## Tuesday, December 13, 2011

### SOLVE - CRUMPLE - TOSS in Algebra 1: hommage à Kate Nowak

Kate Nowak creates some of the most innovative and engaging practice activities anywhere -- especially for those skill/concept areas that are more like scales and arpeggios than like discovery/inquiry lessons. Some skills, like basic math facts, simply need to be practiced. This is true not because students need to be worn down but rather because it takes the mind and body time and first-hand experience to process these as matters of technique. It takes time to get used to the new realities they represent.

Nowhere is this more true than in tinkering with the multiple different forms and components of linear equations in Algebra 1. No sooner have students gotten the hang of finding the intercepts of a line than they're asked to find the slope. They figure out how to find the slope and the y-intercept, and they're given the slope and a non-intercept point. They figure out how to crawl toward slope-intercept form, but fall on their faces when asked to convert to standard form. Standard form, point-slope form, slope-intercept form, two points and no slope, it's a lot of abstraction to juggle. Mastery is part vocabulary work, part detective work, part scales and arpeggios, and part alchemy of different forms. It's a lot to take in.

Enter Kate's Solve - Crumple - Toss activity. I have loved this practice structure since the day I first read about it, but I have struggled with the fact that the most engaging part of the activity destroys the paper trail/evidence. This was less important with high school students, but it is really important with middle schoolers, I find, because they are so much more literal.

For today's linear equation-palooza in class, I created a basic "score sheet" for each student and I numbered each of the quarter sheets on which I glued blocks of problems (4-6 problems per mini-sheet). I also differentiated them from "Basic" level (Basic-1 through -4, Level 2-1 through -4, etc), so that students could choose their own levels. Students were also invited to work in pairs or groups of three because I find it encourages mathematical language use and increases risk-taking. It also seems to be more fun.

After the "Solve" part of the activity, students brought their solved mini-sheets to me to be checked. If they completed the problems correctly, they got a stamp on their score sheet and proceeded to the back of the classroom where I'd set up the Tiny Tykes basketball hoop over the recycling bin. There they completed the "Crumple" and "Toss" stages, awarding themselves a bonus point on the honor system if they made the shot. Then they returned to the buffet table of problems and chose a new mini-sheet.

Because my middle school students like to bank extra credit points toward a test wherever they can, I like to attach these to practice activities such as this one or Dan Meyer's math basketball. Being more literal and concrete than high school students, middle schoolers seem to find great comfort in the idea that they can earn extra credit points ahead of time in case they implode on a quiz or test. What they don't seem to realize -- or maybe they do realize and they just aren't bothered by it -- is that if they participate in the process, they win no matter what. Either they strengthen their skill/concept muscles and perform better and more confidently on the test; or they feel more confident and less pressured because they have banked a few extra-credit points for a rainy day; or both.

It was fun to hear my previously less-engaged students infused with a rush of sudden, unanticipated motivation to tease apart a tangled ball of yarn they have previously been unmotivated -- or uncurious -- to unravel. And something about the arbitrary time pressure of trying to complete as many problem sheets as possible in a short period was also fun for them. I'm feeling a little ambivalent about not having found the secret ingredient of intrinsic motivation in this required blob of material. But I am grateful that, once again, an unexpected game structure generated what the late Gillian Hatch called "an unreasonable amount of practice."

The last word goes to the one student who put it best: "The crumpling is definitely the most satisfying part."

## Wednesday, December 7, 2011

### Something's happening here... what it is ain't exactly clear...

A funny thing happened today on the way to basic linear equation and function skills today in Algebra 1:

students started using precise mathematical language without my having to prod them.

First, a student demonstrating a problem at the board announced matter-of-factly, "Well, first you use the distributive property, making sure not to drop any negative signs. Then you add '2x' to both sides of the equation."

I almost swallowed my own tongue.

Stop, children, what's that sound... everybody look what's going down...

## Tuesday, December 6, 2011

### Another Turning Point in Algebra 1: from larva to butterfly

When things go right in Algebra 1 -- and that is by no means a given for all students in all Algebra 1 classes out in the real world -- there are some truly breathtaking paradigm shifts that take place in student thinking: the moment when a critical mass of students begin to understand that absolute value and inequalities have to do with a relationship with zero; the moment when students begin to grasp the higher concept of groupings (parentheses, brackets, braces, the occasional fraction bar) as having meaning for operations; the light bulb moment they have when they begin to occupy the distributive property.

