cheesemonkey wonders

cheesemonkey wonders

Tuesday, July 31, 2012

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.

Tuesday, July 24, 2012

TMC 12 - Some other "AnyQs" I've always had about "real-world" problems but been too ashamed to admit in public that I have

I am so appreciative of Dan Meyer's digital media problems and set-ups as well as his wholehearted spirit of collegiality. I have made what I'm sure must have been perceived as strange or totally off-the-wall comments or observations, and he has never been anything but gracious, kind, and supportive, both online and in person. Sometimes this has involved beer, but I like to think it has mostly to do with his innately generous and collaborative spirit.

So at my session at Twitter Math Camp 12, I felt brave enough to admit to some of the questions I've found myself having as a non-native speaker of math teaching who walks among you. I confessed that they do not sound like the typical questions I feel are expected to be generated by students, although there are plenty of students in math classrooms who, like me, are non-native speakers.

The perplexing thing is, they generated a lot of interest and conversation about on-ramps for students into a state of flow while doing mathematical activity, so I thought I would make a list of them here. So without editing, here is a list of the questions I prepared as part of my thinking as I was working through the issues of flow for students to whom the physics-oriented world-around-us questions are not the most natural ones to raise.

I often look at Dan's digital media problems and set-ups and find myself wondering...

  • Does it always work that way?
  • Does it ever deviate?
  • Are there any rules of thumb we can abstract from observing this process?
  • Are there any exceptions? If so, what? If not, why not?
  • How long have people known about this?
  • Who first discovered this phenomenon?
  • How was it useful to them in their context?
  • How did they convince others it was an important aspect of the problem?
  • Did the knowledge it represents ever get lost?
  • If so, how/when was it rediscovered?
  • How did this discovery cross culture? How did it cross between different fields of knowledge?
  • What were the cultural barriers/obstacles to wider acceptance of these findings as knowledge?
  • What were the implications of a culture accepting this knowledge?
  • Why do I feel like the only person in the room who ever cares about these questions?
It made me realize I object to the characterization of mathematics as the exclusive slave to physics. It also makes me want to introduce students to other fields (such as economics, financial modeling, forecasting and projections, free cash flow analysis, business planning and marketing planning).

It also made me realize that I am not, in fact, alone.

TMC 12 — impressions and takeaways

So many wonderful blog posts have already come in summarizing what people have taken away from our first Twitter Math Camp! I wanted to write down my own thoughts before any cross-contamination could occur because I am so impressionable by everything you guys say. :-)

In no particular order, these are some of my free associations and thoughts about what I found so valuable about Twitter Math Camp 2012.

TMC was marked by a pervasive spirit of generosity — generosity with ideas, generosity with listening, witnessing, and providing meaningful feedback, generosity with credit, and generosity with time and attention. In turn, the generosity shown by individuals and the collective was met with a truly dumbfounding generosity shown by institutions both private, public, for-profit, and not-for-profit. More on this in a bit.

It's rare to experience a group event that does not contain at least one naysayer or wet blanket, but Twitter Math Camp 2012 defied this trend. It was pervaded by a "can do" attitude from top to bottom, from beginning to end. There were no naysayers, no wet blankets, and also no pity-partiers and no spectators. There wasn't even very much unhealthy attention-seeking behavior. It was a marvel of the power of the word "yes."
No money for a venue? Find one that will host us at no charge (Thank you, Mary Institute and Country Day School of St. Louis — we love you!!!). 
No money for big-name speaker fees? Invite speakers who want to participate and will come to the conference on their own dime. 
No money for supplies? No problem. Invite people who are passionate about overcoming financial obstacles and who will share ways to do things "on the cheap." Or for free. Or people who will say, "Here, I have some extra, have some of mine." 
Nervous about presenting? Don't worry about it. Come and contribute as an audience member. Or volunteer to help out in some other way. Or lurk until you feel ready to jump in.
Also our benefactors were incredibly generous — and some of these insisted on remaining anonymous. I have so much respect for this I cannot begin to describe it. I wish the Gates Foundation had even a few drops of this kind of respect and humility. We were given discounts on commercial products and some free stuff.

And as if that were not enough some anonymous benefactor paid for 40 teachers' dinners at Pi Pizzeria — without even wanting to receive credit! I keep trying to imagine the Gates Foundation working anonymously but it just makes my head explode.

To whatever undercover bodhisattva bought drinks and dinner that night for 40+ excited, exhausted teachers, we all say THANK YOU from the bottom of our hearts.

This was authentically rigorous Professional Development — not the artificial (or faux) rigor of NCLB, standardized testing, PACT, BTSA induction, or most other PD events, conferences, programs, or fads.

