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Sonar the Sheepdog and Toad the Terror take a personality test!

Posted on by Fig Tree

It’s summer vacation, so it’s time to think about…personality tests!

I was speaking with a colleague a few weeks ago about our Myers Briggs types. I have an interest in the MBTI because I’ve spent so much time with Carl Jung, whose writings on the axes of personality were reduced into the 16 Types structure and then commercialized, a process that found new life with the advent of the online personality test. I humor myself in thinking I can find some deeper, fluid truth behind the rigid determinism of the derivative structure, while also successfully avoiding Jung’s persistent sexism. Good luck, chump! Anyway. I like talking about it.

Another colleague chimed in with a comment about astrology, which, look, fair point, but in the hands of someone who’s like “astrology, fine, let’s talk about it,” that comment isn’t a deterrent. She stated that she got a different type every single time she took the test.

This is contrary to my experience, in which I’ve classed myself as a ENFJ persistently over some 20 years: that is “Extraverted-Intuitive-Feeling-Judging”. I wiggled toward “Introverted” for a time, but I think that was wishful thinking on my part more than anything else (more on our subjectivity toward our subjectivity in a later essay, I think). One way to think of this is that my public persona is best compared to a sheep dog named Sonar who is transparent to what everyone (including himself) feels and so is always trying to gather everyone around him into a herd. The dog named Dug from Pixar’s Up comes to mind. Affable and attentive, on-his-sleeve emotional, somewhat dismissible and unserious. That’s my outward persona and captures some truth of how I instinctually engage the world, and it seems like that’s been true for a long time, despite big changes in my life and the long arc of adulthood.

Perhaps because of that disposition, I didn’t ask my colleague any questions, but rather clocked the emotional tone of the comment (i.e. “personality tests make me frowny”) and went about my day — but my curiosity lingered. And here’s another thing I’ve come to think of as an aspect of my personality through the lens of this MBTI type: if my dominant mode of engagement with the world is “extraverted-feeling,” my non-dominant or shadow mode of engagement with the world is “introverted-thinking,” which Jung seemed to think we would experience as something of an attack when it was active. So my curiosity turned this colleagues’ comment over and over in my mind, and with time my thinking became more and more energetic, until another character of mine, one decisively not in my public persona, came to the fore: let’s call him Toad the Terror. Contra the Wind in the Willows character, my Toad the Terror is not all instinct, but he is a breathless and aggressive thinker whose rationality is tempered somewhat by being a Toad with the title “the Terror”. It’s not that he’s angry, he’s actually pure joy, but don’t get in his way. (Dear reader, I always get in his way.)

While Toad the Terror likes to ride the engine of my mind recklessly, he has his uses (“he chanted as he flew, and the car responded with a sonorous drone…). He is, after all, a part of me, and if I can slow him down enough to hear the connections he makes, he brings me all kinds of food for thought.

So I was thinking about this idea that one can get different results on a personality test over time, which on one hand could be a critique of a personality test as hopelessly inaccurate or subjective, and on the other hand could be a critique of the idea…that we stay the same over time! It can do work for both sides. So I wanted to take a step back and think about what we mean by personality.

I’d start with the question: are there invariants to a person’s character, detectable in their behavior, relationships, and self-reflection? What stays the same in a person as they grow? What changes? If a personality test is supposed to tell you something about you as You, how can it best describe those invariants? If your results to a personality test change, does that reflect a changing invariant (gross), or something else?

I’ll start with a safe claim: there are invariants to a person. There are things they do that make them them. These qualities can have two sources, in my thinking: they are either embodied, having been established early in life as our instinctual dispositions on an unconscious level, or they are spiritual, in the sense that they transcend our earthly, temporal form. When I talk about the former, I have the processes of depth and developmental psychology in mind, as well as baser matters like genetics. We’ve been natured, we’ve been nurtured, and the contour of those influences are established early in our human form. When I talk about the latter, I am thinking of the way the author Catherine MacCoun, following Trungpa Rinpoche, talks about “style”, the essence, what we mean when we refer to a person’s spirit. It is not reducible to material, environmental influence. It’s what’s there there.

To that point: I don’t believe these categories of embodied and spiritual are mutually exclusive or independent of one another; it’s just convenient to think of them along these lines. (Spoiler alert, this is not my first dance with dualism in this essay, nor will not be my last. Buckle up!)

The designation of invariants implies the presence of variables. (Please see the spoiler alert above, I known what I’m about.) There are things that change about you. Let’s call them mutables. The embodied and spiritual categories can do some work for me here: what is materially mutable for you is your ever-changing environment and relations. Major changes in your life can change your patterns of behavior, your manner of relating to others, and your values: becoming a parent, falling in love, winning the lottery, experiencing loss or trauma, getting religion, what have you. And what is mutable for you in spirit is that restless ego-persona of yours: the thinker-doer-chooser, the agent at the center of consciousness but not the center of the Self. This character’s fickleness is famed. Descartes was particularly concerned for this fellow, and implied his capacity for being profoundly deceived.

Same caveat here but now in two dimensions: not only does your material environment and relations influence your conscious agency and vice versa, but your experiences in the material world are a road test for your spiritual-invariant style, and your ego-consciousness is always in a tense standoff with your embodied, instinctual navigation of the world: they are two different sets of values, conscious and unconscious, always pulling in tangential or even opposite directions.

I’m going to need a chart! But developing a transcendent meta-structure for personality is beyond the scope of this post. I’m here to talk about the interesting problems of personality tests.

So along comes our modest personality test, which should ideally raise up the invariants of one’s personality, and will have some explaining power to describe how that invariant character navigates the mutables of its life. As busking street performers say: “that ain’t easy!” Not because an exhaustive taxonomy is impossible (MBTI defines 16 different types of people; the Enneagram has 18 when you account for wings; I suppose the Big Five Traits people would claim something like a continuum?), but because personality has one more salient quality: complementarity.

Complementarity is most commonly associated with quantum physics. In that realm, its origin lies in the work of Niels Bohr and Werner Heisenberg, or perhaps earlier, when it became clear that when describing light, it was accurate to describe it as both a wave and a particle, two mutually exclusive ways of being, in order to account for all of its observable behavior. Conversely, if you prioritized one aspect of light too much, you would lose essential behaviors as described by the other aspect. At an early stage of quantum inquiry, classical assumptions did not adequately describe atomic and sub-atomic behavior. At that scale, different rules applied. Following the work of Neil Theise, this idea of focus-on-one-lose-the-other is precisely a problem that occurs at any movement from different scales of organization in the world. The positive product of complementarity is emergence, the appearance of a new observable behavior that could not be predicted on the basis of the prior scale of investigation alone.

For our purposes here, it goes like this. That which is invariant in a person, and that which is mutable, are in a complimentary relationship with one another. Look at one too closely and the other, out of focus, behaves unpredictably and your describing power is diminished. I think that this is the tension that personality tests, and their users, are perpetually caught within. Personality tests need some sense of development or growth within them, while also resting on sound categories of invariant character, to really do the job well. We would need to read them in this way to get anything useful out of it as well. Focus too much on the invariant, and we get caught in determinism. Focus too much on the accidents of the current moment or the present whimsy of the ego, we make personality into a mirror of our circumstances — which I suppose is another kind of determinism! (All of this, it seems, is just as applicable to astrology, and I have a truly marvelous demonstration of this proposition which this margin is too narrow to contain etc.)

Finally, then, to the point! Persistent and dynamic, invariant and mutable, body and spirit, a product of its environment and a free agent: our personality is an emergent property of multi-dimensional web of mutuality, unfolding forth unpredictably from along each axis, not collapsible to any one node. To layer on another physics metaphor, our personality is a three body problem, where the third body is the whole of the other two.

