And *THIS* is why I love the MathTwitterBlogosphere, part 573 – Infinite Tangents interviews Lisa Henry, Part 1

There are some very good things about Halloween on a school day, but a mandatory classroom "party" in advisory last period of the day on a Thursday is not one of them.

When I had finished complaining to myself about the state of my classroom and cleaning up the last of what the 13-year-olds had left behind that really bothered me, I packed up my stuff and got into my car.

And I remembered that I had an Infinite Tangents podcast all cued up for myself — one I'd been saving for a moment when I needed it most. A moment like now.

So I got to spend the drive home with Ashli and Lisa Henry. Part 1. A glorious triumph of delayed gratification.

I feel lucky to have gotten to know Lisa first through Twitter and blogs and then in person at the first Twitter Math Camp in 2012. Lisa has a gift for teaching through community-building, and she has brought this gift to bear on Twitter Math Camp. I admire and appreciate her respectful and inclusive community-building, and it inspires me in my own classroom and in my life.

Now, like most teachers, I come from a family of storytellers, so it's probably no surprise that I love hearing other people tell the stories of events I participated in. I love the prismatic contrasts of perspective and memory – the way something that struck you as essential to an event gets bumped down or deflected sideways in another person's memory due to proximity or overtaking or whatever. So I love hearing Ashli and her guests telling stories of events I remember because that process invokes the same pleasure twice – the memory of the event itself and the joy in the retelling.

My mood lifted considerably as I gained distance from school and lost myself in the conversation and the memories they were weaving on my car stereo.

It was fun to hear about and remember the great Facebook "befriending" moment in 2011 or so—that moment over Christmas Break when a bunch of individuals who'd been nothing more than virtual colleagues on Twitter (but who were still basically strangers) decided to take the seemingly insane step of "friending" each other on Facebook.

It was a moment of enormous risk.

It's one thing to share teaching ideas or goof around on Twitter, but crossing that line between virtual and IRL felt profound. What if these people turned out to be crazy? unpleasant? dangerous? Or even worse — what if they turned out to have different political beliefs than I did?

The risk felt very real at the time, and sometimes it still does. I don't pretend to be something I am not. I am a liberal. I live in San Francisco. I am a practicing Buddhist and a Democrat. My representative in Congress is Nancy Pelosi. I believe in a lot of things I know that a lot of other people in other parts of the country do not.

But the one thing I know in my feet is that I am a teacher — and a learner.

And I knew that all of these other teachers all over the continent who had become my tentative friends and virtual colleagues on Twitter in exploring what it means to teach and learn math were every bit as committed to what that means as I am. So I guess I trusted it. I was willing to go with it, and to push myself beyond my comfort zone for the sake of connecting with a community of like-minded math teachers who want the same things for our kids and for our communities and for our countries — regardless of what we may believe at the grassroots personal level.

And with all of that as background, I have to admit — it was one of the best and most profound decisions I have ever made.

I was one of those crazy ten or fifteen people who was hellbent on attending Twitter Math Camp even if we had to hold it in a yurt outside a garbage dump. I knew that these were people I wanted to be connected to and spend time with and get to know, even if we seem like we'd be completely incompatible based on what you can see from examining our surfaces.

There was a (now-hilarious) period of several months when it seemed as though what my new friends most wanted us to do was to go on a cruise together and do Exeter or PCMI problem sets together. I remember that Julie looked into costs and group rates and I thought to myself, what in the name of everything sacred have I gotten myself into? I hate situations like cruises. I get seasick. I could imagine nothing worse than being trapped on the open ocean for days with people I don't know.

But there was something about the energy of the group that I innately trusted.

I kept my cruise-hating thoughts to myself, but I hung in there because I knew I did not want to miss out on what appeared to be happening. These were people I wanted to spend time with, and I supposed that if that meant I would HAVE to spend time on a cruise ship, I could probably get a prescription for some kind of anti-anxiety medication to have on hand in case I completely freaked out.

And I just hung in there.

Eventually, the cruise ship idea fell apart, thank God, and the math camp idea came together. And nothing has been the same in my life ever since. And it's been good. Very good.

By the time I went through the toll plaza at the city end of the Golden Gate Bridge, I was not only not crabby any more, I was actually happy.

I felt connected to something much larger than my own daily grumbles, and that was enough to wash all the grouchiness away.

By the time I had parked the car, walked the dog, and poured myself a beer, I realized I needed to blog about my drive as a way of remembering what was good and sane and life-affirming about this experience I am having of being part of a worldwide community of math teachers who see teaching as something much larger than what is happening just in our classrooms.

