Beautiful, fluid chaos -- or what "learning in flow" actually looks like to the trained eye

One of the things I like best about my new school are my colleagues. In fact, I don't believe I could stand to teach English (instead of math) if I did not happen to have my particular grade-level team of amazing, insightful, reflective, open-minded collaborative English-teacher colleagues.

I'm not saying that teaching math is one big continuous picnic of sparkly rainbows, unicorns, and effortless class periods of absorptive learning, but in English Language Arts -- particularly at the middle school level -- you have to teach some of the most thought-numbing, soul-dissolving parts of the curriculum ever to torture the human mind. Spelling. Grammar. Vocabulary. I throw up in my mouth a little bit each time I have to schedule time for them on a new weekly assignments calendar. But they're a part of the curriculum that's mandated, and so they have to be taught.  Some things you just have to pinch your nose and swallow as quickly as possible.

On the other hand, or possibly as my reward for fulfilling these less satisfying obligations of my curriculum each week, I get to work with kids on one of the deepest and dearest endeavors of my heart. I get to teach them writing.

Now, one of the things I have learned in my many decades on this planet is that writing -- and learning how to write -- is MESSY. Learning to write a first draft is more about learning how to tolerate the waves of revulsion that come over you as you confront the your own feelings of inadequacy at what you put down on the page than it is about about learning how to structure a proper academic paragraph. In fact, I'm convinced that I could teach a goat to structure a proper academic paragraph. What takes genuine human maturity and emotional/psychological courage is learning to get a first draft down on paper.

For that, you have to gain the willingness to produce what writer Anne Lamott calls "a shitty first draft."

Since I'm not permitted to use that kind of language in a public school classroom with middle schoolers, I use the methods I first learned from, and later taught with, celebrated writing teacher Natalie Goldberg. Her system of "writing practice" emphasizes "separating the creator from the editor," and basically involves a small number of inviolable rules for producing your first draft of an idea. These are:

• keep your hand moving
• don't cross out
• don't worry about spelling, punctuation, grammar, or other rules
• lose control
• don't think
• go for the jugular
• follow and trust where your mind takes you
• give yourself permission to write the worst poop in America / on Planet Earth / in The Milky Way Galaxy

So for first drafts in my classroom, this is how we practice.

We close the door and the windows (so we don't bother anybody trying to do more traditional learning), I make earplugs available to anybody who needs to block out noise in order to think, and I tell my students to let it rip.

As soon as they finish a draft, they can come find me or a peer-editing partner and they or we look at what they have done. First we do so aloud but with no comment until the draft has gotten a first hearing. Natalie says, you can't know what you've written until after you've written it, so first we give it a hearing, then we go to town giving it a quick edit. We look for what our rubric tells us to look for. Then they go back to their desk (or to the floor, or to the back table -- wherever they want to be writing) and they bang out another draft.

The beauty of this system is that it gives them a lot of practice compressed into a very short space of time. Everyone can get a fast, free, immediate edit from a published working writer without time for judgment, shame, or a sense of disgrace to take hold. The kids have very quickly grasped how to use writing practice to harness the flow state, get their juices flowing, and not become too attached to what they've put down on paper. It gives them a wonderful experience of the feedback loop in writing and it gives them immersive time in the flow state that has rapidly improved everyone's basic writing skills noticeably and quickly.

The, um, downside of this system is that while we are having one of these in-class writing workshops, my classroom looks like a chaotic free-for-all. Or so I thought until the other day.

See, when we're doing this, even though I am not actually writing, I fall into the flow state too. I get absorbed in reading, writing, listening, editing, coaching, and cheerleading and I completely lose track of time. In a good way.

But the other day, one of my English colleagues and I were scheduled to trade classes halfway through the period to teach each other's classes part of a jigsaw lesson we were doing. I knew we were doing so, and I had everything ready and prepared, I just lost track of time. So when she arrived in my classroom to trade, she got treated to the sight of me on my knees next to somebody's desk giving one quick edit after another, kids reading aloud and giving each other peer edits, one kid sitting under the phone table next to the flag because he concentrates best down there with earplugs in using an Algebra textbook as his lap desk, and other kids writing (with earplugs in) either alone or together, but in what I imagined to look like total unfettered chaos.

