Week 3 — Talking Points — Desert Island Thinking #MTBoSBlaugust

When I arrived at Princeton, I had been placed with three other roommates in a Gothic dorm suite. I was proud of the things I had accomplished so far. I'd been tied for valedictorian at a huge and competitive public high school, I'd been a soloist at the All-State choral and orchestral concert, and I'd been president of and/or varsity lettered in all my extracurriculars.

So as I discovered that everybody I met had also been valedictorian, editor of the school newspaper, an All-State varsity athlete or musician, etc., I had quite an adjustment. I had to learn how to stay present with my own inner experience and on what was in front of me directly.

I've been thinking about that experience these past two weeks as I have been watched my incoming 9th graders at Lowell adjust to the shock of discovering what it means to arrive at the next level.

The classes are much, much more demanding than they are used to, even at the strongest middle schools. And in addition, as every visitor can see at the front entrance of our school, there is a board that celebrates accomplishments of many of our Lowell graduates since our founding in 1856. There are three Nobel laureates, Pulitzer Prize winners, Broadway and Hollywood stars, admirals and generals and and politicians and world leaders. There are sports legends and pop culture icons, civil rights heroes, the founder of The Gap, and friggin' Lemony Snicket, among others.

Every race, ethnic background, and gender seems to be well-represented.

No wonder my poor kids are freaking out.

Now I try to imagine what it must be like to be one of the very few African-American students in our school. Some of them appear to be doing just fine, but I imagine it is a very strange and disorienting experience to find yourself in what must seem like an endless ocean of whiteness.

We are trying to be intentional in how we are supporting these students and transforming our school culture. We are following best practices and reflecting critically on how we are doing and how we can support their experience. I wish that I could magically airlift in a larger number of faculty of color so that they felt more reflected in the adult community they see all around them. But that is not how public education works. And we have no time to indulge in magical thinking.

So this is the point at which I am introducing some Talking Points on what I like to call desert island thinking. It is the best way I have found to help students to cope with their own feelings of imposter syndrome and the need to be their own best supporters as they enter a completely new territory.

I call it desert island thinking because it is what helped me to cope when I felt overwhelmed and alone as a freshman at Princeton. I reminded myself over and over that, if I were stuck on a desert island, I would want to be with other smart and motivated and hopefully good-hearted people because that would give us our best chances to survive and thrive.

In my teaching life, I think of this as Otter Nation. Our motto is, Hold hands and stick together. When sea otters sleep, they hold hands so they don't drift apart from their tribe. The same is true of us math teachers. We hold hands through the #MTBoS and through #educolor , through Twitter and blogs, and through every social media-based method we can find.

We hold our students in our hearts and try to give them every possible support and advantage we can provide.

For me, a part of that involves helping them to become metacognitively aware and and self-reflective about what they are experiencing and how they can cope with it, how they are brave and well-equipped and the advantages of holding hands and sticking together.

Our Latin Club has hoodies with one of my favorite lines from Virgil's Aeneid emblazoned on the back: forsan et haec olim meminisse iuvabit, which I would loosely translate as, "Perhaps some day we will laugh about this."   This is pretty much where many of my students — and especially my students of color — find themselves at the start of Week 3 too. At this point in Aeneid I, Aeneas and his troops have been driven from their homeland in Troy and find themselves on storm-tossed seas, wondering how they are going to survive.

A growth mindset, and some desert island thinking, along with Talking Points about it, are the best support I can offer them.

"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.

40 days and nights of standardized testing: a reflection

And on the 289th day, God made brownie mix. He divided the mix into the batter & the topping. And God saw the brownie mix, that it was good. And God said, Let the brownie mix be cheap and abundant and distributed to all the grocery stores so that all those who suffer, may make brownies. And the baked brownies He called "one serving," and he forbade the posting of the nutrition facts. And there were brownies, later with toppings, a comfort food.

Chords and Secants and Tangents, oh my!