I admit it -- I'm a sucker when it comes to witnessing a student having a really intense light bulb moment. My own mathematical light bulb moments were very hard-won, so perhaps that gives me a special appreciation for them in others. Still, there's something deeply  moving about the courage it takes to let go of your old frame of reference when you know it's worn out but you don't yet know -- or trust -- what will come in its place. It's a frightening emotional moment in one's learning process, and I know that from first-hand experience in the math classroom.

The closest description I know of how it feels to undergo this transformation comes from A.H. Almaas:
So there is a need for an attitude of allowing, allowing things to emerge, to change, to transform, without anticipating how this should happen. You can direct things only according to the way you are now. You can conceive of the future only according to the blueprints you already know. But real change means that the blueprint will change.
The only thing you can do is to be open and allow things to happen, allow the butterfly to emerge out of the larva and be a different being. You might be amazed, saying, "All this time I thought I had to crawl faster! I didn't know it was possible to fly." It is possible to fly, but if you want to remain a larva, you can learn to crawl a little faster. You can even learn to crawl sideways. But it will never occur to you that you can fly. You see things flying around you but don't think of flying because you haven't got wings. If you allow things to happen, you might find that you do have wings and that you are flying around. (Diamond Heart: Book One,  page 153).
I was privileged to experience the first sparks of such a turning point today in class, as students began to grasp the relationships between and among all the different elements and aspects of linear equations, graphs, and functions they need to be able to take apart and recombine in dozens, if not hundreds, of different ways. Given a linear equation, find its intercepts. Given the intercepts, find the equation of the line. Given the slope of a line and one intercept, find the equation of the line. Given the slope-intercept form of a line, find the standard form. Given the standard form, find the slope-intercept form. Given the slope and some non-intercept point on the line, find me the equation of the line and write it in slope-intercept form. The whole quest involves a collection of movable parts, a juggling act at at first strikes some discouraged students as ludicrous bordering on the impossible. I'll never be able to manipulate all those moving parts, the discouraged student despairs. I'm a larva -- not a butterfly! What kind of crazy-ass thinking are you asking me to engage in here? This is insane! Absurd! The best I can hope for it to crawl a little faster, maybe to be able to crawl sideways and someday do The Twist. But fly in the air like that? Are you totally nuts?

And so it takes a certain amount of what I like to call wallowing. Wallowing in the confusion and the array of perplexing terminology and movable pieces that have to be taken apart and put back together like so many parts of a clock.

I have a friend who is one of those people who can fix literally anything. The fastest way to get something broken fixed is to tell him it's hopelessly broken and can't be fixed. He doesn't know the meaning of the words "can't be fixed." He doesn't trust that as an existential state of being. For him, hearing the words "it can't be fixed" is like somebody double-dog-daring him to prove them wrong. He can't stop himself. He sits with the problem and the pieces and the brokenness until he has resolved it. To him there is no other way.

For me, this situation is exactly the opposite. I look at the broken alarm clock and think to myself, Well, that's clearly hopeless. It must be time to move.

Many of my students feel this way when confronted with the point-slope, point-point, slope-and-intercept, and other linear equation/function/graph skills that are central to Algebra 1. They throw up their hands and yell, "What do you want from me? I'm just a larva, trying to crawl a little faster here? What are you trying to throw me into???"

And so we simply wallow in the mess.

I remind them of my friend Sam Shah's motto, "Take what you don't know, and turn it into what you do know." I suggest some of my friend Avery's habits of mind ideas. I encourage them to tinker with things on scratch paper or graph paper. Make a table. Plug in values. Draw a graph. Try rearranging the elements. See if you can find the x- and y-intercepts.

It doesn't really matter what they do, so long as they do something. And since I won't just give them the answers, they have to practice tinkering and struggling. I believe that learning to struggle with problems is one of the most essential skills a person can develop in life, much less in math.

And a curious thing began to happen in Algebra 1 today. Students began to articulate different distinct patterns in and among the equations and elements. Like, if you are given the equation in slope-intercept form, you don't actually have to DO anything extra to find the slope of the line it represents. It's already there. It's a freebie. There's knowledge there and you get both to use it and to keep it.

