Living close to my own life

Book of Serenity #20: Dizang’s Nearness

Dizang asked Fayan, “Where are you going?”
Fayan said, “Around on pilgrimage.”
Dizang said, “What is the purpose of pilgrimage?”
Fayan said, “I don’t know.”
Dizang said, “Not knowing is nearest.”

I wrote in my previous post of an experience, early in my introductory training for chaplaincy, that gave me space to act, spiritually and meaningfully. That all happened sometime late in the fall of 2010. Within a month of that experience, I was seriously researching seminary programs; within two months, I had applied. Before the year-long chaplaincy training program had ended in June, I was accepted to Union Theological Seminary and I had given notice at my job. Within a year, I was studying theology, Bible, and depth psychology. It was a heady and challenging and rich time and in retrospect I wouldn’t exchange it for any amount of money. Cross-reference: the pearl of great price.

When I think back to then, just over seven years ago now, it’s surprising how quickly it all happened. However, once I had realized the fundamental shift, once I had found the crack in my own resistance and self-doubt, and could see something else for my life on the other side of it, doing the rest was just a matter of course. It took effort and energy and was sometimes difficult —  filling out paperwork, paying application fees, visiting campus, figuring out how to make the money stuff work, etc. — but I think of it this way: the change had already been accomplished. Whatever seminary and pastoral study was for me, I was already in it, and needed only to find a setting where the outer reality matched the prior inner condition. Whatever Union was, I was shown that the decision to go there had already been made.

I knew this, but it was hard to communicate. Leaving my career and livelihood, pursuing a path that had no precedent in my life or anyone else that I knew, among colleagues or friends or family — it was hard to say exactly why I was going to study. Even if I had the language, I wonder if saying, “I need to find a setting where my outer reality matches my inner condition,” would have satisfied anyone’s curiosity or concern.

The responses to “I’m going to seminary,” ran the gamut. My IT coworkers assumed I was going to become a monk. My parents were vocally concerned about how the cost and debt might limit my freedom. You might be surprised to find that seminary is not high on those annoying grad school ROI lists. My friends, with whom I had been most frank about the changes in my spiritual life and ethic, were supportive and encouraging, and asked good questions which I could not easily answer. These were mostly different versions of: what are you going to do with it?

Great question. It created some tension in me, and to hold the space I often said that I was planning on becoming a chaplain after I graduated. I said it enough that I started to believe it. But if anyone had pressed me on it, I would have said — no, probably not. Chaplaincy had brought the fundamental question of my life out into the open, but my sense even then was that chaplaincy itself wouldn’t take me further than that.

In the meantime, which is where we live our lives, it was a good story, in that it was coherent. It went like this:

“When I left teaching to work in IT, I suddenly found myself with something like a 9-5 job and a lot of extra emotional energy that I was no longer expending on the vicissitudes of teaching math to the Youth of America. It was then that I found a rewarding and meaningful meditation practice, and through it I was introduced to a way to manifest that meaning in my day-to-day life: chaplaincy. So I’m going to study theology and psychology so I can become a chaplain.”

Perfectly coherent! Just not really true in the last part. Its merit was that it made more sense than:

“Paul (yes, that Paul) told me that meditation is okay so now I want to think more about that.”

How spiritual! Its merit is that it is descriptive and accurate — but, alas, not compelling unless you are of a particular mindset.

This makes me think of the koan I quoted above, because in retrospect, I think I could have responded to “what are you going to do” with what Fayan says:

“I don’t know.”

This works on levels that I couldn’t express at the time, though I was experiencing them intimately. Of course, there was the element of literally not knowing what was going to happen when I left my job and studied theology. But it is not a small not knowing, like not knowing when the train will come or what’s for dinner tonight. It’s not, “I dunno.”

The not-knowing I was experiencing then was like the experience when you’re walking through the city, and can’t see very far because of the buildings or the contour of the land, but then you turn a corner or come to a little rise, and suddenly you can see the whole at once. You see this vast expanse of people and buildings and streets, in the bowl of a valley, or down miles and miles of a broad avenue, or in some huge open space or park, and suddenly you see the largeness of what you’re in. You behold thousands of lives, interwoven and in motion together. The sky and the earth are broad and incomparable. You have, in a moment: perspective, possibility, and openness.

And if in the moment you see this, someone says, “where exactly will you go in all that,” or, “where’s the nearest subway station,” or, “think there’s a Starbucks with a bathroom somewhere over here?” you might answer with a little smile: I don’t know.

This, as Dizang says, is nearest. Other translations of this koan have Dizang say, “not knowing is closer to the truth,” or “not knowing is most intimate”. As I look back, all of these capture the sense of wonder, the simmering anxiety/excitement, and the sense of being truly close to my own life, more so than I had ever been, in that time.

If you can find a pilgrimage to go on, I recommend it. It was important for me to live not knowing, so I could start learning what was up.

Paul made me a Buddhist

I was reading about the apostle Paul over the holiday, and thinking of his participation in a turning point in my life.

Early in my Buddhist practice I was volunteering as a chaplain-in-training in hospice care, under the guidance of Zen monks. Born a Catholic and uneasy about that tradition’s claim on me, I had found a new and liberating energy in the practice of sitting meditation, an energy that brought me to this chaplaincy training program. I recognized that the urgency of being near death lent my patients clarity, and thought that that clarity would help resolve the question of my life.

This was a misunderstanding, of course. Being with the urgency of dying (which is the same as the urgency of living) doesn’t resolve anything. Only humans can resolve, can make resolutions — but in matters that deserve resolutions, it’s only after struggle, with others and with ourselves. The urgency of life and death, when fully realized, clears a space for conflicting forces within one’s self to come to the fore. The struggle that results when we can no longer hide from this internal tension is, to paraphrase biblical scholar Phyllis Trible, a struggle we have to endure until it blesses us.

So chaplaincy work, which I was sure would speak to me about my life in a new way, actually returned me to exactly the same question of my life, the one that brought me to Church and made me leave Church, the one that made me sit and brought me back to Church, and the one that had me sweating while meditating at home one day a few months into my chaplaincy training.

For a some weeks I had been working with a patient, an older Japanese man that I’ll call Stephen. I characterize him now as a charismatic Christian without a church, a man filled with adoration, despair, insight, loneliness — and cancer. He had a tumor the size of an orange on the side of his throat, that he covered with a napkin that slowly saturated with blood when I visited with him. He had an affection for me but also identified my Buiddhist practice as a smoke-and-mirrors seduction whose architect was the Devil. While I obviously didn’t engage him in these claims, I was hopelessly green and couldn’t move our focus back to him. Further, our visits bothered me well after I left him, and in the words of one of my fellow trainees, I allowed him to completely drape his worldview over me. I never would have done such a thing if it didn’t find something to catch on my own view of myself, some crack in my armor, a jagged edge where a projection like his could find some purchase.