We’re a dance! No wonder those personality test questionnaires are so long. And for my skeptical colleague, I would ask, Sonar the Sheepdog jostling politely with Toad the Terror for the wheel — what has the test always said about you? What does it say now? And does it mean anything for you?

Justice/Religion in Culture/Teaching/Theology/Zen

A Classroom has a Soul

Posted on by Fig Tree

When I was in seminary, I had planned my master’s thesis around the title “Psyche and Spirit in the Classroom.” I see now that this was a skew frame, at an awkward angle, that made it unnecessarily difficult to apply the tools for thinking and seeing that I had gathered in my training. From the perspective of complexity: I was observing the wrong scale. From the perspective of engineering: I had drawn an incomplete system. From the perspective of education and progressive pedagogy, I misunderstood the proper field of reflection on my work as a teacher.

From the perspective of theology, I made a category mistake — what I needed to explore was, “Psyche and Spirit of the Classroom.” To the point: the classroom has a soul, that nexus between the embodied, unconscious constituent elements (psyche) and the animating, holistic awareness (spirit); that heart of being, where will and ideal meet and open the way for action, for reflection, for growth, for compassion, for something new in the world.

The classroom has a soul. Psychodynamically, it has a internal culture, a character, a potential space that holds in tension the inner experience and the outside world, that is made stronger by trust or made weaker (that is, fractured, schizoid) by imposition of the “real world” on it. In Buddhist terms, it is a unity composed of vast diversity, that becomes a harmonious, cacophonous community that realizes the Way (Suzuki Roshi said: “things as it is”). Again from the perspective of complexity, the classroom’s inner experience of of itself is an emergent property of its constituent elements (students and teacher) acting according to a fixed set of simple, local rules. From the perspective of progressive pedagogy: the classroom is a community first, composed of interrelated and interdependent free persons, that engage in democratic process to be accountable to one another and grow their collective wealth.

For all my years as an educator, I have wondered about what a classroom is, what it is for, how it creates change; why students do what they do, and what the teacher can contribute; and finally, what the classroom can create in students to respond to our contemporary crises, adapt as a community, and make progress together. As a math teacher I’ve often started with the distinction between narrow mathematical skills (the “what”) and broader habits of mind (the “how”) but its a natural move to generalize this tension to other subjects, and then of course to a classroom’s or school’s purpose in the context of our culture, society, economy, politics, etc. What are we trying to do here? What will happen no matter what given our structure and the incentives students understand, and what can we actually change in them, and in the world?

Helpfully, to ground this, I have returned repeatedly to thinking about the math classroom, over cycles of reflection, over years and years of practice. To articulate the basic tension, I’ve long relied on Magdalene Lampert’s work (particularly in Teaching Problems and the Problems of Teaching or the essay “When the Problem is Not the Question and the Solution is Not the Answer”) to articulate two goals of my math classroom.

  • Learn the math.
  • Learn how to be the kind of people who learn math.

When I say, “the math” in the first goal, I refer to School Math, a set of procedures and objects that are narrowly defined and even overdetermined in what our society expects of schooling. I say overdetermined, because there are so many factors that narrow what might be called “Mathematics” and its practice to a sequence of “algebra-geometry-calculus-or-statistics” that most people see it as natural; so while educators in literature and history and the languages and arts and sometimes even science can create classrooms with radically different forms and content, while still addressing the heart of their respective content area, math somehow still has to be “the math that I learned when I was in school”. This is the same math whose symbols are used whenever anyone wants to represent the experience of schooling itself: a right triangle with the trigonometric ratios indicated, or an algebraic equation with the omnipresent “x”. Both of these are as natural to some cultural ideal of “schooling” as other symbols that most would recognize as outmoded or traditional, like a diagrammed sentence to teach grammar, or perhaps a book report on George Washington read aloud, more hagiography than history. These images are easy to build upon: red apple on the teacher’s desk; American flag on the wall, next to the clock and the bell; wooden desks in rows, 30 or 35 children directing all eyes at the bespectacled matron at the chalkboard, or frantically scribbling away at an exam, which each will receive back with a circle grade in red pen. (While this collective imagine is familiar even if your schooling didn’t look like it, you will recognize the common experience of all these associating school with being BORING.)

All very evocative; but if I’m thinking of the salient features for my guiding questions here (What is a classroom? Why do students do what they do? What can a classroom do?), I zoom in on a few important details. There’s the top-down instruction, a pedagogy and theory of knowledge that makes students passive receivers of knowledge and the teacher the active possessor of that knowledge, and also the sense that each student is fundamentally making an individual effort (my desk, my test) for an individual outcome (my grade).

The second goal that I have relied upon addresses this while maintaining the individual frame: it asks, what kind of person is a person that learns mathematics? Well, this could be about the qualities of the individual (paying attention, taking notes, completing homework, studying — or even the more progressive-sounding “reflecting” or “taking risks”) but I have always favored an interpretation that bring mathematics forward as an activity practiced in community — we do math when we do math together. So: listening to peers, asking them questions, discussing your own approach, solving problems together, reflecting and sharing in the hopes of moving the work of the class forward. These are communal efforts that, it is assumed, will be reflected in each students’ pursuit of the first goal. In fact, this is often how I’ve framed it for my students when explaining to them the value I find in my discussion-based style of classroom: you will learn the math better here. And on the way, as a nice side result, we’ll do something that looks like how real math is done in community, and will even tie in certain democratic tendencies at the heart of progressive pedagogy.

But truth be told, this doesn’t break out of the persistent individualistic frame that our school’s are created around, and to demonstrate this central truth I don’t have to pull down collective images floating in the ether. On the contrary, I will point out something so obvious that it doesn’t seem to bear repeating: our schools are literally built around a personal effort/reward system. Kids know this in their bones. Any reference to some kind of Good outside of this incentive structure, whether it be a deeper knowledge of math or a comfort with intellectual struggle or some familiarity with democratic process, will always, always be filtered through the individual effort/reward sieve. This is a source of frustration for teachers who believe that learning is something more than an individual effort, and that knowledge worth knowing can be collapsed into the grade-reward — but why? It’s what we’re here to do. It’s a delusion (in the descriptive sense) to imagine schooling as directing its energy anywhere else. And it’s a delusion (in the moral sense) to direct our frustration at students about this! They are doing what we’ve told them. If they think their effort can make the cut, they pursue the reward. If they think their effort cannot make the cut, they reject the reward. This is very rational behavior.

This frustration among teachers makes sense though, because we recognize that this structure that centers individual effort/reward is not necessarily a feature of education, but a human-generated system that has chosen to identify certain priorities at the expense of others. So we can channel that frustration to push back, to say: individual effort/reward is not enough. It comes out of a capitalist and neoliberal system; it is reductive and infantilizing; it is not within the great tradition of human wisdom and its transmission from generation to generation. It reduces teachers to mid-level bureaucrats, petty tyrants of their little domain, demanding obedience and production in exchange for duly-rewarded credentials. Or worse, we become involuntary agents of the market, the point of transaction between “hours of attention begrudgingly paid” and “incremental units of learning”. We lock students in to a economic and political outlook that valorizes infinite growth, bootstrap individualism, constant hustle and all of those consequences we’ve been taught to live with: gross inequality, neverending competition, fossil-fuel dependence, climate change, socialism for the rich and prisons for the poor, the legacies of imperialism and colonialism, and all of the endemic social systems that protect the dominant paradigm

However, those priorities are baked in already! Do we award grades? Yes. Do those grade represent what individual students produced individually? Overwhelmingly, yes. These are the only salient facts here. Everything else is moralistic handwringing — or, when done institutionally, marketing. Our school offers what every other school offers, what any school can possibly offer in our system. Would you like your rugged-individualism-for-profit to be democratically flavored? Would you like the artsy variety? Or perhaps the rigorous variety, of an older vintage? It becomes a kind of consumer preference, and its just as empty.

