Ode on a six-ootsie Tootsie — a love poem to @Trianglemancsd

What an amazing but crazy first week! OK, sure, it was only two days long, but still...

Sick of reading and rereading the various classroom and school rules, I wanted to dive into some mathematics lest I drive myself and my kids totally nuts. So I decided to use Christopher Danielson's Tootsie Roll-sharing problem from his #TMC13 presentation, along with some of his "fun facts" background, as a first math day diagnostic activity and as a platform for introducing my new norms and rubric for collaboration.

Even though I felt like I was just throwing together a slide show launch during my first-period prep, it worked incredibly well!

My Keynote slides and a PDF version of the slide deck are on the Math Teacher Wiki.

Here it is in a nutshell: 

•    Visualize a 6-ootsie Tootsie

•    Now imagine 4 kids who want to share it equally and completely.

•    Can your group come up with AT LEAST TWO WAYS to accomplish this?

Both the 8th graders and the 6th graders had a lot of pretty deep conversations about whether you were thinking of sharing it in terms of number of ootsies or in terms of parts of a Tootsie. Wholes and parts, plus funny-sounding words and the chance to introduce the word synecdoche.

One of the nicest things about doing this was that it helped a lot of kids see that "complicated" and "deeper" are not necessarily the same thing. 

What's not to like?

Collaboration Literacy Part 2 — DRAFT Rubric: essential skills for mathematical learning groups

I have said this before: middle schoolers are extremely concrete thinkers. This is why I find it so helpful to have a clear and concrete rubric I can use to help them to understand assessment of their work as specifically as possible. I'm reasonably happy with the rubric I've revised over the years for problem-solving, as it seems to help students diagnose and understand what went wrong in their individual work and where they need to head. But I've realized I also needed a new rubric — one for what I've been calling "collaboration literacy" in this blog. My students need help naming and understanding the various component skills that make up being a healthy and valuable collaborator.

My draft of this rubric for collaboration, which is grounded in restorative practices, can be found on the MS Math Teacher's wiki. I would very much value your input and feedback on this tool and its ideas.

I don't want to spend a lot of time talking about how and why Complex Instruction does not work for me. Suffice it to say that the rigid assignment of individual roles is a deal breaker. If CI works for you, please accept that I am happy that you have something that works well for you in your teaching practice.

This rubric incorporates a lot of great ideas from a lot of sources I admire deeply, including the restorative practices people everywhere, Dr. Fred Joseph Orr, Max Ray and The Math Forum, Malcolm Swan, Judy Kysh/CPM, Brian R. Lawler, Dan Pink's book Drive, Sam J. Shah, Kate Nowak, Jason Buell, Megan Hayes-Golding, Ashli Black, Grace A. Chen, Breedeen Murray, Avery Pickford, "Sophie Germain," and yes, also the Complex Instruction folks. I hope it is worthy of all that they have taught me.

How Stats Bootcamp Saved My Life — #TMC13

I am trying to make sure I do ten- to fifteen-minute daily writing practices on my session- and topic write-ups from Twitter Math Camp '13 because otherwise I won't end up doing them and I made a promise to myself to try and capture the essence of what was important to me.

Hedge's Statistics Bootcamp session was particularly life-changing for me, primarily in that it saved my life. The CCSS Math 8 standards now require a juicy unit on statistics and probability, which are not my personal strong suit. The truth is, I spent so many years in high-tech marketing I no longer believed in the power of statistics to do anything more than be distorted for various nefarious purposes.

So it was good to go all the way back to the ground and to return to the way of beginner's mind. The term "beginner's mind" caught on due to one of the foundational texts of North American Zen practice, which is Shunryu Suzuki's Zen Mind, Beginner's Mind. If you have not read this, it will teach you everything you need to know about what I find valuable in classroom management (SPOILER ALERT: you will be reading about how "the way to control people is to encourage them to be mischievous. To give your sheep or cows a wide field to wander in is the best way to control them. Then they will be in control in a wider sense"). The key to Zen practice — and to math teaching practice — is always to keep your beginner's mind. As Suzuki Roshi says, "In the beginner's mind there are many possibilities, but in the expert's mind, there are few."

Hedge teaches statistics using what I might call the case method on steroids. She opens with the story of a notorious serial murder trial — a trial that hinged on statistical analysis and interpretation of mortality rates and patterns of nurses' shifts in the VA hospital where the defendant worked. I would describe her Essential Question for the unit as, "How certain is certain enough in matters of life and death decisions?" Revealing one critical piece of statistical evidence after another, she guided our investigation and conversations through the key pieces of evidence in the trial.