What Stephen had found in me, in his suffering and through his significant spiritual insight, was my own doubt and guilt about my own practice. And as good teachers do, he called me on it. Of course, he was not actually my teacher and his assessment was actually a projection, a part of his process of dying slowly and painfully, which arose great doubt and fear in him. However, my work as a chaplain would require me to recognize my own struggle so I could more effectively sit with him in his.

So there I was, at home, meditating, sitting with my own struggle. My doubt was: am I allowed to meditate? Is this a thing that’s okay with God if God exists? You know you’ve reached the question of your life when you keep asking yourself a question that is so completely ridiculous when you think about it objectively, but it will just not leave you alone. It’s because the question itself is just a cover for a subjective reality that has not yet found a fitting expression. I was gripped by this reality but didn’t have the words to confront it consciously, so I struggled with what I had on hand: my sitting practice itself.

Even though meditation had given me new life, I was filled with guilt that it was somehow wrong. And the root subjective experience I had was in fact a feeling that I was wrong: me, sitting there in my me-ness, was wrong. So this was not guilt but shame, more existential and transcendent, that I tried to control by transferring it onto my new spiritual practice. It had been brewing for a while and Stephen gave it the external circumstances to raise it up such that I couldn’t ignore it.

My experience in that moment was: I could not sit. It’s really incredible to write, but that’s exactly what it was. Sitting on a cushion in kneeling position, eyes cast slightly downward, counting my breath, I was so overwhelmed with a feeling of despair and restlessness and doubt that I just couldn’t go on with meditation. I experienced the feelings as a fretting narrative of doubt: What if I’m wrong about all of this? What if sitting it not what I’m supposed to be doing? How can I know what I’m supposed to be doing? Will I be punished for doing things the wrong way? How can this be? What am I supposed to do?

Over and over, this story repeated itself. I couldn’t count my breath to one. I could hardly stay still. The tension became so great that I stopped the meditation. I looked up and thought, what the hell is going on? what is wrong with me? I had found such support in my life from meditation, but what happens when I create a barrier for myself, blocking me from my practice? I was bereft by an opponent sitting exactly in my own shadow, in my own psyche, in my own being. I didn’t know the arc of the struggle, that it was in fact a struggle I was in — as far as I knew, I had just concluded that I couldn’t sit and breathe anymore.

I looked around, despairing. To my left was a small bookcase, and I reached for a book with a big ol’ crucifix on the side of it, John Richard Neuhaus’ Death on a Friday Afternoon. I opened to a random page and found Neuhaus quoting the words of Paul, directed to the Corinthians:

“But with me it is a very small thing that I should be judged by you or by any human court. I do not even judge myself. I am not aware of anything against myself, but I am not thereby acquitted. It is the Lord who judges me. Therefore do not pronounce judgment before the time, before the Lord comes, who will bring to light the things now hidden in darkness and will disclose the purposes of the heart. Then every man will receive his commendation from God.”

Neuhaus names this as the “foundation of a Christian’s freedom,” as opposed to a source of “paralyzing insecurity,” like what I was experiencing right at that moment.

Reading this cracked my anxiety wide open. At one time, it both absolved me of my relentless self-doubt and recrimination, and it gave a transcedent value to the “purposes of the heart,” my longing to be free and live my own life. Naming this desire, and recognizing the small self-concern that obstructed rather than assisted it, allowed me to trust my own expereince, and my own agency in finding the way to that freedom. “I don’t even judge myself!” I think of this now as, being able to trust my own experience as a guide to the purpose of my heart. This spoke exactly to what I had heard as the teachings of the Buddha: be your own lamp.

This did not answer the question once and for all, but it was a pivotal turning point in my Buddhist practice, and my vocation: it gave me space to act. I was, on some fundamental level, in a way that I had not been before, okay. This was both a place to stand, finally, but also a dynamic force — the purposes of the heart are always changing with the world, and keeping close to them provides a kind of motivating energy that prompted the huge external changes in my life: to continue to practice meditation and to serve as chaplain, to go to seminary, to take my Buddhist vows, to be more vulnerable and trusting with others than I ever had before.

One day I’ll have to write more about the irony of Paul making me more Buddhist than ever, and the nature of conversion, or rather, call. And also the irony that I had this very Augustinian call experience without ever having read his Confessions. Seriously. When I finally read it I said, oh shoot.

This makes me think about shame and guilt, and about New Year’s resolutions as well: specifically, my commitment to write more in the New Year. They’re all related. Looking forward to what comes around, even as the news in early 2018 sounds a lot like the news in late 2017: it all looks bad. Thank God for practice, and good books, and friends and loved ones, in the New Year.

Social and Emotional Factors in the Math Classroom (a few initial notes)

I’m trying this thing where I write a quick blog post after an energizing conversation. Wish me luck!

This year at open school night, I gave my students’ parents an idea about who I was and where I came from, on the logic that my professional narrative informs many of my choices in designing my classroom. Rather than providing them with a list of strategies and tools I’m using, I figured I could just tell them why I’m doing what I’m doing, in story form, giving them a better sense of the class, and of me. That seems the most you can get out of open school night: an answer to the question, “who is this person teaching my child math?” So I thought I’d answer it directly.

One of the things I shared with the parents that I had not shared before was my work in chaplaincy and pastoral care. It felt important to say, but it’s so random that I couldn’t leave it as it was — I made a joke out of it. It went something like this:

“When I tell people about the jobs I’ve had, they usually stop me here and say, how did someone who worked as a chaplain go and become a high school math teacher? Then they think for a second and say, actually, I could have used a chaplain in high school math!”

Har. As Open School Night jokes go, it’s not the worst, and I like to think it gets points for uniqueness. Of course, I’m not so sure that I’ve ever actually had this exchange, but people found it funny, so it tells me there’s a seed of truth there.

As I reflect on it, I think there’s more than a seed of truth — and now I have a bit of misgivings about light of it. But it brings an important point to the fore, which if I had to put in one sentence, would be:

The emotional and social life of a math classroom is fundamental to sound progressive pedagogy.

How so? Well, if you found my joke remotely funny, you know the first point.

Math work is frustrating for students.