Here I’d point out that the question, “how do we support individuals in pushing back against the unsustainable and cruel dominant paradigm” is one that most religious institutions exist to answer. It’s an important first step to recognize that when we talk about individual reward/effort incentives in schools, the call is coming from inside the house, and with good reason. I think in our current economic-political-social system, we will not get it outside of the house. It’s what built the house. But the practice of religious communities can help us think about how we might introduce students to something different, something ethical, something new.

I should not have been surprised when I came to that conclusion, that schools can learn something from religion, given my background. Nonetheless it surprised me when I came to it, because I came from a different direction entirely. Let me try to summarize that.

A complex system is one in which units interact according to a simple set of local rules to generate a structure at a higher scale, whose properties we could not necessarily predict based on the individual actors and the rules. The classic example of this is an ant colony, an entity whose famous complexity results, not from the direction of some kind of overmind directing the ant’s efforts, but the cumulative action of each individual ant’s response to those simple, local rules. This makes a colony adaptive to changes in its environment, in order to ensure the colony’s survival, even though no single ant in the colony can be said to be directing that adaptation or could even be said to be aware of the changes necessary to thrive. The colony’s features, its structure, its various functions of self-sustenance, are all emergent properties. And we feel it is accurate and appropriate to speak of the life of the colony on the scale of the collective, just as we can speak of the life of the ant on the scale of the individual unit.

We could go even further and describe a kind of complementarity between ant and colony — in that when we focus on one or the other, we necessarily lose sight of something essential about the subject of our focus. This references one of the roots of complexity theory in the development of quantum theory and indeterminacy. Focus on a light as a particle, and you lose sight of the ways in which it is a wave; focus on an electron’s position, and you lose sight of it’s momentum. This is not a feature of insufficiently accurate measurements, it is a practical limit to what we can perceive when moving between scales of investigation. This complementarity, translated to the example above, says: look at one ant and you don’t see it’s participation in the colony, which is essential to understand its way of being in the world. Likewise, resolve your focus on the colony, and the constituent elements are lost. This can be applied anywhere that scales of investigation are significant. A liver pathologist attends to individual liver cells, as well as the whole organ. To describe the behavior of starlings, we have to zoom out to consider their collective action in contributing to a murmuration.

And as teachers, we have to hold in mind our individual students in tension with the whole classroom. As I read about the various factors that act on our students, the ways in which their broadest behavior patterns are dictated by internal and external factors, I found it more and more helpful to think of my classroom as a complex system, one created collectively by my students (and me!) when we acted according to a set of simple, local rules. I wondered: if I can articulate a set of rules that students know without knowing, could I imagine a way to encourage a countervailing set of rules, that created a different emphasis and balanced our insistent focus on the individual and the market?

You can imagine what my first rule was, given my fixation on individual effort/reward above. But the task is developing the tacit, local rules that act on young people (here I imagine high-school-aged students) that align with the broader task of schools in our culture, which I label here the develop of free persons. Here were the six that I articulated:

Local Rules for the Development of Free Persons

  1. Individual rewards come from individual effort only.
  2. Maintain the social hierarchy.
  3. Produce as efficiently as possible.
  4. Pursue familiar tasks.
  5. In absence of stimulus to keep attention, fall back on bio-factors (tired/hungry/restless)
  6. Keep control by any means necessary.

These need some unpacking, but I’ll just comment on two of them. #3 draws up that we’re talking about the output of artefacts that demonstrate that I know what I’m talking about, and these should be turned out in as little time as possible. Academic dishonesty, which is a huge factor in school (especially now with the widespread availability of AI), enters the game for this reason; and the “efficiency” I indicate here is more about “vulnerability-minimizing effort” than actually doing something that takes less time or energy. For instance, a teacher will behold a students wide-ranging efforts to cheat on a paper or test, and will at some point mutter to themselves, “it would have been easier to just learn the thing!” Yes, but more importantly, no. This would mean the student would be vulnerable to failure. They’re vulnerable to failure if they cheat too, but at least then they deserve it. Failure when you’ve tried is indicative of your failure as a person, a nasty little byproduct of the meritocracy (and neo-Calvinism, while we’re at it).

In fact, #3 along with #2 and #6, are rules that are meant to avoid vulnerability, admitting ignorance, or social tension at any cost. These rules exist for a reason. They are not bad. They are defenses, leaky and inflexible defenses, wielded by young people who haven’t developed a flexible and resilient sense of self yet. Our goal here is not to overthrow or ignore these rules, as if by wishing them gone they will disappear. In fact these rules apply to other groups of people in schools — make it a checklist and bring it to your next faculty meeting, and see how much behavior can be sourced to one or more of these rules!

If these are local rules for free persons, we need the countervailing rule, those which imply the communal, democratic, compassionate causes that we espouse. I countered each of the 6 with its antipode, resulted in:

Six Local Rules for the Development of a Democratic Society

  1. Cultivate communal wealth (unity)
  2. Foster difference among equals (diversity)
  3. Attended to democratic process (solidarity)
  4. Open to newness (not-knowing)
  5. Be present to everything happening right now (bearing witness)
  6. Letting go in action (compassionate or appropriate action)

Each here answers to its companion in the prior list. The parenthetical notes are an alignment of this list with the Three Refuges/Treasures and the Three Tenets of Zen Buddhism. One of the advantages of participating in a community of ethical practice is often someone else has already made the list you need! Unity, diversity, and solidarity correspond to that which a Buddhist takes refuge in, and commits to uphold: Buddha, Dharma, and Sangha. The Three Tenets are more like guides to action — they were the first lesson I learned as I began my practice of contemplative care and chaplaincy in hospices.

The relationship to a religious tradition is also salient on the basis of my connection above — how do you pursue the practice of these local rules in a world that incentivizes their opposites? How do you create a concerted, holistic, communal result in classrooms that contributes in some measure to a healthy democratic society, that balances the emphasis on free individuals, hold them accountable and gives them context to grow in skill, compassion, and wisdom?

This would go a long way to answering the question: What can a classroom do? I’ve already presented a breathless argument for what a classroom is and why students do what they do, so now it’s time to see the potential for change by the teacher — an asymmetric member of that classroom community.

I have two thoughts right now, and I intend to test them this year.

First, I have to say the six rules for democratic society every single day in my classroom. Every. Single. Day. By April my students should have these memorized. I don’t care if they roll their eyes when they say them, or mock my very mockable tone — if they have memorized them by years’ end, they will have them and will be able to lean on them when they need them, likely when they least expect it. It has to become a part of them, just by being in that class every time they are there.

Second, we have to have fun. My class is so not fun. I’ve always put so much stock in an open and dynamic classroom that I never, ever, ask myself, “how can the kids have fun with math?” It’s a blind spot, and a mistake. I think games and fun and play in general allows for a unique but fundamental kind of relationship building. It embodies the principles I’m teaching. It lets in some joy, lends some buoyancy to those local rules. If we have a moment where we successfully realize the communal open rules, and we’ve had some fun, I think the kids are more likely to agree that it’s good that we’ve done it this way.

When I was considering this last point, I remembered a line of poetry I was saw at the head of a chapter in a book I couldn’t remember, but I knew it must be important because I remembered it so well. It was:

On the seashore of endless worlds, children play. -Tagore

I cast about for a bit and fumbled on Google for a while, not quite able to compose the line, but then found a result that hit me like a thunderbolt: it was the psychoanalyst and pediatrician Donald Winnicott, describing the location of cultural experience in Playing and Reality. Here he described play in children as a mediating, third space in between the child’s personal psychic reality and experience, and the real world. In pathological cases, restoring the collapsed third space in a person is the work of a therapist, but in general, we have all relied on this in-between place between inner life and outer reality to become who we are. And it this space writ large that becomes culture.

