Sometimes I teach, and sometimes I just try to get out of the way...

We are in the midst of our giant 8th grade culminating assessment extravaganza — a multi-part project that includes a research paper, a creative/expressive project, a presentation with slides, and several other components I'm spacing out on at the moment.

I have to admit something here: I used to be an unbeliever when it comes to projects.

I used to think they lacked rigor and intellectual heft.

But I was wrong.

Two years of this process has made me a believer in the power of project-based learning.

Sometimes the creative projects are merely terrific, but every year, there are a few that are incredible. This year, this has already happened twice... and only two projects have been turned in so far (they are due on Monday, 22-Apr-13).

Sometimes it is the quiet, timid kid who really blows my mind. Sometimes it is a kid who is kind of rowdy who reveals another, hidden side. But I never fail to be humbled at the potential inside each of these people, and I am honored to teach them.

So this is a reminder to myself that sometimes my job is simply to get out of their way.

Allegory, iambic pentameter, and 8th graders

In 8th grade English we have just started our poetry unit, which is probably my favorite literature unit, and today was probably my favorite lesson of my favorite literature unit.

I had to start by finishing up what I think of as the "poetry bootcamp" section. There are all the basic terms, the mandatory vocabulary, bleep, blorp, bleep, blorp, and a yada yada yada. BO-RING. That is no way to engage 8th graders.

So I took my opening when I got to allegory, which, as I explained to them, is what we call an "extended metaphor," or as I like to think of it, a "story-length metaphor."

Like the fable of The Ugly Duckling.

I am a believer in the power of storytelling and poetry to save lives. They've saved my life many, many times over, and I know many others who've been saved by them as well.

I told them a version of Clarissa Pinkola Estès' version of The Ugly Duckling. I wove the story from the perspective of the bewildered, misfit duckling who cannot belong but who tries so hard to belong until he JUST. CANNOT. EVEN. At which point, he gets driven out of the flock into the landscape of despair.

He wanders through the landscape of despair — through the forest of his fears — until he has reached the end of all that he knows.

Finally, exhausted and hungry, he paddles out on the lake in search of solace and food. As he is paddling around, lost and spent, a pair of magnificent swans paddle up alongside him and ask if they can swim with him.

He looks over his shoulder to see if there is somebody else behind to whom they must be talking. The water is empty.

After many backs and forths, he relents and allows himself to swim with them. And as the sun peeks through the thick cloud cover, the glassy surface of the water turns into a giant reflecting glass, into which he looks, expecting to see his familiar, unlovable image.

But instead, he sees quite another image looking back at him — the reflected image of a third, equally magnificent swan on the lake.

I told them, we all wander lost at some point in our lives, but if we hold on and remain clear about what we are searching for, we will all eventually find our flock, our tribe, our true pack. The people with whom we can be authentic and with whom we belong. Estès talks about "belonging as blessing" as a promise, and I have learned that this is true, even though I always find the needle on my gas gauge quivering around the "E" end of the spectrum by this point in my journey.

On my own path right now, I'm not "there" yet. I don't know where I'll be teaching this time next year, but I do know the shape of this journey, and I understand that now is the moment when I need to redouble my faith in the archetype — even though every fiber of my being is ready to just lie down and allow myself to be eaten by whatever hungry ghosts are passing my way.

I told my students that there are patterns to our experience, just as there are patterns in mathematics and the natural world and in human history. And I think that I told them what I needed to hear for myself, namely, that education and growing up is the process of discovering and learning to trust the patterns that are bigger and greater than our own, fidgety little monkey minds.

Intro to Quadratics — from "drab" to "fab" (or at least, to something less drab)

Recently, I created a new anchor lesson for my Algebra 1 quadratics unit. I found that, while I really liked the sequencing of activities and questioning in the NCTM Illuminations lesson on "Patterns and Functions," I found their situation and set-up simultaneously boring, contrived, and inane.

Actual photograph of San Francisco monkeys

hosting a tea party in the wild

As is so often the case, I find that a certain, judicious sprinkling of silliness and fun in the set-up can really liven up the lesson. A certain amount of contrivance is necessary in many activities, even those that are based on "real-world situations." So why not stretch the real world to make it conform to the needs of my algebra students?