Math is hard, and everyone seems to know it, because people can talk about not really understanding math after sixth grade and they will get a round of affirmation at a cocktail party. Meanwhile, if you say, “I stopped learning how to read in sixth grade,” in the same context, the reaction is very different. So there’s good reason to believe that the idea that math work is hard for students has some cultural capital. As a teacher, I suppose you should be ready to deal with the fact that your students will be frustrated, even if you tell them how to do things very clearly.

Let me push this is a bit further.

Math work should be frustrating for students.

Or at least, good math work should be frustrating, for a time. The productive struggle is a necessity for learning math, because that’s what it takes to build one’s own relationship to the mathematics. That is not easy work, and cannot be easy work, because it requires creativity and discipline and risk-taking.

Now a teacher shouldn’t seek to create unnecessary frustration for students — in a well-designed space for math, the frustration will come naturally. But a teacher must be able, not just to “deal with” the students frustration, but to go further — to tolerate their students’ frustration, giving the students space to work out their own understanding. If the teacher cannot tolerate their students’ frustration, and instead gives into it because of their own anxiety about letting young people be frustrated, the student loses an opportunity to create an authentic connection with the math. There are times when it’s appropriate to alleviate a students’ stress around not yet understanding math, but I believe these are far more rare than most people expect.

So let me bring that together into a third point where the emotional life of the math class is essential:

Teaching math requires a teacher to tolerate their own anxiety about student frustration.

Ultimately, we all became math teachers because we wanted to help young people with math, on some level. If that is part of the original impulse, it’s not surprising that we would be highly uncomfortable with resisting the urge to help. But we can see that the desire to give answers or help anxious students can sometimes handicap students from developing their own capacity to tolerate their frustration and find a way to work through it.

“Less helpful,” is the subtitle to Dan Meyer’s blog. If we overhelp, students will be underserved. If students get used to waiting for a teacher or another authority to swoop in and make their math difficulties go away, they become less able to navigate actual real-world situations where not all the information is provided, where conjectures and estimations are necessary, where the constraints are unclear, or where there are many possible answers that need to be adjudicated and argued depending on the question as hand.

Students need to experience the difficulty of this, which is an emotional task, and teachers need to let students experience the difficulty of this, which is also an emotional task.

And a social one.

Students and teachers need to be able to relate to one another about the frustration of math work.

What needs to be communicated, often through actions more than words, is not just that the teacher expects and accepts and tolerates the students’ frustrations (and anxiety, let’s say it), but further — that the teacher believes the student can work through that frustration and learn something. This pushes the emotional work into a kind of social work. School is about relationships, I saw once. There has to be a level of trust established. The only way a teacher could possibly tolerate a student’s repeated frustration and anxiety is if they trust the student can deal with it productively, and then they have to be able to relate this to the student, over and over again.

And it’s not just about saying it, it’s about meaning it. This is harder than it seems, because it requires the teacher to trust that they themselves could tolerate frustration and anxiety and learn math in this way. I had several beloved but not particularly progressive math teachers when I was growing up. When I think of my formative experience as a math learner, it was when I took on agency for my math learning in college, after I recognized I couldn’t coast by with formulas and shortcuts anymore and had to really study to get at the understanding. That experience of coming-to-agency (which, it so happens, I also mentioned in my Open School Night presentation) is the foundation for my own progressive practice — and even still, I often have a hard time trusting that what I say I believe is really true: that knowledge comes from making sense of one’s own creative experience, and that learning cultivates liberation.

I get the sense, and I think you’ll agree with me, that math seems to be some kind of haven for people who don’t want to think or talk about their feelings, or maybe even don’t want to have much to do with the feelings of others. That’s a stereotype, but it seems to dictate what many people expect of math. However, math brings up lots of feelings, and as teachers we have to be ready to name them and navigate them, and help students hold them without us rushing to fix them. Students need to survive that frustration to discover their own capacities and insights, and we need to protect the space for them to do just that, minding their progress and trusting that, on the most basic level, they already possess what they need and their work is in bringing it to fruition. On good days, I can see that flowering of the free exchange of knowledge in my classes, or rather, I can feel it.

There’s something in Gospel of Thomas about this: “If you bring forth what is within you, what you bring forth will save you. If you do not bring forth what is within you, what is within you will destroy you.” In a theological mode, that captures precisely what I need to create, and protect against, for my math students.

That’s why it’s good for a chaplain to be a math teacher. No joke.

Skillful means for math students and showing up for teacher work

Dear Reader, it is late August! School is beginning soon! For me, that means it’s time to reflect on my goals while I still have the bandwidth to do so.

I ended the last school year feeling overwhelmed with the demands of teaching. Between the changes that I had initiated in my classrooms (trying out different teaching styles, grading systems, and digital platforms), the wide variety of students I was teaching (8th through 11th graders, pre-algebra to pre-calculus), the needs of my students and their families, and the contradictions inherent in teaching progressively in a non-progressive world, it was easy for me to lose sight of the meaning and purpose of my work.

Over the summer, I had a few chances to step back and think. This allowed me to reaffirm my commitment to the work of education by outlining what I want for my students, and how I intend to help them get them there. I made two lists: the first, a set of developmental goals that I have for all of my students; and the second, a set of learning habits specifically geared to their growth as math students, that would help them approach the goals. Here I’ll talk a little about both, in the order I developed them.

Mathematical Habits, or: Skillful Means for Math Students

I developed these early in the summer, at a conference for math teachers at Phillips Exeter Academy in New Hampshire. My workshop leader, Johnothon Sauer, asked our group to answer the question:

What do you want the kids to focus on in your course and your classroom?

The first thing I wrote was the title for my answer to that question: “Skillful Means,” which I had written about just a few weeks before the conference. Skillful means are a set of “practices and habits by which we wake up to what’s real.” I saw his question as an opportunity to describe the development that’s really going on in my classroom (if everything goes as planned), and how I could focus my energy and my students’ energy on that development.

Here’s the list of habitsI want my students to focus on in my math class:

  1. creativity: seeing freshly, using all of their resources (math)
  2. process: conjecture and evidence and revision (math)
  3. communication: speaking and listening and questioning (us)
  4. collaboration/citizenship: mutual support and mutual regard (us)
  5. practice: consistence and persistence in their work and preparation (you)
  6. reflection: meta-cognition and self-knowledge or meaning-making (you)

This is a list of six habits that I want my math students to focus on and cultivate, a tool box of qualities that allowed students to fully engage in their work in math — in short, skillful means to realizing their mature understanding of math.