All afternoon students were figuring little things out like this in class, and it reminded me of the importance of having time and space -- and support -- to wallow in the beautiful, beautiful logic and relationships of algebraic thinking. I realized that I sometimes get convinced that I have to add something external -- something "extra" -- to bring the mathematics to life.

But sometimes all they need is their problems, their minds, and the friction that comes from a little push to help you get to the next level.

## Saturday, December 3, 2011

### 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:

• don't cross out
• don't worry about spelling, punctuation, grammar, or other rules
• lose control
• don't think
• go for the jugular
• 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.

## Sunday, November 6, 2011

### Analysis and Extension of Sam Shah's 'Best Test Question Ever' (a post about a post)

My friend Sam J. Shah recently blogged about his best test question ever, so it was entirely predictable that I would follow along in lockstep as I so often do, stealing and adapting his best ideas in my own teaching practice. What was less foreseeable was that I might actually inquire into and extend what I see working inside this technique and analyze why it works so well. In doing so, my hope is that I (and perhaps others) can get more mileage out of Sam's brilliance.

Based on an idea from another amazing post by fellow Klingon and expatriate math teacher Bowman Dickson, Sam got the idea to order a set of scratch-off stickers and integrate them into a calculus test question. His objective was to address the dysfunctional reaction and misconceptions that many students have whenever their new and emerging understanding gets challenged.

This dysfunctional reaction is a basically a defense mechanism of the unconscious -- formed in response to years of experience in the massively dysfunctional social system of the math classroom. It conditions students, when in doubt, to abandon their own good sense and everything they know in their life outside the math classroom in favor of half-remembered algorithms and recipes that are all too often are at odds with their own emerging reasoning skills and common sense.

But they seem to the unconfident student to be what the teacher is asking for.

Sam's test question had two parts: a first part which asked students to use what they know and have learned to solve a problem of the type they'd been focusing on. There was a sticker covering up something important in the information in Part A of the question, but it had no bearing on the mathematical task being set for them, and so they dutifully ignored the hidden information and simply trusted their own minds to solve the problem.

The genius part comes in Part B, where Sam instructed the students to scratch off the sticker, reveal the hidden information, and evaluate their Part A answer in light of the new information revealed in Part B.

What's genius about the Part B question is that this is an emotional question -- not a mathematical one. By challenging readers to defend or retreat from their previously worked solution, the physical action and the question conspire to introduce fear, uncertainty, and doubt into the reader's process of reflecting on their solution to the question in Part A. And as anyone who has done time in the marketing or political strategy realms knows very well, Fear, Uncertainty, and Doubt are three pillars of influencing consumer (or voter) behavior.

When faced with this kind of challenge, the confident student will furrow her or his brow for a moment, then say, "Not so fast, Mr. Shah. I see what you are trying to do here but it won't work. Not for me. I stand by my answer in Part A and I push back against your clever little ploy to knock me off balance."

The interesting process is what happens when the unconfident student is challenged to reconsider her or his answer to Part A. I say this both as a teacher and as an unconfident student who has spent a lifetime learning how to work with my defense mechanisms when I begin to doubt myself or when my work is challenged. This student's thought process goes more like, "Oh crap. Mr. Shah wouldn't have gone to the trouble to put this sticker here and have me scratch it off to reveal a hidden answer unless he *knew* I would mess up Part A and need to rethink the whole thing. He understands this stuff much better than I do, so there must be a good reason for me to back away from whatever work I did in Part A and figure out how to retrofit my solution to fit the new information just revealed."

It is important and useful to address the emotional reaction of panic and self-doubt here -- not simply the mathematical misconception that reveals the underlying panic and self-doubt. In this case, the misconception is a symptom, not an underlying cause itself.

If we are going to help students develop the courage to trust their own emerging skills and understanding, we need to help them learn how to (a) notice their panic in this kind of situation and (b) address it in a more effective and non-automatic, non-self-abandoning way. As Rudolf Dreikurs would say, we need to encourage our students' courage. And the only sustainable, durable first step that will help them to overcome their unconscious fears is to help them tap into their body-based awareness that they are freaking out.

And this is where Sam has offered a powerful yet simple means to do that -- using only a scratch-off sticker and a thoughtful question.

Once they have noticed that they are freaking out, students have at least 100% more options for next steps in dealing with their mathematical understanding or its lack.

But to move through the emotional blockage, a student first has to notice that the blockage is there.

