WEEK 1 - PROJECT 'MAD MEN' -- Classroom Rules PSA Skits

Leonard Bernstein once said, "To achieve great things, two things are needed — a plan and not quite enough time." I decided to put that principle to the test this first week at my new school by assigning a project on Day 1 that thew together strangers with an absurd but achievable goal: given a particular classroom rule or guideline, create a Public Service Announcement  (i.e., a 30-second "TV commercial" in the form of a skit) whose purpose was to motivate viewers to follow the rules/guidelines for the good of the group.

I created a set-up, instructions, and a rubric for the group project. And my students did not disappoint.

The idea was to get students to think about the consequences of their actions and choices, but their ideas for implementation exceeded even my wildest dreams. Most skits followed a "slice of life" strategy, but the ones that really blew us all away were the ones that parodied existing campaigns.

Two brilliant PSAs started from already-iconic Geico insurance commercials, but the one that left me with tears running down my cheeks was a take-off on Sarah McLachlan's ASPCA spots. The song, "In the arms of the angels..." began playing, and student "Sarah" appears onstage making the exact same kind of appeal she makes in those ads. They had the tone, cadence, and music exactly right, and they clearly understood the emotionally manipulative rhetorical strategy — the seemingly endless list of forms of ignorance designed to eventually provoke self-recognition in almost everyone. Their "mathematical justification" was as follows: the narrator enters and says, "In the past year alone, texting in class tragically cost 5 of Doctor X's students their lives. Remember, think twice before texting in class — there may be fatal consequences for your grade, and for you!

It was pure and inspired genius.

I also loved the spot-on impressions of my teacher persona. One student gave a pitch-perfect parody of my "Function Basics" talk that made me both cringe and laugh my ass off simultaneously.

The best thing about this assignment was that it really pushed the voice of authority downward, into the student community itself. Whatever they made of the experience, they owned it.

I am going to try and remember this for later in the semester, when we've become too routinized.

This is definitely going to be an ongoing part of my repertoire of Day 1 activities. I got through what I neded to,  then gave them the rest of the abbreviated period to collaborate. The time pressure was a thing of art.

It was perfectly imperfect — exactly the way first days ought to be.

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UPDATE:

Here is the link to a generified Word document that you can customize for your own class:

PROJECT MAD MEN- classroom rules PSA generic.doc

And here are the three sample 30-second PSAs I showed my classes to give them ideas:

'You Lost Your Life!' – game show hosted by the Crash Test Dummies (Since Vince & Larry, the Crash Test Dummies, were introduced to the American public in 1985, safety belt usage has increased from 14% to 79%, saving an estimated 85,000 lives, and $3.2 billion in costs to society)
'
What could you buy with the money you save?' - throwing things over a cliff (You could purchase TVs, bicycles, and computers with the money most families spend on wasted electricity)
'Five Seconds' – at highway speeds, the average text takes your eyes off the road for 5 seconds (Five seconds is the average time your eyes are off the road while texting. When traveling at 55mph, that's enough time to cover the length of a football field)

New strategy for introducing INBs: complex instruction approach

After months of not feeling like my best teacher self in the classroom, I got fed up and spent all weekend tearing stuff down and rebuilding from the ground up.

INBs are something I know well — something that work for students. So I decided to take what I had available and, as Sam would say, turn what I DON'T know into what I DO know. Love those Calculus mottos.

So I rebuilt my version of the exponential functions unit in terms of INBs. But that meant, I would have to introduce INBs.

As one girl said, "New marking period, new me!" The kids just went with it and really took to it.

Here is what I did.

ON EACH GROUP TABLE: I placed a sample INB that began with a single-sheet Table of Contents (p. 1), an Exponential Functions pocket page (p. 3), and had pages numbered through page 7. There were TOC sheets and glue sticks on the table.

