Reflection on wallowing after the "Two Faces of 'Smartness'" workshop at the Creating Balance in an Unjust World conference

So yesterday I was at the Creating Balance in an Unjust World conference on math and social justice in San Francisco with Jason Buell (@jybuell) and Grace Chen (@graceachen), and I finally got to meet Brian Lawler of CSU San Marcos (@blaw0013) and Bryan Meyer (@doingmath) in person. They are (of course!) both terrific. I came away so impressed with Brian Lawler — a wonderful math education teacher and researcher as well as a fun guy and a total mensch, in addition to being my friend Sophie (@sophgermain) Germain's mentor. You should definitely follow him on Twitter if you're not already.

He and Jason and I crashed the "Two Faces of 'Smartness'" workshop session yesterday right after lunch, which was beautifully given by Nicole Louie and Evra Baldinger.  It was glorious to do math on the floor with Brian and Jason at the back of a classroom where about fifty math teachers from around the country had crammed ourselves in because we wanted to learn about this and well, honestly, we just didn't care about having to sit on the floor.

What was wonderful about it?

Well, first they are both such amazing, caring, reflective teachers and mathematicians. We were given an Algebra 1-style complex instruction group task and we worked on it deeply, in our own ways, for 15 or 20 minutes. There was so much respect for the others in the group, along with deep listening and amazing mathematical and teacherly thinking.

Some of that wonderfulness was wonderful for me was because of my own issues over the years with shame about my own mathematical thinking processes, which are usually quite different from those of other mathematicians and math thinkers I work with. Even after many years of intensive work, I still have a conditioned habit of abandoning my own thinking in favor of somebody else's — anybody else's — especially if they seem confident about their thinking. I have a sense that this is similar to what our discouraged math students often experience, the ones who prefer English class or music or social studies, because I was one of those students myself.

Jason is a middle school science teacher, so he also has a slightly different way of looking at math than Brian or I do. At one point he suggested that we verify our idea by counting the squares. Brian and I looked at each other dumbfounded for a moment, since that had not occurred to either one of us. I exclaimed, "What a great idea! It's so science-y!"

We laughed, counted, and continued our work together.

There can be such joy in a group task like that, but not if the group's working structure is set up with rigid norms that limit individual students' participation. Frankly, I just hate the "assigned roles" kind of group work because I find that it fails to reflect -- or prepare students for -- the kind of group work that happens in a real-world collaborative setting such as a software design meeting. There, engineers and product marketers and managers come together but are not restricted in their participatory roles. No one is limited to being a "recorder" or a "task manager." One person presents a starting point to kick things off, and from there everybody just jumps in with the best they have.

That's how we were working on the floor together yesterday. It was an organic, free-flowing process, and as a result, both the learning and the mathematical conversation were far more authentic than I've usually experienced in this kind of work.

There were also rat-holes — glorious rat-holes! — we chased down. At one point we had even (temporarily) convinced ourselves of the possibility of a quadratic formulation of the rule, even though we'd been told (by the title of the worksheet) that this was a linear growth function. After a few minutes, we punctured the balloon of that idea, and felt a little deflated ourselves. We'd been working for several minutes straight but unlike most of the other table groups, we had still not called the teacher over for even our first of three check-ins. I hung my head in discouragement. "We are fucked," I said. But then we laughed again, brushed ourselves off, and picked back up where we'd last seen something productive.

The end of the workshop activity involved reflection on what the others in our group had contributed to the process in a method known in complex instruction as "assigning competence." You highlight one of the key competencies that another group member demonstrated and you tie it to a positive learning consequence to which it had led us. For example, I appreciated how Jason had brought in ideas from the real-world thinking of science because it had added rigor and a verification mindset to our process. Brian appreciated how I'd been able to stay with my confusion and keep articulating it in a way that made my process visible and available for investigation.

This pleased me because it is something important I think I have to contribute. I call it my process of "wallowing." I have a deep and self-aware willingness to wallow in my mathematics.

One of the other teachers in the room asked me to say more about what "wallowing" meant, and at first I felt overwhelmingly self-conscious about speaking up. But then I remembered that (a) I was being asked by other math teachers who are passionately interested in understanding different ways of reaching students who have their own unusual relationships to mathematics, and (b) I had Brian Lawler and Jason Buell on either side as my wing men, and come on, who wouldn't find uncharacteristic courage in that situation?

So I told him that for me — and in my classroom — wallowing means learning how to be actively confused and developing a comfort and a willingness to stay present with that confusion while doing mathematics.

In much school mathematics, appearing confused is a frequent and constant source of unspoken shame. And so most people with any amount of self-regard quickly learn how to cover it up and hide it from view. I went through much of high school disguising my confusion and shame as thoughtful reflection. I became a master of avoiding humiliation in class by keeping my confusion well-hidden. If I didn't get *caught* being confused, then I couldn't be humiliated or shamed about it.

Later I would work through my confusion privately so I could show up in class always and only being able to raise my hand about something I felt I understood cold.

So I believe there needs to be a culture of allowing for wallowing in active confusion in our math classrooms. We should not be too quick to dismiss confusion or try to resolve it or spackle over it.  I would even argue we need to consider it a badge of honor and an activity worthy of our time, consideration, and cultivation. The only way to cultivate curiosity is to cultivate an environment that is supportive of wallowing — active engagement and presence in the process of being confused.