So this is my "One Good Thing" for the day. Thank you, MathTwitterBlogoSphere, for being there on the other end of the Twitter line whenever I need to feel connected.

Gasshō.

Twitter Math Camp 2013 — reflections on a sustainable model of hope

At Twitter Math Camp 2013 (#TMC13) this morning, I was both amused and inspired to read these two tweets — one by one of my math ed inspirations and another by a colleague I could not respect any more than I do and whom I can also call a friend:

Ann and I having great time in Philly at Twitter Math Camp - amazing ideas and energy! Massive hope for what is possible.
— Steve Leinwand (@steve_leinwand) July 27, 2013

You guys, we gave @steve_leinwand hope. We can go home now.
— Kate Nowak (@k8nowak) July 27, 2013

Like my spiritual and general life role model, Wile E. Coyote, I am invariably hopeful in a small sense that this will FINALLY be the moment — that perfect moment when all my best-laid "plans" will do the trick and I will, at long last, have the solid, effortlessly nourishing, and unshakable ground beneath my feet that I crave (and that I believe I so richly deserve).

But years of experience have taught me that that is the "hope" of an Indulging Baby — a person who looks like an adult on the outside, but who really walks around believing that my every problem, need, and desire in life should be solved by benevolent and invisible external forces. This is in harmony with my frequent conviction that my life really ought to operate like one of those behavioral experiments in which, each time I press the correct lever, the Universe promptly and consistently rewards me with a food pellet.

So I'm sure you can imagine my annoyance with the reality that life — and teaching — refuse to cooperate with my first-draft of things.

For the second year in a row, I have blown away by what I receive at Twitter Math Camp. The best, the most creative, the most resourceful, and the deepest-thinking math teacher I know in the English-speaking world show up and share with me their 'A' game. This is not so much a blessing to me as what I would describe as a complete fucking miracle. In sharing, in presenting, in participating, and in attending, every single person at this conference gives me a richer PD experience than many teachers ever get in an entire lifetime.

And in a sense, that is the point.

For me, this conference is about refilling the well at The Great Oasis of The Impeccable Warriors. There pretty much are no Indulging Babies here at TMC. If you want somebody to take care of you and make you feel better and wipe your butt, well, this is not going to be the place for you. Everybody here is truly impeccable. To me, that means that everybody does the very best they can in whatever situation they are in. It's a stone soup mindset. If everybody has crap, then we will be eating crap soup that night. But if everybody brings one small, precious ingredient to the soup, then we will be eating like royalty — or at least, like Silicon Valley-based organizations that are overfunded by the Bill and Melinda Gates Foundation (use your imagination, or consult @fnoschese's Twitter feed and/or blog).

That is not to say that everything is perfect. People are still people, which means we can all sometimes be thoughtless, stupid, impulsive, stubborn, rude, and a whole host of other things.

But what makes this work, I think, is that everybody here owns their own "stuff" and is willing to be accountable for what they put into the communal mystic cookpot.

The truth behind the truth is, I brought my 'A' game too. I worked for three months on my sessions, planning, preparing, reflecting. You guys are my tweeps. My tribe. Even though I had an almost totally crappy year, I did not want to let you down. And I have learned that I will get back in proportion to what I put in (cf. CCSSM 8.F.1 and 8.F.3, and passim).

So my challenge to everybody who is attending Twitter Math Camp for the first year this year is to reflect on this question:

Now that you have fifty percent as much experience with TMC as even the most experienced Twitter Math Campers among us, how are YOU going to help make Twitter Math Camp just as amazing next year?

I strongly believe that the people who show up for something are exactly the right people. So, hey — welcome to the club of Impeccable Math Camp Warriors! You certainly have something important to contribute, or you would not be here reading this.

You don't have to answer this question right now. But if you want this to be here next year — both for yourself and for others — it is important to hold this question in your heart as you process the experiences you've had these past several days.

I believe that hope is a process, not a destination, and I believe that what Steve Leinwand was responding to was the awesome force field of being in the presence of 125 impeccable warriors all being impeccable together — 125 math teachers who don't simply complain about what a mess things are, but rather who each grab a mop and say, oh, I see— I'll do it.

An act of wisdom

"One thing I know for sure is that when you are hungry, it is an act of wisdom each time you turn down a spoonful if you know that the food is poisoned."                            

— Anne Lamott, Operating Instructions

There are some truths you have to live, even when that path is hard. For me, this is one of those times. I have this quote hanging over my desk, which is helpful because I have really had to live it this school year. Every morning I need to remind myself of the wisdom and sanity of this perspective.

For me, this truth is bedrock. 