SMART BOARD: on the projector, I put a countdown timer (set for 15 minutes) and an agenda slide that said,

• New seats!
• Choose a notebook! Good colors still available!
• Make your notebook look like the sample notebook on your table 

As soon as the bell rang, I hit Start on the timer, which counted down like a bomb in a James Bond movie.

Alfred Hitchcock once said, if you want to create suspense, place a ticking time bomb under a card table at which four people are playing bridge. This seemed like good advice for introducing INBs to my students.

I think because it was a familiar, group work task approach to an unfamiliar problem, all the kids simply went went with it. "How did you make the pocket? Do you fold it this way? Where does the table of contents go? What does 'TOC' mean? What goes on page 5?" And so on and so on.

I circulated, taking attendance and making notes about participation. When students would ask me a question about how to do something, I would ask them first, "Is this a group question?" If not, they knew what was going to happen. If it was, I was happy to help them get unstuck.

Then came the acid test: the actual note-taking.

I was concerned, but they were riveted. They felt a lot more ownership over their own learning process.

There are still plenty of groupworthy tasks coming up, but at least now they have a container for their notes and reflection process.

I'm going to do a "Five Things" reflection (trace your hand on a RHS page and write down five important things from the day's lesson or group work) and notes for a "Four Summary Statements" poster, but I finally feel like I have a framework to help kids organize their learning.

I've even created a web site with links to photos of my master INB in case they miss class and need to copy the notes. Here's a link to the Box.com photo files, along with a picture of page 5:

We only got through half as much as I wanted us to get through, but they were amazed at how many notes we had in such a small and convenient space.

It feels good to be back!

Teaching Mathalicious' "Harmony of Numbers" lesson on ratios, part 1 (grade 6, CCSSM 6.RP anchor lesson)

I started teaching Mathalicious' Harmony of Numbers lesson in my 6th grade classes today, and I wanted to capture some of my thoughts before I pass out for the night.

The Good — Engagement & Inclusion
First of all, let's talk engagement. This made a fabulous anchor lesson for introducing ratios. The lesson opens with a highly unusual video of a musical number that every middle school student in America knows — One Direction's "What Makes You Beautiful."

You'll just have to watch the video for yourself to see how the surprise of this song gets revealed.

What I wish I could capture — but I can only describe — was the excitement in the room as my 6th graders realized what song was being played. It took about eight measures for the realization to kick in. Imagine a room full of South Park characters all clapping their hands to their cheeks and turning around with delight to see whether or not I really understood the religious experience I was sharing with them.

Every kid in the room was mesmerized. Even my most challenging, least engaged, most bored "I hate math" kids were riveted to the idea that music might be connected to math. It passed the Dan Pink Drive test because suddenly even the reluctant learners were choosing to be curious about something in math class. My assessment: A+

We started with a deliberately inclusive activity to kick things off — one whole-class round of Noticing and Wondering (h/t to the Math Forum). Sorry for the blurry photography of my white board notes. They noticed all kinds of really interesting things and everybody participated:

From noticing and wondering, we began to circle in on length of piano strings and pitch of notes. This was a very natural and easy transition, perhaps since so many of the students (and I) are also musicians of different sorts. Five guys, one piano, dozens of different sounds, what's not to like?

The Not Actually 'Bad,' But Somehow Slightly Less Good
One thing I noticed right away was that, while the scale of the drawings on the worksheet worked out very neatly, it was kinda small for 6th graders to work with. The range of fine motor skills in any classroom of 6th graders is incredibly wide. At one end of the spectrum, you have students who can draw the most elaborate dragons or mermaids, complete with highly refined textures and details of the scales on either creature. At the other end of the spectrum, you have the students I've come to think of as the "mashers," "stompers," and "pluckers." These are the kids who haven't yet connected with the fine motor skills and tend to mash, crush, or stomp on things accidentally. Some will pluck out the erasers from the pencils in frustration ("Damn you, pointy pencil tip!!!").