Considering this in the light of complexity and emergence, I saw the development of classroom culture with individual students as the creation of a emergent, sentient entity at a higher scale of inquiry. The third space created communally, the place where students explore and play among themselves and with elements in the world around them, is the soul of the classroom. What is necessary to foster this space, to protect it from fracturing into unrelated component pieces, is trust. Winnicott, in his dense and evocative style, says that it is here that experience “creates living” — and so in some sense, the classroom itself is alive, has consciousness, adapts to changes, can grow. The one, out of the many, harmonizing as a community.

So! The classroom has a soul, the beginning and end of my process here, and a surprising combination of my reading of complexity, theology, progressive pedagogy, depth psychology, and the Dharma. I thought to call it “The Classroom as Buddha” or “The Classroom as Sentient Being” or “The Classroom as Cosmos” — but then I thought, it was there at the beginning! I just had to turn it, just so.

Teaching

On listening in math

Posted on by Fig Tree

I met with a student for extra help. Call her K.

K is in 9th grade this year, is new to the school, and has returned her last two math quizzes blank. To her credit, this is her third week in a row visiting me on a Friday afternoon for help. K maintains a healthy distance from her effort, using every cue she can muster to let me know she would rather be elsewhere. Nonetheless, she is here, along with a classmate of hers who is similarly struggling. I’m thinking of two episodes from our 40 minutes together.

First, we were working through this equation,

0 = 9x + 18

and we had established what to add and when, resolving the statement to

-18 = 9x

At this point K answered by saying “x is -2.” She explained that she recognized immediately that 9 times 2 is 18, and since -18 was our goal, the 2 also had to be negative.

When I introduced the way in which she had implicitly used division, she wondered why we would even talk about division here, as she read the whole thing as a multiplication problem. Of course, she is right. I explained the power of algebraic method to work in every situation, even when the numbers are beyond our immediate arithmetic access. I think I offered an equation like 3.181740 = 9.1308x, which you might run into on a lazy Sunday afternoon, as one does. She remained skeptical, which I’m starting to understand is a strength of hers.

Second, we were looking at a somewhat more complicated equation, which it turns is the same equation as the first one (I had my reasons):

4x + 10 = -5x – 8

This task would be filed under “solving a multistep equation” in a textbook or an online math tutorial. K and her classmate are both stumped about a next step here. The classmate proposes “combining like terms” and “moving” terms about, in such a way that the equality is not maintained. I try to explain that this is a priority, though I’m not sure they recognize the urgency behind that particular value.

K makes an attempt and suggests adding 10 to both sides. This would result in

4x + 20 = -5x +2

I respond with what I believe will show them the most efficient route to solving the equation, by which I mean generating a statement of “x = -2”. It’s boilerplate algebra teacher stuff: we want to “get all the x’s to one side and all the numbers to the other side” by “doing the opposite operation of what’s there” and finally “getting x alone.”

The algebra we’re doing here is review, so in class I am less interested in exploring the philosophical implications of the algebra. This is all the more true with students who are struggling to demonstrate their understanding on quizzes and show up at extra help. However, because I am the teacher that I am, and I am generally unsuccessful in having them just “do the math”. And as it turns out, this is the kind of thing kids often do like talking about, when they forget their dyspeptic attitude toward school math for a moment. For instance, both of my 9th grade math classes have already grappled with the ambiguity around, for instance, “-5x – 8” being the same as “-5x + -8” and the implications of that fact for algebraic manipulation, without much prompting from me. And as we’ll see here, extra help doesn’t turn off anyone’s meaning-making capacities.

K regards the problem after I’ve done my bit and says, “But isn’t adding 10 still correct?” Had I been sitting I would have fallen out of my chair, because of course she’s right. Again.

I suspect the word she was looking for was “true” rather than “correct” — it’s true to say that adding any value to both sides of the given equation will maintain the relationship described. The high school textbook name for this is the “additive property of equality”, which if you’ve ever tried to teach directly you know is a slog, because students are both like “what” and “duh” and “why even bother stating that” — all valid responses. But as truth has a tendency to do, it’ll come up in our work no matter what, sometimes to our chagrin.

That she wanted to describe it as “correct” is interesting, since I’m sure that not a few math teachers would respond by saying “no” — simply because adding 10 to both sides of the given equation will get you no closer to resolving the statement to its simplest expression. That my only purpose in working with algebra and equations is to find “the answer” rather than exploring the qualities of number itself is worth some self-reflection.

I try to capture much of this by saying, “Yes! That is still a true statement that maintains the relationship here. Good point. And also, our goal here is to find a value for x. Let’s talk about how to do that.” In my minds eye, I see her shrug wryly as if to say, “what if we just called it a day?”

Conversations with my math students, especially in small groups, often put me in mind of what I learned when I was training as a chaplain. There is this idea that as much as possible we don’t want to impose our own theological perspective on the patient, and instead let them tell their story themselves — a story that on one hand, they can’t help but communicate, but on the other, can be brought to conscious reflection if a proper space is opened for it. Much of the work of chaplaincy is waiting patiently for subtle cues that suggest that you have a green light to explore further, without steamrolling anyone with your agenda.

I was never much good at this. In the lingo, I had trouble stepping into my “pastoral authority”. But I can see that my own struggles with that patience and guidance live on in my work as a math teacher — where listening is so easily bypassed in favor of telling, and where students have stories to tell about how they understand so much more math than our narrow schoolish exercises could possibly bring to the surface.

In math teaching, as in chaplaincy, we have a responsibility to cultivate that meaning-making. For math teachers, perhaps more than chaplains, the struggle is even in recognizing that the meaning-making is happened. But the kids can’t not tell their stories.

Religion in Culture/Zen

American Psyche

Posted on by Fig Tree
“Biden and Trump Say They’re Fighting for America’s ‘Soul.’ What Does That Mean?” New York Times, 10/17/2020

Originally posted on 10/18/2020, thought I’d share it here.

In the ancient Greek used in the Gospels, the word for soul is “psyche”, as contrasted with the word for spirit: “pneuma”. The latter suggests a relationship to wind — and thus Jesus in the 3rd chapter of John could be saying, “the wind blows where it will” just as much as, “the spirit goes where it will.” Both get to the point. Spirit is animating and non-material, and in personal terms, it’s connected to the breath.

Psyche is interesting because it is related to the Greek word for “cold”. It suggests a parallel relationship: soul manifests where the spirit goes, just as coolness manifests where the wind blows. As the spirit inhabits the body, the soul comes into being, an emergent property of the meeting of spirit and matter.

Psyche is obviously the root of “psychology” but also suggests (as modern depth psych traditions have) a broader quality of human being than brain function, closer to the Buddhist use of “Mind” or “Heart-Mind”. It’s the total, embodied, You: conscious and unconscious process combined, everything you know and don’t know about how you are in the world.

Now as I’ve always thought about it, there’s no sense in talking about the healing of the spirit — the spirit is pure energy, radiant, expansive and irreducible. The soul, however, it rooted in material, “fleshly” or “incarnate”. It’s healthy functioning, like the flow of a river or the growth of a plant, can be blocked, warped, or split. In every case, spirit will manifest as fully as it can, filling whatever container it finds.