Once you get to circles, chords, tangents, secants, arcs, and angles in Geometry, it's all just a nightmare of things to memorize — which means things to forget or confuse.

Rather than have students memorize this mishmash of formulas, I decided to have them focus on recognizing situations and relationships. And a good way to do that is with a four-door foldable.

Make it and use it.

Humans are tool-using animals. So let's do this thing!

Doors #1, 2, 3, and 4 each have only a diagram on their front door with color-coding because, as my brilliant colleague Alex Wilson always says, "Color tells the story."

Inside the door, we wrote as little as we possibly could. At the top we wrote our own description of the situation depicted on the door of the foldable. What's the situation? Intersecting chords. What is significant? Angle measures and arc lengths. What's the relationship? Color-code the formula.

Move on to Door #2.

We did the same thing with the chord, secant, and tangent segment theorems.

These two foldables are the only tools students can use (plus a calculator) for all of the investigations we have done with this section. They are learning to use it like a field guide — a field guide to angles and arcs, chords, secants, tangents. I hear conversation snippets like, "No, that can't be right because this is an intersecting secant and tangent situation."

My favorite is the "two tangents from an external point" set-up, which we have dubbed the "party hat situation" in which n = m (all tangents from an external point being congruent).

A big part of the success of this activity seems to come from teaching students how to make tools and to advocate for their own learning. Help them make their tools, set them loose, and get out of their way.

That's a pretty good strategy for teaching anything, I think.

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.

"The organism moves towards health" — reflections on TMC14

Everybody is writing blog posts about feeling like a fraud after an amazing experience at Twitter Math Camp 2014. Impostor syndrome. I feel like a fraud too, at least, most of the time, but I am trying to practice refraining from my conditioned habits of reacting automatically and giving in in response to that defense mechanism. I am practicing not-reacting. I am trying to notice the positive energy that is there and to just allow it. I am trying to allow myself to experience myself as a competent, good-enough teacher I have respect for and want to continue to be.

me practicing accepting myself as a competent,
good-enough teacher, seen here
with supportive tweeps & a giant margarita

What worked in the Group Work Working Group session was setting up a structure to sustain that positive energy of presence. Having learned how to do that is a huge gift I have given myself over the past 25 years of dharma practice. It's a "gift" that comes from working very hard at being present and practicing every day, rain or shine, whether I feel like it or not, whether I do it well or do it badly. I follow the three teachings my teacher Natalie Goldberg learned from her teacher Katagiri Roshi: Continue under all circumstances. Don't be tossed away. Make positive effort for the good. I have done that in my practice every single day for over 25 years. It's the one thing I know in my feet that I am good at.

starting with restorative classroom circles

So I decided to bring THAT to Twitter Math Camp this year.

The structure works because it is a structure for teaching and sustaining presence — learning to be present with an open heart. I have dharma sisters and brothers all over the world, but when we practice together online, we practice asynchronously — each of us on our own, in our own lives, in our own homes. When we come together using the asynchronous forum of online communication, we maintain that same structure of presence. Write when you write. Read when you read. Listen when you listen.

No comment.

using the Talking Points structure; no comment

"No comment" is the most important part of the structure, and the hardest part to implement online in a forum like Twitter, which is designed to support comments. "No comment" is about allow there to be space for everyone. It is about all being present together authentically and about staying present with whatever arises. THAT is the thing that most adolescents don't get exposed to in their lives, and it is the thing that can make the greatest possible difference in the quality of their experience — both in the math classroom and everywhere else in their lives.

Most people in our culture don't have a lot of experience in being present and staying present. It takes an enormous amount of energy to learn how to stay present and not flinch. But do that with anything you love and you will have a magical experience. Do that with math, and you'll unlock the treasures of your amazing human mind. But being present with others in a big open space is hard. At first it can be scary. It's very naked. That is why the structure of "no comment" is so important. It helps to create a shared space of emotional safety. It gets everybody focused on their own stuff and supports dropping the "act" you bring to most in-person interactions. That's why it's good to do so right from the start. It's about reframing our conditioned habits of personality.