This made me want to rethink the tools and scales of the modeling. It might be good to have an actual manipulative with bigger units (still to scale). Cutting things out is a good way for students this age to experience the idea of units and compatible units. Simply measuring and mentally parceling out segments is a little tough for this age group. Ironically, within a year or so, this difficulty seems to disappear. I'm sure there are a lot of great suggestions for ways to make this process of connecting the measurements to the ratios through a more physically accessible manipulative or model. But then again, I'm just one teacher, so what do I really know? My assessment: B

The Not Ugly, But Still Challenging Truth
The most difficult thing about this lesson is that 6th graders go S L O W L Y. Really slowly. My students' fastest pace was still about three times longer than the initial plan.

I am fortunate that this pacing is OK for me and my students. They need to wallow in this stuff, so I will simply take more time to let them marinate. We'll try to invent some new manipulatives for this, and I'll blog about them in a follow-up.

But the reality is that this lesson is going to take us three full periods to get through. They will be three awesome, deeply engaging learning episodes filled with deep connections as well as begging to have me play the video again (Seriously? Three times is not enough for you people???).

Even though this is a much bigger time requirement, I still give this aspect of the lesson an A+. Getting reluctant learners to be curious about something they're very well defended against is a big victory.

I'm excited to see what happens tomorrow! Thanks, Mathalicious!

Substitution with stars

This one is for Max, who asked about it on Twitter, and for Ashli, who interviewed me for her Infinite Tangents podcasts.

As Ashli and I were talking about some of the struggles we see as young adolescents make the transition from concrete thinking to abstraction, I mentioned substitution.

For many learners, there comes a point in their journey when abstraction shows up as a very polite ladder to be scaled. But for others (and I count myself among this number), abstraction showed up as the edge of a cliff looking out over a giant canyon chasm. A chasm without a bridge.

This chasm appears whenever students need to apply the substitution property of equality — namely, the principle that if one algebraic expression is equivalent to another, then that equivalence will be durable enough to withstand the seismic shift that might occur if one were asked to make it in order to solve a system of equations.

Here is how I have tinkered with the concept and procedures.

Most kids understand the idea that a dollar is worth one hundred cents and that one hundred cents is equivalent to the value of one dollar. I would characterize this as a robust conceptual understanding of the ideas of substitution and of equivalence.

One dime is equivalent to ten cents. Seventy-five pennies are equivalent to three quarters. You get the idea.

We play a game. "I have in my hand a dollar bill. Here are the rules. When George's face is up, it's worth one dollar. When George is face down, it's worth one hundred cents. Now, here's my question."

I pause.

"Do you care which side is facing up when I hand it to you?"

No one has yet told me they care.

"OK. So now, let's say that I take this little green paper star I have here on the document camera. Everybody take a little paper star in whatever color you like."

Autonomy and choice are important. I have a student pass around a bowl of brightly colored little paper stars I made using a Martha Stewart shape punch I got at Michael's.

Everybody chooses a star and wonders what kind of crazy thing I am going to have them do next.

We consider a system of equations which I have them write down in their INB (on a right-hand-side page):

We use some noticing and wondering on this little gem, and eventually we identify that y is, in fact, equivalent to 11x – 16.

On one side of our little paper star, we write "y" while on the other side, we write "11x-16":

I think this becomes a tangible metaphor for the process we are considering. The important thing seems to be, we are all taking a step out over the edge of the cliff together.

We flip our little stars over on our desks several times. This seems to give everybody a chance to get comfortable with things. One side up displays "y." The other side up displays "11x–16." Over and over and over. The more students handle their tools, the more comfortable they get with the concepts and ideas they represent.

Then we rewrite equation #1 on our INB page a little bigger and with a properly labeled blank where the "y" lived just a few short moments ago:

"Hey, look!" somebody usually says. "It looks like a Mad Lib!"

Exactly. It looks like a Mad Lib. Gauss probably starts spinning in his grave.