The fact that we know and follow each other's teaching practice and reflections, based on years of engagement in the Twitterblogosphere, I found myself starting every conversation in the middle of engagement. There was no need to negotiate or argue for your priorities. They were simply accepted as legitimate because you had showed up.

I also found myself starting from a position of believing in the possibility and potential of each session topic. When @mgolding presented on INs (Interactive Notebooks), I dropped directly in concentration and went with it. When @jreulbach demonstrated how she helps middle schoolers translate words into math or uses foldables to teach them to slow down and honor a process, I took careful notes. When @bowmanimal led us through ways to use Geogebra in different kinds of lessons, I was willing to follow him anywhere (except to see Magic Mike, but that's a different story). The ability to dispense with the "literature review" and "topic justification" portion of each talk probably freed up 30% more time than is usual at a conference or PD event.

We came together as a community of committed individuals in an expression of healthy interdependency.

In contrast to the dangerous and destructive rhetoric of doing more, more, more with less, less, less and "to hell with what is good for the teachers," we supported one another and respected people's boundaries and limits. No shame, no blame. Taking good care of oneself is the best way to ensure that we will have energy to expend on behalf of our students, schools, and communities. As the great Jungian analyst and cantadora Clarissa Pinkola Estes has written, "Insist on a balance between pedestrian responsibility and personal rapture. Protect the soul. Insist on quality creative life."

I felt encouraged to trust that what I find truly useful will be of benefit to others too, and may even become more useful after I receive positive, constructive feedback.

Attendees came as they truly are in their real teaching lives. It was possible to have a deep, genuine conversation with anybody at any time on any given day.


There was a wide and generous interest in what others had to say at Twitter Math Camp — not simply politeness or compliance with the expected social norms of a PD or a typical conference event.

People talked about what actually works and inquired into why.

It didn't matter who you were with — new, old, young, mid-career, career-switcher. Everybody brought their A-game and shared it without hesitation.

Everyone's voice and presence was valued equally (okay, maybe @samjshah's voice and presence were valued a little more than the rest of ours were, but then, he is worth it). Everyone was valued and recognized as an equal.

No airy-fairy ivory tower research perspectives about the way things are supposed to unfold. This was the real deal.

Everyone at TMC12 understood that effective teaching and learning are much more than any single technique, tactic, or flavor of the month. These were teachers who were "all in" in their engagement. I felt proud to be a part of this.

Monday, July 23, 2012

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.

Thursday, July 19, 2012

TMC 12 - Day 1 - working the Exeter problems

We spent this morning in self-selected groups, working on Exeter Math 1, Math 2, or Math 3 problems. I worked in the Math 1 group. We agreed to work in a free-form way on the first four pages of the Exeter Math 1 problems, with discussion, collaboration, and analysis in any way we wanted.

I am still digesting and processing my experience, but here are some of the things I noticed.

My general feeling is that the Math 1 problems are all about cultivating independence. The sequence begins with an investigation into rates, but the work requires the learner to actively use what you know.

No spoon-feeding, no spectators.

As a learner, I found I had to focus on reading, interpreting, and decoding problems, listing information (what do I know? what do I need to know?), organizing it, and identifying my objective in the process. I also noticed that everything went more smoothly when I gave names to things and actively identified equivalences. Naming things and identifying parts of the problems gave me a way into organizing my information and my thinking.

I enjoyed working through problems and brainstorming about methods/strategies. I am now wondering, how I can use problems like these to cultivate independence and problem-solving with my students? How much scaffolding would middle-schoolers need to get started?

One of the things I am really interested in is how @k8nowak uses this kind of method to set up some "productive struggle" for a lesson. Oo, I think I'll go over to the other table and ask her!

Sunday, July 15, 2012

On being a non-native speaker in search of autonomy in the math classroom

I have a confession to make — I'm less like you than you might have thought.

I was never one of the students for whom mathematics came naturally. If I worked really hard and did twice as much practice as the worst "good" math students in my classes, then I was able to keep up. But I never experienced math the way so many of you describe your experiences of it. Don't get me wrong — I've always envied you. But I always seemed to need many more hours of privacy and "think time" and lots of step-by-step review of my own notes and rewriting what seemed to me to have happened in class. Slowly the ideas and understanding would grind their way into my body and mind, punctuated by multiple nights of dream-time reorganization of my learning efforts, until I could clumsily work along with the rest of you top students.

Carlos Castaneda makes a distinction between "stalkers" and "dreamers" — those who learn by pursuing their learning like hunters, finding and identifying and following their learning clues like predators hunting their prey, patiently tracking ideas through the jungle until their arrow meets the target and it becomes theirs. And then there are the "dreamers" — like me — who stumble along in mortal terror and confusion until we become one with the mud and the mystery.