I resigned from my current school in March to remove myself from a toxic situation that is still unfolding. My conscience told me I could not be a part of the direction that is being pursued.

I had to turn down the spoonful to save my soul because I knew in my bones that the food being offered had been poisoned.

Hence my current job search.

I may have resigned that position, but there is no way on earth I am going to leave this profession.

I am a very effective and highly qualified teacher of mathematics, which is an area of desperate need and critical shortage around here. But we are living through an extraordinary period of economic uncertainty and complete political insanity — a time in which our leaders oscillate between one extreme of grandiose talk about "reforming" public education and its opposite of all-out panic at the crisis-level reality of our schools' current situation. 

Our leaders are lost, and our children are bearing the brunt.

The Serenity Prayer instructs me to accept the things I cannot change, the courage to reach out and change the things I can affect, and the wisdom to discern the difference between these two very different kinds of things. 

So as I apply for new jobs and do interviews and give demo lessons, I am also choosing moment by moment to renew my focus on growing and improving my practice as a teacher of mathematics.

And as I do this — even as I fret or worry about finding a new position — a curious thing keeps happening: I keep falling in love with math teaching all over again.

I've created a really great project-based learning (PBL) version of the Barbie Bungee activity (see here and here and here and of course, here), and I'm doing the same thing for the Double Stuf Oreo measurement extravaganza I plan to guide my students through this week. I am learning a ton about differentiation through teaching problem-solving from the online course I am taking from Max Ray at The Math Forum, even though I feel like I can never do enough of the coursework. And Kate Nowak (now of Mathalicious!) and I are having a blast brainstorming our 'PCMI Problem-Solving, TMC-style' problem-solving session for Twitter Math Camp '13 in late-night Google doc chat sessions.

I am hoping that all of this work will be of benefit to me in the fall, but the reality is, of course, that there are no guarantees.

I remind myself daily of the three great teachings my own teacher Natalie Goldberg passed on to me from her root teacher Katagiri Roshi. These are:

•  Continue under all circumstances
•  Don't be tossed away
•  Make positive effort for the good

I am working on writing up and sharing all these lesson ideas and learnings that I'm figuring out, but to be honest, I am struggling to find the time right now. So I am taking good notes to help me write up these blog posts over the summer.

I also remind myself of my amazing good fortune to have my tribe of math teacher-bloggers in the math twitterblogosphere. You support and inspire me every day, and my gratitude for you is bottomless.

Thoughts On Making Math Tasks "Stickier"

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

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

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

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

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

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

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

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

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

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

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

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

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

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

"My work here is done."

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

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! :)

And this is why I teach...

It was another crappy Friday in an arithmetic series of crappy Fridays that were running together and threatening to define the limit of my patience for fall trimester as x approaches a mid-sized number that is nowhere near infinity. So I have no idea what possessed me to wake up even earlier than usual to pull together an extra day's practice activity for my right-after-lunch class of rumpled and discouraged algebra students — the ones who believe to their core that California's Algebra 1 requirement is God's own punishment for unremembered karmic crimes they must have committed in previous lifetimes.

But I did it.

The topic was solving and graphing compound inequalities — a skill set that must be mastered in order to have any hope of making sense of and mastering the next topic traditional algebra curricula force-feed to our students: the dreaded topic of absolute value inequalities.

There's really nothing I can say to convince a roomful of skeptical eighth graders that compound inequalities will prove not only useful in business planning (which, after all, is simply algebra writ large across the canvas of the economy) but also amusing and possibly even interesting little puzzles to delight the mind.

To this group of students, they're simply another hoop to be jumped through.

So something in me understood that I needed to reframe the task for them, and to do so using Dan Pink's ideas about intrinsic motivation from his book Drive.

Nothing unlocks the eighth grade mind like an authentic offer of autonomy. As I explained recently to a room of educators at a mindfulness meditation training, middle school students suffer emotionally as much as adults, but they have comparatively little autonomy. A little well-targeted compassion about this can carry you for miles with them, though I usually forget this in the heat of working with them.

For this reason, I like to save practice structures such as Kate Nowak's Solve—Crumple—Toss for a moment when they are desperately needed. I have learned to withhold my Tiny Tykes basketball hoop for moments like this, when students need a little burst of wonder in the math classroom. And so even though I was tired and very crabby about the ever-increasing darkness over these mornings, I pushed myself to pull together a graduated, differentiated set of "solve and graph" practice problems to get this group of students over the hump of their own resistance and into the flow experience of practicing computation and analysis.

And oh, was it worth it, in the end.

