Thoughts On Making Math Tasks "Stickier"

Last year, the book that changed my teaching practice the most was definitely Dan Pink's Drive: The Surprising Truth About What Motivates Us. It helped me to think through how I wanted to structure classroom tasks in order to maximize intrinsic motivation and engagement.

This year, the book that is influencing my teaching practice the most would have to be Made To Stick: Why Some Ideas Survive and Others Die by Chip and Dan Heath. I bought it to read on my Kindle, and I kind of regret that now because it is one of those books (like Drive) that really needs to be waved around at meaningful PD events.

The Heath brothers' thesis is basically that any idea, task, or activity can be made "stickier" by applying six basic principles of stickiness. Their big six are:

1. Simple
2. Unexpected
3. Concrete
4. Credible
5. Emotional
6. Story

The writer in me is bothered by the failure of parallel structure in the last item on this list (Seriously? SERIOUSLY? Would it have killed you to have used a sixth adjective rather than five adjectives and one noun? OTOH, that does make the list a little stickier for me, because my visceral quality of my reaction only adds to the concreteness of my experience, so there is that). But that is a small price to pay for a very useful and compact rubric. It also fits in with nicely with a lot of the brain-based learning ideas that @mgolding and @jreulbach first turned me on to.

This framework can also help us to understand — and hopefully to improve —a lot of so-so ideas that start with a seed of stickiness but haven't yet achieved their optimal sticky potential.

I wanted to write out some of what I mean here.

For example, I have often waxed poetic about Dan Meyer's Graphing Stories, which are a little jewel of stickiness when introducing the practice of graphing situations, yet I find a lot of the other Three-Act Tasks to be curiously flat for me and non-engaging. Some of this has to do with the fact that I am not a particularly visual learner, but I also think there is some value in analyzing my own experience as a formerly discouraged math learner. I have learned that if I can't get myself to be curious and engaged about something, I can't really manage to engage anybody else either.

Made To Stick has given me a vocabulary for analyzing some of what goes wrong for me and what goes right with certain math tasks. The six principles framework are very valuable for me in this regard, both descriptively and prescriptively. For example, Dan's original Graphing Stories lesson meets all of the Heath brothers' criteria. It is simple, unexpected, concrete, credible, emotional, and narrative. The lesson anchors the learning in students' own experience, then opens an unexpected "curiosity gap" in students' knowledge by pointing out some specific bits of knowledge they do not have but could actually reach for if they were simply to reach for it a little bit.

But I would argue that the place where this lesson succeeds most strongly is in its concreteness, which is implemented through Dan's cleverly designed and integrated handout. At first glance, this looks like just another boring student worksheet. But actually, through its clever design and tie-in to the videos, it becomes a concrete, tangible tool that students use to expose and investigate their own curiosity gaps for themselves.

Students discover their own knowledge gap through two distinct, but related physical, sensory moments: the first, when they anchor their own experiences of walking in the forest, crossing over a bridge, and peering out over the railing as they pass over (sorry, bad Passover pun), and the second, when they glance down at the physical worksheet and pencil in their own hands and are asked to connect what they saw with what they must now do.

This connection in the present moment to the students' own physical, tangible experience must not be underestimated.

Watching the video — even watching a worldclass piece of cinematography — is a relatively passive sensory experience for most of us.

But opening a gap between what I see as a viewer and what I hold in my hands — or what I taste (Double-Stuf Oreos!), smell, feel, or hear — and I'm yours forever.

"My work here is done."

This way of thinking has given me a much deeper understanding of why my lessons that integrate two or three sensory modalities always seem to be stickier than my lessons that rely on just one modality. Even when the manipulatives I introduce might seem contrived or artificial, there is value in introducing a second or third sensory dimension to my tasks. In so doing, they both (a) add another access point for students I have not yet reached and (b) expose the gap in students' knowledge by bringing in their present-moment sensory experiences. And these two dimensions can make an enormous different in students' emotional engagement in a math task.

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.

Radio Silence Does Not Mean Nothing Is Happening...

Wow, did I ever fall off the radar.

Plop. That "splat" you might have heard was me, falling off the blogging radar.

But I'm back, baby.

Last night I had the most wonderful dinner with @btwnthenumbers and @woutgeo and @mythagon, who was in town for a conference/collaborative meeting, and I tell you, it pretty much restored my faith in teaching, in mathematics, and probably in all of humanity.

I have been working at a near-frantic pace these last five weeks, prepping, teaching, grading, not grading, having parent conferences, having meetings with parents and the principal, having meetings with parents and principal and superintendent, going to IEP meetings, collaborating with my department members to write goals that will help us to align our curriculum with the Common Core, and generally dealing with all those things that go haywire as soon as you start to nail down some satisfying, finite part of your teaching.

In other words, just like you, life has been kicking my ass.

But between last night and this morning's drive to work something shifted. Something sane and healthy intervened.

That something was my connection with the Twitter- blogo-sphere.

Whenever I'm feeling exhausted and run over with skid marks across my face and body, connection with my tweeps -- any connection -- seems to be the best medicine. I don't know why this is true; I only know that it is so. Remembering this makes me think of a quote I have from von Neumann hanging in the ring of inspiring quotes that encircles my classroom: "In mathematics, you don't understand things; you just get used to them." Some days that's how I feel about things in my classroom or in my school or in my life.

I only know that five or ten minutes of venting to my tweeps about an impossible situation -- even when @woutgeo is only half-listening because (a) the Giants are sucking pretty hard against the Cardinals and because (b) my venting is both predictable and boring -- it helped just to have reconnected with the connection. In Jakobsonian structuralist linguistics, this kind of communicative connection is known as a "phatic utterance" (look it up, Riemann, I have to look up all of your crap).

By this morning, I was feeling reasonably happy driving to work for a 7:30 a.m. meeting. I was not totally thrilled about the hour or having to buy gas at that hour or the price of gas for that matter, but I felt pretty great about car-dancing in the dark to Ace of Base's "The Sign" and remembering car-dancing at #TMC12 with @mgolding and @samjshah and @jreulbach and @ bowmanimal on the way to do Exeter problem sets. And I felt great when @rdkpickle's sweet soprano voice was joined by @SweenWSweens and @jreulbach singing "Tweet Me Maybe." And I even laughed when the theme from Sesame Street came on. iPod's "shuffle" feature has a somewhat perverse sense of humor.

OK, and one other thing I have learned is that my dog always knows when it's time for me to end a blog post. Just now he jumped up on my lap and pounded the laptop keyboard with his giant panda bear paw:

34ycvzn

So that's my cue to wrap this up.

I just want to say, if you are feeling alone or frustrated or exasperated and you are reading this, then for the sake of everything we hold dear, please reach out to someone else who is of like mind. "It's hard to teach right... in isolaaaaaaaaation.... So here's some PD.... just like vacation!"

Tweet me maybe, tweeps. Over and out for now.

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.

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.