Dreaming is Hard, But It's the Only Way to Make Something — BSU Design Thinking, Part 1

This is the first of a series of posts I am writing for myself so that I can remember how I've been using design thinking in my work with our Black Student Union (BSU) program.
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One of the things Steve Jobs always valued about me was my ability to mobilize a huge group of people to do impossibly large things. In college, I ran an opera company. In the 1990s, I started NeXTWORLD Expo (which signaled the inflection point that would eventually lead NeXT to save Apple). In the 2000s, I was a co-founder of a women's wilderness retreat. And in the 2010s, I helped to start Twitter Math Camp.

Now I am one of the faculty leaders of the equity steering committee at my very old, historically entrenched, very large, racially and ethnically complicated academic magnet school. Three years ago, we embarked on a five-year process of school culture transformation to make it a more welcoming place, both for our students of color and for our faculty and support staff of color. Our students' families and communities are engaged, our PTSA is an active participant, and our 40,000-member alumni association is also involved. We are up to our eyeballs in the process of waking up to the toxic soup of systemic racism that we all swim in. I have often used the Zen metaphor of fish not noticing the water that they are swimming in, but I've come to realize that systemic racism is a polluted condition of that water. Our goal is to learn how to notice the pollution and to stop polluting the water further. We need, as the Tao Te Ching says, to let the mud settle and the water run clear.

The goal is not only to disrupt the trance of inequities that we all walk around in; the goal is also to  create a healthy and sustainable school culture in which learners from marginalized communities are entitled to thrive.

The progress is slow. The work is grueling. But there is also a lot of heart in our community, and sometimes that opens up an occasional moment of grace. So when our Black students told us what they needed, I took them seriously.

Raising money and helping them organize to achieve their deep dreams are things I know how to help with. So back in September, I got busy doing what I knew how to help with. The BSU officers and I met in our classroom to work together on envisioning and fundraising and mapping out our plans.

The envisioning is always harder than the fundraising, but when you are discouraged, it looks like the opposite is true. That is part of how the status quo and the power structure maintain their hold. The status quo wants you to believe that money is the problem, but I'll let you in on the secret: money is almost never the problem. The reason nine out of ten start-up efforts fail is not for lack of money; they fail for lack of imagination. This is one of the illusions that Design Thinking can help thinkers to break out of. The imagining is the hardest part because it requires us to go against the psychological and emotional defense mechanisms that keep us locked in our "safe" but disempowered crouch. They keep us thinking and dreaming small, when what we really need to do is to take the risk of thinking and dreaming big.

So the BSU officers and I engaged in a first draft envisioning and imagining conversation. This was some of the most exciting but complicated — and emotionally exhausting — work of my teaching career so far.

"What do you want to accomplish?"
"We want jackets."
I scribble on my list. "Done. What else?"
They were stumped.
"What else?"
"But we can't afford jackets. We need to have more bake sales."
"Don't worry about the money. That's my job. What do you want to  do??"
They thought for a minute.
Um, maybe a camping trip."
I write this down. "Good. What else?"

For thirty minutes, I pushed them and insisted they just toss out crazy ideas. No self-defeating talk about implementation, just make a list. Brainstorming rules. No judgment. Don't think.

And they starting coming up with ideas. College visits. Service projects in their neighborhoods. A Senior Showcase. An assembly.

"Good, good, good. What else?"

Every time they used the word "But..." I cut them off. "We're not talking about that right now. We're talking about deep dreams and making a list. What else?"

It was bewildering to them. They've been conditioned not to dream and I was prodding them to reconnect with this basic human capacity.  Honestly, I don't know if we could have gotten anywhere if there had not already been a years-long foundation of mutual trust woven between and among the five or six of us. They know I'm a little nuts, but they also know that they can trust me. They know that when I screw up, they can call me on it and I will own it and apologize for it. We've been blundering along together for years. I taught all of these girls as freshmen and sophomores, and I've been mentoring them, tutoring them, coaching them, writing letters of recommendation for them, and pushing them to reach high for all the time they've been at our school. And now they are on their way to becoming persons of power — the scientists and artists and politicians and engineers they are determined to become.

But the academic stuff turns out to be the easier piece. Dreaming is a different kind of path, and it's one that usually only the kids with privilege get mentored into. I was breaking this boundary, and it felt dangerous. That is almost always the way I know when I'm doing the right thing. As George Lucas once said, "When people tell you it's impossible, you're on the right track."

Once we had a huge list, we did some analysis on it. What are the must-haves? What are the nice-to-haves? What are the pieces we can live without if we have to? We prioritized. We negotiated. We gave things up; then we put them back onto the list. We organized them into categories. We identified the critical path. We flagged the dependencies. "This thing has to come before that thing. This thing can't happen unless that thing happens first."

It took a long time to get them into flow. There is a suspension of disbelief that has to happen during the envisioning phase. Otherwise nothing happens. They started getting involved in the process. Their body language loosened up. They leaned into the discussions. They started to lose their inhibitions about jumping up, grabbing a whiteboard marker, and drawing a matrix or a diagram on the board. Developing the comfort and safety and confidence to break the rules of compliant and oppressive forms of discussion is a giant step towards true empowerment. We began to make progress.

Finally, we got to a place where we could begin packaging up what we had thought of and started productizing it. Our first "product" would be a Black History Month program for the school. With each step, we asked ourselves, How will students benefit from this? How will the school benefit? What are the tangible and intangible outcomes? How will we be laying the groundwork so that future cohorts of the BSU will be able to replicate this program and grow it over time?

We started building a grant proposal draft and a spreadsheet on our BSU Google classroom. Parents requested permission to join the documents and spreadsheets and chats and I was thrilled. Request for access messages started popping up and I approved them as fast as they came in. Click. Click. Click. The parents mostly lurked and marveled at their children's boldness and imagination. They expressed their excitement and gratitude at Back To School Night, but I turned it right back on them. It was their children doing the amazing stuff. I was only the facilitator.

The kids occasionally panicked. "I don't have time to work on the grant proposal! I have a chem lab due and a mock trial event in LA and a basketball game on Wednesday. I don't know how this is going to get done."

And I did what I had been trained to do as a manager of large teams. I pitched in. I did whatever parts of the work I could help with. "Don't worry about it. I'll write a draft and people can edit it in the Google doc. We'll make it happen. This is the power of teams."

And we did it. In the end, I wrote the grants for their ideas. I interfaced with the power structure. And I got them the money.

Then the real work could begin.

The Festival of Reassessment (SBG)

December is when I am truly grateful for strong routines. They mean I can split the class up and still count on everything moving forward. I am running behind in my pacing, so I needed to set up a mass SBG reassessment opportunity for slope skills yesterday. I set up all the reassessors along the window side of the classroom and all of the non-reassessors on the hallway side of the room. The non-reassessors worked on linear systems skills and problem-based learning while the reassessors worked on demonstrating mastery of slope skills.

Whenever a reassessing student finished their work, they brought it up to be rechecked. I went through it right then and there while they watched. “Uh huh... uh huh... uh huh...” until “Oh noooooo! Why is this negative?!?!? It ruins everything! Go back and fix it!!!” And then the next student moved forward in the queue.