"Can we play Mad Libs?" "I love Mad Libs!" "We did Mad Libs in fifth grade!" "We have a lot of Mad Libs at my house!" "I'll bring in my Mad Libs books!" "No, mine!"

It usually takes a few minutes to calm the people down. This is middle school.

I now ask students to place their star y-side-up in the blank staring back at us.

Then it's time to ask everybody to buckle up. "Are you ready?"

When everybody can assure me that they are ready, we flip the star. Flip it! For good measure, we tape it down with Scotch tape. Very satisfying.

A little distributive property action, a little combining of like terms, and our usual fancy footwork to finish solving for x.

Some students stick with substitution stars for every single problem they encounter for a week. Maybe two. I let them use the stars for as long as they want. I consider them a form of algebraic training wheels, like all good manipulatives. But eventually, everybody gets comfortable making the shift to abstraction and the Ziploc bag of little stars goes back into my rolling backpack for another year.

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I'd like to thank the Academy and Martha Stewart for my fabulous star puncher, without which, this idea would never have arisen.

I wore out my first star puncher, so I've added a link above for my new paper punch that works much better for making substitution stars. Only eight bucks at Amazon. What's not to like? :)

Sometimes I teach, and sometimes I just try to get out of the way...

We are in the midst of our giant 8th grade culminating assessment extravaganza — a multi-part project that includes a research paper, a creative/expressive project, a presentation with slides, and several other components I'm spacing out on at the moment.

I have to admit something here: I used to be an unbeliever when it comes to projects.

I used to think they lacked rigor and intellectual heft.

But I was wrong.

Two years of this process has made me a believer in the power of project-based learning.

Sometimes the creative projects are merely terrific, but every year, there are a few that are incredible. This year, this has already happened twice... and only two projects have been turned in so far (they are due on Monday, 22-Apr-13).

Sometimes it is the quiet, timid kid who really blows my mind. Sometimes it is a kid who is kind of rowdy who reveals another, hidden side. But I never fail to be humbled at the potential inside each of these people, and I am honored to teach them.

So this is a reminder to myself that sometimes my job is simply to get out of their way.

Intro to Quadratics — from "drab" to "fab" (or at least, to something less drab)

Recently, I created a new anchor lesson for my Algebra 1 quadratics unit. I found that, while I really liked the sequencing of activities and questioning in the NCTM Illuminations lesson on "Patterns and Functions," I found their situation and set-up simultaneously boring, contrived, and inane.

Actual photograph of San Francisco monkeys

hosting a tea party in the wild

As is so often the case, I find that a certain, judicious sprinkling of silliness and fun in the set-up can really liven up the lesson. A certain amount of contrivance is necessary in many activities, even those that are based on "real-world situations." So why not stretch the real world to make it conform to the needs of my algebra students?

The Made To Stick elements are all here: multiple access points are provided through manipulatives, storytelling, and humor.

My student investigation sheet, Table for Eighteen... Monkeys is available on Box.com. A PDF of the Table Tiles master is available here on Box.com
here.

Tiny plastic monkeys sold separately. :)

UPDATE: Worksheets now also on the Math Teacher's Wiki, at http://msmathwiki.pbworks.com/w/page/55614036/Algebra%201#view=page

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.

Standards-Based Grading, or How Teaching For Mastery is Different

Teaching for mastery is different.

Teaching for mastery especially means giving up a lot of old and cherished assumptions about assessment. Anybody who has adopted SBG in any way can attest to this. But I am continually amazed at how unwilling many of us can be to letting go of old, ineffective methods, beliefs, and assumptions about assessment.

At its essence, valuing mastery means not only tracking relative mastery but also accepting mastery as the measure of student success in our classrooms. And that means letting go of the value we have always placed on the routinized behavior of the the dutiful student.

This is is probably the hardest shift of all.