I get lofty and abstract enough talking about the *human* soul, so thinking about a *national* soul gives me a touch of vertigo, but I guess I’ll say that 2020 brings to light the splits in our national psyche, makes the unconscious realities that many of us white Americans have been unable or refused to see. The Battle for the Soul is not new! The callous Id-hero in Trump just raised it up, and Biden’s bantery wounded-healer offers both acknowledgement of that reality but also normalcy — — and that’s where this article helps, because when the shadow in the soul comes to light, the question is not, “how do we put this where we can’t see it anymore,” but, “this is us, too — what do we do with it?” If this nation has a soul, it’s made of *all* the parts, even those we don’t care to see it those that create *terrible* suffering. I think of the Buddhist warning about anger: “both pushing away and embracing is dangerous, for it’s like a great fire.

“So just “return” is not enough. This article frames the battle for soul with: “what do we want to *become*?” What broader, equitable vision does all this conflict and suffering point toward? I think of the 1619 Project, when it said, America wasn’t a democracy until Black Americans made it one” — out of that oppression came a closer iteration of true freedom.

What is this soul, and what labor will bring forward something new in the world?

Justice/Teaching/Theology

Confronting Whiteness with White Students

Posted on by Fig Tree

In January of 2020, I co-facilitated a two-day workshop on whiteness, race, and racism with a group of white high school students. I had designed the workshop with my collaborator, an English teacher who had long been a partner in discussing racism and our experience as white educators. We wrote that our intended audience was “white students who feel the need to explore their racial identity and become effective anti-racist allies to people of color.” We wanted to look at our experiences of being white, briefly survey the history of race, roleplay situations to practice calling in our white peers, and plan to turn our learning into action.

We had tried before to work with a group of white students, but it never got legs. This time, I felt a renewed urgency for that work.

The necessity of white antiracist spaces

Over the preceding two years, I had worked on a handful of faculty committees focused on racial identity and equity in our school. In that time, I came to see that the onus of talking about race and structural racism at our progressive, independent school fell almost exclusively to students of color.

Every year, the school set aside a day to program student-led discussions about racism and other systems of oppression as they manifest in our community. I was working on the faculty committee to organize it, and I quickly had to reckon with the fact that this day would be the first and only time white students would be gathered in an intentionally white space to talk about their experience of race. As I knew from being in those rooms in previous years, many would check out. Some would just not come to school for that day.

Students of color, on the other hand, would wonder what purpose this one day could serve for them, when they were constantly immersed in this exact conversation. Every other day of the year, in a variety of affinity groups, in their classes, and in weekly assemblies, they were tasked with exploring and expressing racism’s impact on their lives. If their white peers were present, they were responsible for communicating this experience in a way the white students found palatable. And they were doing this work while being subjected to frequent microaggressions, like those documented earlier this summer by the collection of “Black-at” Instagram accounts.

(To address the concerns of the students of color on the day of programming, the affinity spaces for people of color were devoted to “coalition building”, in which students across different racial and ethnic identities could have discussions together. The issue of white students joining this kind of conversation once a year remained.)

This changed my orientation when thinking about race at my school. I knew just enough to recognize the historical irony of people of color having to do all of the work, given that race was invention of white people intent on maintaining their power. This latest manifestation of that system is that race is a problem for people of color, so people of color have to do the work. But this has it backwards: white people are the source of race and racist ideas, and so it’s their work to undo it. To put it succinctly:

“I’m only black because you think you’re white.”

James Baldwin

Some white students, faculty, and administrators would have recognized the dynamic Baldwin names here, but the crux of it was lacking in the general white consciousness of the school community. There were frequent (if uneven) attempts to foreground matter of race and equity in our pedagogy, curriculum, and community practices — but there was no regular, faculty-mediated space for white students to talk about their whiteness, and to build skills to work against it.

It seemed necessary to develop white anti-racist student leaders, who would publicly do the work of calling in their fellow white students, while supporting and being accountable to their fellow students of color. The workshop seemed like a good start.

Our approach to the workshop

That month, I attended a one-day workshop led by the Center of Racial Justice in Education called “Talking about Race for Educators”, and I adapted the general structure and content of that workshop for a group of high school students. My collaborator and I brought in ideas from prior race-equity workshops at our school, practices in our classrooms, and other professional experiences to develop the program. I leaned on my experience as a chaplain resident in hospitals, my training in theology, and my Zen Buddhist practice as well. We prepared to open a space for white students to talk about their whiteness. We also anticipated, as facilitators, being vulnerable and sharing our own realizations about being white educators. We were thrilled when seven students signed up, just enough to justify the workshop. We were finally going to make this happen!

Our general structure was to first focus on our experience as white people: in the context of our families, of society, and in the school community. Then we zoomed out and talked about the historical roots of the idea of race in the modern West, and the different valences on which racism manifests now, from internalized to societal racism. With that set of ideas in mind, we read about microaggressions that students of color have reported in our school, and roleplayed talking to white peers about microaggressions they had committed. Finally, we laid plans for creating a regular organization of white students that would continue to focus on whiteness and racism in the school, hold itself accountable to students of color, and plan for antiracist action.

Theological tangent: The Fruits of Confronting Whiteness

This workshop was a powerful experience unlike any I’ve had in fourteen years working as an educator. I was moved by the students’ willingness to listen and to share. There were moments that were uncomfortable and challenging, and others that were energizing and, frankly, joyful.

There is some suspicion about a group of white people having a good time talking about race. This suspicion is justified! The way I’ve made sense of it is that it is a joyful thing to name the truth of your life, and that that joy has to be earned, by acknowledging the harm in which you’ve participated. That joy denotes an openness to what’s new, to a newly found ability to act. At best, what comes from confronting whiteness is an experience of liberation, by recognizing something that has restrained you.

What is restraining about whiteness? It’s obviosuly not conventional restraint: whiteness is something that gives white people power. But there is a cost to that power. There is a sense in which what you’ve gained, what you claim as yours fair and square, was won by brute force, violence, and cheating. That creates an underlying fear that keeps us in line and working for whiteness because it benefits us, and because we can’t fathom what will happen if we let go of it.

But if there’s a space where we can let go of it, if only for a moment, we get a glimpse of what it would be like to not rely on fear to live our lives.

In some ways, this is a kind of once-and-for-all experience: you can’t undo what you’ve come to know, it’s yours forever, and it suggests the potential for authentic connection within yourself and with others. In other ways, this experience requires maintenance, by constantly revisiting and reflecting on your experience of whiteness. Otherwise, the overwhelming flow of the material realities of our lives overcome what little progress we’ve made in seeing and knowing what’s true. Fear takes back the wheel that it’s held it for so long.

However, we can name the fear as a part of ourselves and move toward wholeness again — which is required, ultimately, for right relation with other white people and with people of color. Until we name the fear, the anger, the defensiveness, the dismissiveness, we can’t own it. When we name it, when we own it, then we can let it go and act against it.

The Best Laid Plans, 2020 Edition

At the end of the workshop, we discussed starting a white anti-racist student group to meet regularly. The students committed to having a discussion with one peer about being white at our school.

The next day I went to a NYSAIS meeting of white antiracist educators in New York independent schools (loosely organizing under the acronym, WARE), focused on structuring white anti-racist spaces. This built on what I had learned from the CRJE, and offered something of a model for regular meetings with white students committed to anti-racist action. Because we were in the middle of busy trimester already, my collaborator and I figured that, if we waited for the new trimester, it would allow us to open the group to the high school community. So we looked to the spring trimester to establish a regular group meeting.

The NYSAIS workshop was on February 1st, 2020, twelve days after the first diagnosis of infection from coronavirus was given in the United States.

Of course, as the winter trimester came to a close in mid-March, the arrival of coronavirus in New York City swiftly upended any normal expectation of what school would be in the spring. We returned from break in early April, and spent that month adjusting to a new online reality for school against the backdrop of dreadful news and the sounds of sirens out our windows.