We went through this process of working and my checking and sending kids back for about 40 minutes. “Nooooo!!!” I would circle something and pretend to freak out, sending them back to fix stuff. It became a carnival. “AAACK!" I would say. "Go back and fix this!” Seeing this happen in real-time changed kids’ relationships with their misconceptions. It reminded me of piano practice as a child. Something would splatter in the midst of a phrase or figure and I would have to go back to the beginning, willing the figure to come out right through my fingers on the keyboard.

We kept going until all 12 students had triumphed over slope and point-slope form. What I loved about this process was how it transformed the social focus of the process of understanding to us (the whole class) against the skills. Kids were going wild and cheering when somebody finally triumphed over the "slope and point-slope” process, jumping up and down and hugging their newly non-reassessing classmates and friends.

The goal became one of getting everybody in the classroom over the finish line. From individual mastery to collective. Students stopped focusing on who had status in the classroom and who did not. They stopped thinking about their place in the social hierarchy and instead lost themselves in the flow of doing this f***ing slope and linear equation problem.

And then as each new classmate finally triumphed over the skill, the whole class felt truly victorious.

Everybody got the individualized attention they needed as they drove their skills forward, and we also bonded as a collective community, advancing our work as a group.

In these divisive times, I think this might be an important process to cultivate.

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.

First thoughts on completing Exeter Math 1

I just finished doing the 2010 edition of Math 1 (91pages) today.  Now begins the synthesizing and summarizing, which I will put into blog posts.

Math 1 is an Algebra 1 course that includes an incredibly deep coverage of proportional reasoning, in addition to the usual linear, quadratic, and exponential function topics.

I did Math 1 because most of our incoming students are incredibly bright and hard-working but they were not the math monsters in their middle schools. They have many of the typical middle school gaps, but they are much more sophisticated than most 9th grade Algebra 1 students. So the fact that Math 1 is a REALLY TOUGH course that dives very deep into Algebra 1 material is a great thing because it will give my students the deep rich course they deserve, even though they are placed into Algebra 1 based on their current skill level.

My Algebra 1 learners find themselves stuck in a ZPD no-man's-land: their ZPD as math learners is nowhere near their ZPD as readers. 

This presents a huge problem in the classroom. The math in CPM Algebra 1, for example, is rich and interesting, but the text is written for reluctant readers, discouraged readers, and English Language Learners, which is a huge turn-off for the vast majority of my enthusiastic and highly capable readers.

They feel insulted by it, and they are not shy about expressing these feelings. So my student population tends to dismiss it and resist it, even if they really do need to learn the content. This raises the question of how best to serve a population of learners who need to be challenged with greater nuance in textual interpretation and presentation in an introductory high school math class.

For all of these reasons, Math 1 is going to form a terrific problem-based “spine” for my Algebra 1 classes. The problem sequences are rich and interesting and engaging with sophisticated contexts, though they start from first principles. They develop to a point where even a mathematically sophisticated adult will find them very challenging.

To get started, I printed all pages of the problem sets, answer keys, and commentaries and created a binder with the following sections:

1 - Problem Sets plus glossary at the end

2 - Commentaries

3 - My Worked Solutions (for each page of problems, I have one stapled cluster of my worked solution pages)

4 - Answer Keys

I did all of my work on three-hole binder paper, with each new page from the problem set being its own stapled packet (or "blob") in the Worked Solutions section. 

Whatever problem set I was working on I would take out of the binder along with the relevant answer key page. That way I could work on binder paper without having to carry the whole damn binder around all the time. Much of this work was done on a lap desk with my iPhone/Desmos for graphing, my TI-83-plus (sorry, Eli) for computation, and my monkey pencil case including my mechanical pencil, my ProRadian protractor, and my colored pencils.

A lot of people have asked me why I started at the end and worked from the end forwards, about 10 pages at a time. The answer has two parts: (1) whenever I started from the beginning, I bogged down or got sidetracked; and (2)  it enabled me to see where we were going and where students would end up. By seeing where they would land at the end of the course, I could better understand how things worked from the beginning.

More thoughts coming soon, but I wanted to capture these ideas right away. If you have specific questions you'd like to discuss, please put them into the comments section below.

"Find What You Love; Do More of It"— #MTBoS Edition, a report from the field

While my friend @TrianglemanCSD Christopher Danielson is holding down the fort at the Minnesota State Fair and the Math On A Stick exhibit, I'm in my third full week of school avec students, and I realized I needed to peel off another layer of my persona and take his advice from his keynote address at #TMC15:

Find what you love; do more of it.

I love storytelling and stories. I come from a family of storytellers, where dinnertime was always a time of sharing stories.

I also love history — ancient history — and I know more about it than I usually give myself credit for.

So I did more of both of those things today. In my Algebra 1 class, no less.

It felt like a huge risk. But I decided to feel the fear and do it anyway.

So I told them what I have long known about the origins of algebra and equations. In its earliest uses, "algebra" means "balance." An equation is a metaphor for what everyone in the ancient world knew and understood with their own inherent sense-making and mathematical reasoning: just as a vendor at a market weighs out what a customer wants to buy — weighs it out with standards-based measures that are sanctioned by governments and universally accepted — so too is an equation a representation of these scales... and our goal is to balance out abstract or concrete quantities using that familiar structure from daily life.

I asked students what they knew about weighing and measuring and they told me honestly what their experiences have been at the farmer's markets all over our city.

We investigated what we knew about what happens when you place a known amount of weights on one side of a balance, and we imagined — and in some cases, acted out — what happens as you pour a continuous quantity of something onto the other side of the balance.

We talked about what it means to bring a scale into balance and we applied what we knew — the best we had — to the ideas at hand.

We talked about national and international standards bodies and about how even a perfect model degrades over time, which is why it needs to be monitored and occasionally replenished.

And so, by the time we got to the addition, subtraction, multiplication, and division properties of equality, we were already deep into our own connections with the metaphor and with the human history of algebra and with our own active and vivid imaginations.

By the end of class, nobody even complained about having to do the 2-2 homework. I am hoping that's because it was a little more deeply connected to their humanness than it ever had been before.

What it means to be a part of a learning community - Tribal Elder Edition

One interesting moment from the Oregon Math Network Conference this past week:

Bill McCallum was leading a large-ish session on building a culture of collaboration through jointly investigating student work.

Fawn (@fawnpnguyen) and I were sitting side by side at a table off to the side, each of us prepping madly for our next sessions. But neither of us could resist the lure of student work. We set our own presentations aside and pulled up the examples of middle school student work on Fawn's computer.

The task for the teachers in the room involved making sense of middle school students' written-out interpretations of different possible takes on how to simplify the expression

                  7 – 2 ( 3 – 8x)

Being experienced teachers of middle school math students, Fawn and I were both immediately captivated.

"Look at how this student identified right away that the value being distributed is a negative 2 — not just a 2," she said. "They noticed that part of it right away."

I nodded.

I noticed the student's language, which indicated a little mid-process magical thinking about the how to distribute multiplication over subtraction: "...because you use order of operations";  "you always do the problem inside the parentheses first"; "...but then "it's a problem that you've got  – 2 on the outside and – 8x on the inside."

"The student is using these phrases as magical incantations," I said. "The rules are still spells to him or her." Fawn agreed.