As I shifted over to SBG, I noticed how much of our system of math teaching is organized around students being merely dutiful: sitting still, listening quietly, practicing silently, accepting information without challenge. It's a model of student passivity that places everybody into the known and accepted hierarchy. The "good" students land at the top. The "middle" students land in the middle. And the "weak" students land at the bottom.

But as we all know from having inherited, taught, and assessed these students, this schema does not measure mastery, skill, or comprehension. Dutiful students often lack conceptual understanding or procedural skills. They often have distorted memories of algorithms they heard about but never owned.

Changing over to an SBG system of teaching and assessment has meant that I have to create conditions under which any student — even ones with problem behavior or lack of "dutiful-ness" — can achieve mastery.

To me, this idea exposes the biggest flaw in the existing system. If a teacher or administrator decides from the outset that a given student is a "B-" student, then what reason does that student have to make the effort necessary for improvement?

This system also fails to allow for individual (or group) movement up the fixed staircase of the classroom hierarchy, except for improvements in "dutiful-ness." And it seems to me that if we want to improve access and equity to mathematics for all students, this is the single biggest obstacle we face.

It also seems to me that we need to consider the possibility that any hierarchical model might be transformed from a staircase to an escalator, in which all students can be expected to reach the target floor or level of skills and understanding. And that means we will have to allow for the possibility that all students in a class demonstrate the mastery that is asked in a way that permits them to receive a higher score than the "B-" or "B+" that they have always been pigeonholed into.

What We Actively Value, Versus What We Tell Students We Value

Lately I've become acutely aware of what I actively value in my classroom, which has entailed an uncomfortable amount of noticing the conditioned habits of my teacher personality. I don't collect and stamp homework assignments. I don't have each day's agenda and objective for the day neatly written on the whiteboard by the time the first bell rings. My classroom is pretty messy most of the time. I don't have a good system for filing away those last three copies of every handout for future use. I took great permission from @mgolding's system of daily handouts using her Container Store hanging file system: basically, the handouts migrate downward one pocket until there are no pockets left, at which point they go into the recycling bin.

I've made my peace with these tradeoffs because I discovered early on that if I was allotting attention to those things, then that was attention I wasn't allotting to the things I actually do value.

I adopted an SBG assessment system because it aligns my grading/scoring system with the things I actually value: mastery, effort, and perseverance. And also presence — being fully present with the activity we are doing that I actually care about. And as I've noticed that, I have noticed something else I feel good about in my classroom: my kids know that those are the things I value. Which that means they don't waste valuable life-energy bullshitting me about the small stuff we all know I don't really care about.

This has led to a lot of interesting progress with students I didn't expect to make progress with. Less successful students who don't feel shamed stick around to ask questions and engage in meaningful academic inquiry. They come to my room during their study hall periods to follow up, get help on missed or misunderstood assignments, or ask for additional work they can do to improve their understanding.

Not their grade -- their understanding. Their performance.

I am not used to this, and it causes me a lot of inconvenience. 

Students who have a reputation for giving up and giving in ask me if they can write another draft, reassess their missed algebra skills/concepts questions, and take greater ownership of their learning in my classroom. My ego would like to think this is because I'm such a highly effective teacher, but in actuality, I think it's more that my walk is becoming more aligned with my talk. I care about mastery and effort and perseverance, which means that those are the things I respond to.

What I did not realize until this afternoon is that this also means that I don't respond to things that are NOT those things. Which means that my kids are not expending any effort pretending to care about things around me that they really don't care about either. There is a focus on the work, and there is not a focus on things that are not the work. This may sound obvious, but actually it's not -- or at least, it wasn't for me. It took me years to discover that I'd been walking around in a consensual trance all my life.

This kind of awareness is challenging, to be sure, but it is also incredibly freeing. Students spend a huge part of every school day pretending to care about things that don't actually matter to them. Fitting in, pleasing teachers, winning points. Some of it is necessary but much of it they know to be complete and utter crap.