The boys who are my most discouraged and resistant learners came alive when they understood that a little athletic silliness was to be their reward for persevering through something they considered too boring to give in to. They suddenly came alive with cries of, "Dr. X— watch this shot!" from halfway across the room. One boy who can rarely be convinced to do the minimum amount of classwork completed every problem I provided, then started tutoring other students in how to graph the solution sets and perform a proper crumpled-paper jump shot.

The girls in the class got into it too, but they seemed more excited about the possibility of using my self-inking date stamp to stamp their score sheets. So I gladly handed over the date stamp to whoever wanted to stamp their own successfully solved and graphed inequalities.

I was far more interested in reviewing their mathematics with them. One of the things I love best about practice structures like this one is that they give me an excuse to engage one on one with discouraged students under a time crunch pressure that adds a different dimension to their motivation. Suddenly they not only want to understand what they have done, but they want to understand it quickly, dammit, so they can move on to another problem, another solution, another graph, another bonus point.

Ultimately, Solve—Crumple—Toss becomes an occasion for conceptual breakthroughs in understanding.

I can't tell you why this happens. I can only tell you that it does happen — often. It makes me feel lighter, more buoyant about teaching them algebra. And it makes them feel happier too.

I wanted to write this down so I could capture it and remember this for a few weeks from now, when it stays darker even longer in the mornings and when I feel crappier and crabbier and more forgetful.

Radio Silence Does Not Mean Nothing Is Happening...

Wow, did I ever fall off the radar.

Plop. That "splat" you might have heard was me, falling off the blogging radar.

But I'm back, baby.

Last night I had the most wonderful dinner with @btwnthenumbers and @woutgeo and @mythagon, who was in town for a conference/collaborative meeting, and I tell you, it pretty much restored my faith in teaching, in mathematics, and probably in all of humanity.

I have been working at a near-frantic pace these last five weeks, prepping, teaching, grading, not grading, having parent conferences, having meetings with parents and the principal, having meetings with parents and principal and superintendent, going to IEP meetings, collaborating with my department members to write goals that will help us to align our curriculum with the Common Core, and generally dealing with all those things that go haywire as soon as you start to nail down some satisfying, finite part of your teaching.

In other words, just like you, life has been kicking my ass.

But between last night and this morning's drive to work something shifted. Something sane and healthy intervened.

That something was my connection with the Twitter- blogo-sphere.

Whenever I'm feeling exhausted and run over with skid marks across my face and body, connection with my tweeps -- any connection -- seems to be the best medicine. I don't know why this is true; I only know that it is so. Remembering this makes me think of a quote I have from von Neumann hanging in the ring of inspiring quotes that encircles my classroom: "In mathematics, you don't understand things; you just get used to them." Some days that's how I feel about things in my classroom or in my school or in my life.

I only know that five or ten minutes of venting to my tweeps about an impossible situation -- even when @woutgeo is only half-listening because (a) the Giants are sucking pretty hard against the Cardinals and because (b) my venting is both predictable and boring -- it helped just to have reconnected with the connection. In Jakobsonian structuralist linguistics, this kind of communicative connection is known as a "phatic utterance" (look it up, Riemann, I have to look up all of your crap).

By this morning, I was feeling reasonably happy driving to work for a 7:30 a.m. meeting. I was not totally thrilled about the hour or having to buy gas at that hour or the price of gas for that matter, but I felt pretty great about car-dancing in the dark to Ace of Base's "The Sign" and remembering car-dancing at #TMC12 with @mgolding and @samjshah and @jreulbach and @ bowmanimal on the way to do Exeter problem sets. And I felt great when @rdkpickle's sweet soprano voice was joined by @SweenWSweens and @jreulbach singing "Tweet Me Maybe." And I even laughed when the theme from Sesame Street came on. iPod's "shuffle" feature has a somewhat perverse sense of humor.

OK, and one other thing I have learned is that my dog always knows when it's time for me to end a blog post. Just now he jumped up on my lap and pounded the laptop keyboard with his giant panda bear paw:

34ycvzn

So that's my cue to wrap this up.

I just want to say, if you are feeling alone or frustrated or exasperated and you are reading this, then for the sake of everything we hold dear, please reach out to someone else who is of like mind. "It's hard to teach right... in isolaaaaaaaaation.... So here's some PD.... just like vacation!"

Tweet me maybe, tweeps. Over and out for now.

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.

On choosing sanity, and on modeling this choice for our students

I want to talk a bit about sanity — not because I think I'm an expert (I'm not; no one is) but because I have come to understand sanity as a choice we make moment by moment, and because, in so doing, I have seen how we either model — or do not model — it for our students in our classrooms and in our lives. And this is an enormous part of the social and emotional life training they either receive or do not receive in this crucial part of their lives.