Very quickly, the timed structure and the practice of "no comment" makes the practice of presence very freeing. You begin to relax into that big open space. You become curious. Your defenses soften. You begin to notice the interesting patterns of your own mind. Best self and worst self. Curious self and bored self. Zen mind and monkey mind. Defense mechanisms, such as snark.

collaborative mathematics
using the Talking Points structure; no comment

The practice of "no comment" creates a space in which the authentic thoughts of your own amazing human mind can arise and step forward. And we honor that process by persisting in not-commenting as we continue.

Natalie describes this process as stepping forward with your own mind.

Once you get a taste for being present, you'll naturally begin to crave it more. That is something I count on in my classroom management practice. Fred always said, "The organism moves towards health." That is one of his greatest teachings for me. "The organism moves towards health" means that, in the process of growing up, we all fall away from the naturally sane and healthy patterns of our organism. "Fight or flight" is a falling away from the natural discharge cycle of "rest and digest" we experienced as infants. When you're hungry, you eat. When you're tired, you sleep. Fred said there is a deeper wisdom inside us that is always available for us to tap back into. It's like an underground stream that is part of our psychological and emotional water table. When we practice being present through structures like Talking Points or meditation or writing practice, it feels like a homecoming — a homecoming to a natural state that is healthy and inquisitive and curious to see what will happen next. It is a natural reconnection with our own inner growth mindset that is our birthright — not some artificial fantasy state we impose on students from without by telling them to have one.

assigning competence after group work & 
observation; still no comment

A growth mindset is just the psyche's way of attuning to the fundamental idea that our organism moves naturally in the direction of health if we will let it — if we can get out of its way and allow it to unfold as it needs to. Allowing means learning to refrain from interfering with that natural movement, and so we use structures that make it manageable for ordinary human beings like us to access the extraordinary ocean of intellectual and creative possibility that is mathematics.

Ten minutes at a time is about what I can muster, I have learned over the years.

Kate test-driving a geometry task using the
Talking Points structure; still no comment

In my experience teaching meditation and writing practice and other structures that cultivate presence, I have found it is about what most people can handle. Ten minutes of Talking Points, no comment — GO. Ten minutes of writing practice — keep your hand moving, no comment, GO. Ten minutes of mathematical conversation, no comment, GO. Learning how to be present with the big, scary openness of not-knowing is no small thing. That is why we zone out, check our phones a hundred times an hour, play video games, watch TV, assault-eat, numb out, zone out, distract ourselves. We all crave the real stuff, but connecting with it feels like sticking a butter knife into the electrical socket. So we break it into more manageable chunks. We set a limit for ourselves and dive in for a limited period. We practice being present for ten minutes at a time. And then we give ourselves and our students a break. It helps us build our tolerance for the intensity of presence and it builds our courage to come back and try it again the next time.

Natalie says that monkey mind is the guardian at the gate, protecting the treasures of our heart and strengthening us for the challenge of opening ourselves to presence and to Big Mind. The structure of "no comment" makes it feel safe for us to touch in to that fire at the center of our being. It helps us to close the gap between what we THINK we've been doing and what we have ACTUALLY done. For me, it's about strengthening students' courage to open their hearts to contact with their amazing mathematical minds — with what my friend Max Ray of The Math Forum at Drexel calls their "mathematical imaginations." We math teachers know the secret that everyone has this mathematical imagination. Our greatest challenge is to get students to trust that they have it too and can access it safely and reliably.

________________________________________

TRY THIS
Read Taming Your Gremlin by Rick Carson.

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.

Building concept maps is harder than it looks

I'm having students create a concept map as a summative assessment for our Complex Numbers unit and... w o w — there is all kinds of learning going on.