We both recognized these pieces of productive struggle from our own students's journeys. We dissolved into flow as we started talking about different ways to provoke authentic insight and discovery in our students. This is what is fun about getting together with kindred teacher spirits. It gives us the chance to share a deep kind of noticing that happens automatically during the school year, when we are trying to avoid drowning in the sheer overwhelming volume of student work.

While we'd been lost in analyzing, noticing, and wondering — and unnoticed by us — Bill had stepped closer to eavesdrop on our conversation and to join in the fun. At a certain point, he stepped right into the flow of conversation, offering his own noticings and wonderings about the students' wordings and insights. Several times we all burst out laughing — not at the student's work but at our own pure delight in it. Even after all this time, we can all still be captivated by adolescent mathematical thinking.

Well into his late 80s, Michelangelo was often heard to repeat the motto, "Ancora imparo" — "I am still learning." That is a concise summary of the delight that all teachers feel when we get the chance to sit together as a part of a learning community and think about teaching and learning together. This is the best teaching and learning reminder I know, and I always feel blessed when I have one of these flashes of self-remembering during one of these moments. So I wanted to capture this one.

The deeper wisdom of the body in math class

This post is for Malke.

As I was eavesdropping on a recent conversation between Lani Horn (@tchmathculture) and Malke Rosenfeld (@mathinyourfeet), I received a pointer to an article summarizing recent research that shows that kids with ADHD actually need to squirm in order to learn.

This makes sense to me. The deeper wisdom of the body is usually overlooked in thinking about teaching, learning, and assessment in mathematics. And yet, it can provide a vital link for our students in claiming their mathematics as well as their humanity.

I was thinking about this on Friday afternoon when I tweeted out the following:

I love the dulcet tones of compasses, rulers, & pencils during a Friday afternoon constructions quiz. #geomchat

Malke tweeted back:

I love that they are doing all that by hand. And that there are dulcet tones. :)

I responded:

Geo has affirmed my belief in the life made by hand. Huge benefits to Ss [students] from physically constructing their understanding.

I had another in a series of lightbulb moments this past month about what How People Learn says about externalizing our understanding.

And ever the good online learning partner, Malke tweeted back:

have you blogged about it?

So here I am.

In How People Learn, the authors talk about how we can use skits, presentations, and posters in group work to help students externalize their emerging understanding. This makes sense to me. In order to learn something, one first has to notice it, and that means developing a metacognitive self-awareness of the process and how it’s going.

Over the last few years, I have found that teaching students to use foldables, INBs (Interactive Notebooks), guided note-taking, and physical constructions is another extremely rich field of helping students to externalize their emerging understanding — only in these cases, they are externalizing their understanding through physical, kinesthetic processes — not just through talk, listening, and presentation processes.

The physical dimension is a good grounding for conceptual understanding. Teaching students how to literally use their tools can be a multidimensional process of making their learning both physical and tangible. Flipping open a flap or a page in a composition book is a physical manifestation of the process of retrieval or comparison or evaluation. Likewise, the process of using patty paper as a tracing medium to externalize the concept of superposition and projection of a figure to confirm congruence is a way of helping students to slow down their speeding monkey minds and to become present with the mathematics that are right in front of them.

When I tuned in to the clatter of compasses, rulers, and pencils on Friday, I really noticed how deeply engaged my students were with the geometry they were working on. Their body postures indicated how deeply immersed they were in the experience of flow: set your compass opening to an appropriate width and draw an arc across the angle you want to copy. Stab the endpoint of the segment where you want to create a new copy of your original angle and swipe the same arc there. Go back to the first angle. Refine your compass opening so that it now matches the width between the intersections of your arc and the original angle. Shift your paper, stab at the lower intersection of your copied angle-in-process and swipe an arc that will intersect with the arc you just drew there. Drop your compass; pick up your straight edge. Carefully draw a line to connect the endpoint of your target segment with the intersection of the arcs you have drawn, completing the terminal side/ ray you need to draw. Drop the straight edge; position the patty paper over your original angle and use your straight edge to trace it. Drop the straight edge and carefully slide your traced angle over your constructed angle. Does it match your figure perfectly?

The concentration etched on their brows matched the precision of their work on the page in front of them. Bisect an angle. Construct the perpendicular bisector of a segment. Construct a parallel line through an external point by using it to define an angle that you can copy.

Hopping from one stone to the next, you can cross an entire river. By placing one foot on the Earth after another in a pattern of glide reflections, you can complete a journey of a thousand miles or more.

That is one of the lessons of deductive and spatial reasoning at the heart of any good Geometry course. Noticing that it is happening in my classroom — really happening through physical, mental, and whole-hearted engagement — is one of the greatest blessings of being a teacher.


On Talking Points, disidentification, meditation, and the need for a structure

One of the things I have noticed with discouraged math learners and Talking Points — or other disidentification techniques — is that students often express a kind of euphoria afterwards. “That was so much fun!” they will often say (or yell).

This is a result of the disidentification process. They are not accustomed to speaking in their own authentic voices in math class. They have become conditioned to attending math class under what Brousseau called “the didactic contract.” Under the didactic contract — the implied contract to which they have become conditioned — they are required to check their authentic self at the door, with all its attendant messiness, blurting-out, hesitant and half-formed ideas. Instead, the didactic contract demands that they conform to very narrow ideas of what a “good math student” is supposed to do: Sit down. Shut up. Pay attention. Get the right answer. Don’t ask why.

There’s no point in our denying that this is what most math students have become acculturated to. They didn’t make up these requirements themselves. Somewhere along the way, everybody encounters a math learning environment in which these are the expectations.

This situation is what the great Swiss psychoanalyst Alice Miller spoke of in her book, The Drama of the Gifted Child. In an adult-centered, authoritarian society (which most societies are), the social constructs are organized to side always with the adult/parent/teacher instead of with the child. And in fact, as Miller’s work showed, not just *instead of* the child, but at the child’s expense.

This is the general situation for discouraged learners in math classes. Many students perceive early on that their authentic selves are not welcome here. They quickly learn to wear a mask in math class and to pretend to be smart, compliant, and “mathematical” — in other words, to adopt a false persona in math class.

The problem for us as math teachers is that it is not easy to crack through this false self. Disidentification is not an easy or a straightforward process. The psyche adopts these masks as defense mechanisms — and for very good, if outdated, psychological and emotional reasons: fear of abandonment, fear of humiliation, fear of shaming, fear of annihilation.

These may be outdated, outmoded fears by the time a student reaches middle school or high school, but that does not make them any less real or active in the present moment. For a traumatized math learner, they are the most real thing in their world during 5th period.

In their own different ways, the psychologists Eugene Gendlin, A.H. Almaas, and Francine Shapiro have all posited that trauma in the past forms a kind of “stuck place” in the human mind/brain/psyche. Whenever we encounter a stimulus that “triggers” that stuck place, we “flash back” to the moment of trauma and our defense mechanisms lock into place.

This is what makes disidentification so difficult to achieve in practice. A defended psyche is not a receptive psyche. And a student may *hear* that s/he needs to adopt a growth mindset in math class, but s/he hears this message from his or her bunker, thirty feet under ground and behind several feet of concrete protective functions.