By the end of April, the community had scrambled to some semblance of normalcy, or at least as much as a society-wide disruption would allow. We suspected that we would be online for the rest of the year. Grade policies for this trimester were established, as were class routines. This gave me space to think about the white antiracist group again. Despite the times, I didn’t want to lose the momentum that this group of young people had found, especially since it took so long to get off the ground.

I reached out to my collaborator to try and start the meetings, but she was now working from home while providing schooling and daycare to her two young children. So I reached out to the students, and in the first week of May we began regular meetings of what I was calling OWAL: Organizing White Antiracist Leaders. A small, regular group met weekly through the rest of the year. Since we were meeting outside of the regular school club structure (and because we were all spending hours on Zoom every day already), I limited the meetings to half an hour each. My intent was to keep the momentum going and prepare for a formal beginning in the fall.

In the meantime, I structured things to keep whiteness front and center in my students’ perspectives.

Structuring White Antiracist Meetings

I followed the guidance of peers doing this work in other schools and the professional trainers who work with the CRJE and WARE in structuring these weekly meetings. My priority was on our experience of whiteness, by which I mean we focused on personal narratives and feelings in situations where our whiteness seemed to matter.

This is powerful, simply because white people do not explicitly think of themselves as “white” — they think of themselves as “people”. “Race” is a phenomena assigned to others. Intellectually, we know we’re white, but the relevance is not immediately clear. Naming our whiteness as a relevant factor in our lives allows us to see that we have been treated differently than people of color, that we harbor racist assumptions, or that we have have hurt people of color in our lives despite our best intentions.

Because I was keeping the meetings brief, I imagined the whole meeting as a share, guided by one prompt: “What has your experience of whiteness been like recently?” Generally, I won’t define whiteness for them, but ask them to think about a time their whiteness seemed relevant. Despite our blinders on this matter, our whiteness is a fact of our existence, which means it’s something we can talk about as experiencing.

Three evasions to talking about whiteness…

This task is hard for the kind of white students I work with, and I think this applies to broader population of liberal white adults as well (including me). White students find ways around it, and so do white adults.

We are conditioned to not see race and not talk about it. Race is always something that happens to someone else. And for many of us, raised in good white liberal households and educated by good white liberal history teachers, we have a set of stories we tell ourselves about what race is and who perpetuates racism. These stories have titles like:

  • “Racism is what Southern bigots and far-right Republicans do”
  • “The Civil Rights movement peacefully and decisively defeated racism”
  • “Racism can’t survive where white people are nice and well-meaning”
  • “Race is a social construct and so it’s not real”
  • “Everyone has to face adversity, but we all have to find a way to adjust”
  • “Obviously racism is bad, but these protests/social media posts/assemblies/classes are not productive”

Although each one has a seed of truth, they are so taken out of context that their relevance is distorted. These are deployed in the same way some Christians will deploy verses or even single sentences in the Bible: as a bludgeon to end discussion. In both cases we can call this proof-texting. In the white liberal version of this, race and racism are ideas that fit into a tidy intellectual structure, one that conveniently places responsibility for racism elsewhere — on bigoted white people, or on people of color. And its cumulative effect is: even when race is the topic of discussion, we white people find ways to avoid a personal accounting of it.

If we can sidestep the temptation of proof-texting and talk about a personal experience where our whiteness is relevant, white students and adults will point out what other white people have done, and usually what they have done wrong. It’s an opportunity for judgment on others (and implicitly a claim of innocence for ourselves). Or, if we do talk about an experience we ourselves had, our account will be inseparable from our rationalization of our actions, without a chance to explore what actually happened. This is kind of the opposite of proof-texting: instead of too little context to sharpen our comment into a weapon, we give too much to use it as a shield.

I’m not asking them for an accounting of either right and wrong, or of what other people do, or of bromides gathered from the history books. I’m asking these students for their experience of whiteness. I’m asking them to swim against the stream of their conditioning, to unlearn a subconscious program that insists: do not talk about race, except along these safe parameters, and change the topic as quickly as possible. My role is to support them so they can break out of the routines of proof-texting, judgment, and rationalization.

So: how to do that? How to get them out of their heads?

…and one way to bypass evasions!

One way to short-circuit proof-texting, judgments, and rationalizations, and to keep the focus on one’s own experience, is to ground ourselves in our feelings, in our actual embodied life. So I insist that the students talk about how it feels to be white. Either I elaborate on the prompt to request this, or I ask follow-up questions about what it felt like to be in the situation described. The effect this has is moving past our ideas of things and get to our actual response to them.

Why? White feelings can often derail conversations about race, so why center them here? This is most painfully true in mixed-race spaces where even a comment about racism or a modest proposal to support students or teachers of color can lead to defensive responses from white people. In that case, white feelings are used as a tool to erase the needs of people of color to protect the comfort of white people.

What I’m talking about here is naming the feelings themselves, in a space of white people listening to and acknowledging those feelings as real. There is nothing right or wrong about a feeling. It just is what it is. A feeling can lead to actions that we can judge as good or bad, or as helpful or harmful depending on our goal. Some feelings should be cultivated for action, others should be restrained. But if we can’t even say “this thing made me feel this way,” we won’t be able to truly reckon with what happened or learn how to respond next time. We’ll fall back on proof-texts and rationalization again, instead of talking about what actually happened.

What is required, and what we’re looking to cultivate

Doing this requires vulnerability, trust, and humility — qualities that are rare in your average high school classroom, but essential to seeing this crucial aspect of our lives. The goal of the white antiracist space is to foster these qualities, so we can actually talk about our experience of whiteness, and then address the ways we perpetuate racism. Once we do that, it becomes more clear what action should follow, and when we hold ourselves accountable to our peers of color, we needn’t burden them with these unprocessed feelings.

So this is what we did each week over the course of May 2020. The meetings were modestly attended and felt good. We were treading water, making it through the hardest and strangest term of school anyone had ever seen. My only plan was to identify a handful of student leaders by June who would help facilitate these meetings in the coming school year. Then we could leave the spring behind, happily.

Nonstop 2020, and 2020 is Nothing New

I shouldn’t have been surprised by what happened next. That I was surprised makes it clear why I, personally, need white antiracist spaces. That feeling of surprise is something I could stand to reflect on.

Doubling down on a bit of white myopia, I thought it was going to be “Central Park Karen” who made the big splash the week after Memorial Day. I was so busy reading the news and Tweets about that encounter that the early reports of George Floyd’s death sailed right past me. When I met with the white students that week, one of them talked about George Floyd’s murder, and she was the first person I spoke with who used that word to describe what had happened (in case I suggested otherwise above, the kids who are actually doing the work are just as often out ahead of me). The next night, a police precinct in Minnesota was on fire. The night after that and for the weekend, it seemed like the whole country was.

“Now is the time to talk about what we are actually talking about,” was the headline of an article by Chimamanda Ngozi Aditchie after the 2016 election. The phrase occurred to me that week, the last week of school, because suddenly everything we had been discussing since January seemed plain and clear right in front of us: the blinding and binding effect of whiteness, the long, repetitive history of race, the many layers of racism in our contemporary life, and the need for action.

Our last white antiracist meeting of the year was well attended, and there were several other mediated spaces that the school organized for white students that were modeled somewhat on the work we had done in the winter and spring. I was grateful that I had pushed ahead with the work when I did in April — otherwise, we would have been left scrambling again.

But that’s the thing of it, isn’t it? There is nothing so predictable in our public life than racist violence, than racism’s persistent and consistent through-line in our national narrative. When this happens, when suddenly everyone is talking about race, we need to be preparing for the next time it happens. We have to be marching in formation already, not redeploying every time we’re surprised by the grimly predictable.