The Made To Stick elements are all here: multiple access points are provided through manipulatives, storytelling, and humor.

My student investigation sheet, Table for Eighteen... Monkeys is available on Box.com. A PDF of the Table Tiles master is available here on Box.com
here.

Tiny plastic monkeys sold separately. :)

UPDATE: Worksheets now also on the Math Teacher's Wiki, at http://msmathwiki.pbworks.com/w/page/55614036/Algebra%201#view=page

Thoughts On Making Math Tasks "Stickier"

Last year, the book that changed my teaching practice the most was definitely Dan Pink's Drive: The Surprising Truth About What Motivates Us. It helped me to think through how I wanted to structure classroom tasks in order to maximize intrinsic motivation and engagement.

This year, the book that is influencing my teaching practice the most would have to be Made To Stick: Why Some Ideas Survive and Others Die by Chip and Dan Heath. I bought it to read on my Kindle, and I kind of regret that now because it is one of those books (like Drive) that really needs to be waved around at meaningful PD events.

The Heath brothers' thesis is basically that any idea, task, or activity can be made "stickier" by applying six basic principles of stickiness. Their big six are:

1. Simple
2. Unexpected
3. Concrete
4. Credible
5. Emotional
6. Story

The writer in me is bothered by the failure of parallel structure in the last item on this list (Seriously? SERIOUSLY? Would it have killed you to have used a sixth adjective rather than five adjectives and one noun? OTOH, that does make the list a little stickier for me, because my visceral quality of my reaction only adds to the concreteness of my experience, so there is that). But that is a small price to pay for a very useful and compact rubric. It also fits in with nicely with a lot of the brain-based learning ideas that @mgolding and @jreulbach first turned me on to.

This framework can also help us to understand — and hopefully to improve —a lot of so-so ideas that start with a seed of stickiness but haven't yet achieved their optimal sticky potential.

I wanted to write out some of what I mean here.

For example, I have often waxed poetic about Dan Meyer's Graphing Stories, which are a little jewel of stickiness when introducing the practice of graphing situations, yet I find a lot of the other Three-Act Tasks to be curiously flat for me and non-engaging. Some of this has to do with the fact that I am not a particularly visual learner, but I also think there is some value in analyzing my own experience as a formerly discouraged math learner. I have learned that if I can't get myself to be curious and engaged about something, I can't really manage to engage anybody else either.

Made To Stick has given me a vocabulary for analyzing some of what goes wrong for me and what goes right with certain math tasks. The six principles framework are very valuable for me in this regard, both descriptively and prescriptively. For example, Dan's original Graphing Stories lesson meets all of the Heath brothers' criteria. It is simple, unexpected, concrete, credible, emotional, and narrative. The lesson anchors the learning in students' own experience, then opens an unexpected "curiosity gap" in students' knowledge by pointing out some specific bits of knowledge they do not have but could actually reach for if they were simply to reach for it a little bit.

But I would argue that the place where this lesson succeeds most strongly is in its concreteness, which is implemented through Dan's cleverly designed and integrated handout. At first glance, this looks like just another boring student worksheet. But actually, through its clever design and tie-in to the videos, it becomes a concrete, tangible tool that students use to expose and investigate their own curiosity gaps for themselves.

Students discover their own knowledge gap through two distinct, but related physical, sensory moments: the first, when they anchor their own experiences of walking in the forest, crossing over a bridge, and peering out over the railing as they pass over (sorry, bad Passover pun), and the second, when they glance down at the physical worksheet and pencil in their own hands and are asked to connect what they saw with what they must now do.

This connection in the present moment to the students' own physical, tangible experience must not be underestimated.

Watching the video — even watching a worldclass piece of cinematography — is a relatively passive sensory experience for most of us.

But opening a gap between what I see as a viewer and what I hold in my hands — or what I taste (Double-Stuf Oreos!), smell, feel, or hear — and I'm yours forever.

"My work here is done."

This way of thinking has given me a much deeper understanding of why my lessons that integrate two or three sensory modalities always seem to be stickier than my lessons that rely on just one modality. Even when the manipulatives I introduce might seem contrived or artificial, there is value in introducing a second or third sensory dimension to my tasks. In so doing, they both (a) add another access point for students I have not yet reached and (b) expose the gap in students' knowledge by bringing in their present-moment sensory experiences. And these two dimensions can make an enormous different in students' emotional engagement in a math task.