And so, Sam, this is why I am, as always, your biggest fan.

## Sunday, October 23, 2011

### 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!

## Saturday, October 1, 2011

### Tikkun olam, cheesemonkey-style, or why I became a public school teacher

This was my first Rosh Hashanah as a full-time teacher and it got me thinking, as Rosh Hashanah always does, about the obligations we have for tikkun olam, the obligation we hold as human beings to repair the world. But this year it also got me reflecting specifically on why I became a public school teacher.

To be truthful, I became a teacher because I am ashamed of what my generation and I have done in our society with what we were given.

As a alumna of Silicon Valley and of some truly amazing companies, I'm proud of the cultures, technologies, and connections we created in the world.

But I am also disgusted by some of the other things my classmates and fellow Ivy League alumni bought into: greed and the amoral free-for-all that brought us the banking collapse, Bear Stearns, Lehman Brothers, Teach For America. The Gates Foundation.

Way to grab power and simply install yourselves as the new assholes-in-chief, guys. Nicely played.

As Elizabeth Warren rightly points out, nobody who has done well in our society has done so alone. I know I didn't. Everyone stands on the shoulders of infrastructure and investments made by previous generations.

My new colleagues and school community are wonderful and I feel lucky to be doing my part every day in a place that values what I am doing and why and gives me the support I need to do my job. But it also gave me cause to reflect on the fact that I'm just one bee in a world-enveloping hive.

When I get frustrated or discouraged, I try to remind myself that it took a long time for things to get this completely fucked up, so it shouldn't surprise anybody that it's going to take us some time to get things back on track. But at least there is a core of us out there, doing this work, every day.

So my advice to all in this new school year is that, if you notice that things have turned into a giant pile of shit, don't just stand there on the sidelines, kvetching, pointing fingers, and throwing money onto the pile.

Grab a shovel and start digging.

## Tuesday, August 30, 2011

### Something I really did right: Day 1 lesson on really working the rubric

I know I said I was going to go to bed at 8:07, but I wanted to capture and share the essence of something I really did right today in my (mixed 7th and 8th grade) Algebra 1 class.

It was an actual mini-lesson on interpreting -- and more importantly, on using -- the five-point rubric my teammates and I adopted.

Here is my version of the rubric (as a PDF): Rubric handout - Algebra.pdf

WHAT I DID
After the syllabus and the course requirements, I handed out the rubric and had the kids read the bulleted description of each element of a full-credit five-point answer.

We discussed each element, most of which were familiar to all students, but then I really stayed with the topic of "presenting one's work in a neat, organized, and logical manner according to the standards recognized by mathematicians around the world."

My kids are from very varied backgrounds, so we talked about how mathematics has become a lingua franca in our modern world -- so much so that a math teacher in Russia or in Egypt or in India or in Italy could easily read and assess the essence of a math problem written out by a well-trained student who does not speak the same language they do. We marveled at this for a bit (they're very smart and curious middle schoolers!).

Then this was the piece that really pinned the whole thing home.

HAVE THE STUDENTS ASSESS A WORKED PROBLEM USING THE FIVE-POINT RUBRIC
I wrote a very elementary prealgebra problem on the board and told them that the solution I was about to show them was presented on a math assignment turned in by one Hermione Granger. I told them that they were going to have to assess Hermione's work on the problem and justify their score using the rubric we had just reviewed.

Now, of course, being Hermione, she was very meticulous in solving problem #4, showing every step of her work, spacing her work out on the page so that it was easily readable, lining up the equals signs so that equivalence was as visually obvious as it was algebraically.

Then I asked them to give this work a score.

I was really excited by how engaged they were in assessing Hermione's work. One student gave it a five, and then another agreed, citing each of the criteria in the rubric in turn. Then one of the eighth-graders said, in summary, that this made sense because she had shown both that she understood what she was doing AND that she understood that how she presented her work was important in communicating to others that she understood the value in communicating clearly, logically, and neatly.

Needless to say, I was dumbfounded.

I then showed how Ron Weasley had approached the same problem. Unfortunately, Ron started by labeling his paper from 1 to 22, and squashed in problem #4 to fit the meager space he had left on the page, writing smaller and smaller until he had to have his solution creep up the right-hand margin of the page toward where the paper was dated in handwriting so cramped it verged on mental-patient scribblings. He circled his answer near the top of the page.

