to follow.

As always, let me know what you think and what happens if you use this!

Proof Portfolios

Over the last five years of teaching proofs in Geometry, I have learned two things: (1) the most effective student understanding comes from writing about their proof process, not from the proving itself, and (2) the most effective feedback process for students is a peer-to-peer reciprocal feedback process.

So this year, when I had to be out of school for a few days, I designed a Proof Portfolio project for them to do in my absence.

Each day had four small, reasonable proofs students had to do — and they could collaborate on these. But then... they had to write a number of short-answer reflections to analysis questions based on their own proofs in the day's set.

In addition, they had to find a peer to trade with and to give a rubric-based peer review and reflection.

In my class, they did this for several consecutive days. I made it worth a quiz/project grade.

When I returned, there was a great deal of wailing and moaning and gnashing of teeth about How Hard This Project Was and How Hard They All Worked.

It was clear that this project was a rite of passage for my classes.

But as I'm reading their work, I am blown away by how much they seem to have learned!

Their mastery of proof is not perfect. But it is authentic and it is growing. And to me, that is the most important point at this stage.

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I made up four days' worth of activities. Each day is two double-sided pages (proofs & reflections).

Here is a link to the G-drive folder with the four PDFs:

https://drive.google.com/open?id=1Mcb-AueXujpiWI2wD1FkuXAGTtWFjKAY

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More photos:

The New Normal

By U.S. standards, San Francisco is a large, densely populated city, but geographically, we are really quite small — only 7 x 7, as the saying goes. We are also both a city and a county, the only one in California. Which means that everybody knows somebody at any given school.

Last week, a gun went off at in a classroom at one of our sister high schools across the city. This happened around 11:15 a.m. Naturally, the ninth-grade students in my classroom knew about it by around 11:20.

"It was a freshman." 

"It was in the bathroom." 

"No, it was in a classroom. They're on lockdown."

"He had a Spiderman backpack."

"My cousin goes to school there there."

 It was scary to know about while it was happening. Everybody does lockdown drills and everybody complains about them, but nobody would have objected if it had been a lockdown for real in our own school.

After a few minutes of frantic following the thread of what was known, I turned off the lights. "Let's stop and take a moment to meditate and send them good energy."

One boy with a blue sweatshirt and a worried look said, "Like, should we pray for them?"

I said, "If that is what your heart tells you to do in this moment, then you should do that." He nodded, closed his eyes, and laced his fingers together with practiced intensity.

I guided students into a brief mindfulness meditation. We laid our phones face down on our desks, and I gave them the instruction on how to do meditation, focusing their attention on their breath coming in and out at their nose. Thirty-six wired, anxious fourteen-year-olds and I spent the next two minutes anchoring our crazy, overstimulated monkey minds together in our breath.

I felt the mood loosen in the room; then I flipped the light back on and we returned to our lesson.

I kept an eye on my Twitter feed, and when class was drawing to a close, I told them that the police had apparently secured the gun and the area and that they were just waiting for the all clear.

A few years ago, I would have lost the focus of the students and not been able to redirect it. Now I know better what to do and how to do it.

I just wish this weren't happening as much as it seems to be in our country.

First week and AVID strategies

I made it through the first week! And the chairs never had to get unstuck from the floor!

I did so much more metacognitive work this week than I’ve ever done before. Every day we did a say-do-mean summary at the end (My notes say... This enables me to... This means that...). Every day I tied our essential question to our work and to our metacognitive goals. And every day I used 10-2 processing to keep the pace up and get kids collaborating instead of relying on me. For every ten minutes of notes, I gave two minutes of processing time to catch up and collaborate on making their notes accurate. When my Geometry students asked what the terms were going to be on Friday’s vocabulary quiz, I didn’t answer that question. Instead, I instructed them to take two minutes to compare notes at their tables. See if anybody caught something you missed. Make sure everybody has everything they should have in their notes.

And they did it.

This was a powerful learning for me.

Until now, I used to answer those questions.

Now I am encouraging self-reliance and resourcefulness and a thinking classroom instead. I am doing this every place I can.

It’s a small instructional shift towards resourcefulness, but it feels seismic. I definitely want persistence, but not thoughtless persistance. I want to cultivate thoughtful persistence and resourceful persistance. You have super-smart classmates. Use them as an additional resource. Use them as a primary resource.

I felt so proud of my kids this week, it gave me energy. Even though I was exhausted, it gave me energy.

Now I am sitting in my favorite place in the world with my sofa and my fireplace and my music and my dog. The sun is burning away at the fog. The beginnings of a good new year.

A Course in Thinking

This blog post is also a session at Sam Shah's The Virtual Conference of Mathematical Flavors 

In a conference on flavors of mathematical teaching and learning, you could be forgiven for expecting every session to address some version of the age-old arguments about whether there are math people and non-math people, about whether it is better to have a growth mindset or a fixed mindset, or about whether mathematics is the most beautiful of all the disciplines we teach in school.

Which is probably why I feel so hesitant to confess my dirty little secret. In my classroom, I teach mathematics as one of the humanities.

The fact is that math is a human activity. If you are human, you cannot escape it. And what I have come to value the most about the opportunity to teach mathematics is that it has become one of the most pivotal ways in which we transmit the culture and values we cherish the most. For me, some of those values include respect, communication, empathy, understanding, persuasion, civil disagreement, persistence, deep listening, reassessing, and changing one’s mind. Math class gives me an opportunity to share all of these aspects of being human and living together in human culture.

So I’ve rewritten the introduction to my course syllabus to emphasize some of the things about which I feel most strongly — and which I believe are the most powerful and important things I have to share with my students over the course of the next year.

I listen to hear your thoughts.

_____________________________________________

This is a course about thinking.

You are here to learn how to think better and to use your thinking to accomplish things in the world.

The essence of thinking is sense-making. To make sense of things, you have to understand them, which means you have to want to understand them. One of our mottos in this class is, You gotta wanna.  This is as important in mathematics as in everything else.

So everything in this class is about making sense of things. In mathematics — as in life — we mostly make sense of problems. If you do not yet know that life presents a steady stream of problems to be solved, you will soon. 

In this class, we happen to use mathematics  as a ground for thinking. I will tell you a secret up front: I don’t actually care if you  ever “use” this stuff ever again or not... so please don’t waste time asking me that question. It is a boring and senseless question. What I care about passionately is that you learn how to think and communicate at a more advanced level than you are capable of right now. 

And that is what we are going to work on.

Thinking better is a set of skills you can actually learn and use at this school. It is the appropriate focus of math class.

Since you are going to be thinking for the rest of your lives, you are going to need to make sense of things you don’t initially understand. And then you’re going to have to persuade other people that your thinking is right. So your goal in this course should be to grow as an active sense-maker who is skilled in using these tools of thinking.

You should also learn to treat your thinking with respect. The mind is a muscle, and this school is a place where we work to strengthen our thinking muscles. That means we need to develop strength, flexibility, and endurance in our thinking — in other words, you need to become a strong thinker, a flexible thinker, and a persistent thinker. You also need to become a good collaborator, which means you need to become a better listener.


While there are no guarantees, I can promise you that if you focus on these goals here, you will do well in this class, and these skills will carry you very far in your life.