"Wallowing" is a better description of how my primary learning state in mathematics proceeds. Day after day, I'm confused, mute, and incapable, unaware that I'm holding my breath like a deer in the "fight or flight" state, and praying that the teacher will not discover the secret shame that my body and my unconscious mind are desperately trying to conceal — the fact that I don't learn mathematics the way you are trying to teach me, the way you yourself learn mathematics. I wallow and I continue to wallow until the mysterious alchemy of osmotic transfer has occurred, until I have absorbed the mathematics as the mathematics have absorbed me.

I've always worried that my sense-making-reason-making-understanding mechanisms are defective because they don't accept the inputs being provided as the sole ingredients required for my learning. My body-mind cannot seem to identify them as nutrition. Sometimes it reacts to them as if they were pathogens I must be protected against. And that reaction triggers the fight-or-flight response, and I find myself once again holding very, very still to avoid your displeasure, disappointment, and frustration — and your discovery.

This is the curious thing for me about walking among you these days — I am a non-native speaker of this language of mathematics and mathematics teaching that we share. You speak to me as if I too grew up with this language, played with it from infancy, organizing my toys and numbers and ideas in my nest as you did. You speak to me as if I too were a native speaker, as if numbers were my first language. The other day Kate tweeted that her mom teases her that, when she starts teaching in the Southern Hemisphere, she may begin to swirl in the opposite direction from the way she has always operated up here, that, say, she will go from being someone who is naturally brilliant at learning and teaching mathematics to someone who is suddenly "good at poetry and relationships." When I heard that, I found myself wondering if I would experience the same thing if I moved that far south, but in reverse — if I would suddenly become someone who is naturally fluent in mathematics and does not speak it with a funny accent.

As a learner, I listen, I tinker, I do, I experiment, I reverse my thinking, I try to find a pattern, plus I take copious notes along the way so I can use them later to wallow in the material privately until I begin to feel the signs of absorption. I know that I will need time and space to live with my confusion, to wrestle with it, to struggle, and to hand off the baton of responsibility to my subconscious mind to rearrange the learning while my conscious mind and body take a break. Like the student volunteers in Robert Stickgold's sleep research lab at Harvard, playing a downhill skiing simulation video game before napping and playing again to assess their improved results, I need time and space for my unconscious mind to reorganize my daily fragments of learning. I need time and space to sink down into that primal, mysterious, adaptive soup before I will be able to notice that I am holding my breath once again in a fight-or-flight reaction.

Only then will I be able to breathe again and relax.

I don't know why learning mathematics is this way for me. I only know that it is. And I that gives me the confidence to say out loud that, as a learner, it simply doesn't work for me to be told to relax or to follow someone else's investigative process. It isn't always sufficient for someone like me to be invited into your curiosity about the purpose of mathematics—no matter how engaging your digital media representations are. Likewise, it isn't always sufficient for someone like me to be invited to pave a pathway to confidence through mastery of a checklist of concepts or procedures.

What does give me confidence — as well as engagement and determination — is being trusted and granted the autonomy to trust my own learning process and my own deeper wisdom about my own learning.

Of course, the tricky thing about cultivating autonomy, though, is that autonomy is by definition an all-or-nothing proposition. As a teacher, you can't grant autonomy cautiously or halfway, and you can't assume you know what another person needs in order to feel autonomous in their learning activity. If there is one thing I have learned from twenty-plus years of meditation practice and teaching, it is this:
You can't control somebody else's autonomy. You can only cease to interfere with their learning process.
This is why reframing strategies — such as games and game-like activity structures — can be such powerful additions to the learning environment. They free learners to choose a different focus for their conscious attention — something other than their ability to understand or not understand the learning target. For the especially shut-down or anxious learners, such reframing activities give our conscious minds a displacement activity (finding the treasure, completing a turn in a game) that keeps it busy and out of our hair while our unconscious minds and bodies can help us organize and reorganize the material before us into understanding.

Reframing strategies are also valuable in encouraging autonomy in capable and curious students, providing variety and texture to their experience as well. But most importantly, by engaging everyone in the room in their own personal and collective pursuit and experience of flow, they help to create the social and emotional conditions under which students can experience lasting and meaningful engagement.

What I am arguing here is that a key to developing a sense of autonomy in our math classrooms is to harness reframing strategies that support the greatest number of students in experiencing the flow state while doing mathematics as much of the time as is possible.

By blending these strategies with those that cultivate a sense of purpose (such as Dan Meyer's digital media + "Any Questions?"), and with those that, like SBG, clean up the tense and often fraught expectations and communication of mastery, I believe we can dramatically boost the percentage of students in the room who feel autonomous and taste a sense of flow while doing mathematics.

And that, it seems to me, should be the goal we are targeting.

Saturday, July 7, 2012

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.