Then I asked them to assess his work using the rubric.

The students had a hilarious time criticizing the insane-looking presentation of the work. Much hilarity was had at poor Ron's expense, which was fine, since he is a fictional character without actual human emotions.

CONSOLIDATION OF LEARNING
To drive my point home, I took Dreikurs' strategy of using natural and logical consequences as a framing device and asked the class about the different choices Hermione and Ron had made in how they presented their work and their answers.

Everybody agreed that Ron had made lazy, poor choices because even though he had arrived at the "correct" answer, he had done so in a way that sabotaged his own efforts to do well in the class.

There was a lot of repetitive, reinforcing discussion of this point and we concluded that in a situation where you have control over choices (such as how to present your work), it would be foolish and short-sighted to sabotage your chance to have your learning be recognized by a scorer just because you're feeling a little inconvenienced.

And THAT was exactly the point I was hoping they would discover for themselves. Low-cost, high-impact point made.

And now I'm really going to bed.

UPDATE: 14-Sep-11
I created a completely generic downloadable version of my 5-point rubric as a PDF which you are welcome to use / steal. It's on the Math Teacher's Wiki at:  Rubric-5-point-generic.pdf

## Sunday, August 28, 2011

### The Unspoken/Unconscious Curriculum - keeping it both urgent AND important

Setting up my new classroom has caused me to think a lot about what is often called "the hidden curriculum" or "the unspoken curriculum" — the idea that we speak volumes about what value through the unconscious messages we send kids through the way we organize our classrooms, our schools, and our teaching.

Wikipedia has a nice brief overview of the idea of the hidden curriculum:

http://en.wikipedia.org/wiki/Hidden_curriculum

When I first arrived at my new school and got my classroom, it took me several days to figure out why I felt so depressed whenever I unlocked my classroom. It was only after about a day of taking down the previous occupant's wall hangings that it hit me: everything hanging up was about rules, schedules, and basic skills. Without saying so explicitly in words, it all said, "I the teacher am more concerned with managing your behavior than I am with inspiring your learning." It said, "I too am counting the minutes until the end-of-day bell rings."

It was a big "Ouch" moment.

Now teachers don't do this because they are bad people or boring people. It is simply a conditioned habit of teaching behavior. It's a trance (or a ditch) we've fallen into. But as my mentor always says, "Noticing shifts the energy." And once I've noticed it, I can address it.

So I made a radical U-turn in my classroom design and decorating philosophy. As much as it bothers me to have disorganized shelves and messy cabinets, this both more urgent AND more important:

In my classroom, I want students to be focused on things that are both urgent AND important.

I'll add some pictures later but I wanted to get these thoughts down. In the meantime, I'm wondering, what unspoken curriculum is being emphasized in your classroom?