Meditation With Middle Schoolers – Episode Pi Minus 3: Sending and Taking

So on Friday my 8th graders’ giant research papers were due, and this is the week that high school acceptances go out. The 8th graders are stressed to the max. When the bell rang, my Advisory students begged. “Can we meditate? PLEEEEEEEASE?”

And as I always do when they request to do mindfulness meditation, I put on my mental robes and teach them this practice that has saved me so many times.
This morning I taught them the practice of lojong, which is a Tibetan form of mindfulness that translates loosely into “sending and taking.” The idea is that you breathe in the suffering that is out there, and you breathe out the peacefulness that is needed.
I sat on the staging table at the front of the room, folded my legs, and rang the singing bowl before giving them the instruction. “Close your eyes, and focus your attention on your breath coming in and out at your nose.” I waited for them to get very still, which inevitable helps them to get very, very quiet. “Think of someone who is very precious to you,” I began, “and when you breathe in, imagine yourself breathing in their pain and suffering and anxiety.”

Being middle schoolers, they have a lot of friends who are also suffering. The silence was so profound I could hear my own pulse.

“And while you are doing this practice for someone you care about very much, I will be doing this practice up here on this table for you — breathing in your anxiety and breathing peacefulness into your lives.” I gave them some guided instruction in imagining how it feels to receive this kind of heartfulness, and in noticing how it feels to send it out.

Turns out, it is very healing.

When I gave the instruction for closing the meditation, students stayed still even after they opened their eyes. One girl exclaimed, “That was magical!” The other students all nodded.

I told them, “This practice is always available to you, and all this week I will be doing this practice and sending peacefulness energy to you — wherever you are, all the time, every day.”

I rang the bell and gave them a deep gassho (bow) out of gratitude. There are times that remind me why I teach, and no hostile or ignorant third parties can take that away. I remembered something my teacher Dr. Fred Joseph Orr always said to me, “In a contest between the imagination and the will, the imagination will always win.” And here he would pause before finishing. “ALWAYS.”

Reflection on wallowing after the "Two Faces of 'Smartness'" workshop at the Creating Balance in an Unjust World conference

So yesterday I was at the Creating Balance in an Unjust World conference on math and social justice in San Francisco with Jason Buell (@jybuell) and Grace Chen (@graceachen), and I finally got to meet Brian Lawler of CSU San Marcos (@blaw0013) and Bryan Meyer (@doingmath) in person. They are (of course!) both terrific. I came away so impressed with Brian Lawler — a wonderful math education teacher and researcher as well as a fun guy and a total mensch, in addition to being my friend Sophie (@sophgermain) Germain's mentor. You should definitely follow him on Twitter if you're not already.

He and Jason and I crashed the "Two Faces of 'Smartness'" workshop session yesterday right after lunch, which was beautifully given by Nicole Louie and Evra Baldinger.  It was glorious to do math on the floor with Brian and Jason at the back of a classroom where about fifty math teachers from around the country had crammed ourselves in because we wanted to learn about this and well, honestly, we just didn't care about having to sit on the floor.

What was wonderful about it?

Well, first they are both such amazing, caring, reflective teachers and mathematicians. We were given an Algebra 1-style complex instruction group task and we worked on it deeply, in our own ways, for 15 or 20 minutes. There was so much respect for the others in the group, along with deep listening and amazing mathematical and teacherly thinking.

Some of that wonderfulness was wonderful for me was because of my own issues over the years with shame about my own mathematical thinking processes, which are usually quite different from those of other mathematicians and math thinkers I work with. Even after many years of intensive work, I still have a conditioned habit of abandoning my own thinking in favor of somebody else's — anybody else's — especially if they seem confident about their thinking. I have a sense that this is similar to what our discouraged math students often experience, the ones who prefer English class or music or social studies, because I was one of those students myself.

Jason is a middle school science teacher, so he also has a slightly different way of looking at math than Brian or I do. At one point he suggested that we verify our idea by counting the squares. Brian and I looked at each other dumbfounded for a moment, since that had not occurred to either one of us. I exclaimed, "What a great idea! It's so science-y!"