After I rattled these off, I labeled each with one of the three parenthetical notes (math, us, you). Math focused on a fundamentally mathematical practice (creative problem solving and the process of developing one’s own ideas in math), us focused on one’s relationship with a community of math-workers (communication and collaboration/citizenship), and you focused on the students themselves (the individual practice of working on math on one’s own, and the reflection on what one has done and how one has changed in that work).

I imagined these being most useful as framing my feedback to the students. While I would offer graded feedback for the understanding they could show me of the various math skills and content we were spending all of our time discussing in class, these six habits would be how I talked to students about the quality of their work. I would write their comments based on these habits, and talk to their advisers and parents in these terms. With a consistent structure, I can communicate to them what I think is important about doing math, with the hopes that it will change how they think about math and what they do to study it.

Thus the Habits — skillful means. But as it turns out I needed something more, and it was going to follow me around until I could articulate it.

Goals for All Students, or: Showing Up for Work with Young People

So I was on a silent retreat, meditating for about six hours a day, and running a lot of stories over and over in my head about how to do what I want with my life.

Ever since I decided to go to seminary almost seven years ago, I have known that my life was going to take a different path than I had imagined, but it’s taken a long time for that to really take shape. When I finished seminary three years ago, I didn’t have a clear picture of the kind of work that would hold my desire to discuss and pursue meaning and development and being — which I’ve taken to calling soul-work. I ended up returning to the math classroom, but it was financial need (read: student debt) as much as authentic interest that brought me there. I’m happy where I am, but I know that there’s a broader project that I’ve only just begun to explore.

And when you’re meditating for six hours a day, you’ve find yourself with a lot of time to think about what you could be doing or should have done. Thankfully, you also have a lot of time to practice, dropping your awareness down below the thought, and below the attached feelings of doubt, or anxiety, or fear, or regret that seem to arise with the thought, and staying with the experience in your body, right at that moment, not trying to drive off the thought but also not letting it drive you off. Just staying with it and sitting with it, not separating from it or giving in to it.

I had about a day’s worth of meditation wracked with some kind of anxiety in the category of how-can-I-do-what-I-really-want, and I kept up the practice, met with a teacher to talk about it, and kept on sitting, until that moment at 6:35 in the morning, with the rising sun tapping me on the shoulder, when I felt a shift within me that broke that whole story I was telling myself wide open. Rather than the same old narrative of how I can I get to something that’s not yet here, I beheld the question:

Where is the soul-work in your role right now, as middle and high school math teacher?

The answer, dear reader, will not surprise you in the slightest, but it struck me like the bright ocher of the wall in front of me, which had been in front of me all that time but I only really saw at that precise moment.

The soul-work I have now occurs exactly in my relationship with my students, where I find them right now, and what I want them to grow into and become. I was reminded earlier in the summer: school is about relationships. And I could make space for that relational work, the central work of a teacher, if I could articulate the goals that I have for my students across the board. This was a way of truly showing up for my work as a teacher, to practice soul-work exactly where I found myself.

Having been cracked open by the August sun and a wall, I struggled mightily to not immediately start making the list of goals I have for all students, since I was still technically meditating, in a room full of silent meditating people. Practice was still practice. So I held off for a bit, unsuccessfully, but relieved that a change had come.

When I finally sat down to articulate my goals for all students over the course of a school year, this is what I wrote:

  1. Intellectual: Demonstrate proficiency/mastery in all of the content-based learning goals of their course of study
  2. Academic: Develop student skills for the effective, organized practice, absorption, and retention of the content
  3. Social: Interact with peers in small groups productively and equitably
  4. Psycho-spiritual: Practice and reflect on your capacity for creative, authentic work

While the intellectual and academic goals are obviously important, they are balanced with broader social and psycho-spiritual goals that are meant to address the whole student. Similar to the skillful means above, these would help me structure how I talk about my students’ work with them over the course of the year — but these are not means, these are ends. These are what we’re going for. I can see where my students are with each of these, and push their growth where they need it.

I want my students to know more math; I want them to know how to study and understand math, I want them to be able to develop math with and support/be supported by their peers, and I want them to realize themselves as mathematical beings, so to speak.

Everything I’m doing with them is bent toward these goals. When I lose sight of these because I have a fancy new idea about pedagogy, or I’ve read an article about trends in education or politics that make me angry, or I’ve had a conversation with a parent or colleague go in difficult direction, I can remind myself that I’m here to move my students toward these four goals by equipping them with the six skillful means listed above.

Then, rather than pushing away the work because I don’t like it, or getting lost in the work and missing the forest for the trees, I can simply meet the work where it is, renewing my vow to help my students realize the fullness of their participation in math, and the part of their being which is fulfilled by its study. Hopefully, I can continue to respond to them with intelligence and compassion, and bear witness to the reality and potential of their lives.

Well-wishes to all teachers, students, and families — and really anyone who will experience some challenging growth this season. You’re not alone.

Teaching and Skillful Means

The end of the school year is the best time to think about the next school year, since obviously I’ve got nothing else going on. I’m working on a few things to reboot and overhaul my classroom practices, but also looking into ways to stay excited about math and connect it to something meaningful. This can lead to some wide-ranging book-browsing, with some interesting results. For instance:

I was standing in the Strand, reading a copy of Quantum Mechanics: The Theoretical Minimum and I was wondering why I was reading it at all. I don’t teach quantum mechanics, let alone science, and it isn’t the kind of book one picks up casually. It’s not a beach read — but then again, I’m not much of a beach-reader!

I’ve been interested in quantum physics for a while. I read a lot about it when I was in college, and have become more interested in it again as of late while listening to the lectures of Neil Theise, a liver pathologist and senior student at the Village Zendo, where I practice. He has written and spoken about intersections between modern science and traditional systems of wisdom. I find him most exciting when he talks about Fundamental Awareness, which relates the findings of quantum physics to the primarily Eastern philosophical and religious idea that consciousness/awareness is not an emergent property of matter but in fact fundamental to the structure of the universe. When I first heard him speak about it, it opened a world of speculation in old interests of mine through the lens of my meditation practice.

Initially, though, I was so excited about the ideas that I didn’t see its relationship to mediation. It was all so cerebral and abstract, and I loved it — but what does it have to do with sitting on your cushion? He said: the whole philosophical construct is kind of skillful means, fulfilled and personalized by one’s disciplined practice with the Zen community. He said, more directly, “the universe has made one request of me, that I be aware. This is one way to know that, and meditation is my way to practice that.”