Raise periscope. Spot the threat. Lower periscope and retreat.

Evolutionary psychologists consider this fight-flight-freeze response and its replay during anxiety dreams as a most ancient form of threat rehearsal. Knowing what they know from their previous experience, the protective functions of the psyche leap into action and do their best to make sure we remain vigilant and safe from incoming threats. They perceive this to be a matter of survival, which is why they go to such great lengths to make sure we perceive it that way too whenever we step over the threshhold into math class.

So the first order of business in the process of disidentification is to establish trust and to form a safe — and sane — alliance with all learners. If math class is to become a growth mindset place for all students, then it must first be established as a safe place in which to remove our masks and to return to being our deeper, authentic, creative selves.

To make any place safe for the authentic self to come out, it helps to have a structure in place. That way, the structure can provide the psychological and emotional safety (and freedom) in which we can drop down into our authentic selves.

In all forms of mindfulness meditation, this structure consists of three things: a posture, an anchor, and a timed period.

In Zen, we sit on a black cushion in the lotus or half-lotus position (or forward on a chair with both feet flat on the floor). We place our hands on our knees or in the cosmic mudra and we face a white wall. We lower our gaze to a 45-degree angle with the floor, and we anchor our attention on our breath.

Whenever our attention wanders — and monkey mind guarantees that it will inevitably wander — we gently redirect it back to our breathing.

The Vietnamese Zen teacher Thich Nhat Hanh teaches the use of a gatha, or mindfulness verse, as an attentional aid during meditation. With each in-breath or out-breath, one thinks a line of a simple verse:

Breathing in, I calm my mind.
Breathing out, I smile.
Dwelling in the present moment,
I know that this is a wonderful moment.

Which reduces to:

In,
Out.
Present moment,
Wonderful moment.

I’ll say this about Thich Nhat Hanh: you have to be a pretty evolved being to be able to teach this kind of clarity and sanity to the very countries that launched your own into chaos.

We do all of this for the whole timed period, whether it is ten minutes or 45 or an hour. Gradually, with patience and lovingkindness, we learn how to do this for longer and longer periods, until the timed period we are working with is every day for the rest of our lives.

We do this because this is our structure.

To the uninitiated, a structure might seem to be a rigid thing, but that is a misunderstanding, and I will tell you the secret: it is actually the essence of freedom.

It gives our defense mechanisms and our wounded child ego-self-psyche something important to do while we drop down into the vulnerable place where our authentic self is kept safe — beneath all those layers of protective functions, social masks, people-pleasing, snark, and our “on-stage” personas.

The structure makes it safe for a human being to reconnect with that deeper, authentic self.

So it is natural to experience a kind of euphoria afterwards. Our culture generally doesn’t encourage us to connect with our authentic selves, so when we do, many people experience it as a kind of homecoming. Intuitively, we know that it is the source of all our greatest ideas and energy and creative fire. Finally, it is a relief to drop the masks we wear and to just be fully and authentically ourselves.

The Enlightenment poet Friedrich Schiller described this experience of flow as arising from the competing impulses toward being present and toward thinking, which operate in a kind of luminous reciprocity, with their harmonious interaction producing a third impulse which he terms the Spieltrieb (or 'play impulse'):

Irresistibly seized and attracted by the one quality, and held at a distance by the other, we find ourselves at the same time in a condition of utter rest and extreme movement, and the result is that wonderful emotion for which reason has no conception and language no name.

                       — Friedrich Schiller, Twelfth Letter on the Aesthetic Education of Man

When the mind is both fully at play and fully at rest in this way, it is at home. 

And when this experience happens in math class, students are growing and truly experiencing mathematics.

This is the sanest, healthiest, richest, most creative human state I know — and I want all of my students to experience it in my math class. Only then can they connect with the growth mindset and the mathematics that are their birthright.

But the key to unlocking that moment is through structure. And for me, in my math classes, that structure is Talking Points.

Models of exploratory talk from my youth — the NeXT years

In planning the group work morning session, I keep asking myself what I want group work to look like — and more importantly, to feel like — for my students. So far, the best description I have found in the literature comes from Douglas Barnes, by way of Neil Mercer (of Cambridge University) and Malcolm Swan and the Thinking Together project in the UK.

So far, Barnes’ conception of exploratory talk, as fleshed out by Mercer and Swan in their research, has come closer than anything else to what I first experienced in the most creative and effective engineering cultures in my adult life.

Lately I have come to the realization that what I really want to prepare my students for is the kind of passionate, creative, and incredibly effective exploratory talk culture that first electrified me during the three years I worked for Steve Jobs at NeXT.

Steve was a master of exploratory talk skills, though he was definitely stronger on the concept development side of things than he was on the social and emotional skills. But more than anybody else I have ever known, Steve valued exploratory talk. In many ways large and small, he worshipped it. And so did we. That was a big part of how I — and many others of us — justified putting up with the craziness we endured while working for him during that period. In search of the “insanely great,” Steve was open to crossing over into the extreme. You had to really want to be there.

Steve’s primary mode of exploratory talk was what could best be described as “gladiatorial.” You had to be willing to die in the arena — and die over, and over, and over again over weeks or months or even years. If you knew what you were talking about — and were prepared to defend your ideas to the death — then you were equipped to step into the arena. However, you also had to be prepared to get bloodied. The emotional toll was tremendous, and many of the most brilliant thinkers I knew at NeXT were simply not willing or able to go into the ring. They stayed as long as they could and made amazing contributions to the experience while still preserving their souls and their sanity. As I grew up, I began to understand that the price of Steve’s mode of exploratory talk was exclusion. Like him, most of the people who were willing to engage in that exchange were white men. I was unusual in that regard because I was not. Most of the leaders of Apple are still primarily white men.

One of the most powerful things about Steve’s engagement in exploratory talk was they when you were right about something, he would eventually come back and give credit (or take credit himself while in proximity to you). As many others have said, he did not do this with a tremendous amount of grace. He could be awkward and blunt and cruel and manipulative. But he could also be deeply and sincerely celebratory of your best work, and a big part of his genius was in being able to bring together some of the brightest, most intensely creative people in the business — the ones with the best ideas and the most flexible skills and the ability to get shit done. And he was a genius at launching us all into combat.

When I joined NeXT, I knew that I was going there to connect with the people I would be starting other companies with and working with for the rest of my life. That belief proved to be true. To this day, the ex-NeXT network remains my most active and cherished alumni group. I started other software companies with exNeXTers, and I worked with some of those who later took over Apple. We shared (and continue to share) a common framework — a common way of engaging in exploratory talk that is recognizable by us all. It’s a sixth sense about a kind of passionate and engaged exploratory talk in which the participants are fully present, and totally bringing their ‘A game’ to the conversation.

In the years after leaving NeXT, most of us refined our processes of exploratory talk in ways that made the process gentler and more generous, more nurturing. Steve’s way was just too damaging. It also left too many brilliant minds and voices out of too many conversations — conversations that would have benefited from the contributions of people who were less combat-averse than the rest of us.

For my own part, I found that mindfulness, restorative practices and good therapy really helped.