We laughed, counted, and continued our work together.

There can be such joy in a group task like that, but not if the group's working structure is set up with rigid norms that limit individual students' participation. Frankly, I just hate the "assigned roles" kind of group work because I find that it fails to reflect -- or prepare students for -- the kind of group work that happens in a real-world collaborative setting such as a software design meeting. There, engineers and product marketers and managers come together but are not restricted in their participatory roles. No one is limited to being a "recorder" or a "task manager." One person presents a starting point to kick things off, and from there everybody just jumps in with the best they have.

That's how we were working on the floor together yesterday. It was an organic, free-flowing process, and as a result, both the learning and the mathematical conversation were far more authentic than I've usually experienced in this kind of work.

There were also rat-holes — glorious rat-holes! — we chased down. At one point we had even (temporarily) convinced ourselves of the possibility of a quadratic formulation of the rule, even though we'd been told (by the title of the worksheet) that this was a linear growth function. After a few minutes, we punctured the balloon of that idea, and felt a little deflated ourselves. We'd been working for several minutes straight but unlike most of the other table groups, we had still not called the teacher over for even our first of three check-ins. I hung my head in discouragement. "We are fucked," I said. But then we laughed again, brushed ourselves off, and picked back up where we'd last seen something productive.

The end of the workshop activity involved reflection on what the others in our group had contributed to the process in a method known in complex instruction as "assigning competence." You highlight one of the key competencies that another group member demonstrated and you tie it to a positive learning consequence to which it had led us. For example, I appreciated how Jason had brought in ideas from the real-world thinking of science because it had added rigor and a verification mindset to our process. Brian appreciated how I'd been able to stay with my confusion and keep articulating it in a way that made my process visible and available for investigation.

This pleased me because it is something important I think I have to contribute. I call it my process of "wallowing." I have a deep and self-aware willingness to wallow in my mathematics.

One of the other teachers in the room asked me to say more about what "wallowing" meant, and at first I felt overwhelmingly self-conscious about speaking up. But then I remembered that (a) I was being asked by other math teachers who are passionately interested in understanding different ways of reaching students who have their own unusual relationships to mathematics, and (b) I had Brian Lawler and Jason Buell on either side as my wing men, and come on, who wouldn't find uncharacteristic courage in that situation?

So I told him that for me — and in my classroom — wallowing means learning how to be actively confused and developing a comfort and a willingness to stay present with that confusion while doing mathematics.

In much school mathematics, appearing confused is a frequent and constant source of unspoken shame. And so most people with any amount of self-regard quickly learn how to cover it up and hide it from view. I went through much of high school disguising my confusion and shame as thoughtful reflection. I became a master of avoiding humiliation in class by keeping my confusion well-hidden. If I didn't get *caught* being confused, then I couldn't be humiliated or shamed about it.

Later I would work through my confusion privately so I could show up in class always and only being able to raise my hand about something I felt I understood cold.

So I believe there needs to be a culture of allowing for wallowing in active confusion in our math classrooms. We should not be too quick to dismiss confusion or try to resolve it or spackle over it.  I would even argue we need to consider it a badge of honor and an activity worthy of our time, consideration, and cultivation. The only way to cultivate curiosity is to cultivate an environment that is supportive of wallowing — active engagement and presence in the process of being confused.

It is the deepest form of mathematical engagement I know, and it is thrilling, inspiring, and honoring to be a part of it. When a student experiences that euphoric, lightbulb moment of authentic, personal insight, we can be assured that the understanding it signals is not only deep but also durable. This is true because when you are actively confused about something, you are fully engaged in making your own mathematics. Whether it is a "big" idea or a "little" procedure, these moments of insight are the source of all intrinsic motivation. And isn't this the kind of reflective, metacognitive insight about student learning processes that we are hoping to cultivate?

Go graph yourself!

Yesterday I used masking tape to turn the floor of my classroom into a coordinate plane. 

Students had to graph themselves, then find the slope of the line between themselves and various other points in the room. A good time was had by all, and a few insights were had.

Today I think we will also graph all the bits of trash that usually get left on the floor by lunch time. That will give us time to set up for a fierce game of Coordinate Plane Battleship.

Oh, the things we do to promote a deeper conceptual understanding! :)