Fortunately, this teacher is both an enlightened person and a reflective practitioner in her teaching, so she was absorbed for a few minutes just watching what was going on, taking it all in and finding it extremely effective and engaging.

Then she came over, tapped me on the shoulder, and reminded me that we needed to switch classrooms and finish the jigsaw activity.

At lunch later, she told me how much she had enjoyed getting the chance to watch our process unnoticed because it gave her a totally different vision of what an in-class writing workshop could be.

That made me feel both grateful and relieved, since I had felt certain that doing what I was doing was the straightest path to getting myself fired (except for the part about my kids' writing improving more and faster than many other teachers' classes).

Anyway, it was really interesting to have been observed while I myself was in the flow state.

Renegade Math Teacher Brings SBG into the English Classroom: Film at 11

SBG works so well in my Algebra classroom I've been looking for ways it could transfer into my eighth-grade English classroom -- especially with regard to writing. One of the hardest things about teaching persuasive or expository writing is that each "skill" is composed of multiple, discrete sub-skills, each of which could itself be broken down further into tinier and tinier (i.e., more refined) sub-skills. In many ways, it's an M.C. Escher-like process -- a mise en abîme of nested skills.

BACKGROUND

Our school and district use our own combination of two methods that work for us, adapted through our own collaborative practice, reflection, and research over many years to fit our district goals and population. As a starting point and foundation, we use the Jane Schaffer method for teaching the actual composition process and a slightly modified version of 6 Traits program for assessing the finished product (or the work-in-progress). 

What I like about the 6 Traits assessment system is that it has a strong SBG orientation. It is a rubric-based system that assesses idea development, organization, voice, word choice, sentence fluency, and conventions -- the main basic categories that young writers need to master to produce both competent and coherent arguments, paragraphs, and essays. In our district, we have whittled it down to a four-point scale, which gives most middle schoolers a fighting chance of making sense of their scores.

What I like less about the 6 Traits assessment system is the complexity and denseness of its rubric. As Edward Tufte, the infographics pioneer might say, its information density approaches near-total opacity.

While I appreciate that its authors are trying to be comprehensive, my experience is that, for a middle school or high school student trying to juggle the many skills that come into play in writing a persuasive paragraph, it's just too damned complicated.

MY IDEA

One of the things I've noticed early on in this school year is that even our strongest writing students tend to have only a tenuous grasp of what makes an effective topic sentence. And having taught literature at the university level, I have seen how this confusion tends to persist and worsen over time.

So my goal was to come up with an activity that integrated two tools I've found useful in SBG in the math classroom: (1) a clear, simple, compelling four-point rubric for judging the effectiveness of a topic sentence, and (2) an activity to give students practice in judging a wide range of topic sentences, along with practice in using the rubric as a basic for analyzing, debating, and justifying their assessments of each one.

With that in mind, I created the two tools which are attached here: a Topic Sentence Rubric and a "Judging Topic Sentences" activity for use in pairs or small groups. The "Judging Topic Sentences" activity sheet includes twenty topic sentences I wrote based on a recent writing prompt for that staple of the eighth-grade English curriculum, "Flowers for Algernon." The writing prompt (which was deliberately broadly written) asked the student to compose a persuasive paragraph regarding the author's message in the story about cruelty toward people with mental disabilities. 

I gave them 30 minutes in class to work together on the assessing activity before we came back together as a whole class to discuss and give closure to the process.

RESULTS

What was fascinating as I circulated among the groups was how quickly everybody grabbed hold of the idea of using criteria from the rubric as the basis of their judgments. Suddenly I was hearing arguments about how, yes, a certain claim was definitely true and supportable but was basically pretty trivial! I was also hearing students argue that another example made an "original and juicy claim," but that it was awfully long and wordy and could easily be improved with better word choice and sentence construction.

When we came back together as a class, I asked for examples of the worst topic sentence on the list and the best. The discussion was productive in that it brought students to an understanding that an "OK" topic sentence could kick off a really great paragraph if the writer used all the tools at his or her disposal. It also made them realize that a truly outstanding topic sentence could launch a truly mediocre paragraph if it was followed by weak use of evidence from the text and lame or badly written analysis and interpretation.

