Compound Inequalities Treasure Map

Never underestimate the power of novelty to help you engage certain students.

I just spent the last hour and a half-long block period with my jaw on the floor, watching in amazement as my most discouraged, 12th grade College Prep Math students worked productively and peacefully on, of all things, the analysis and solving of compound inequalities.

During my prep, I turned a boring worksheet into a treasure map. And that turned a boring requirement into a very peaceful and enjoyable period.

As she was leaving, one girl asked, Could we please do more work like this?

I'll take that as a compliment!

TMC 12 SESSION: Increasing intrinsic motivation using the ideas in Dan Pink's Drive

Dan Pink's bestselling book Drive: ___  has given the business world new ways to think about increasing intrinsic motivation in the workplace, but his ideas have resonance in math education too. The purpose of my Twitter Math Camp 12 session was to summarize the main ideas in Drive and to talk about how I have applied them to the specific situation of the math classroom.

In the model he sets out, Pink presents three fundamental pillars of intrinsic motivation:

• AUTONOMY, which he defines as "behaving with a full sense of volition and choice” as opposed to feeling pushed around by “external pressure toward specific outcomes” (Drive, p. 88). 
• MASTERY, which is a growth mindset in the model of Carol Dweck's work, a way of thinking about one's work that requires both effort and engagement. He also describes mastery as "an asymptote," an impulse that moves toward an ideal of perfect oneness without ever fully achieving it (Drive, pp. 118, 122, & 124).
• PURPOSE, a sense of being connected to the why of what one is doing (Drive, p. 233).

All three of these elements support the development of FLOW — a profound human state of "optimal experience" which was first studied in depth by the renowned psychologist Mihalyi Csikszentmihalyi (pronounced "chick-sent-me-high").

Flow is what many of us who teach math feel when we lose ourselves in doing mathematics, and my argument in this presentation is that helping our students to experience the flow state while they're doing math should be our top priority when thinking about motivation.

We can help students tap into the flow state by using Pink's three elements of intrinsic motivation to create "on ramps" for students to the flow experience.

PURPOSE is a terrific building block for many of our most capable students, but for the discouraged or disengaged student, it is necessary but not sufficient. What Can You Do With This?, Three-Act Digital Problems, and AnyQs? activities can be helpful in cultivating a sense of purpose in students, but it is important to keep in mind that there are other factors — including social, emotional, and psychological factors — at work with our most discouraged students.

Using a Standards-Based Grading framework helps students understand talk about MASTERY by clarifying expectations and improving communication between and among students, teachers, and parents.

AUTONOMY is the hardest of the three elements to encourage, so I spent most of my talk about ways to develop a sense of autonomy with math students.

There are two parts to autonomy: (1) an outer component and (2) an inner component. The EXTERNAL part can be built up by disrupting student expectations through alternative  activity structures. Games, game-like activity structures, treasure hunts, creating foldables, making up dances or songs, creating and performing skits or puppet shows that demonstrate definitions or processes, and other such reframing activities redirect student attention away from what causes them anxiety or trauma and toward something that allows them to relax and let doing mathematics be simply a means to an end. REFRAMING can be a crucial part of helping students find themselves in flow while doing mathematics.

The INTERNAL component of boosting autonomy has to do with helping students to NOTICE their fears or reactive responses and ALLOWING there to be space for their authentic feelings and conditioned reactions. We can support students by not taking their reactions/reflexes personally and by noticing our own reactions/reflexive responses to different kinds of disengagement we experience from students. Encouraging a posture of noticing and allowing enables us to help students loosen their identification with past negative experiences and open up space for newer, positive experiences to overwrite those in their minds and bodies.

By honoring and encouraging the flow state in our students while they are engaged in mathematics, we can help them to renegotiate their relationship with math class. And that creates space for the positive and self-reinforcing intrinsic motivation that will help them get out of their own way and find lifelong success with mathematics.

On choosing sanity, and on modeling this choice for our students

I want to talk a bit about sanity — not because I think I'm an expert (I'm not; no one is) but because I have come to understand sanity as a choice we make moment by moment, and because, in so doing, I have seen how we either model — or do not model — it for our students in our classrooms and in our lives. And this is an enormous part of the social and emotional life training they either receive or do not receive in this crucial part of their lives.