But none of us were ever willing to give up the electric quality of those product development conversations. They were incandescent. They left you hungry for more. After the meetings ended, we would all crawl back to our offices, drained and exhausted. But under the surface, we were all making notes, sketching ideas, and plotting our next pitches.

Hours or days later, somebody would pull you into their office to show you something they’d hacked together on their own time, working through some unresolved part of the central idea. That was how you prepared for combat in the arena — you tested your ideas against the best minds you knew. You forged alliances.

Some parts of this process were hilarious. My friend Henry hacked together a UI (user interface) component out of the AppKit to demonstrate some point he’d been trying to convey. In the last piece of his model, there was a pulldown menu of possible actions this one modal dialog allowed you to select. The last of the possible action options in the menu was often, “Drive an 18-inch spike through my brain.” The standard buttons at the bottom right of the dialog window were ‘Cancel’ and “OK.”

For me, this is the ideal of the kind of exploratory talk conversation I want my students to taste in my classroom. I want them to experience that process of brainstorming that takes you out of your own skin — and even out of your own mind — into a kind of magical space that Neil Mercer has termed “interthinking.” It’s that experience of being part of a Bigger Mind than your own individual, cognitive awareness. Brainstorming your way into truly great ideas takes a lot more commitment to flow and to “allowing” than most cognitive psychologists and theorists are comfortable talking about.

But that’s where all the payoff is.

Compound Inequalities Treasure Map

Never underestimate the power of novelty to help you engage certain students.

I just spent the last hour and a half-long block period with my jaw on the floor, watching in amazement as my most discouraged, 12th grade College Prep Math students worked productively and peacefully on, of all things, the analysis and solving of compound inequalities.

During my prep, I turned a boring worksheet into a treasure map. And that turned a boring requirement into a very peaceful and enjoyable period.

As she was leaving, one girl asked, Could we please do more work like this?

I'll take that as a compliment!

"Wow, what a great question!" or Repeat After Me: A Unit Test is Still a Learning Opportunity"

I have met teachers who refuse to answer questions of any kind at all during tests, and I admit that this puzzles me because from where I sit, those are some of the highest-leverage teaching and learning opportunities I will ever have.

I just hate to waste them.

For they are the moments when I have my students' complete and undivided attention.

And that means they are my best hope for encouraging and guiding students in the process of productive struggle.

During a test, I will happily entertain anybody's question about anything. Really. Ask me anything. I will gladly offer encouragement and encourage their courage because for many students, THAT is the moment at which they are most deeply engaged and present in the process of struggling with their learning.

But I am apparently the most frustrating person in the world because the best answer I will ever give students is to say, "THAT is a GREAT QUESTION!"

I smile and nod and encourage them and urge them to keep going. And at first, they really think they hate me for it.

During today's Math 8 test, kids kept asking questions and I kept answering, "That is a GREAT question! What a terrific insight!" and leaving to move on to the next questioner. "But is this RIGHT?" They would ask, sounding wounded. And I would say, "You are asking a FANTASTIC question! Keep going!" and move right along.

Finally somebody thought to ask me in a tiny and supplicating voice, "Dr. S, is THIS a good question to ask?" And I peered over and looked at their paper and exclaimed, "Yes! That is a super-fantastic question!"

I was certainly the most annoying person in the room, but they are starting to catch on to this whole productive struggle business. Eventually it became a humorous trope. "Oh, yeah — don't bother asking. I'm sure that's a really GREAT question."

To which I would chime in, "Yes — it really IS a super-great question!"

Don't get me wrong — this is NOT an easy thing to do. It takes strength and practice and intestinal fortitude. It will never be featured as "great classroom action." But it is the most precious and valuable thing I know how to offer my students.

I can say this because I have also been on the receiving end of this kind of teaching. It is a teaching about the value of struggle. It is an incredibly precious gift, but nobody can ever explain it to you. You actually have to experience it in order to understand what a profound act of respect it is for the primacy and centrality of your own personal experience to your own personal learning.

I spent plenty of years complaining bitterly about meditation teachers who practiced this kind of bounded containment. But I sat with it. I stayed with it. I learned first to accept it, and then to embrace it. After a lot of struggle, it humbled me. It changed me in ways big and small. It opened my heart and empowered me to discover the value of struggling within my own life's journey, as well as in subjects like mathematics. That kind of preciousness and wholeheartedness is all too rare in America, but I hope that all human beings will at least taste it at some point in their lives.

So even though it was in some ways a crappy day and a frustrating day and an exasperating day, it was also a kind of gift day too. I want to remember that.

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.

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! :)

What We Actively Value, Versus What We Tell Students We Value

Lately I've become acutely aware of what I actively value in my classroom, which has entailed an uncomfortable amount of noticing the conditioned habits of my teacher personality. I don't collect and stamp homework assignments. I don't have each day's agenda and objective for the day neatly written on the whiteboard by the time the first bell rings. My classroom is pretty messy most of the time. I don't have a good system for filing away those last three copies of every handout for future use. I took great permission from @mgolding's system of daily handouts using her Container Store hanging file system: basically, the handouts migrate downward one pocket until there are no pockets left, at which point they go into the recycling bin.

I've made my peace with these tradeoffs because I discovered early on that if I was allotting attention to those things, then that was attention I wasn't allotting to the things I actually do value.

I adopted an SBG assessment system because it aligns my grading/scoring system with the things I actually value: mastery, effort, and perseverance. And also presence — being fully present with the activity we are doing that I actually care about. And as I've noticed that, I have noticed something else I feel good about in my classroom: my kids know that those are the things I value. Which that means they don't waste valuable life-energy bullshitting me about the small stuff we all know I don't really care about.

This has led to a lot of interesting progress with students I didn't expect to make progress with. Less successful students who don't feel shamed stick around to ask questions and engage in meaningful academic inquiry. They come to my room during their study hall periods to follow up, get help on missed or misunderstood assignments, or ask for additional work they can do to improve their understanding.

Not their grade -- their understanding. Their performance.

I am not used to this, and it causes me a lot of inconvenience. 

Students who have a reputation for giving up and giving in ask me if they can write another draft, reassess their missed algebra skills/concepts questions, and take greater ownership of their learning in my classroom. My ego would like to think this is because I'm such a highly effective teacher, but in actuality, I think it's more that my walk is becoming more aligned with my talk. I care about mastery and effort and perseverance, which means that those are the things I respond to.

What I did not realize until this afternoon is that this also means that I don't respond to things that are NOT those things. Which means that my kids are not expending any effort pretending to care about things around me that they really don't care about either. There is a focus on the work, and there is not a focus on things that are not the work. This may sound obvious, but actually it's not -- or at least, it wasn't for me. It took me years to discover that I'd been walking around in a consensual trance all my life.

This kind of awareness is challenging, to be sure, but it is also incredibly freeing. Students spend a huge part of every school day pretending to care about things that don't actually matter to them. Fitting in, pleasing teachers, winning points. Some of it is necessary but much of it they know to be complete and utter crap.

Ten, fifteen, forty, or fifty minutes of being authentically engaged in something that matters to somebody is a huge thing. Ten, fifteen, forty, or fifty minutes of authentic interaction with someone who is trying to focus as sincerely as possible on what actually matters in this life is even bigger.