Staying Present in the Cycle of Beginning and Ending

So the question becomes: how can we be ready in the new school year?

I think the student work should continue in the same way: I’ll ask students to share their experience of whiteness. With more time in a meeting, we can transition to roleplaying situations to orient ourselves toward action, calling in our white peers, and being accountable to our peers of color.

Having the same structure to each meeting is important to me: as one white colleague put it, we are trying to make a routine of looking for and talking about our whiteness, of normalizing that reflection. We could have read all of the books on the anti-racist reading lists and we could have gone to all of the protests; we could have appropriately and authentically reflected on our complicity with white supremacy many times over. But as another white colleague of mine has said: everyday, when we wake up, we still have to recommit to the work. Everyday, we will still wake up white.

I’ve been meeting with different groups of white faculty and staff across my school this summer to support one another in the work, and their thoughts have helped flesh out what my collaborator and I had been pursuing in January. Another faculty member (another English teacher, they’re the best) joined me to facilitate the white antiracist student space near the end of the year. And two white students volunteered to facilitate the white antiracist students group in the fall, and we’ll have a regular meeting time.

Commitment is not the end. It’s the first step.

Justice/Zen

Clouds of Witness

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I was in Austin, Texas for a few days before I really looked up at the sky. I saw churning clouds under a hot sun, a favorite object of contemplation of mine in the summer months. In New York City, the tall clouds create airborne ridges and peaks that put you at the floor of an enormous valley of your own imaging, the lowest layers of which are the concrete and glass facades that give you no long-view vantage other than skywards. It’s all up and down in New York, a continuum from you to the lowest edge of the sun.

Texas was not as flat as I expected, but you are acutely aware of its horizontal breadth when you fly in. Once on the ground, observing clouds becomes less about their stratospheric reach and more about their flow over the surface of the hot land. In a dry climate, those clouds are the most immediate river. But they are a river without banks, a river that floods so comprehensively that it’s nothing but the flood. Clouds suggest a vast oceanic current, alerting us to the easily forgotten fact that our atmosphere is a positive entity, a real presence of fluid, always mixing and changing and interacting.  Clouds just allow this process to catch a little visible light, and pull back the curtain on a tense and temporary equilibrium. 

At this one particular moment that I happened to look up, at a glance I saw a cloud communing with itself, arms expanding and contracting, regions withdrawing and or reaching beyond their capacity to cohere, this continent of vapor giving and taking from the invisible sea around it. A very hot day seems to stifle activity for the land-bound, especially humans, dogs, and the leaves of trees on a day with no breeze. But that direct draught of radiation — light, UV, infrared, all of it —  into the atmosphere has just the opposite effect. The sky becomes an expansive reservoir of potential energy, pushing the balance of countless gaseous exchanges in one direction or another. Midday clouds and nighttime storms and hazes at dawn are all manifestations of this enormous exchange that flows around us all the time.

Ocean of clouds over Oklahoma, 6/2/19

A cloud is not its own. It’s a greeting card from a chemical sea in which you make your whole life. There is no life beyond its boundary. I’m thinking now of the experience some astronauts describe in beholding the entirety of human life curved along the very top layer of a minor sphere of rock, and the terms of frankly spiritual awe it inspires in them. A part of this kind of awe is a sense of contingency, perhaps absolute contingency: we rely on this Earth for every aspect of our being, and without it we are really, truly without refuge. In a turn that is so self-serving that it is other-serving, since it finds that soft vein of reality where self and other, individual and society, human and Earth, are not separate at all, this kind of Earth-reverence becomes a motivation to serve, to act with compassion and energy and skill to protect and sustain that which has protected and sustained us.

In Buddhism, we call this “vowing to save numberless sentient beings.” It follows from the historical activity of the Buddha stepping off of his seat of enlightenment to engage the world. In Christianity, I would identify it as the source of a creation theology, one that names this fleshly, material life and world as Good, if challenging and inertial at times.

What the clouds show is that we needn’t go to space to experience a sense of awe-inspiring contingency. Astronauts might see that terra is not as firma as we think, and is in fact a small shelter of life in a dark cold chaos. Likewise, the realization that we swim about in a chemically active sea that is ever so finely balanced to a narrow band of conditions for this life to be possible, leads me to some combination of gratitude, contingency, and frankly, terror.

To be full of awe is to feel at least a little awful, and in the Bible, we can read a line describing fear of the LORD as awe, as well. To realize that the source and sustenance of your life is contingent is not sentimentality, meant to foster some shallow sense of ease. I experience it as a charge. The religious impulse must address the full range of human contingency, by raising up fundamental realities, the deep veins of our being, the structural truths of our lives. Brought into the materialist context of American life, that means saying basic facts like a mantra, until they start to change our choices — that is, until they start to inform ethical action. To wit:

  • The air I breathe is active and present. It positively promotes my own life. It is not neutral, not background, but only becomes that when I take it for granted.
  • Furthermore, its narrow balance is neither preordained not guaranteed. There is no reason that life should exist on this Earth, and no automatic break if we push our active chemical balance too far one way or the other. Balance — in chemistry, in ecosystems, and in political affairs and social relations — is descriptive and not normative. If things happen to be balanced, it’s not because they’re supposed to be.
  • Once I realize this, life’s contingency comes home to me. I swim in a sea of my own making now, and really of our own making. The deep veins connect us.

“A single garment of destiny” binds us, Martin Luther King Jr. said. His witness is all the more crucial now, as we come into consciousness of how we are changing our ocean of air. To summarize two centuries of climate science: we’ve expanded its capacity to retain energy. Really, it is its own kind of awe-inspiring, to see how our impressive industry, the same tools of skill and effort we would rely upon to save all beings, has influenced so profoundly and so suddenly this sea of air in which we all swim.

And we expand King’s meaning to this whole fluid knit of Earth and air, recognizing we are not somehow separate from them, and all of their material and matter and energy. Earth-and-us are one intermingled system, always influencing and responding in a sequence that is endless in extension, across time and everywhere right now. Our relation to the Earth is itself a complex and active sea, and it’s one that we are, for now, quite lost in. Some among us drown as a result. Our compassion fails when we don’t look to see how our actions play out.

It was skill and effort that brought us here. And it is those qualities guided by compassion, that are our hope.

A single cloud can be a witness to this teaching, to this reality. It has its being in the vast dynamic exchange of the air, water, and dust and is in fact just an extension of that exchange. In the same way, we are a part of all of this. We can direct our actions best when we are clear-eyed, but we can’t always know the outcomes. This leads to a kind of modesty that informs our compassionate action, both to act with some caution and also to recognize that it’s not always up to us.

So I’ll breathe my air a little more deeply, moving the gratitude of such a largesse of life into the foreground of my day. Like my breath, it starts right at the tip of my nose, and is always there for me. I wonder how sensing this atmospheric contingency changes me? Knowing that the contingency of each breath is shared by all, and that we all have some active part to play in its sustenance, the tension in my chest softens, and air in me can once again flow freely.

Teaching

Anxiety and Frustration in the Math Classroom: My NCTM Presentation, Fall 2018

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It’s been a while! Playing a little catch up. First:

Below is the slideshow I presented at the NCTM Regional Conference this past November in Seattle. It’s spare in the beginning because I mostly had teachers speaking in dyads — one person tells a story, and the other person repeats it back to them as closely as they can, and then they switch. Then it goes on to content on the basis of that exchange.

It’s also available at this link.

This was my first time presenting to an NCTM crowd, and my first time getting legs under this longer project of mine: how to think of student anxiety from a depth perspective, as something that we can work with and that requires us to reflect on our own practice.

Surely I won’t feel any anxiety in a workshop on anxiety, right?