 

Students are working in groups and can use all their notes and assignments from the unit. Some kids jumped right in and started hacking away. Others whined and asked why we couldn't just have a normal test.

We are using Post-Its, scissors, pencils, and paper to do our constructions.

In-process projects range from amazing to struggling, but what impresses me most is how much the work reveals about what students are figuring out and how each student is understanding and constructing meaning in their learning. It also demands that learners own their own learning.

Because this is so revealing, I am probably going to use concept maps both as formative assessments before and during the unit as well as using them as a 'ways of understanding' tool to help them consolidate their learning.

BREAKING: OK, this activity is definitely a keeper. Students are really digesting their learning, talking about it, debating how to represent it, and clarifying areas of confusion for themselves. Here is an outstanding example from today:

Writing Kids Notes

So much is not going right in my new classroom, but some things are. One thing that is going right is my off-stage strategy of writing kids notes. Megan Hayes-Golding blogged about her teacher notecards a year ago, and right away I stole the idea. Megan is a genius. They are comic strip-style notecards with "Dr. S" at the top of the main thought bubble, surrounded by comic strip energy.

What do I write notes for? The answer is as individual as the kids themselves. Sometimes I write a note to compliment a student on her renewed focus in class. Other times I will write a note to thank a student for a particularly insightful contribution to our discussion or to our classroom community.

Sometimes I write a note to encourage a student's courage:

Dear ___ — 

Thank you for asking Mr. X if you could come to my room during 4th period for help with your completing the square homework. I was proud of you for advocating for yourself when you were not sure what to do. Once we got to the bottom of that one piece of confused thinking, you were completing the square like a champ. For future reference, once Mr. X has called over, you don't have to wait outside the door to come in — you can just come right in.

Keep at it, ___. This new approach you are trying out is really working. — Dr. S

Another powerful kind of note is an apology for something boneheaded or inadvertent that I have done.

Dear ___

I am writing to apologize for calling you __ [another student's name] the other day in class. I felt bad all day about that because I value you so much for all the energy and effort you bring to our class. I never want to hurt your feelings, but I could see that when I made that mistake, it really hurt your feelings. I hope you will accept my sincere apology for my actions.  — Dr. S 

In my new school setting, I notice a thousand times a day how teacher energy and attention and support are a form of currency in the classroom and whole-school economy. Notes become talismans that support new behaviors and learning patterns and most importantly, courage. They are tangible artifacts of social and emotional learning that is every bit as hard-won for a student's mathematical and academic development as their mathematical skills.

Whatever the circumstances from which they come, I want all of my students to grow up into compassionate and mindful persons of power in their communities.

Sometimes the competencies we need most to cultivate within students are social and emotional. Many times I notice that the lack of well-developed psychological or emotional resiliency blocks a student from being fully present in their mathematics and from taking even small risks with their learning. And if we want students to be accountable for their behaviors, then we also need to model being accountable for our own.

Dear ___,   Thank you for telling me what is not working for you in our class. In addition to showing great courage in your learning, you have also saved me from wasting more of everybody's time using the same old failed teaching ideas. From now on, I am going to do more direct instruction and note-taking practice at the beginning of class first — before we break into group work. I think that will help you and the whole class to get the main idea students need to be successful with our investigations and practice problems. Thank you for helping me to understand what is not working for you so I can find a way to do it better. — Dr. S

Notes can become treasures that help students remember to advocate for themselves. There's nothing secret inside their envelopes, but they heighten kids' awareness that something important has been going on and that I have noticed it. Most of my students have never been noticed at school for much of anything. But because they are amazing and growing human beings, they want it. Some of them want it bad. And that is a big part of the culture I am trying to create. I want students to want to receive positive acknowledgment of something they have done in class.

"Dr. S! Percy is trying to look at my letter!"

"Percy! Leave Q's letter alone! That is her stuff!" 

Sometimes this system of accountability touches a nerve. Sometimes it touches a heart.

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.

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?