Ten, fifteen, forty, or fifty minutes of being authentically engaged in something that matters to somebody is a huge thing. Ten, fifteen, forty, or fifty minutes of authentic interaction with someone who is trying to focus as sincerely as possible on what actually matters in this life is even bigger.

I learned this lesson from years of experience with my mentor and teacher, Dr. Fred Joseph Orr — mind to mind, and heart to heart, though it took years to digest, and quite frankly, I'm still digesting. I'll probably be digesting for the rest of my life. No one had ever paid that kind of focused, intensive, thoughtful, and bounded attention and awareness in my presence before. And it made me discover how it feels to feel alive. I only discovered how precious that kind of awareness was -- and still is -- once that chapter of my life ended and a new chapter had begun.

I was noticing all this today during a test in which some of my lowest-performing students were asking for "help" with certain problems. I noticed that each time I came over in response to their request, they were not so much asking for assistance as asking for a kind of authentic engagement and support that was neither judging nor doing for them but simply witnessing their effort with presence. What I noticed today inside myself — and what distinguished this from mere adolescent attention-seekig behavior — was my own felt sense of a embodied memory of seeking out this kind of authentic connection in my own work with Fred. And this felt sense gave me the motivation to allow that connection and that presence. I trusted something inside my own inherent, intelligent functioning that told me to allow the connection rather than to pull back and resist. It was a subtle and quiet movement inside me, and I'm still figuring out what exactly was going on.

How many times have I mistaken noise for the signal? Do discouraged students ask because they hang on to the sane and healthy hope that they can learn and connect and make progress? Fred always told me, "The organism moves toward health," and I grew to believe him. I wonder if this is what my discouraged students are really asking for when they ostensibly make a seemingly attention-seeking request for something called "help."

Life on the Number Line - board game for real numbers #made4math

UPDATE: Here is a working link to the zip file: https://drive.google.com/open?id=0B8XS5HkHe5eNNy10MWZVSDNKNnc

Last year I blogged about my work on a Number Sense Boot Camp, so I won't rehash all of that here. This year I want to give the follow-up on how I used it last year, what I learned, and how I'm going to use it this year in Algebra 1.

This was my breakthrough unit last year with my students. It anchored our entire Chapter 2 - Real Numbers unit and really solidified both conceptual understanding and procedural fluency in working with real numbers, the real number line, operations on real numbers, and both talking and writing about working with real numbers. We named it Life on the Number Line.

Here's how the actual gameboards, cards, and blank worksheets looks in action (sans students):

I sure hope I didn't make a bonehead mistake in my example problem!

The most effective thing about this activity was that it compressed a great deal of different dimensions of learning into the same activity, requiring learners to work simultaneously with the same material in multiple dimensions. So for example, they had to think about positive and negative numbers directionally in addition to using them computationally. They had to translate from words into math and then calculate (and sometimes reason) their way to a conclusion. They had to represent ideas in visual, verbal, and oral ways. And they had to check their own work to confirm whether or not they could move on, as no external answer key was provided.

Since they played Life on the Number Line for multiple days in groups of three or four players comprising a team who were "competing" in our class standings, learners felt that the game gave them an enormous amount of practice in a very short amount of time. Students also said afterwards that they had liked this activity because it helped them feel very confident about working with the number line and with negative numbers in different contexts.

I also introduced the idea of working toward extra credit as a form of "self-investment" with this game. For each team that completed and checked some large number of problems, I allowed them to earn five extra-credit points that they could "bank" toward the upcoming chapter test. Everyone had to work every problem, and I collected worksheets each day to confirm the work done and the class standings.

What I loved about this idea was that students won either way — either they had the security blanket of knowing they could screw up a test question without it signifying the end of the world, or they got so much practice during class activities that they didn't end up actually needing the five extra credit points!