It is the deepest form of mathematical engagement I know, and it is thrilling, inspiring, and honoring to be a part of it. When a student experiences that euphoric, lightbulb moment of authentic, personal insight, we can be assured that the understanding it signals is not only deep but also durable. This is true because when you are actively confused about something, you are fully engaged in making your own mathematics. Whether it is a "big" idea or a "little" procedure, these moments of insight are the source of all intrinsic motivation. And isn't this the kind of reflective, metacognitive insight about student learning processes that we are hoping to cultivate?

What We Actively Value, Versus What We Tell Students We Value

Lately I've become acutely aware of what I actively value in my classroom, which has entailed an uncomfortable amount of noticing the conditioned habits of my teacher personality. I don't collect and stamp homework assignments. I don't have each day's agenda and objective for the day neatly written on the whiteboard by the time the first bell rings. My classroom is pretty messy most of the time. I don't have a good system for filing away those last three copies of every handout for future use. I took great permission from @mgolding's system of daily handouts using her Container Store hanging file system: basically, the handouts migrate downward one pocket until there are no pockets left, at which point they go into the recycling bin.

I've made my peace with these tradeoffs because I discovered early on that if I was allotting attention to those things, then that was attention I wasn't allotting to the things I actually do value.

I adopted an SBG assessment system because it aligns my grading/scoring system with the things I actually value: mastery, effort, and perseverance. And also presence — being fully present with the activity we are doing that I actually care about. And as I've noticed that, I have noticed something else I feel good about in my classroom: my kids know that those are the things I value. Which that means they don't waste valuable life-energy bullshitting me about the small stuff we all know I don't really care about.

This has led to a lot of interesting progress with students I didn't expect to make progress with. Less successful students who don't feel shamed stick around to ask questions and engage in meaningful academic inquiry. They come to my room during their study hall periods to follow up, get help on missed or misunderstood assignments, or ask for additional work they can do to improve their understanding.

Not their grade -- their understanding. Their performance.

I am not used to this, and it causes me a lot of inconvenience. 

Students who have a reputation for giving up and giving in ask me if they can write another draft, reassess their missed algebra skills/concepts questions, and take greater ownership of their learning in my classroom. My ego would like to think this is because I'm such a highly effective teacher, but in actuality, I think it's more that my walk is becoming more aligned with my talk. I care about mastery and effort and perseverance, which means that those are the things I respond to.

What I did not realize until this afternoon is that this also means that I don't respond to things that are NOT those things. Which means that my kids are not expending any effort pretending to care about things around me that they really don't care about either. There is a focus on the work, and there is not a focus on things that are not the work. This may sound obvious, but actually it's not -- or at least, it wasn't for me. It took me years to discover that I'd been walking around in a consensual trance all my life.

This kind of awareness is challenging, to be sure, but it is also incredibly freeing. Students spend a huge part of every school day pretending to care about things that don't actually matter to them. Fitting in, pleasing teachers, winning points. Some of it is necessary but much of it they know to be complete and utter crap.

Ten, fifteen, forty, or fifty minutes of being authentically engaged in something that matters to somebody is a huge thing. Ten, fifteen, forty, or fifty minutes of authentic interaction with someone who is trying to focus as sincerely as possible on what actually matters in this life is even bigger.

I learned this lesson from years of experience with my mentor and teacher, Dr. Fred Joseph Orr — mind to mind, and heart to heart, though it took years to digest, and quite frankly, I'm still digesting. I'll probably be digesting for the rest of my life. No one had ever paid that kind of focused, intensive, thoughtful, and bounded attention and awareness in my presence before. And it made me discover how it feels to feel alive. I only discovered how precious that kind of awareness was -- and still is -- once that chapter of my life ended and a new chapter had begun.

I was noticing all this today during a test in which some of my lowest-performing students were asking for "help" with certain problems. I noticed that each time I came over in response to their request, they were not so much asking for assistance as asking for a kind of authentic engagement and support that was neither judging nor doing for them but simply witnessing their effort with presence. What I noticed today inside myself — and what distinguished this from mere adolescent attention-seekig behavior — was my own felt sense of a embodied memory of seeking out this kind of authentic connection in my own work with Fred. And this felt sense gave me the motivation to allow that connection and that presence. I trusted something inside my own inherent, intelligent functioning that told me to allow the connection rather than to pull back and resist. It was a subtle and quiet movement inside me, and I'm still figuring out what exactly was going on.

How many times have I mistaken noise for the signal? Do discouraged students ask because they hang on to the sane and healthy hope that they can learn and connect and make progress? Fred always told me, "The organism moves toward health," and I grew to believe him. I wonder if this is what my discouraged students are really asking for when they ostensibly make a seemingly attention-seeking request for something called "help."

And this is why I teach...

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

But I did it.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

• Does it always work that way?
• Does it ever deviate?
• Are there any rules of thumb we can abstract from observing this process?
• Are there any exceptions? If so, what? If not, why not?
• How long have people known about this?
• Who first discovered this phenomenon?
• How was it useful to them in their context?
• How did they convince others it was an important aspect of the problem?
• Did the knowledge it represents ever get lost?
• If so, how/when was it rediscovered?
• How did this discovery cross culture? How did it cross between different fields of knowledge?
• What were the cultural barriers/obstacles to wider acceptance of these findings as knowledge?
• What were the implications of a culture accepting this knowledge?
• Why do I feel like the only person in the room who ever cares about these questions?

It made me realize I object to the characterization of mathematics as the exclusive slave to physics. It also makes me want to introduce students to other fields (such as economics, financial modeling, forecasting and projections, free cash flow analysis, business planning and marketing planning).

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