So I read about quantum mechanics now, about the fact that consciousness cannot be removed from consideration in objective observations, and I think about my practice and my participation in the world.

But I wanted something a little more: I wanted something related to my math teaching. Still, I was holding this book, getting excited about its ideas and its math and its spiritual implications, and still I was feeling like, this is related! How?

Standing there reading about spin and the states of quantum systems, and moving through this fog of anticipation and mild befuddlement, the words skillful means suddenly hit me. I think I actually said “Oh!” out loud.

If science and quantum physics is related to skillful means and ethical action, so is math teaching. In fact, every discipline is related by skillful means, the practices and habits by which we wake up to what’s real. So I asked these two questions of myself, as a math teacher:

  1. how can a math class be taught with skillful means?
  2. how can a math class sustain and develop skillful means in my students?

Both questions are related to having some understanding about reality, about “Things As It Is,” as Suzuki Roshi once said. For a long time I’ve wondered how to combine my Zen practice, my theological and depth-psychological education, and my teaching vocation together. These central questions move me toward that.

I remembered a line from a mentor of mine, Ann Ulanov, about why she writes texts that combine theology and psychology to “see how one discipline can feed another, without collapsing or dishonoring one either.” How can we bring one field into fruitful conversation with another?

Anyway, those two questions are the broad questions I’ll be asking as I prepare for teaching next year. Now I just have to get to the summer!

 

Math, in search of meaning

What does math mean? And what should it mean for my students?

The answer to both these questions is up for grabs and not initially apparent. It requires an interpretation – the technical question is, what hermeneutic do we apply to math? How do we “read” math in a way that makes sense for us?

Math developed over time, and we can say things about who developed it, how they developed it, and can condense and summarize their work in retrospect. It is also utilized now for a variety of reasons. The interpretative question implies that neither set of facts – how math developed, or how it is used now – offer a definitive answer to a question of meaning and norm: what does math mean and what should it mean for us now?

Math, perhaps more than any other traditional secondary school subject, elicits reactions among people that emphasize its universality, objectivity, and invariance – and that these qualities are by far the most important thing about it. Ruminations on math in this key end up sounding grand and cosmic: math is a universal language, math is the underlying structure of natural laws, etc.

In this reading, the context in which math takes place is less important that the content that math delivers. Human disposition and purpose does not impact math’s impartiality. The only important context for math is the one in which it was developed – before now. The work has been done and we are responsible to the edifice that our ancestors have left.

In a million implicit or explicit ways, you can hear the argument that the math we receive now would be the same math no matter who came up with it or when they came up with it. In this frame of thought, reforming math education is unnecessary at best, and at worst obscures math’s universality and objectivity in the name of some lesser purpose (often, politics, or worse, political correctness). This explains much of the resistance to math reform. It is also a sensibility prominent among students. “Why don’t you just teach us the math,” frustrated students of mine have asked (they present themselves as experts of knowing math when they see it – but perhaps not yet hermeneutics).

In other fields of study, an emphasis on the message that takes no account of the messenger or the community receiving the message has been called “orthodoxy,” for better or worse, but that’s not quite specific enough. We’re talking about the interpretation of a text – mathematical statements, objects, and conjectures – so the term I’ll use has more to do with a lens, or a reading stance than a whole worldview.

I’ll call what I’ve described here: Mathematical Literalism. In this reading, the primary meaning of math is its universality and invariance, and students should approach it with humility and with an intention to take in the received wisdom. Furthermore, those students who by talent and effort can approach it are honored as having some special capacity for abstraction, which is often a cipher for general intelligence.

This is one interpretation of math. Another is functional and gives more attention to what math can accomplish when put into real-world applications (I mean this colloquially, as in, talking about math in close relation to stuff, as opposed to the category of math textbook word problems that are not-so-affectionately labeled, ”pseudocontexts”). Here, math is most often seen in service of the sciences, engineering, economics, and finance. Its universality is acknowledged, but mostly in that it delivers reliable quantification and abstraction that makes valuable tasks accessible. The context of mathematics matters, but not the context of its historical development – only the context where math finds its expression in the field. This is often measured in material terms.

Those who speak of math with this frame in mind are attentive to the demands of a modern economy and a computerized, data-driven society, one which the digital revolution is constantly transforming. There are also aware that education, especially in applied and technical fields, opens up career opportunities for students that are selective and profitable. The important context, again, is in the future – and is measured by material gain.

This kind of reading of math I call Mathematical Materialism. The primary meaning of math is how we may use it, and it should be approached by students with a practical and ends-driven spirit. Those who find success in this way are valued for the material benefit they have created – no small distinction in our materialist, pragmatic culture.

Clearly, these two interpretations are not mutually exclusive. Most people do not think too much about math, and if pressed on the matter will say some combination of: math is math, and if you can do it you’re pretty smart; you will probably be able to find a good job, and the social value of that work will allow give you the means to live a happy life. The broader American values of practicality, hard work, individualism, and material success all participate in promoting these two readings of math.

There is another reading of math that acknowledges the data that Literalism and Materialism start with, but goes in a different direction. We can find a helpful middle route between these two hermeneutics by noting where they locate the most important context for mathematical work.

Literalism puts the important context in the past: the work has been done, and now we have math and we have to absorb it. Materialism puts the important context in the future: it’ll be worthwhile math when it’s put in service of some project with results.

In between these two, we have the context of the present: the important work to be done for students of mathematics is the work that is done right now. Its meaning is in its actualization, and not in its majestic existence or its material expression.

What would we call a reading that makes its present context a priority? It would focus our intention not on retracing past steps or the preparation for future steps, but instead on the mathematical process as it is pursued in your math classroom, or your child’s math classroom, right now.

I propose Mathematical Praxis as a middle-way interpretation of math, between Literalism and Materialism. I think this implies what I intend – that our proper reading of math requires us to engage in mathematical activity, and the activity is more important than the content or the product. The meaning of math is found in its process – the only meaning is the meaning you create in doing it, right now.

This interpretation of math would not dismiss its historical development, or its potential products – but it would approach them in right relation with math as a present and creative intellectual activity, an activity that requires practice, a space for which needs to be cleared in a young person’s developing mind. In fact, without engaging in creative mathematical activity, students can neither appreciate the work and ingenuity of mathematicians past (and locate them in a variety of locations, not just in the ancient Greeks and early modern Europeans), nor can they be expected to skillfully (and compassionately) apply mathematics to its practical ends. Surely some do, but a privileged few. If math is powerful and valuable, it must be shared equitably and made accessible to all.