One of the things I love best about blogs and Twitter Math Camp is that they give me a chance to experience the art of "the reveal" — more specifically, how other teachers handle "reveals" in their classrooms. Over the years, I have stolen adopted many of Sam's techniques for building reveals into his artful guided student investigation worksheets. Hedge handles reveals by demanding self-restraint. In this lesson, she provided each group with  three large manila envelopes labeled A, B, and C, and she starts class with her norms and consequences — namely, that you don't open anything until HEDGE SAYS it's time to do so. Failure to comply with this norm will result in a massive public test of physical fitness, such as giving her 20 pushups on the spot (I used to think this was a violation of the Geneva Conventions, but now I know better). Layer by layer, she has students uncover each next piece of evidence, which serves as a landing on a giant staircase of learning.

I want to be clear: this method is not "sage on the stage" so much as it is "trustworthy tour guide on a once-in-a-lifetime tour. She makes sure that her charges don't miss anything important along the way. I believe this is  our job — to set up experiences for our students so that they can uncover and develop what they need at each step. It's about helping kids to develop their capacity to slow down and attend to the world around them one thing at a time.

This is not something students can get from a MOOC or a videogame or other prepackaged online learning technique. It's a transfer of human praxis that happens mind to mind and heart to heart. This is why we say that the best teachers inspire.

Piece by piece, Hedge had us work through the statistical evidence and probabilities in the trial. She showed us how many parts of the trial hinged on competing interpretations of the statistical evidence by the lawyers, but the statistician expert witnesses each side employed, and ultimately, by the jury. I

I will definitely be adapting this unit for Math 8.

Twitter Math Camp 2013 — reflections on a sustainable model of hope

At Twitter Math Camp 2013 (#TMC13) this morning, I was both amused and inspired to read these two tweets — one by one of my math ed inspirations and another by a colleague I could not respect any more than I do and whom I can also call a friend:

Ann and I having great time in Philly at Twitter Math Camp - amazing ideas and energy! Massive hope for what is possible.
— Steve Leinwand (@steve_leinwand) July 27, 2013

You guys, we gave @steve_leinwand hope. We can go home now.
— Kate Nowak (@k8nowak) July 27, 2013

Like my spiritual and general life role model, Wile E. Coyote, I am invariably hopeful in a small sense that this will FINALLY be the moment — that perfect moment when all my best-laid "plans" will do the trick and I will, at long last, have the solid, effortlessly nourishing, and unshakable ground beneath my feet that I crave (and that I believe I so richly deserve).

But years of experience have taught me that that is the "hope" of an Indulging Baby — a person who looks like an adult on the outside, but who really walks around believing that my every problem, need, and desire in life should be solved by benevolent and invisible external forces. This is in harmony with my frequent conviction that my life really ought to operate like one of those behavioral experiments in which, each time I press the correct lever, the Universe promptly and consistently rewards me with a food pellet.

So I'm sure you can imagine my annoyance with the reality that life — and teaching — refuse to cooperate with my first-draft of things.

For the second year in a row, I have blown away by what I receive at Twitter Math Camp. The best, the most creative, the most resourceful, and the deepest-thinking math teacher I know in the English-speaking world show up and share with me their 'A' game. This is not so much a blessing to me as what I would describe as a complete fucking miracle. In sharing, in presenting, in participating, and in attending, every single person at this conference gives me a richer PD experience than many teachers ever get in an entire lifetime.

And in a sense, that is the point.

For me, this conference is about refilling the well at The Great Oasis of The Impeccable Warriors. There pretty much are no Indulging Babies here at TMC. If you want somebody to take care of you and make you feel better and wipe your butt, well, this is not going to be the place for you. Everybody here is truly impeccable. To me, that means that everybody does the very best they can in whatever situation they are in. It's a stone soup mindset. If everybody has crap, then we will be eating crap soup that night. But if everybody brings one small, precious ingredient to the soup, then we will be eating like royalty — or at least, like Silicon Valley-based organizations that are overfunded by the Bill and Melinda Gates Foundation (use your imagination, or consult @fnoschese's Twitter feed and/or blog).

That is not to say that everything is perfect. People are still people, which means we can all sometimes be thoughtless, stupid, impulsive, stubborn, rude, and a whole host of other things.

But what makes this work, I think, is that everybody here owns their own "stuff" and is willing to be accountable for what they put into the communal mystic cookpot.