Students reported that they felt this system gave them an added incentive to find their own intrinsic motivation in playing the game at each new level because it gave them feelings of autonomy, mastery, and purpose in their practice work.

The game boards were beautifully laminated by our fabulous office aide but do not have to be mounted or laminated. The generic/blank worksheets gave students (and me) a clear way of tracking and analyzing their work. And the game cards progressed each day to present a new set of tasks and challenges.

All of these materials are now also posted on the Math Teacher Wiki.

Let me know how these work for you!

UPDATE 10/27/2016: Here is a working link to a zip file of all the components for this: https://drive.google.com/open?id=0B8XS5HkHe5eNNy10MWZVSDNKNnc

WEEK 1: 'Words into Math' Block Game | #made4math

In keeping with my Week 1 emphasis in Algebra 1 on activating prior knowledge of how to translate words into mathematical expressions, equations, or inequalities (or at least gelling some of it back into place), I've also created a "Block" game for practicing 'Words into Math' in my Algebra 1 classes. There are two levels of game cards that correspond to Lessons 1.3 and 1.4 in McDougall Littell Algebra 1 California edition (for those of you playing along at home).

This is a variation on Maria Anderson's wonderful, tic-tac-toe-style "blocking games" (Antiderivative Block, Factor Pair Block, and Exponent Block — using her generic gameboard, rules, and my own game cards for each of these first three games of hers on her web site).

The game can be played in any number of ways — either competitive or collaborative. Students can compete against each other — tic-tac-toe style — to get four of their counters in a row. Or they can simply take turns choosing the problem and working on solving each problem on the whole board.

I've created two levels of "Words into Math Block": Level 1 (purple problem cards) and Level 2 (green problem cards). I use Maria's generic PDF gameboard and print or copy them on colored cardstock or paper. I have learned the hard way to give each level its own color ID as soon as I create the game cards so I can easily recreate the card sets later whenever I need to.

I allow students to use whatever resources they need to during practice activities, so I expect to see those nifty Troublesome Phrase Translator slider sleeves flying during these two days. :-)

All of my materials, plus the photo above (in case you need a model) are on the Math Teacher Wiki.

Students really love these block games! I have a bunch of different "counters" that they can use as their game board markers: little stars (Woodsies from Michael's), circles, and hearts, colorful foam planet/star clusters, and various kinds of beans.

I'm hoping to get my students to be less flummoxed by mathematical language by giving them practice in using it early and often. Enjoy!

Intermezzo - summer reading seminar on The Curious Incident of the Dog in the Night-Time

One of the things I sometimes forget that I love about teaching English is the fact that I get to get adolescents talking and thinking about issues we all feel deeply about. The cool thing about sparking these conversations with young adolescents (by which I mean secondary students, as opposed to college students) is that most of them are just waking up to these issues for the first time in their lives, which means passions run deep. And that means they are ripe for thinking deeply about these issues — more deeply than we often give them credit for.

In my seminar this afternoon on The Curious Incident of the Dog in the Night-Time, I wanted to get students to develop for themselves a question that I think is fundamental to citizenship in a functioning democracy — specifically, who is it who, in different contexts, gets to decide what is to be considered "normal," and therefore acceptable?

The Curious Incident is an interesting reading choice for incoming 9th graders because the narrator, Christopher, is a young man on the autistic spectrum who easily qualifies in students' eyes as an outsider. In spite of extremely high math and science aptitude and achievement (preparing to take his maths A-levels at age 15), he is prevented from attending a mainstream secondary school. Instead, his social and emotional impairments have caused him to be marginalized into a special needs school where even he can see that most of the students are far less socially and emotionally functional than he is.

The students in my seminar are outgoing 8th graders I have known for a full year now. Because I teach both math and English, I have actually taught most of them for at least one period a day, and in many cases, for two periods a day. Which is to say, I know them unusually well for a casual summer reading seminar. I also know the ELA curriculum they have all just finished working through because I helped to develop some of it, and this gave me a lot of touchstones to draw on in our discussions. However, I would like to point out that this kind of lesson could work well with almost any group of students, since it centers on one of the main issues in adolescent life: namely, issues of fairness.