## Monday, August 8, 2011

### Favorite Tweets: Predictable Tweets Edition

 fnoschese Khaaaaaaan! @fnoschese #predictabletweets 8/6/11 5:44 PM

 fnoschese My life with 5 sons! @dcox21 #predictabletweets 8/6/11 5:58 PM
 park_star Unicorns! @cheesemonkeysf #predictabletweets 8/6/11 6:04 PM
 dandersod I (went/ate/listened to) to some totally awesome (bar/snackfood/indie band) only found in Brooklyn. @sarcasymptote #predictabletweets 8/6/11 6:10 PM
 dandersod I (went/ate/listened to) to some totally awesome (bar/snackfood/indie band) only found in Brooklyn. @sarcasymptote #predictabletweets 8/6/11 6:10 PM
 cheesemonkeysf @dandersod @sarcasymptote Then I passed out on my couch only to wake up covered in Doritos & Nutella. #predictabletweets 8/6/11 6:36 PM
 dandersod Sarcastic smart comment. @dcox21 #predictabletweets 8/6/11 6:19 PM
 cheesemonkeysf @park_star I love B but he is driving me batty! #predictabletweets #inanadorableway 8/6/11 6:37 PM
 cheesemonkeysf @park_star It could just as well have been "Cute baby behavior captured and shared on Instagram!" #predictabletweets 8/6/11 6:40 PM
 cheesemonkeysf @samjshah I just finished another fantastic book -- my __th of the year! #predictabletweets 8/6/11 6:41 PM
 cheesemonkeysf @ddmeyer Flying from to and boy are my arms tired! #predictabletweets 8/6/11 6:42 PM
 cheesemonkeysf @cheesemonkeysf Making brownies. #predictabletweets 8/6/11 7:43 PM
 calcpage @fnoschese If Lucy had lived 100 years, she would have been 100 years old (today)! #predictabletweets #fb #in 8/6/11 8:29 PM
 dcox21 I'm trying to read but this Dora the Explorer night light is causing a glare on my iTouch. @jybuell #predictabletweets 8/6/11 8:40 PM
 dcox21 Khan uses the wrong kind of modeling. @fnoschese #predictabletweets 8/6/11 8:41 PM
 dcox21 I finished this Euler problem during the second intermission. @dandersod #predictabletweets 8/6/11 8:42 PM
 dcox21 Where's the ^@*&%# cheese puffs. @sarcasymptote #predictabletweets 8/6/11 8:43 PM
 stardiverr Khan Academy Sucks! @fnoschese #predictabletweets ;P 8/7/11 6:19 AM
 park_star Check out my awesome hair! @k8nowak #predictabletweets 8/7/11 8:58 AM
 cheesemonkeysf @fnoschese Angry Birds in the physics classroom. #predictabletweets 8/7/11 9:03 AM
 cheesemonkeysf @druinok @fouss Love to laminate. #predictabletweets 8/7/11 9:08 AM
 cheesemonkeysf @druinok Yet another amazing discovery to share about classroom organization. #predictabletweets 8/7/11 9:08 AM
 cheesemonkeysf @park_star It's been hours since B did something mischievous. I'm afraid to look. #predictabletweets 8/7/11 9:09 AM
 cheesemonkeysf @lmhenry9 Sharing something genuinely valuable and insightful about teaching. #predictabletweets 8/7/11 9:11 AM
 cheesemonkeysf @jreulbach New idea for distracting three high-energy sons while sharing great ideas & funny stuff on Twitter & iPad. #predictabletweets 8/7/11 9:13 AM
 EmergentMath @cheesemonkeysf "#predictable tweets" #predictabletweets (did I just BLOW YOUR MIND?) 8/7/11 9:14 AM
 cheesemonkeysf @samjshah Time to blame someone on Twitter for something that's annoying me. #predictabletweets #followedbypetulanthashtag 8/7/11 9:15 AM
 cheesemonkeysf @samjshah Justin Bieber #predictabletweets 8/7/11 9:29 AM
 cheesemonkeysf @sarcasymptote AM I THE ONLY F***ING TEACHER IN MY BUILDING WHO KNOWS HOW TO READ????? #predictabletweets 8/7/11 9:30 AM
 cheesemonkeysf @fnoschese Now I'm going to pretend I'm a serious teacher who didn't start the whole #predictabletweets thing in the first place. #whome 8/7/11 9:38 AM
 samjshah @ddmeyer watch this video of paint drying #anyqs #predictabletweets 8/7/11 9:41 AM
 lostinrecursion @ddmeyer watch this video of paint drying #anyqs #predictabletweets 8/7/11 9:41 AM
 samjshah @ThinkThankThunk just had a sdnt discover the higgs boson. also, here's 2 blog posts and a 10,000 line program i wrote #predictabletweets 8/7/11 9:39 AM
 samjshah @k8nowak frak! school's making us listen to a consultant talk abt withitbutwithoutitness. let's mock it relentlessly NOW #predictabletweets 8/7/11 9:36 AM
 samjshah @jreulbach im on the dock with wine whining about my neighbor's LAME party. oh, also here's a math song i wrote. #predictabletweets 8/7/11 9:34 AM
 samjshah @sarcasymptote i am not a hipster. i play the ukulele, wear cardigans, live in wburg, have a beard, drink in dives #predictabletweets 8/7/11 9:32 AM
 calcdave @Mythagon I've had that same problem! Have you tried... #predictabletweets 8/7/11 9:49 AM
 calcdave @EDTECHHULK SOMEONE SAY TECH SOLVE ALL WORLD PROBLEMS. SMASH! #predictabletweets 8/7/11 9:51 AM
 cheesemonkeysf @fouss Ran 312.2 miles. #predictabletweets 8/7/11 8:58 AM
 cheesemonkeysf @sophgermain Something dry and witty, signed "Love, me." #predictabletweets 8/7/11 8:57 AM