I learned this lesson from years of experience with my mentor and teacher, Dr. Fred Joseph Orr — mind to mind, and heart to heart, though it took years to digest, and quite frankly, I'm still digesting. I'll probably be digesting for the rest of my life. No one had ever paid that kind of focused, intensive, thoughtful, and bounded attention and awareness in my presence before. And it made me discover how it feels to feel alive. I only discovered how precious that kind of awareness was -- and still is -- once that chapter of my life ended and a new chapter had begun.

I was noticing all this today during a test in which some of my lowest-performing students were asking for "help" with certain problems. I noticed that each time I came over in response to their request, they were not so much asking for assistance as asking for a kind of authentic engagement and support that was neither judging nor doing for them but simply witnessing their effort with presence. What I noticed today inside myself — and what distinguished this from mere adolescent attention-seekig behavior — was my own felt sense of a embodied memory of seeking out this kind of authentic connection in my own work with Fred. And this felt sense gave me the motivation to allow that connection and that presence. I trusted something inside my own inherent, intelligent functioning that told me to allow the connection rather than to pull back and resist. It was a subtle and quiet movement inside me, and I'm still figuring out what exactly was going on.

How many times have I mistaken noise for the signal? Do discouraged students ask because they hang on to the sane and healthy hope that they can learn and connect and make progress? Fred always told me, "The organism moves toward health," and I grew to believe him. I wonder if this is what my discouraged students are really asking for when they ostensibly make a seemingly attention-seeking request for something called "help."

Intermezzo - summer reading seminar on The Curious Incident of the Dog in the Night-Time

One of the things I sometimes forget that I love about teaching English is the fact that I get to get adolescents talking and thinking about issues we all feel deeply about. The cool thing about sparking these conversations with young adolescents (by which I mean secondary students, as opposed to college students) is that most of them are just waking up to these issues for the first time in their lives, which means passions run deep. And that means they are ripe for thinking deeply about these issues — more deeply than we often give them credit for.

In my seminar this afternoon on The Curious Incident of the Dog in the Night-Time, I wanted to get students to develop for themselves a question that I think is fundamental to citizenship in a functioning democracy — specifically, who is it who, in different contexts, gets to decide what is to be considered "normal," and therefore acceptable?

The Curious Incident is an interesting reading choice for incoming 9th graders because the narrator, Christopher, is a young man on the autistic spectrum who easily qualifies in students' eyes as an outsider. In spite of extremely high math and science aptitude and achievement (preparing to take his maths A-levels at age 15), he is prevented from attending a mainstream secondary school. Instead, his social and emotional impairments have caused him to be marginalized into a special needs school where even he can see that most of the students are far less socially and emotionally functional than he is.

The students in my seminar are outgoing 8th graders I have known for a full year now. Because I teach both math and English, I have actually taught most of them for at least one period a day, and in many cases, for two periods a day. Which is to say, I know them unusually well for a casual summer reading seminar. I also know the ELA curriculum they have all just finished working through because I helped to develop some of it, and this gave me a lot of touchstones to draw on in our discussions. However, I would like to point out that this kind of lesson could work well with almost any group of students, since it centers on one of the main issues in adolescent life: namely, issues of fairness.

The activity I set up for today involved small groups doing "detective work" on five related thematic issues in the novel and then sharing out their findings with the rest of the group. The five thematic areas were:

• Belief systems: conventional religious beliefs versus Christopher's own unique belief system
• "Normal" behavior and how we judge differences in the behavior of others
• The nature of human memory: Christopher's beliefs about his own memory and other people's
• The significance of Christopher's dream in the novel
• The interrelated issues of truth, truthfulness, and trust

To get things started, I modeled the investigative process using issue #2 - what is considered "normal" behavior and who gets to decide whose behavior in a society will be considered "normal" and whose will be considered "deviant" (or sub-normal). Students needed a little more context on what autism is and how it can affect a young person socially, so we did a little quick internet-based research (thank you, iPhone!) on the autistic spectrum and what it means to be higher-functioning or less-high-functioning. Students zoomed in on the exact contradiction I had hoped — but have learned never to expect— they would target: the question of varying standards of "Behavior" that govern the judgment of and consequences for actions of adults (such as Christopher's father) and those of a kid like Christopher himself. Fairness is something that most adolescents feel strongly about, even when they are generally treated quite fairly, as most of these students usually are. [SPOILER ALERT: stop reading here if you haven't read the novel and don't want to know what happens as it progresses].

The kids were really quite exercised about the fact that while Christopher was the one labeled as having "Problem Behavior," his father committed a number of acts that we all agreed had to qualify as "Problem Behavior," including (a) killing an innocent dog, (b) lying to his son about the boy's mother being dead, and (c) hiding her letters to him to maintain the lie of her having died of an improbable illness. These were just the big issues.

So we circled around until we needed to land on a word they did not yet have in their vocabulary: arbitrary. Our dictionary manager looked the word up and read its several definitions to the group while we tried it on for size. "Arbitrary" definitely seemed to fit the contradictory categorizations of behavior of adults versus of Christopher in the novel. There was no way around the fact that the rules seemed both arbitrary and easily manipulated by the adults — far more easily than by Christopher himself. The notion that society's rules are subjective constructs, influenced by the personal beliefs and opinions of human beings, struck them as a significant new insight.

This part of the discussion led to a second insight I'd been hoping we might arrive at: the fact that whoever is in power gets to determine what will be considered normal. The idea of differences in power is something most of these students have not encountered much, except in the context of adults/parents versus adolescents/children. So for many of them, it was a new idea to think that these inequities could extend outside of families to other social relationships and interactions.

Their investigations and presentations were rich and quite thorough. To save time, I provided more scaffolding in the worksheets (chapter and/or page references) than I would have if we had been doing the project over several class periods. Still, I was pleased that they were able to reread their sections closely, draw on their annotations and notes, and quickly assemble arguments about each of these thematic areas that were supported by evidence from the text.

Having just come back from Twitter Math Camp, and still being immersed in rich dialogue about math pedagogy and equity, the conversation reminded me that every subject area in which we teach is a powerful opportunity to engage with students. At Twitter Math Camp, I loved being able to drop directly into the middle of an ongoing conversation I've been having with colleagues in the Math Twitterblogosphere for months or years in the virtual realm. In our seminar today, I loved being able to drop directly back into pretty advanced investigation with these students because I had already done so much formative assessment with them over the past year in this same kind of context.

These conversations are a gift of deep teaching and learning, and they are a reminder of what gets lost when policymakers become enchanted with the kind of magical thinking that allows them to chase the illusions of quick fixes and silver bullets such as plopping kids down in front of a giant library of videotaped lectures. Developing a library of tutorial videos may be a worthwhile archival goal, but it is no substitute for the magic that can happen when good and authentic teaching connects with a ready student.

TMC 12 SESSION: Increasing intrinsic motivation using the ideas in Dan Pink's Drive

Dan Pink's bestselling book Drive: ___  has given the business world new ways to think about increasing intrinsic motivation in the workplace, but his ideas have resonance in math education too. The purpose of my Twitter Math Camp 12 session was to summarize the main ideas in Drive and to talk about how I have applied them to the specific situation of the math classroom.