I teach middle schoolers, or rather, I should confess that they teach me. Every student and every class is a mirror in which I can see what I am teaching them. Perhaps because their access to it is new, middle school students have a finely tuned hypocrisy detector. More so than any of the high school or university students I've ever taught, middle school students want to see who "walks their talk." Do so, I have learned, and they will follow you anywhere. Fail to do so at your own peril.

So a big part of this year's learning, for me, has been learning how to tune in to what I am actually doing and checking in on whether this is consistent with the social and emotional lessons on appropriate self-care I am trying to teach. Sometimes that has meant being the adult in their lives who tells them to stop the madness. The only way to stop the war is to stop fighting, stop struggling, stop efforting. There really are only so many hours of the day, and for middle schoolers, about eight of those need to be spent sleeping. That means every piece of homework can't always get done every day all the time. Sometimes a person has to choose sanity. So I try to understand that and allow for it, because learning to allow space for all of life is something they are going to have to learn if they are going to do better in running this world than we have done so far.

I've also had to learn how to trust my training and my gut. I was blessed to study for over ten years with a pioneer in integrating social and emotional intelligence and mindfulness into learning environments ranging from special education to mainstream classrooms to therapy situations. You probably haven't heard of him because he has spent his life being what I think of as a guerrilla bodhisattva — a pioneering educational psychologist and an undercover evangelist for social and emotional health in daily life. His name is Dr. Fred Joseph Orr, and I am blessed to count myself among his students. Actually, we think of ourselves as his disciples, though he would undoubtedly discourage that characterization. But it's a fair one. He taught us to integrate teachings from whatever sources might be beneficial to ourselves and our communities — teachings from Adlerian psychology, spiritual development, meditation, yoga, Buddhism, his own mischievous sense of humor and spirit of adventure, writing as a practice, the practice of joy and creativity in whatever form they might take, and environmental restoration and ecological rebalancing. I came to him as a writer, writing teacher, and longtime meditation practitioner, but I quickly became much more than that under his mentorship. And it was the kind of mentorship that is a true spiritual gift — the kind you can only repay by sharing it with others. In his life, he suffered in ways that most of us would find unimaginable, and yet he remains the most radiant and joyful person I have ever known. And although his active teaching practice has been cut short by a medical condition that has become the focus of his own personal life practice, his students carry on his great efforts, sharing the learning and the gifts we received from his teachings. His teaching of us was an investment in the future and a labor of love. I wake up every morning determined to be worthy of the effort, love, and energy he poured into teaching me.

There's an urban fable Fred used as a teaching tale. It's known as The Hundredth Monkey principle. It began in the 1950s as a call to end the escalating nuclear arms race, but Fred believes it has broader applicability as a model for how human awareness and sanity can be activated too, and I have come to believe this too. The idea is simple, yet profound: when a critical mass of individuals' consciousness gets raised, it inevitably triggers a paradigm shift in the dominant culture. So this turns out to be a more leveraged model for social change than the conventional wisdom tends to think, for when we direct the focus of our daily efforts on helping individuals and small groups to shift their energies, awareness, and attention, we are doing our part to put our culture on the path that leads toward greater sanity, in addition to greater achievement.

So what does all this squishy-sounding woo-woo stuff have to do with teaching and learning mathematics?

I believe it provides us with an on-ramp, a way to reach the hearts and minds of the students who are most discouraged and shut down in the math classroom. It's differentiated for the most capable students because most of them have never been given tools to cultivate self-awareness and other-awareness as a part of their learning. And by learning — and by teaching these discouraged students how — to cultivate their social and emotional intelligence in how they engage in mathematical practice in our classrooms, we can change their relationship with mathematical studies to one based on what the American Tibetan Buddhist teacher Pema Chodron describes as "unconditional friendliness."

Over the last couple of days, as I've begun my yearly summer rituals of cooking and storing school lunches in the freezer for days when I need the loving self-care of hand-made soup in the middle of my day, I have realized that this is the heart of my Twitter Math Camp talk. My topic is Dan Pink's book, Drive: The Surprising Truth About What Motivates Us, and how to use his ideas about intrinsic motivation to reach the discouraged math learners in our classrooms. I've begun to understand how Fred's work with me is an arrow that flies straight to the bullseye of this target, and it's given me some hopefully valuable insight into how to create the toughest of Pink's three pillars of intrinsic motivation. That pillar is autonomy, and I'll write more about it in an upcoming post as I flesh out my talk with ideas and activities.

In the meantime, I'm going to let my subconscious mind work on the problems while my conscious mind takes a nap.