My fellow eighth-grade English teachers used this activity in their own way over the next few days and found it to be very helpful in getting students to think about what makes a strong and effective topic sentence.

So now it looks as though it will become a regular part of our writing curriculum. 

Another triumph for SBG!

WARNING: This post contains math education heresy

I am so tired of math teachers and teacher educators telling me memorization doesn't work that I am willing to take a reckless step into the fray.

My purpose in this post to demystify this dangerous misunderstanding and to say that memorization of basic facts not only can work but indeed does work and works well -- as long as several essential conditions are met.

First, a definition. When I talk about memorization, I am NOT suggesting that one can achieve mastery by rote memorization of the proof of the Fundamental Theorem of Galois theory.

Rather, I am referring to an active process of integrating certain basic, rudimentary facts into one's mind and body, both backwards and forwards. By this, I mean that, given a vocabulary word, one can produce the definition, and similarly, given the definition, one can produce the vocabulary word. Or given a basic multiplication fact, one can produce the product and similarly, given a composite number, one can produce its basic factors.

 I am talking about filling in basic math facts. Expanding critical vocabulary. And solidifying basic mathematical skills that are often missing in the high school math student. 

Facility with this kind of memorization is the sine qua non to serious foreign language study as an adult, since it is simply not practical to put yourself into the way of enough quality adult conversations to absorb all the vocabulary one will need to read, write, think, and speak another language with the basic fluency that is required if you are going to be dropped into another culture. But it IS possible to approximate that vocabulary and bring its user closer and closer to a level of acceptable fluency.

This is how I both learned and taught Italian and Latin, as well as a number of other languages as a Comparative Literature scholar. It is also how the Peace Corps trains its Corps members in preparation for their overseas, language-intensive assignments. 

I was schooled in the Rassias Method, a highly dramatic, intensive, and effective technique of drilling students in the language classroom to approximate and accelerate the contexts of listening and speaking another language. It does so through very strategic, high-energy, rapid-fire, and theatrical drilling and practice techniques.

http://rassias.dartmouth.edu

Approximating contexts is important because, as Skemp puts it, purely instrumental learning without any relational context is just pointless. But I believe many of my colleagues and math education instructors have misunderstood this critical distinction. The way I read it, Skemp is not suggesting that there is NO room or role for instrumental learning. He is asserting that instrumental learning is insufficient without relational learning as well.

This intersection between instrumental and relational learning is where the Rassias Method really shines. One thing I used in my math classes this past year was the Rassias strategy of "flooding" students (my term, not Rassias') with productive opportunities in order to burn those facts and skills into their minds and bodies. But even more important than the drill itself is the process of breaking down student inhibition in the classroom.

This strategy is key.

Discouragement is always accompanied by inhibition. And the only way I've ever found to break down inhibition in this regard -- my own as well as that of my students --  is to insist on lots and LOTS of participation and practice -- with no chance of opting out.

The Rassias Method taught me to use a technique that blends rapid-fire drill with micro-contexts and an often humorous dramatic flair to create a heightened emotional charge in the classroom in which anyone could be called on at any moment to produce anything that is being asked for. It encourages learners to engage, to enjoy, and to stop worrying about producing the right answer because it creates dozens and dozens of chances to produce the right answer. It accomplishes this goal by flooding learners with basic language demands, all the while heightening drama, motivation, and interest in success while simultaneously lowering the stakes of failure. 

To put it another way, trying becomes more important than succeeding -- because eventual success is assumed.

Here is an example of how I used this in teaching my Italian language classes at Stanford.

One of the biggest hurdles in learning Italian is mastering its complicated matrix of prepositional contractions. Wikipedia has a reasonable summary of this matrix here:

http://en.wikipedia.org/wiki/Contraction_(grammar)#Italian

In Italian, a number of key basic prepositions are ALWAYS merged with the direct article preceding the noun that is the object of that preposition. So for example, to say that something is "on the table," you need to merge the preposition for "on" (in this case, "su") with the direct article "la" ("the") that precedes the noun "tavola" ("table"): in other words you need to say that something is "sulla tavola" ("on the table') instead of "su la tavola."