In the model he sets out, Pink presents three fundamental pillars of intrinsic motivation:

• AUTONOMY, which he defines as "behaving with a full sense of volition and choice” as opposed to feeling pushed around by “external pressure toward specific outcomes” (Drive, p. 88). 
• MASTERY, which is a growth mindset in the model of Carol Dweck's work, a way of thinking about one's work that requires both effort and engagement. He also describes mastery as "an asymptote," an impulse that moves toward an ideal of perfect oneness without ever fully achieving it (Drive, pp. 118, 122, & 124).
• PURPOSE, a sense of being connected to the why of what one is doing (Drive, p. 233).

All three of these elements support the development of FLOW — a profound human state of "optimal experience" which was first studied in depth by the renowned psychologist Mihalyi Csikszentmihalyi (pronounced "chick-sent-me-high").

Flow is what many of us who teach math feel when we lose ourselves in doing mathematics, and my argument in this presentation is that helping our students to experience the flow state while they're doing math should be our top priority when thinking about motivation.

We can help students tap into the flow state by using Pink's three elements of intrinsic motivation to create "on ramps" for students to the flow experience.

PURPOSE is a terrific building block for many of our most capable students, but for the discouraged or disengaged student, it is necessary but not sufficient. What Can You Do With This?, Three-Act Digital Problems, and AnyQs? activities can be helpful in cultivating a sense of purpose in students, but it is important to keep in mind that there are other factors — including social, emotional, and psychological factors — at work with our most discouraged students.

Using a Standards-Based Grading framework helps students understand talk about MASTERY by clarifying expectations and improving communication between and among students, teachers, and parents.

AUTONOMY is the hardest of the three elements to encourage, so I spent most of my talk about ways to develop a sense of autonomy with math students.

There are two parts to autonomy: (1) an outer component and (2) an inner component. The EXTERNAL part can be built up by disrupting student expectations through alternative  activity structures. Games, game-like activity structures, treasure hunts, creating foldables, making up dances or songs, creating and performing skits or puppet shows that demonstrate definitions or processes, and other such reframing activities redirect student attention away from what causes them anxiety or trauma and toward something that allows them to relax and let doing mathematics be simply a means to an end. REFRAMING can be a crucial part of helping students find themselves in flow while doing mathematics.

The INTERNAL component of boosting autonomy has to do with helping students to NOTICE their fears or reactive responses and ALLOWING there to be space for their authentic feelings and conditioned reactions. We can support students by not taking their reactions/reflexes personally and by noticing our own reactions/reflexive responses to different kinds of disengagement we experience from students. Encouraging a posture of noticing and allowing enables us to help students loosen their identification with past negative experiences and open up space for newer, positive experiences to overwrite those in their minds and bodies.

By honoring and encouraging the flow state in our students while they are engaged in mathematics, we can help them to renegotiate their relationship with math class. And that creates space for the positive and self-reinforcing intrinsic motivation that will help them get out of their own way and find lifelong success with mathematics.

Rational Expressions Treasure Hunt (or, Intrinsic Motivation for the Intrinsically Unmotivat-able Bits)

We are coming up on our state testing window (STAR testing in California, ugh), which means it's time to finish "covering" all the so-called key standards material in preparation for the last-minute test prep and hand-wringing.

In our Algebra 1 curriculum, the last unit before state testing is the Rational Expressions unit, which I find to be one of those inherently frustrating and procedural sections.

The good news of the rational expressions unit is that it gives Algebra 1 students an opportunity to see how some of the foundational skills and concepts they've been learning can come together to provide some very sophisticated conceptual and computational tools.

The bad news is, students are tired -- tired of the routine of observation - guided practice - independent practice - followed by a chapter test. And they're just plain tired in the sense that they've absorbed a lot in every class they're in and basically their brains are kind of full.

So I reviewed my notes on Dan Pink's book Drive to see how I could weave together his ideas of autonomy, mastery, and purpose. And that gave me the following ideas:

• AUTONOMY - students needed a unit which relies more on self-checking than on getting a teacher seal of approval (or a rubber stamp);
• MASTERY - students seemed to need a unit which would emphasize tracking their mastery of skills and concepts, which meant giving them lots of opportunities both to do and to spot patterns in their doing;
• PURPOSE - students needed a sense of purpose to the overall activity, rather than the "bigger picture" sense of Dan Meyer's WCYDWT (What Can You Do With This?) -  to provide some light-hearted gratification or, as some might put it, a cheap thrill. :-)

As these ideas whirled around, I felt envious of Kate Nowak's wonderful circumcenters lesson (from Geometry) that harnessed fun clues with the need to draw circumcenters on a map of the school as a motivation for hunting down numbered markers which she had tucked around the school.

It occurred to me that I could use a treasure hunt idea (organized more as a geocaching or letterboxing hunt) as an intrinsically self-motivating reward system -- coupled with a series of self-check-able problem sets/worksheets -- to give students a little break from routine and a reason to work together purposefully to practice simplifying rational expressions and finding the excluded values.

So here are the components I created:

1. a set of graduated worksheets (one for each day) for them to use as practice problems
2. a handwritten Answer Key that I slipped into sheet protectors and tacked up on the front bulletin board for students to check their work against
3. a "rubber-stamping station" where I or they would stamp their completed AND checked worksheets to place in their...
4. group folder
5. a Ziploc bag or sheet protector stapled to the inside of the group folder where they could store their treasure tokens
6. a set of "clue" cards, one for each worksheet's treasure token, that students would take together with a...
7. Hall Passes (which clearly states that I have given them permission to snuffle around in the designated area to find their treasure tokens and come back to my classroom)
8. one weatherproof plastic Gladware container PER treasure box/worksheet to contain the treasure tokens for each worksheet/level (I used Woodsies stars that I bought at Michael's and labeled them 11-2a or 11-2b to correspond to their worksheets, but you could also use punched-out paper or cardboard shapes of any type); treasure boxes were labeled with masking tape and also contained a marker and an index card on which students would write their group's initials when they removed a token

A couple of observations. First of all, your "clue cards" will be different from mine based on your school and where you wish to send your students on their searching. Being a California indoor-outdoor type of school that is built into a hillside, we have a lot of beautifully xeriscaped/landscaped pocket gardens that made for good treasure box hiding places. So my clues said stuff like, "Facing room ELEVEN, TWO TIMES TEN paces or so to your right, you'll find a bathtub fit for a bird. Look below the bushes behind..." Or "Head toward LUCKY 13 and look for the LAVENDER HEDGE. The treasure box is tucked behind..."

Students responded positively to this shift toward autonomy. They delight in completing a practice task that grants them permission to snuffle around a little outside in the fresh air. And they seem to love unraveling the clues, maybe because they love reading and thinking about themselves and their own environment. The Hall Pass requirement gave them a clear set of expectations and accountability, and even my least accountable students have been taking it seriously, which is a refreshing change of pace for all of us.

Their assessment will come from my review of their group project folder -- its tokens, its completed and corrected worksheets, and the presence or absence of worksheets for each student in the group.

The worksheets and sample hall passes and clues are up on Box.net

NCTM Standard 7: fostering "positive dispositions toward mathematics"

Standard 7 for the National Council of Teachers of Mathematics measures whether well-qualified math teachers "support a positive disposition toward mathematical processes and mathematical learning." But their criteria and performance indicators don't exactly reach through the screen, grab me by my shoulders, and inspire me to inspire my kids to love mathematics. They seem more like a floor than a ceiling, and personally, my desire is to aim higher than that.