I teach middle schoolers, or rather, I should confess that they teach me. Every student and every class is a mirror in which I can see what I am teaching them. Perhaps because their access to it is new, middle school students have a finely tuned hypocrisy detector. More so than any of the high school or university students I've ever taught, middle school students want to see who "walks their talk." Do so, I have learned, and they will follow you anywhere. Fail to do so at your own peril.

So a big part of this year's learning, for me, has been learning how to tune in to what I am actually doing and checking in on whether this is consistent with the social and emotional lessons on appropriate self-care I am trying to teach. Sometimes that has meant being the adult in their lives who tells them to stop the madness. The only way to stop the war is to stop fighting, stop struggling, stop efforting. There really are only so many hours of the day, and for middle schoolers, about eight of those need to be spent sleeping. That means every piece of homework can't always get done every day all the time. Sometimes a person has to choose sanity. So I try to understand that and allow for it, because learning to allow space for all of life is something they are going to have to learn if they are going to do better in running this world than we have done so far.

I've also had to learn how to trust my training and my gut. I was blessed to study for over ten years with a pioneer in integrating social and emotional intelligence and mindfulness into learning environments ranging from special education to mainstream classrooms to therapy situations. You probably haven't heard of him because he has spent his life being what I think of as a guerrilla bodhisattva — a pioneering educational psychologist and an undercover evangelist for social and emotional health in daily life. His name is Dr. Fred Joseph Orr, and I am blessed to count myself among his students. Actually, we think of ourselves as his disciples, though he would undoubtedly discourage that characterization. But it's a fair one. He taught us to integrate teachings from whatever sources might be beneficial to ourselves and our communities — teachings from Adlerian psychology, spiritual development, meditation, yoga, Buddhism, his own mischievous sense of humor and spirit of adventure, writing as a practice, the practice of joy and creativity in whatever form they might take, and environmental restoration and ecological rebalancing. I came to him as a writer, writing teacher, and longtime meditation practitioner, but I quickly became much more than that under his mentorship. And it was the kind of mentorship that is a true spiritual gift — the kind you can only repay by sharing it with others. In his life, he suffered in ways that most of us would find unimaginable, and yet he remains the most radiant and joyful person I have ever known. And although his active teaching practice has been cut short by a medical condition that has become the focus of his own personal life practice, his students carry on his great efforts, sharing the learning and the gifts we received from his teachings. His teaching of us was an investment in the future and a labor of love. I wake up every morning determined to be worthy of the effort, love, and energy he poured into teaching me.

There's an urban fable Fred used as a teaching tale. It's known as The Hundredth Monkey principle. It began in the 1950s as a call to end the escalating nuclear arms race, but Fred believes it has broader applicability as a model for how human awareness and sanity can be activated too, and I have come to believe this too. The idea is simple, yet profound: when a critical mass of individuals' consciousness gets raised, it inevitably triggers a paradigm shift in the dominant culture. So this turns out to be a more leveraged model for social change than the conventional wisdom tends to think, for when we direct the focus of our daily efforts on helping individuals and small groups to shift their energies, awareness, and attention, we are doing our part to put our culture on the path that leads toward greater sanity, in addition to greater achievement.

So what does all this squishy-sounding woo-woo stuff have to do with teaching and learning mathematics?

I believe it provides us with an on-ramp, a way to reach the hearts and minds of the students who are most discouraged and shut down in the math classroom. It's differentiated for the most capable students because most of them have never been given tools to cultivate self-awareness and other-awareness as a part of their learning. And by learning — and by teaching these discouraged students how — to cultivate their social and emotional intelligence in how they engage in mathematical practice in our classrooms, we can change their relationship with mathematical studies to one based on what the American Tibetan Buddhist teacher Pema Chodron describes as "unconditional friendliness."

Over the last couple of days, as I've begun my yearly summer rituals of cooking and storing school lunches in the freezer for days when I need the loving self-care of hand-made soup in the middle of my day, I have realized that this is the heart of my Twitter Math Camp talk. My topic is Dan Pink's book, Drive: The Surprising Truth About What Motivates Us, and how to use his ideas about intrinsic motivation to reach the discouraged math learners in our classrooms. I've begun to understand how Fred's work with me is an arrow that flies straight to the bullseye of this target, and it's given me some hopefully valuable insight into how to create the toughest of Pink's three pillars of intrinsic motivation. That pillar is autonomy, and I'll write more about it in an upcoming post as I flesh out my talk with ideas and activities.