Practically speaking, this roughly six-by-eight matrix of prepositions and direct articles needs to be absolutely second nature for a speaker who wishes to be able to produce and recognize the right prepositional contraction for the job.

Basically, the prepositional contractions are the times tables / multiplication facts of the Italian language.

To get students using these, one Rassias technique I used involved a little plastic elephant, whom I named Signor Elefante, which I held in different positions with respect to a festive-looking cardboard box and drilled my students, asking, "Dov'è Signor Elefante?" ("Where is Signor Elefante?"). Or as we say in edu-speak, I used situational motivation (for a good discussion of situational motivation, see Wilhelm and Smith, "What Teachers Need to Know About Motivation," Voices from the Middle, Vol. 13, No. 4, May 2006).

Sometimes Signor Elefante was "nella scatola" ("in the box"), sometimes he was "sulla scatola" ("on the box"), sometimes he was "vicino alla scatola" ("near the box") or "lontano dalla scatola" ("far away from the box"). Sometimes he was "sotto la scatola" ("under the box") or "alla porta" ("at the door"). Occasionally he was "sulla lavagna" ("on the chalkboard"). He got himself into some pretty wacky prepositionally contracted situations. But after a lot of practice and inhibition-destruction -- as well as their own practice at home with flash cards -- locating Signor Elefante in time and space became more and more natural for my students. They got themselves over this major linguistic hurdle and developed their own relationship with the prepositional contractions.

They blended instrumental learning techniques with relational learning to generate understanding and fluency that was more than the sum of its parts.

In my math classes last year, I found that many of my lowest-achieving students responded well to this kind of approach to remediation. Even my higher-achieving students responded well to this approach. In fact, the most important the thing I discovered this past year is that many students have no idea how to practice basic techniques... but they get excited by the results they can achieve once someone shows them how memorize and assimilate bits of information like this.

Now since in spite of my best efforts I am bound to be misunderstood and misquoted, I'll restate this as plainly as possible: I'm not talking about using memorization with higher-level thinking and problem-solving. I am, however, talking about using these techniques as a strategic intervention to help students remediate and give them the tools and techniques they will need to fill in the gaps and potholes that riddle their elementary mathematical preparation. 

Confidence with the basics is a necessary condition to cultivating curiosity and persistence about mathematics. I speak from my own experience as well as that of my students.  Mastery of basic tools and techniques, combined with a lowering of inhibitions, is a foundation upon which confidence and curiosity can grow. And that can be the basis for a turnaround to success in high school mathematics -- regardless of where students are starting from.

Unmediated Experience, part 2 — another use of primary texts in the math classroom

While gathering problems for my logarithms and exponential functions unit from some of my favorite textbook sources, I noticed that John Napier's birth and death dates (1550-1617) looked kind of familiar — really familiar, in fact.

In fact, they're almost the same as Shakespeare's birth and death dates (1564-1616).

And they're awfully close to Galileo's birth and death dates too (1564-1642).

So why not at least mention the historical context of logarithms?

Getting students writing and reflecting in math class

I used this idea in Algebra 2 during our polynomial graph sketching unit to support their conceptual understanding of end behavior, and it worked surprisingly well.

Most of my students had not had much truck with the idea of infinity, much less with the idea of approaching it, so we started by talking about how the graph of a function is a representation of a specific story — like a novel — or like the life story of a human being. Every person's life story is completely unique, yet everyone has an experience of both birth and death (the beginning and end being like end behavior). Everyone's birth story may be different -- some people are born in a taxi cab, some are born at home, some are born in a hospital, some are born under water, and yet every single one of these births has the very fact of having gone through birth in common. Similarly, death is the ultimate "end behavior" of life. We cannot know exactly how or when a specific person's death may come, but we do know that it is going to happen some time after they have been born and have lived for some duration of time.

We also talked about the movement of a function graph across the axis at its x-intercepts — how at certain key transformative moments, a person's life crosses from negative into positive territory -- or it may move in the opposite direction.