Take Time to Save Time – Hall of Fame reference sheets

Inevitably, teachers get known for their mottos. Sam's mottos are justifiably world-famous. Personally, I love "Don't be a hero." Mine are known mostly around my school, but it is interesting to see how they trickle down into students' unconscious minds.

Color telling the story

Mottos pay off. My favorite is one I stole from my former colleague Alex Wilson: "Color tells the story." I don't understand how anybody can do math at a deep conceptual level without colored pencils. Color really does tell the story, especially in Geometry (see popular worked example at right).


One of my best math class mottos comes from published patterns for knitting. It is, "Take time to save time." In knitting, this means to make sure that the tension of your actual knitted work — your hands, your needles, your yarn — match the tension or gauge described in the knitting pattern. There are no shortcuts here. My knitting gauge tends to be extremely big or loose compared to most pattern-makers. I often have to use much smaller needles than specified in order to achieve a good match with the specified knitting gauge.

In my classroom, "Take time to save time" means, synthesize your learning into a reference sheet. For all tests but the final, I allow students to have and make a half-page reference sheet.  The first rule is, you can have anything you want except a photocopy of my work on your reference half-sheet. The second rule is, if you have more than a half sheet of 8.5 x 11 inch paper, then I get to tear it in half and choose which half you get. This rule gets tested even when I emphasize it. Every year somebody tests this rule. "But Dr. S! I only wrote a half-page worth of stuff on the paper!" It doesn't matter. I usually rip the whole thing lengthwise so they only get the right-hand half of the paper.

It makes its point.

In knitting, this point gets made by the scale and size of your finished object. If you insist on not checking your gauge, at some point, you will end up with a finger-puppet-sized sweater or a scarf the size of Lake Tahoe.

Clearly this student is going to ace the final.

In our classes, this point gets made by your performance on our common final exam. Students who have been practicing making clear, concise, summaries and examples of their work and key points tend to turn in consistently strong performances. So on the final, I allow a full-page reference sheet (both sides). I emphatically want students to consolidate their understanding and create their own examples. That is where the learning happens.

So I was thrilled today when I asked to see examples of in-progress reference sheets. Many of them made my Hall Of Fame request to scan for posterity. This Algebra 1 student has totally nailed her understanding of mixture problems. This is the best example I've seen of a student consolidating her understanding of these modeling challenges.

Allegory, iambic pentameter, and 8th graders

In 8th grade English we have just started our poetry unit, which is probably my favorite literature unit, and today was probably my favorite lesson of my favorite literature unit.

I had to start by finishing up what I think of as the "poetry bootcamp" section. There are all the basic terms, the mandatory vocabulary, bleep, blorp, bleep, blorp, and a yada yada yada. BO-RING. That is no way to engage 8th graders.

So I took my opening when I got to allegory, which, as I explained to them, is what we call an "extended metaphor," or as I like to think of it, a "story-length metaphor."

Like the fable of The Ugly Duckling.

I am a believer in the power of storytelling and poetry to save lives. They've saved my life many, many times over, and I know many others who've been saved by them as well.

I told them a version of Clarissa Pinkola Estès' version of The Ugly Duckling. I wove the story from the perspective of the bewildered, misfit duckling who cannot belong but who tries so hard to belong until he JUST. CANNOT. EVEN. At which point, he gets driven out of the flock into the landscape of despair.

He wanders through the landscape of despair — through the forest of his fears — until he has reached the end of all that he knows.

Finally, exhausted and hungry, he paddles out on the lake in search of solace and food. As he is paddling around, lost and spent, a pair of magnificent swans paddle up alongside him and ask if they can swim with him.

He looks over his shoulder to see if there is somebody else behind to whom they must be talking. The water is empty.

After many backs and forths, he relents and allows himself to swim with them. And as the sun peeks through the thick cloud cover, the glassy surface of the water turns into a giant reflecting glass, into which he looks, expecting to see his familiar, unlovable image.

But instead, he sees quite another image looking back at him — the reflected image of a third, equally magnificent swan on the lake.

I told them, we all wander lost at some point in our lives, but if we hold on and remain clear about what we are searching for, we will all eventually find our flock, our tribe, our true pack. The people with whom we can be authentic and with whom we belong. Estès talks about "belonging as blessing" as a promise, and I have learned that this is true, even though I always find the needle on my gas gauge quivering around the "E" end of the spectrum by this point in my journey.

On my own path right now, I'm not "there" yet. I don't know where I'll be teaching this time next year, but I do know the shape of this journey, and I understand that now is the moment when I need to redouble my faith in the archetype — even though every fiber of my being is ready to just lie down and allow myself to be eaten by whatever hungry ghosts are passing my way.

I told my students that there are patterns to our experience, just as there are patterns in mathematics and the natural world and in human history. And I think that I told them what I needed to hear for myself, namely, that education and growing up is the process of discovering and learning to trust the patterns that are bigger and greater than our own, fidgety little monkey minds.

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.