The truth behind the truth is, I brought my 'A' game too. I worked for three months on my sessions, planning, preparing, reflecting. You guys are my tweeps. My tribe. Even though I had an almost totally crappy year, I did not want to let you down. And I have learned that I will get back in proportion to what I put in (cf. CCSSM 8.F.1 and 8.F.3, and passim).

So my challenge to everybody who is attending Twitter Math Camp for the first year this year is to reflect on this question:

Now that you have fifty percent as much experience with TMC as even the most experienced Twitter Math Campers among us, how are YOU going to help make Twitter Math Camp just as amazing next year?

I strongly believe that the people who show up for something are exactly the right people. So, hey — welcome to the club of Impeccable Math Camp Warriors! You certainly have something important to contribute, or you would not be here reading this.

You don't have to answer this question right now. But if you want this to be here next year — both for yourself and for others — it is important to hold this question in your heart as you process the experiences you've had these past several days.

I believe that hope is a process, not a destination, and I believe that what Steve Leinwand was responding to was the awesome force field of being in the presence of 125 impeccable warriors all being impeccable together — 125 math teachers who don't simply complain about what a mess things are, but rather who each grab a mop and say, oh, I see— I'll do it.

Collaboration Literacy — essential skills in mathematical learning groups (i.e., shared mathematical thinking)

It has long been clear to me that there are important skills of interdependence that I value in mathematical group work, but I have always been dissatisfied with the assumptions inherent in the existing models. My dissatisfaction always stems from conflicts with some of my deepest-held values about collaboration and about learning about collaboration.

Sam's post on Participation Quizzes was the first model I ever heard about that felt harmonious with what I know about healthy collaboration. I love the idea of using formative assessment of a group's collaborative interactions as a lens for viewing the mathematical learning that was going on. But I also know myself well enough as a teacher to know that I need a clearer, more explicit framework in my head so I can be both clear and intentional about the skills I am cultivating and encouraging.

Fawn's epic and brilliant deconstruction of successful in-class activities the other day referenced a touchstone work that I too really value: Malcolm Swan's Improving Learning in Mathematics manifesto. This time through, though, I was struck by four skill areas for group work that Swan touches on but does not develop.

These, I have realized, form the basis of a set of group work skills I could envision developing into a rubric for participation quizzes as well as a set of foundational "collaboration literacy" skills I could wrap my mind and heart around.

Here are the four skill areas I am thinking about for the collaboration skills rubric, along with my early commentary and thoughts:

• SHARING SKILLS — in other words, developing a sense of inclusiveness as a member of a mathematical learning group. These skills include: demonstrating patience when others have difficulty putting their ideas into words; allowing others adequate time to express their own ideas; not moving on until everyone understands; and actively making sure that everyone understands why or how a piece of shared thinking/reasoning is so
• PARTICIPATING SKILLS — developing your own agency as a math learner (i.e., making your own personal contributions to the group's shared thinking). Skills include: overcoming shyness to share your thinking with the group; managing your desire to take the microphone more than your share of the time; genuinely "showing up" with your own unique insights and gifts as a thinker; encouraging and supporting others as they speak their ideas, confusion, or questions.
• LISTENING SKILLS — developing your own openness as a collaborator. Skills here include: listening actively and deeply; not simply waiting for your turn to talk; making eye contact with those who are speaking; asking clarifying questions; disagreeing respectfully; and agreeing and extending others' thinking.
• EXPLORATORY TALK SKILLS — developing your voice as a math learner and as a member of a learning group. The phrase "exploratory talk" comes from Swan's discussion (page 37), and I think it encapsulates the qualities we are looking for when we ask students to collaborate to develop a shared understanding. These are areas where I believe The Math Forum's work really shines. Skills here include: noticing and wondering; extracting information and a question; paraphrasing or rephrasing; acting out a problem; plus making explicit transitions from one topic to the next and preventing transitions from occurring until the whole group is ready to move on. 

I envision self-assessment and peer assessment being vital parts of the process in addition to teacher assessments of individuals and groups.

I am particularly excited about ways to integrate thinking from restorative practices into this framework for mathematical learning groups because I believe they hold a lot of promise for improving the quality of student interaction.

I hope there will be a vigorous discussion in the comments!

Quotes hanging over and around my desk — or, what the MTBoS means to me

I got a new job today, plus I had a birthday earlier this week, plus Topper had a hot date in Doodle Land, so I've been noticeably in the bleachers of the latest debates about the mathtwitterblogosphere, what it is, what it means, what's good about it, what's not so good about it, and so on... and so on... and so on.

It's probably just as well. I don't find myself to be particularly constructive when I'm tired and strung out and stressed.