Math is a verb, something that students do. It’s meaning is not prescribed or premeditated. It has meaning only in as much as it’s free act of creative intellect. Experiencing this, students can start to answer a question they are rarely asked: what does math mean?

Math Class for America

So the election happened.

Today, the students at my school felt scared, sad, angry, anxious, and confused, but gave such energetic and clear expression to so many sides of the matter at hand, and spoke bravely and listened to one another compassionately. They opened a space to share and acknowledge how they were feeling, and started looking for ways to channel these feelings into action.

What they reminded me was, you don’t decide events, and you don’t even decide how you feel as a result of those events, but you can choose how you respond to events and how to use your feelings. Right now, the students chose to speak and share, and when we had spent the morning on that, to return to math class and do some good work. At the end of the day, I’d ask students: how are you? And they go — okay. And give a knowing smile. I was so impressed.

My classroom is 100% where I want to be right now. When we finally got into it after the (important, crucial, timely) whole-class conversations, whole-school sit-ins, viewing of speeches and lots of hugging and passing around of tissues — when I finally got with my students, in a math class, working on math — I saw my work there in a whole new light.

What I want to teach my students is: how to reason together; how to listen; how to argue your point with supporting evidence; how to evaluate and adjudicate contradictory evidence, and how to change your mind publicly, without fear. That’s what math is about, really. Its content is all shapes, numbers, and patterns, but its method is democratic dialogue, the communal probing of understanding and implicitly, the establishment of meaning.

That’s what we need. Math class is a microcosm. If we can’t listen to someone with a different idea of how to plot a range of values graphically on a number line, or are not willing to admit the possibility that our solution is incomplete or incorrect — how do we propose to do such things around the economy, immigration, global warming?

Their work is all in groups this year, but I’ve always been a little hands off in terms of guiding them on how to do this — which is ridiculous, because who knows naturally how to work in a group? No one (cf. the 2016 election, The United States Congress, etc.). So I got into it with them, directing them in ways I had not before. This seemed important today, of all days.

I went from group to group as they tried to build a consensus around their solutions to the homework. Let me tell you, they were not having it. It’s so hard just to listen to one another and go at the pace that your neighbor is going. They bounce around unpredictably in their work. They skip questions that they don’t understand without much attempt to try. They see any kind of extra detail in note-taking, or writing out their reasoning as an impossible and unnecessary expense of energy. Same with suggesting their answers to other students and listening to the responses. But of course when they don’t do these things, all kinds of ridiculousness ensues. Several times I’ve had students present their ideas on a problem to the whole class, only to have members of their own group disagree with them. I’m like — how did you get through 30 minutes of group work without mentioning your differences on this problem, which was one of three you had the task of discussing??

I know why, of course. Listening closely is hard. Hearing critique and mustering a thoughtful response is even harder. It’s easier to let someone just tell you their answer if they speak it with enough authority, and even easier still to be satisfied with your own understanding and not probe any further.

Our responsibility as citizens is all of the hard things, though — arguing our case, listening to that of our opponent, and sincerely evaluating the two along side one another. How often does that happen, I wonder? More practice would be better. Starting with the young is good, too.

Cornel West wrote an editorial last week about the spiritual blackout in America, and I’ve returned to it frequently. Dr. West tells us about Plato’s critique of democracy — its potential for corruption and manipulation by elites and charismatic politicians, its weak spot for ignorance and mob rule — and offers us John Dewey’s response, that a democracy must foster in its citizenry critical intelligence, moral compassion, and a mature sense of history. That’s the purpose of democratic education, and democratic math education (or as I called it today, Math for America, or at other times People’s Math) can do all three.

The ability to make, evaluate, and revise arguments using evidence and in collaboration with others is precisely critical intelligence.

The act of listening and attending to one another’s ideas builds a spirit of moral compassion, because we learn that other minds work like ours, make brilliant leaps and careless errors like ours, and have the potential for growth like ours.

And in as much as a math class encourages students to participate in the creation of mathematics, rather than the rote absorption and recitations of formulas and vocabulary, it brings students into a truly universal, historical human dialogue that can be both humbling and empowering — this is a mature sense of history. I am receiving what was handed down to me, and I am handing it down myself.

Teaching helps. I’m glad when I emerged for my commute today into a sad, early morning cloud and a subway full of people not looking at one another, I knew I was going to a place where I could put my anger and sadness to good political use: teaching math.

Theological values in secular math education

Before continuing to look at math education in the light of, on one hand, a drastically uncertain future, and on the other, values inherent in that work that we would want to endure in our students (that is, values that are somehow ultimate), I thought I’d develop a little scheme for talking about theological values that are swimming around in a math class already. You don’t need the language of theology to describe them, but that’s what I’m doing, to give them some ground beyond the smaller contingencies of our present education system.

For my wider project here, I’m writing secular theology — theology that takes as its goal some coherence with non-theological language, and has some cruciality for situations that are commonly taken as non-theological.

Allied to that goal, having more to do with my own perspective than any necessary feature of secular theology, I’m writing in a dual-belonging frame — making use of both Christian and Buddhist concepts to cast some light on those typically non-theological, secular issues. That these concepts have some analgous relationship is interesting in itself, but that argument will be more implicit in what I write. Think of this as fair use. (I’d like to build more on the idea that a interreligious dialogue must become a secular dialogue, to find common language — but that’s for some other time.)

So, here’s how I’m laying out theological values for my present purposes. Let’s start with the theological virtues of Hope, Faith and Love (c.f. Paul and Thomas Aquinas). As I think interreligiously, triune concepts are helpful markers. Of course Christianity is replete with them, but they crop up in Buddhism as well. I’m thinking now of the Three Pure Precepts or Three Tenets of Zen — Not knowing, Bearing Witness, and Compassionate Action. Putting these two triune structures alongside one another illuminate them both. To wit:

Hope and Not-knowing — this is a fundamental openness to reality, a stance of accepting rather than controlling things as they are.

Faith and Bearing Witness — this suggests a trust and commitment to what is disclosed when we see with the eyes of Hope and Not-Knowing.

Love and Compassionate Action — this is the appropriate response when the previous two are realized. I’ve also seen that last phrase as “appropriate action” or “appropriate response,” which suggests a fundmental relationship with what is really true and love/compassion. There’s nothing special about it — love is actually what’s up. We needn’t reach for it or create it, it’s inherent in what’s happening, and when we respond with it we’re responding in perfect harmony to/with the situation. You don’t have to work too hard to see this play out in the Christian system, either. The other thing that’s important about these is: they’re fundamentally communal.