 cheesemonkeysf RT self: @jybuell Just overheard #cubelady say #predictabletweets 8/7/11 8:48 AM
 calcdave @rdkpickle You guys, I missed the convo again because I was listening to some cool band that plays in 17/5 #predictabletweets 8/7/11 9:54 AM

 samjshah @cheesemonkeysf finished knitting another dodecahedron. #predictabletweets 8/7/11 9:00 AM
 Fouss Bret Michaels rocks! @Mseiler #predictabletweets 8/7/11 11:19 AM
 Fouss Making some random food that no one else has ever heard of. @cheesemonkeysf #predictabletweets 8/7/11 11:18 AM

 jbrtva @cheesemonkeysf I'm loving the #predictabletweets posts 8/7/11 11:58 AM

 jillbacklund @cheesemonkeysf: How bad can things be when you have 11,842 -10n won tons in your freezer? #predictabletweets" (on nth day of school) 8/7/11 12:08 PM

 cheesemonkeysf “@calcdave: You can pick yr online friends, you can pick yr nose, but you can't pick yr online friends' noses” #predictabletweets 8/7/11 1:17 PM

 park_star @sophgermain aren't they close or something? How long can it take to move into Hogwarts? #isntthereaspellforthat 8/7/11 12:55 PM

 lostinrecursion @lostinrecursion oh no! Something about my flight. Blah blah. #predictabletweets 8/7/11 2:14 PM

 calcdave @vihartvihart Just doodled a solution to P=NP while bored in MATH527. #predictabletweets 8/7/11 12:54 PM

 calcdave @rjallain New blog about reanalyzing this viral video (that Mythbusters messed up) using Tracker. #predictabletweets 8/7/11 12:48 PM

 calcdave @sumidiot 30 miles in 1:22:05. Felt like I was going faster, but not bad for morning run. #predictabletweets 8/7/11 12:32 PM

 calcdave @MSeiler Your printer is fine, just "Open Up and Say... Ahh!" #predictabletweets 8/7/11 12:30 PM

 calcdave @CardsChic On a fieldtrip with the kids, but did you see that Westbrook slider? #predictabletweets 8/7/11 12:27 PM

 Fouss [insert something totally off the wall but brilliant here] @calcdave #predictabletweets 8/7/11 12:26 PM

 calcdave @SweenWSweens Just popping in to say that I have a dance that will show students how to conceptualize the 4th dimension #predictabletweets 8/7/11 12:24 PM

 sarcasymptote @jreulbach OMG!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! hi!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! #predictabletweets 8/7/11 12:14 PM

 calcdave @CmonMattTHINK How many sudoku solutions have a box with the numbers in order? #predictabletweets 8/7/11 12:21 PM

 calcdave @chrislehmann Philly sports! Also, my adorable kid. #predictabletweets 8/7/11 12:22 PM

 sarcasymptote @calcdave oh, predicting tweets? kind of like this youtube video? http://t.co/fV0kidU #predictabletweets 8/7/11 12:17 PM

 calcdave @approx_normal Was somewhere normal and did something confusingly crazy. The world is different down here. #predictabletweets 8/7/11 12:15 PM

 calcdave @lmhenry9 Did anybody actually read the chapter this week? #sbarbook #predictabletweets 8/7/11 12:13 PM

 sarcasymptote @park_star I'm going to get instant frostbite if I go outside, but it's ok bc we have socialist healthcare! #predictabletweets 8/7/11 12:06 PM

 dethornSTEM @GoGoAliza New blog post about life and NYC and theatre! #predictabletweets 8/7/11 3:16 PM

 cheesemonkeysf @sophgermain -> Amazeballs. #predictabletweets 8/7/11 3:14 PM

 dethornSTEM @paulshakesby The Paul Shakesby Daily is out! #predictabletweets #tooeasy 8/7/11 3:19 PM

 dandersod Hating khan doing yoga while taking care of adorababy. @fnoschesek8nowakpark_star #mergedtweets 8/7/11 3:42 PM

 calcdave "This unicorn on my knit cap vomited sparkles all over my book!" @cheesesamjshahmonkeysf #mergedtweets 8/7/11 4:05 PM

 sockington check check check is this thing on OH WAIT IT'S A PILLOW fair enough FLUMP zzzzz 8/5/11 4:42 AM