One of the ways in which a positive disposition is fostered is by building a strong and positive learning alliance with my students. In a therapeutic situation, the establishment of a therapeutic alliance is a critical step. The client must believe that the therapist believes in them and in their commitment to change. The great Jungian analyst, teacher, and storyteller Clarissa Pinkola Estés says that nobody can truly accomplish great things completely on their own steam. The same is true for students in the math classroom. When they know in their bones that I am rooting for them, they begin to feel that success in mathematics is possible. That doesn't mean I don't "display attention to equity/diversity" or "use stimulating curricula" and "effective teaching strategies," as NCTM standard number 7 demands. It means that every day, in every way, I try to demonstrate my own commitment to being in their corner and cheering for them.

Another way in which I can help foster positive disposition toward mathematics is through sharing my own enjoyment of the processes we investigate. To me, positive disposition is about cultivating curiosity and patience. I find that when I model my own process of enjoyment, I give them a window into what their own relationships to mathematics can look like.

And so I consider it a wise investment of time and energy to cultivate positive dispositions wherever I can, regardless of a student's success or lack of sucess so far in Algebra, and I see it paying off in little and big ways throughout the year.

One experiment in building positive disposition I've been trying lately is something I ripped off borrowed from Sam Shah -- the use of motivational buttons. Inspired by Sam's lead, I made up some motivational buttons for students to wear during tests:

If students wear their Algebra Warrior! button during tests, I give them an extra credit point on the test. I gave these out during our last test and made everybody "take the pledge" to wear their button during tests, including the state standardized tests this year.

Still, I recognize that they are middle school students who can (a) lose anything and (b) easily be distracted even from things that are important to them.

So I was pleased when at least 80% of each class showed up eager to show me that they were wearing their Algebra Warrior! buttons for the test on Friday.

It's a tiny thing, but it's a tangible way of getting them to practice demonstrating their commitment to being impeccable warriors in mathematics. Like warriors putting on armor to do battle, my little Algebra Warriors put on their buttons and remember to form an alliance with themselves — to advocate for themselves and remember that they are connecting with something much bigger than their fear or confidence whenever they do mathematics.

Beautiful, fluid chaos -- or what "learning in flow" actually looks like to the trained eye

One of the things I like best about my new school are my colleagues. In fact, I don't believe I could stand to teach English (instead of math) if I did not happen to have my particular grade-level team of amazing, insightful, reflective, open-minded collaborative English-teacher colleagues.

I'm not saying that teaching math is one big continuous picnic of sparkly rainbows, unicorns, and effortless class periods of absorptive learning, but in English Language Arts -- particularly at the middle school level -- you have to teach some of the most thought-numbing, soul-dissolving parts of the curriculum ever to torture the human mind. Spelling. Grammar. Vocabulary. I throw up in my mouth a little bit each time I have to schedule time for them on a new weekly assignments calendar. But they're a part of the curriculum that's mandated, and so they have to be taught.  Some things you just have to pinch your nose and swallow as quickly as possible.

On the other hand, or possibly as my reward for fulfilling these less satisfying obligations of my curriculum each week, I get to work with kids on one of the deepest and dearest endeavors of my heart. I get to teach them writing.

Now, one of the things I have learned in my many decades on this planet is that writing -- and learning how to write -- is MESSY. Learning to write a first draft is more about learning how to tolerate the waves of revulsion that come over you as you confront the your own feelings of inadequacy at what you put down on the page than it is about about learning how to structure a proper academic paragraph. In fact, I'm convinced that I could teach a goat to structure a proper academic paragraph. What takes genuine human maturity and emotional/psychological courage is learning to get a first draft down on paper.

For that, you have to gain the willingness to produce what writer Anne Lamott calls "a shitty first draft."

Since I'm not permitted to use that kind of language in a public school classroom with middle schoolers, I use the methods I first learned from, and later taught with, celebrated writing teacher Natalie Goldberg. Her system of "writing practice" emphasizes "separating the creator from the editor," and basically involves a small number of inviolable rules for producing your first draft of an idea. These are:

• keep your hand moving
• don't cross out
• don't worry about spelling, punctuation, grammar, or other rules
• lose control
• don't think
• go for the jugular
• follow and trust where your mind takes you
• give yourself permission to write the worst poop in America / on Planet Earth / in The Milky Way Galaxy

So for first drafts in my classroom, this is how we practice.

We close the door and the windows (so we don't bother anybody trying to do more traditional learning), I make earplugs available to anybody who needs to block out noise in order to think, and I tell my students to let it rip.

As soon as they finish a draft, they can come find me or a peer-editing partner and they or we look at what they have done. First we do so aloud but with no comment until the draft has gotten a first hearing. Natalie says, you can't know what you've written until after you've written it, so first we give it a hearing, then we go to town giving it a quick edit. We look for what our rubric tells us to look for. Then they go back to their desk (or to the floor, or to the back table -- wherever they want to be writing) and they bang out another draft.

The beauty of this system is that it gives them a lot of practice compressed into a very short space of time. Everyone can get a fast, free, immediate edit from a published working writer without time for judgment, shame, or a sense of disgrace to take hold. The kids have very quickly grasped how to use writing practice to harness the flow state, get their juices flowing, and not become too attached to what they've put down on paper. It gives them a wonderful experience of the feedback loop in writing and it gives them immersive time in the flow state that has rapidly improved everyone's basic writing skills noticeably and quickly.

The, um, downside of this system is that while we are having one of these in-class writing workshops, my classroom looks like a chaotic free-for-all. Or so I thought until the other day.

See, when we're doing this, even though I am not actually writing, I fall into the flow state too. I get absorbed in reading, writing, listening, editing, coaching, and cheerleading and I completely lose track of time. In a good way.

But the other day, one of my English colleagues and I were scheduled to trade classes halfway through the period to teach each other's classes part of a jigsaw lesson we were doing. I knew we were doing so, and I had everything ready and prepared, I just lost track of time. So when she arrived in my classroom to trade, she got treated to the sight of me on my knees next to somebody's desk giving one quick edit after another, kids reading aloud and giving each other peer edits, one kid sitting under the phone table next to the flag because he concentrates best down there with earplugs in using an Algebra textbook as his lap desk, and other kids writing (with earplugs in) either alone or together, but in what I imagined to look like total unfettered chaos.

Fortunately, this teacher is both an enlightened person and a reflective practitioner in her teaching, so she was absorbed for a few minutes just watching what was going on, taking it all in and finding it extremely effective and engaging.

Then she came over, tapped me on the shoulder, and reminded me that we needed to switch classrooms and finish the jigsaw activity.

At lunch later, she told me how much she had enjoyed getting the chance to watch our process unnoticed because it gave her a totally different vision of what an in-class writing workshop could be.

That made me feel both grateful and relieved, since I had felt certain that doing what I was doing was the straightest path to getting myself fired (except for the part about my kids' writing improving more and faster than many other teachers' classes).

Anyway, it was really interesting to have been observed while I myself was in the flow state.