So there are your three Buddhist-Christian theological values. Now for a more absurd sleight of hand, I move them into the math classroom.

For reasons I can’t quite articulate, I’ve made these axial — each pair create a pair of balancing forces which I’m aruging I want my math students to develop and realize (again, in a completely secular context).

How do Hope and Not-Knowing map onto my math class? As patience and urgency. My students must learn to watch carefully and quietly, but with intention. The tension between these two describe a kind of temper that is always watching and ready. Confronted with a problem (mathematical, theological, or otherwise), this temper is your starting point — before you reach out to work with it, you need to face it squarely. It takes a long time to really understand a mathematical concept, with lots of little and big errors and adjustments along the way. Frequent re-doing means you need to hold that frustration with patience but also feel the internal pull to keep on trying. This is also called active attention.

How do Faith and Bearing Witness map onto my math class? As risk-taking and reflection. More active thatn the previous, this is a commitment, a trust, and a relationship with the object. It is partially a leap, an acknowledgement that we don’t know everything, but it is not reckless or unprecedented. It is based on prior experience, but requires some kind of break with that old evidence because: something new is here. Mathematical risk-taking is trying different approaches, testing with your mind different avenues, trusting that you can learn something by trying, but also trusting that your own experience is not completely irrelevant in this context.  Reflection implies the stepping back and seeing what’s happening, where the problem is and where you are, and where what you know runs up against what it presents as unknown.

How do Love and Compassionate Action map onto my math class? As argument and listening. Love and Compassioante Action are both ethical responses to the situation of the community, and transferred to the community of a math class, our commitment to one another is to argue and to listen. Argue, in terms of presenting statements with reasons that can be contested or agreed upon; listen, in terms of receiving the statements of others carefully and with attention. In math, this grows out of the previous two. If you’re paying close attention to what’s happening in working through a math problem, and if you’re trying things and thinking about what you’ve done, it’s natural in community to simply extend those processes to others: by taking in arguments and responding to them.

We often think of mathematical dialogue as purely intellectual, and place love and compassion in the realm of the heart — but I wonder what mathematical dialogue stands to gain from growing out of the heart-mind? That reflection might lead us to critique the current individualized, competitive system of education, that in my opinion handicaps math education more severely than other disciplines.

So that’s my preliminary Buddhist-Christian analysis of theological values found in a secular math classroom, that math students can be developing and realizing all the time. Note that these are probably values that apply to any discipline that requires dialogue — doing it in math would mean, we’re working with numbers and shapes and patterns. But that doesn’t mean we can’t do it with openness, trust, commitment, and love.

Math for the End of the World (Part I): Rising Seas, Hope, and Math Education

…or, Eschatonimatics? Apocalyptic Curves? Oh these are truly terrible.

When I last wrote about the PBL method of teaching math, I said that I often thought of this approach as Peoples’ Math (for it’s non-hierarchical structure emphasizing co-creation) and as Not Knowing Math (for it’s emphasis on students producing, rather than absorbing rotely, the math — and the necessity for patience and openness with the struggle to know something for one’s self).

I also think of it as Math for the End of the World, and I think of it this way more often than the other two.

A word or two about what I mean about the End of the World.

When I think about the end of the world, I do not have the literal reading of John’s Apocalypse in mind (though my thought and that text are not as divergent as it might appear at first glance), and I’m not touching on the question of Christian vs. non-Christian, sin vs. salvation, justice vs. mercy, and so on. No — for me, the End of the World is more mundane and less dramatic than that (at least in the single-event sense), and can be described in far greater detail than Revelation expresses. This particular End represents such an unusual and existential crisis to us that it seems to require a different way of thinking together as a human species, a different relationship to the biosphere to which we owe our entire existence, and so requires a departure from our business-as-usual assumptions about economy, industry, politics — and education, including math education.

The End of the World I’m talking about is human-produced, carbon-emission-driven global warming. It won’t destroy the planet in raw physical terms, and it likely won’t be a sudden confrontation with dramatic change, but it will radically alter that human-constructed habitat, the World. A better phrase for it would be the End of History, and this makes more explicit that what we’ve been doing is going to have to be radically different from what we do next, after some point at which everything we’ve come to assume about the Earth’s providence gets thrown into question.

As a wayward student of environemental engineering, and a waywayward student of Christian theology, it might not come as a surprise that I think about my current work in math education through this lens. Climate change presents an existential crisis, one that offers not just a personal end but an Ultimate End — all of humanity is threatened, and this inspires reflection in any and all fields of acitivty.

I first came across this kind of reflection in Roy Scranton’s essay in the Times, Learning How to Die in the Anthropocene. Scranton, an English professor and writer, is an Iraq War vet, so his lens compared the day-to-day threat of navigating the roads of occupied Baghdad to the broader, inescapable threat of rising seas and more severe weather patterns (i.e. Katrina). The connnection is particularly salient — the Pentagon has been pointing out the destabilizing potential of global climate change, as Scranton discusses. But he further develops the idea that this crisis has material and political consequences but also philosophical ones — confronting these changes, we ask what does it means to die? This leads inevitably to the question, what does it mean to live? He presents this as a fundamentally philosophical, humanistic question, one that is as confounding and as likely to capture our anxious attention as how to keep saltwater out of New York City’s very vulnerable subway tubes.

The Janus question of “how to die/how to live” first struck me when working as a hospice chaplain. Patients facing death reflect on the only thing they can in light of the ultimate: their life. In that context, I did not consider this process philosohical (though it can be) so much as spiritual and theological.

The questions are: how do we make meaning in the face of the ultimate, that which transcends but still participates in the smaller narrative of our lives? Why does a forward projection to the End lead us inevitably to a backwards reflection of the Beginning? What part does the Ultimate play in our mundane day-to-day? How does the Ultimate reach out to us, here and now? I think these are theological questions, given cruciality by spirutal experience and reflection, and they have a helpful place in our communal exploration of a world we’ve set on a rapidly changing course.

In grad school, I wrote for a Biblical interpretation class a global warming interpretation of one of Jesus’ prophetic utterances regarding the Second Coming, and the troubles that would precede this final act of God in history. Luke (21:25) says it: “There will be signs in the sun, moon and stars. On earth, the nations will be in anguish and perplexity at the roaring and tossing of the sea.”

I wrote that our fear of the danger to come should inspire a changing attitude to our world, our activities, and to one another. Less consumption, less material obsession, less exploitation; more compassion, more creative expression, more community.

But my professor corrected me — you can’t scare people into acting justly, even when the stakes are all human life, everywhere.