In the meantime, I'm going to let my subconscious mind work on the problems while my conscious mind takes a nap.

Rational Expressions Treasure Hunt (or, Intrinsic Motivation for the Intrinsically Unmotivat-able Bits)

We are coming up on our state testing window (STAR testing in California, ugh), which means it's time to finish "covering" all the so-called key standards material in preparation for the last-minute test prep and hand-wringing.

In our Algebra 1 curriculum, the last unit before state testing is the Rational Expressions unit, which I find to be one of those inherently frustrating and procedural sections.

The good news of the rational expressions unit is that it gives Algebra 1 students an opportunity to see how some of the foundational skills and concepts they've been learning can come together to provide some very sophisticated conceptual and computational tools.

The bad news is, students are tired -- tired of the routine of observation - guided practice - independent practice - followed by a chapter test. And they're just plain tired in the sense that they've absorbed a lot in every class they're in and basically their brains are kind of full.

So I reviewed my notes on Dan Pink's book Drive to see how I could weave together his ideas of autonomy, mastery, and purpose. And that gave me the following ideas:

• AUTONOMY - students needed a unit which relies more on self-checking than on getting a teacher seal of approval (or a rubber stamp);
• MASTERY - students seemed to need a unit which would emphasize tracking their mastery of skills and concepts, which meant giving them lots of opportunities both to do and to spot patterns in their doing;
• PURPOSE - students needed a sense of purpose to the overall activity, rather than the "bigger picture" sense of Dan Meyer's WCYDWT (What Can You Do With This?) -  to provide some light-hearted gratification or, as some might put it, a cheap thrill. :-)

As these ideas whirled around, I felt envious of Kate Nowak's wonderful circumcenters lesson (from Geometry) that harnessed fun clues with the need to draw circumcenters on a map of the school as a motivation for hunting down numbered markers which she had tucked around the school.

It occurred to me that I could use a treasure hunt idea (organized more as a geocaching or letterboxing hunt) as an intrinsically self-motivating reward system -- coupled with a series of self-check-able problem sets/worksheets -- to give students a little break from routine and a reason to work together purposefully to practice simplifying rational expressions and finding the excluded values.

So here are the components I created:

1. a set of graduated worksheets (one for each day) for them to use as practice problems
2. a handwritten Answer Key that I slipped into sheet protectors and tacked up on the front bulletin board for students to check their work against
3. a "rubber-stamping station" where I or they would stamp their completed AND checked worksheets to place in their...
4. group folder
5. a Ziploc bag or sheet protector stapled to the inside of the group folder where they could store their treasure tokens
6. a set of "clue" cards, one for each worksheet's treasure token, that students would take together with a...
7. Hall Passes (which clearly states that I have given them permission to snuffle around in the designated area to find their treasure tokens and come back to my classroom)
8. one weatherproof plastic Gladware container PER treasure box/worksheet to contain the treasure tokens for each worksheet/level (I used Woodsies stars that I bought at Michael's and labeled them 11-2a or 11-2b to correspond to their worksheets, but you could also use punched-out paper or cardboard shapes of any type); treasure boxes were labeled with masking tape and also contained a marker and an index card on which students would write their group's initials when they removed a token

A couple of observations. First of all, your "clue cards" will be different from mine based on your school and where you wish to send your students on their searching. Being a California indoor-outdoor type of school that is built into a hillside, we have a lot of beautifully xeriscaped/landscaped pocket gardens that made for good treasure box hiding places. So my clues said stuff like, "Facing room ELEVEN, TWO TIMES TEN paces or so to your right, you'll find a bathtub fit for a bird. Look below the bushes behind..." Or "Head toward LUCKY 13 and look for the LAVENDER HEDGE. The treasure box is tucked behind..."

Students responded positively to this shift toward autonomy. They delight in completing a practice task that grants them permission to snuffle around a little outside in the fresh air. And they seem to love unraveling the clues, maybe because they love reading and thinking about themselves and their own environment. The Hall Pass requirement gave them a clear set of expectations and accountability, and even my least accountable students have been taking it seriously, which is a refreshing change of pace for all of us.

Their assessment will come from my review of their group project folder -- its tokens, its completed and corrected worksheets, and the presence or absence of worksheets for each student in the group.

The worksheets and sample hall passes and clues are up on Box.net