The activity I set up for today involved small groups doing "detective work" on five related thematic issues in the novel and then sharing out their findings with the rest of the group. The five thematic areas were:

• Belief systems: conventional religious beliefs versus Christopher's own unique belief system
• "Normal" behavior and how we judge differences in the behavior of others
• The nature of human memory: Christopher's beliefs about his own memory and other people's
• The significance of Christopher's dream in the novel
• The interrelated issues of truth, truthfulness, and trust

To get things started, I modeled the investigative process using issue #2 - what is considered "normal" behavior and who gets to decide whose behavior in a society will be considered "normal" and whose will be considered "deviant" (or sub-normal). Students needed a little more context on what autism is and how it can affect a young person socially, so we did a little quick internet-based research (thank you, iPhone!) on the autistic spectrum and what it means to be higher-functioning or less-high-functioning. Students zoomed in on the exact contradiction I had hoped — but have learned never to expect— they would target: the question of varying standards of "Behavior" that govern the judgment of and consequences for actions of adults (such as Christopher's father) and those of a kid like Christopher himself. Fairness is something that most adolescents feel strongly about, even when they are generally treated quite fairly, as most of these students usually are. [SPOILER ALERT: stop reading here if you haven't read the novel and don't want to know what happens as it progresses].

The kids were really quite exercised about the fact that while Christopher was the one labeled as having "Problem Behavior," his father committed a number of acts that we all agreed had to qualify as "Problem Behavior," including (a) killing an innocent dog, (b) lying to his son about the boy's mother being dead, and (c) hiding her letters to him to maintain the lie of her having died of an improbable illness. These were just the big issues.

So we circled around until we needed to land on a word they did not yet have in their vocabulary: arbitrary. Our dictionary manager looked the word up and read its several definitions to the group while we tried it on for size. "Arbitrary" definitely seemed to fit the contradictory categorizations of behavior of adults versus of Christopher in the novel. There was no way around the fact that the rules seemed both arbitrary and easily manipulated by the adults — far more easily than by Christopher himself. The notion that society's rules are subjective constructs, influenced by the personal beliefs and opinions of human beings, struck them as a significant new insight.

This part of the discussion led to a second insight I'd been hoping we might arrive at: the fact that whoever is in power gets to determine what will be considered normal. The idea of differences in power is something most of these students have not encountered much, except in the context of adults/parents versus adolescents/children. So for many of them, it was a new idea to think that these inequities could extend outside of families to other social relationships and interactions.

Their investigations and presentations were rich and quite thorough. To save time, I provided more scaffolding in the worksheets (chapter and/or page references) than I would have if we had been doing the project over several class periods. Still, I was pleased that they were able to reread their sections closely, draw on their annotations and notes, and quickly assemble arguments about each of these thematic areas that were supported by evidence from the text.

Having just come back from Twitter Math Camp, and still being immersed in rich dialogue about math pedagogy and equity, the conversation reminded me that every subject area in which we teach is a powerful opportunity to engage with students. At Twitter Math Camp, I loved being able to drop directly into the middle of an ongoing conversation I've been having with colleagues in the Math Twitterblogosphere for months or years in the virtual realm. In our seminar today, I loved being able to drop directly back into pretty advanced investigation with these students because I had already done so much formative assessment with them over the past year in this same kind of context.

These conversations are a gift of deep teaching and learning, and they are a reminder of what gets lost when policymakers become enchanted with the kind of magical thinking that allows them to chase the illusions of quick fixes and silver bullets such as plopping kids down in front of a giant library of videotaped lectures. Developing a library of tutorial videos may be a worthwhile archival goal, but it is no substitute for the magic that can happen when good and authentic teaching connects with a ready student.