I was flumoxed, but I see what he was talking about. The chiding moralism of “you’re gonna get yours, fools,” rarely inspires lasting change. Just because science is on your side does not give you a right to be a jerk to your benighted neighbors. 

It seems that Christian reflection on the End Times (bear with me if you’re not a Christian), starts from a place of hope, not fear. Roger Haight summarizes Karl Rahner’s description of hope:

Hope…refers to the fundamental openness of the human spirit…hope desginates a region of human existence from which both faith and love are elicited. Hope reaches back into the human spirit as inner freedom that characterizes reflective consciousness.

This makes me think of the Zen precept of not-knowing — a fundamental openness of being, toward all being, exercised freely. This is a disposition that leads to a renewed commitment (for Christians, faith; for Zen Buddhists, bearing witness) and a guide for action (for Christians, love; for Zen Buddhists, compassionate or appropriate response). It’s nice when these two very different religions seem to agree on a deeper, objective dynamic in human encounter with the ultimate. It suggests a further expansion of these questions into secular realms of knowledge and action.

A question that has pursued Christian theology from its earliest days is: how does this exercise of human freedom influence the outcome of all things? What part of the World’s ultimate fate is our work, and what part of it is given to us freely? This is Paul on circumcision; this is the Augustinian/Pelagian controversy; this is the Reformation question of works-righteousness. More recently, Juan Luis Segundo asked: what of our work will endure into the life to come? How do we know what we do will be a part of the Eschaton? If nothing, then why do anything at all?

Moving from the Christian reflection to a more secular one: if you agree that climate change is real and as bad as it seems, then we’re facing a radically different world to come. It is worth asking: what of our work will endure into that different world? What can we create, in a spirit of openness and hope rather than fear and reaction, that will buoy the spirit of life and the floruishing human community? What part do we play in this cycle of life and death that we influence and receive so intimately and so globally?

That brings me to my math class, a space that is already open to my reflection, and where meaning is always alive, whether I notice it at the time or not. Conveniently, unexpectedly, I’ve already described PBL math as a method that encourages an openness, not-knowing, that corresponds to hope. Does it make sense to practice hope? I think so.

But there’s more here to explore — if we see the world’s situation as it is now, what would we want to instill in our students to survive what seems liklely to bring calamity and chaos, and certainly will affect the poor and marginalized of the world disproportionately. What do we want to teach our students, when we are facing a radical change in everything we know and assume about human responsibility and sustenance?

I don’t know! But I can see two preliminary avenues of questioning:

1) How is math itself related to the project of human flourishing? (problem solving! reasoning from evidence! resilience and community support! listening, being flexible, accepting new conditions, and taking worthwhile risks!)

And 2) what kind of space best communicates this to students, and helps them practice it, such that it sticks — that will communicate a transcendent value that is enduring, that approaches us from beyond our suffering world and helps us face it?

Next time. I need a sandwich.

To teach the right answers for the wrong reasons/my own experience is not for all seasons

(With apologies to T.S. Eliot…)

My students sometimes ask if I actually like math, or what brought me to be a math teacher. I have struggled to answer, and for a long time I thought it was because I actually didn’t like math. But that’s not quite it. I didn’t want to share because I understood on some level that what I gathered from my years of success in math classes was not at all what I wanted them to gather.

What drew me to math is precisely that quality that most people ascribe to it: it’s very neat packaging of the complexities of the world into some lines of scratchwork, terminating in a simple and correct answer.

I was very good at this. It was also bullshit.

I got some hint of this in college, when procedure or example pronblems could no longer guarantee success. I learned dramatically the need for a more open-ended, heuristic approach, which usually went hand in hand with group work. Sure, there were still right answers, but the path to them was not linear, and was not supported by faithfully copying every word uttered in a lecture, either.

Right answers even become dubious in the lauded “real world” problems so commonly proposed in math education. True, in as much as math models the world, you can model more or less successfully, and this is central to all kinds of endeavors. But the path there is not a path you can follow by rote, so much as one you must create by walking it. It is a creative act, both in that you are making something new, and that you are pursuing your own authentic approach in doing so. 

In this way, mathematics is as intuitive and subjective as any creative form. Because it can model the world, it has some value as a clarifying tool, and its basic tools (number, shape, pattern) are such ubiquitous tools to human thought that we can speak of their objectivity. But this is true of the humanities as well — equally subjective and objective, equally intuitive and intellectual, equally individual and communal; and completely, fundamentally creative.

This practice requires a classroom characterized by fruitful disorder, skillfully channeled; conjectures that are open to constant revision; and my student talk, thoughts, and attitudes being the engines that drive the class.

But this is not why I became a math teacher! I became a math teacher because I remembered loving its false order and its neatly packaged right answers! But what I found when I was a math teacher long enough to catch my breath and look around was:

  1. The surprising diversity with which students can understand any topic no matter how simple I assume it is: from trigonometry to linear modeling to fractions to multiplication, if you have 25 students, you have 25 ways of understanding and expressing those concepts. I’m still be surprised by the insights and ingenuity that even my most struggling students can share.
  2. The baffling resistance that students will put up to even the most simplified expressions of some idea. This can be interpreted as some kind of childish willfulness, or it can indicate that there’s something lacking in the approach. While the habit in our field is the former ( the so-called deficincy model of teaching, conveniently pathologizing the child), I think the latter is more generous and closer to the truth.

Both of these contradicted my model of Math-as-Truth-with-a-capital-T. There was more diversity and complexity than I expected, and when I tried to push those differences aside, it only created fruitless anxiety — for both my students and me.

So my idea of what I’m doing and why it’s important has changed — but habit lives in the body, and is not so easily moved. It is not unlike an emotional/psychological defense, which had its place in its time, and must have helped me at some point, but has outgrown its use.

Luckily, habitual patterns can be addressed with practice as well. Intentional, mindful, even humble practice. As often happens, my students are my best teachers, revealing the emotional patterns that I long ago learned to suppress or manage. They will learn to manage them as well, but this can be done a way that affirms their authentic approaches to thought and creativity. Listening to them, giving due dignity to their thought process and their feelings, they can be cultivated for self-possession, a confidence given naturally and not reliant on any correct answer, and found again and again within the support of a community.

That’s a math class, right there. As a math teacher, my role is to embody that practice while handling the tools of mathematics. Even in the most supportive professional environment it can be hard to remember and to return to that practice, because it is at odds with what I value as a math student.

The hardest thing about teaching math isn’t the students, or the math. It’s getting out of my own way.