TMC #14 Group Work Working Group Morning Session – Annotated References & Framework

I'm having a lot of fun planning the Group Work Working Group morning session for Twitter Math Camp 2014, and it's time to start sharing.

Here is the background material I'm using for developing the group work morning sessions. Please note that this is NOT required reading!  Recreational reading only! So please don't freak out!  :)

I wanted to give people a sense of the framework and background I'd like us to start from so attendees can decide whether this morning session will be right for them. I also wanted to provide links and titles to valuable materials.

These are listed in order of relevance to the Group Work Working Group morning session — they are not in formal bibliographical form.

National Academies Press, How People Learn (downloadable PDF here)
This amazing free book provides the framework within which we'll consider the use of group work. I am especially keen for us to explore how we can develop and implement tasks that fit within their (approximately) four-stage cycle for optimizing learning with understanding while also fitting with our own individual school and district requirements. In a nutshell, the four stages are as follows:

STAGE 1 - a hands-on introductory task designed to uncover & organize prior knowledge (in which collaboration cultivates exploratory talk to uncover and organize existing knowledge)

STAGE 2 - initial provision of a new expert model (with scaffolding & metacognitive practices) to help students organize, scaffold, & develop new knowledge (in which collaboration provides a setting to externalize mental processes and to negotiate understanding)

STAGE 3 - what HPL refers to as "'deliberate practice' with metacognitive self-monitoring" (in which collaboration provides a context for advancing through the 3 stages of fluency with metacognitive practices)

STAGE 4 - transfer tasks to extend and apply this new knowledge & understanding in new and unfamiliar non-routine contexts

Malcolm Swan, "Collaborative Learning in Mathematics" (downloadable PDF here)
A short and highly readable summary of Swan's instructional design strategy for collaborative tasks, including notes on his five types of mathematical activities that constitute the bulk of the Shell Centre's formative assessment MAP tasks and lessons.

Malcolm Swan, Improving learning in mathematics: challenges and strategies (downloadable PDF here)
An in-depth introduction to Swan's approach to designing and using the kind of rich tasks offered by the Shell Centre and the MARS and MAP tasks.

Chris Bills, Liz Bills, Anne Watson, & John Mason, Thinkers (can be purchased from ATM here)
The richest source book imaginable for ideas for activities to stimulate mathematical thinking. Often credited by Malcolm Swan and Dylan Wiliam.

Anne Watson & John Mason, Questions and Prompts for Mathematical Thinking (can be purchased from ATM here)
The richest source book imaginable for variations on questioning and prompting strategies.

Dylan Wiliam, Embedded Formative Assessment
This book is a gold mine. Don't leave home without it.

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?