I have one of the TMC12 photos from last summer hanging over my desk, along with a number of quotes all around that remind me, among other things, what I value about the MTBoS. Today they feel wiser about the whole thing than I do:

"I was a late bloomer. But anyone who blooms at all, ever, is very lucky."
    — Sharon Olds

"Success is going from failure to failure without loss of enthusiasm."
    — Winston Churchill

"Ancora imparo." ["I am still learning."]
     — Michelangelo at age 87

"If you bring forth what is within you, what you bring forth will save you."
     — The Gospel of Thomas

"Rock bottom became the solid foundation on which I rebuilt my life."
     — J.K. Rowling

Welcome difficulty.
Learn the alchemy
True human beings know.
The moment you accept what troubles you've been given,
The door opens.
    — Rumi

My learning to swim drowns no one.

     — Dr. Fred Joseph Orr


"There are years that ask the questions and years that answer."
     — Zora Neale Hurston

"Continue under all circumstances.
  Don't be tossed away.
  Make positive effort for the good."
    — Dainin Katagiri Roshi

"We're lost. But we are making good time."
     — Yogi Berra

"Tell me, what is it you plan to do
 with your one wild and precious life?"
     — Mary Oliver

Oreos, Barbies, and Essential Questions: framing projects for differentiated learning

The Oreos lesson/unit has been going swimmingly. Students loved the project and the poster, though I'm feeling a little bored with my project ideas right now. Not every project culminates in making a poster. I have a bunch of other ideas I want to write about in another blog post, but that is not where I am headed in this post.

What I want to ponder is, I wonder if we have not been making our Essential Questions (EQs) in mathematics too small. Too narrow. Ever since my Global Math presentation (the one where I had the epic #micfail that left me playing Harpo to Daniel and Tina's Groucho and Chico), I have been thinking about Understanding by Design more and more, and that has led me to ask myself if I don't need to make my Essential Questions in math lessons a whole lot bigger and deeper. There are so many ways to bring the real world into my math classroom, and one of those ways is to frame our work using questions that adolescents are obsessed with thinking about in their everyday lives — questions such as, How dangerous is too dangerous? How do we define what is fair? truthful?

These EQs can form a frame around the activities we do to connect the mathematics to the real world around us. They help provide a situational motivation for learning — and for wallowing in — the mathematics that starts from a place where all students are naturally. And they also make the work we do more, well, essential.

Some of my "major" Oreo lesson EQs blossomed into, Are Nabisco's claims about their Double Stuf Oreo products fair? Are they truthful? just? And my "minor" EQs started revolving around, How can systems of linear equations in two variables help us to model and assess the validity of this claim in the real world?

I am finding more and more that when I frame our work in this way, I hear less and less of the question, "When am I ever going to use this?" And frankly, that's less wear and tear on my soul as a teacher.

With Barbie Bungee, in addition to creating an occasion for more practice in reading aloud and practicing decoding and interpretation skills, I used my situation set-up to raise the EQ, how dangerous is too dangerous? This is a question every adolescent has had to wrestle with since the dawn of time (or at least, since the dawn of puberty as a social construct). In their effort to keep him safe, Siddhartha's parents built him a golden cage of pleasure palaces and theme parks so he would marry and have a life there and never want to leave home. And I can only imagine what Moses' parents must have gone through ("Put down that rod! You're going to put someone's eye out with that thing!").

And the things that matter about that question are (a) the assertion you come up with and (b) the way you marshall concrete evidence and interpretive scaffolding and support to persuade someone else (such as your parents) of the validity and rightness of your assertion.

Coming from a writerly and an entrepreneurial background, I often find that the math of a thing — the essential mathematics of a thing — comes down to what I can persuade someone else of. 

For example, How dangerous is too dangerous? 

Well, it turns out that 28 rubber bands can be empirically demonstrated to be one rubber band too many. With 27 rubber bands, Barbie can have a thrilling — but still safe enough — ride, but at 28, she cracks her head open on the sidewalk, the lawsuits begin, and her parents return to her graveside frequently to tell her "I told you so!" throughout eternity.

And isn't that something we ALL dread?

With the Oreos experiment, the EQs were, Am I being cheated? Are Double Stufs, in fact, double? Is this fair? Is this a good deal? and of course, also, "Does this seem universally and predictably true?"

These are questions every adolescent wallows in every day of their lives. How many times a day do YOU hear, "But that's not FAIR!" or "Mr. C decided such and such. Do you think that is FAIR?"

Fairness is about our own personal beliefs and interpretations of the evidence in light of our own experiences in our world. And only you can answer a question like that for yourself.