People came to it! It was great! Look at all these curious math teachers! They didn’t realize it, but I was going to make one of them talk for a long time, and the other listen in total silence.

I’ll be presenting a broader version of the same presentation to general ed teachers at the PEN conference in Minneapolis/St. Paul this October. I am personally feeling some anxiety about that! Fruitful anxiety! The best kind.

Justice/Teaching

Math as Witness: who counts? who doesn’t?

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I ended the school year with a surprising burst of energy after the students left for the summer. I slogged my way through two straight days of comment-writing. These can be draining (imagine making 58 short but meaningful phone calls with the promise of near-zero response), but if I can create space for it, they become an opportunity to reflect on my students’ actual experience of my class, contra whatever expectations or descriptions I offered at the outset. The natural move then is to think about what I want them to actually experience next year.

Right on the heels of my comment-writing, I spent two days with a group of colleagues from my school developing a pilot service learning program that we would each enact in our classrooms next year.  I took a smattering of ideas and conversations and threaded them together into a strand that I called, “Math as Witness”. In my math classes, and especially my 11th grade Discrete Math elective, I envisioned a program that started with my students’ attentive presence with a marginalized community, and then moved to their study of Discrete Math topics: voting theory, apportionment (and with it, gerrymandering), combinatorics and probability, game theory, and graph theory. On one hand, this would deepen and give real-world urgency to their study of math; on the other, it would open a space for them to offer their knowledge so as to assist a marginalized population somehow. Transcending both of those goals, the students would come to care for the community, and as an expression of that care, know more of it though the lens of mathematics.

That was the plan after a few iterations, and as plans go it sounds grand. But I needed two things: the community, and the math!

There is no shortage of marginalized communities that might benefit from accessing the conclusions of discrete math, and especially those that are related to the day’s pressing issues. Immigration, voting, representation, income and opportunity, all of which can be analyzed along lines of race, class, gender, or immigration status — these would all be at home in a Discrete Math problem set. But after spending two days talking to colleagues from across the disciplinary spectrum, I needed to really get into the math itself.

And so at just the right time, I went to a math conference! The 2018 PBL Math Teaching Summit (organized by Dr. Carmel Schettino) gathered a group of teachers committed to a problem-based philosophy and practice in math education. While not geared to Discrete Math, service learning, or justice-themed mathematics, the PBL crowd is energized, creative, and committed to classrooms that decenter the teacher in favor of non-hierarchical, student-driven mathematical construction. Throw an allied project out there, and you’re bound to get something back.

Also, if you’re working on a problem of your own, I find that spending time with energized math educators talking about problems is a really nice way to get some juice in your parallel process. I experienced exactly that kind of sideways creativity at the PBL Summit. Alongside whatever I jotted down from presentations, I was scribbling marginal notes about math, service, and justice.

What came from this was not a list of learning objectives or a text or set of problems all ready for September, but instead a philosophical center of gravity for the entire discrete-math-as-witness project: Who counts? and who doesn’t?

The topics of Discrete Math all dance around the question of counting: counting to express the popular will (voting), and the problems of doing so in a representative government (apportionment and gerrymandering); counting the available options from a wider range of possible groupings (combinatorics), and determining the likelihood of some outcomes over others (probability); and the condensation of human conflict, competition, and cooperation into a set of metrics (game theory).

In a service-learning context concerned with social justice, this has to be pushed a step beyond what we’re counting or how we’re counting it. Who in our society counts? Which is the same question as, who doesn’t count? How is that counting or non-counting justified? What do different ways of counting suggest about the decision of who is counted and who is not? And then, was it a decision? Who made it? Why?

Math teacher-talk had me all excited about this, without anyone saying a word about it. It was a good couple of days.

That’s where I was at, and then I went to Alabama.

I’d been to Alabama once before, for a wedding, and now I was going again, for a wedding. I’ll spare you the carpetbagger musings on Alabama in June, except to say Alabama humidity is different than ours. New York summertime humidity is ocean-based, but in Alabama it comes right out of the earth and grass and trees. This has good and bad sides to it. At its best, New York humidity (yes I just wrote that) is salty and fresh; it makes you sanguine. Alabama humidity is all-pervasive. Surrender to it and you become one with it and all it embraces, Whitman-like: red soil, pines, ponds greener than the trees, and the trees are green AF.

At its worst, that salty New York humidity is penetrating and corrosive. In Alabama, it is oppressive and inescapable.

After wedding and family time were over in Auburn, we drove down I-85 to Montgomery to see the Legacy Museum. Physical monuments to black suffering at the hands of (and black resilience in the face of) white supremacy are surprisingly hard to find in this nation established on a foundation of slave labor, even in my dear Yankee homeland. When a brick-and-mortar instance of that witness presents itself to you in the heart of the community that birthed the modern civil rights movement, it’s the right move.

I’m reminded again and again these days about the importance of art in learning and knowing — and with art I will include museum curation and monument design (obviously). I would like to communicate to you my experience of exploring the Legacy Museum (“From Enslavement to Mass Incarceration”), which told me everything I know already but immersed me in it in a way I hadn’t felt before — which meant, of course, I was feeling it rather than thinking it — but the words will fail me. Some combination of sadness, horror, self-consciousness, anger, and sobriety.

More poignant than that, more penetrating and overwhelming, was the National Memorial for Peace and Justice, dedicated to remembering the pervasive terror campaign of lynching that many, but mostly black Americans, were subjected to over the last two centuries. I’ve had a fine chance to keep lynching at an arm’s length for much of my educated life, one of those nice that’s-a-southern-thing habits that my northeastern brethren permit themselves from time to time. The Memorial, with its hoist metal blocks, rusting with the same color as blood and that Alabama soil, arrayed so that we have a sense of their number all at once, makes what was for me a distant abstraction into a crucial reflection of our current situation, and it implicates everyone. The arm’s-length attitude is a privilege, one not afforded African Americans, and one that everyone needs to confront, or else that legacy of violence stays underground, in the water supply, wreaking havoc. Since I returned to New York, I reached for Dr. James Cone’s The Cross and the Lynching Tree, in which he says:

I wrestle with questions about black dignity in a world of white supremacy because I believe that the cultural and religious resources in the black experience could help all Americans cope with the legacy of white supremacy and also deal with what is called “the war on terror.” If white Americans could look at the terror they inflicted on their own black population — slavery, segregation, and lynching — then they might be able to understand what is coming at them from others. Black people know something of terror because we have been dealing with legal and extralegal white terror for several centuries. Nothing was more terrifying than the lynching tree.

So, after a week in between two years but also its own moment, I woke up in Brooklyn this morning. The chorus from “Ella’s Song” was on repeat in my mind’s ear and I still had a palpable feeling of lowering my head under a matrix of metal boxes in midair. I’m looking at my notes about Math as Witness from less than a week ago, though it seems like longer. I suppose it’s my first day of summer vacation proper, a time to rest but also to read and write and think.

I’m thinking of voting rights, and the contrary movement to restrict them in this country, under the banner of ending (nearly non-existent) voter fraud. I’m thinking of Dr. Cone’s comment about the war on terror in relation to lynchings, and remembering that ICE was founded not so long ago under the aegis of the Department of Homeland Security — so we can begin to see how the present crackdown on immigration is a part of this wider campaign against the shadowy, threatening Other, conceived here as the foreigner, there as the entrenched black community, elsewhere (and perhaps throughout) as the poor and powerless. I’m thinking about the fragility of a democratic republic, how easy it can be for a few powerful interests to play the numbers, to determine the rules of counting, and decide the outcome before the question is even asked.

I’m wondering how I can best help my students use math to start asking, and answering, the questions:

Who counts? and who doesn’t? And what do we do about it?