More Hands on the Lever: 12 Hours in August

    Last spring, when a supervisor asked me to present a summer workshop on how to implement 3-Act tasks and estimation180 in elementary classrooms, my first response was, "Theresa has to do it with me."  My second was, "We'll need more than just one day."  Theresa was ready and willing, the supervisor agreed, and here's how it got advertised:

   In late June Theresa and I outlined our plan, using what we had learned from running our PLC.  We would have 12 hours over 3 days in early August.  Our audience would be a mix of  K-5 classroom teachers, district instructional coaches, and fellow math specialists.  Since all but 3 of the 24 teachers attending would have little or no 3-Act or estimation180 experience, I started to think of the workshop as "Intro to MTBoS", with the image of someone dipping their toe into the water.
     We decided to start everyone off with a 3-Act, then work backwards and deconstruct the process by focusing on the important parts of Act 1: noticing and wondering and estimating.  We'd do a 3-Act each day, allow for plenty of discussion and text study, and build in time for teachers to find resources in the computer lab.
   And then I went to Twitter Math Camp.

Everyone raising their hand paid for their room or travel to attend #tmc15. What do you notice and wonder? pic.twitter.com/nNOJfCNj6x

— Levi Patrick (@_levi_) July 25, 2015

      Being immersed in that amazing community of 200 committed, smart, funny, passionate, and inclusive educators, and watching their presentations,  made me realize that what Theresa and I had planned just wasn't going to cut it.  We needed more.  Pumped on adrenaline, my mind raced most of the days and nights in Claremont:

@JSchwartz10a at least you got some sleep. My roommate liked to get up at 4am. @Veganmathbeagle @cmmteach

— Graham Fletcher (@gfletchy) August 6, 2015

     I was determined to bring more of the TMC excitement back to New Jersey.  Fortunately, I still had about a week to prepare, and TMC attendee Brian Bushart was already running a PD session in his district and blogging about it.  Although I was afraid we might be pressed for time, Theresa agreed to two important additions:

• Putting a frame around the workshop by demonstrating how the instructional practices and activities we were promoting would help students (and their teachers) build a healthy and positive emotional relationship to math.  This was something we had done in the PLC, and that Brian had done in his training.
• Introducing the participants to important MTBoS figures by 1) calling them out by name, and 2) interspersing video clips throughout the PD experience.

Day 1:

    We kicked things off with an extended quote from Tracy Zager's Shadowcon talk, "Breaking the Cycle".  Tracy was generous in allowing me to use some of her slides, and the sometimes hard to confront facts regarding elementary school teachers and math anxiety was put on the table within minutes of our 8:30 AM start.  Although I had made my own struggle with math anxiety public in a post last year, most of the teachers present were unfamiliar with my story, and I took the opportunity to recount my unpleasant experiences in school, complete with evidence:

One example, taken from my first grade report card.  The older I got, the more confused I became.

     During the discussion that followed, some participants admitted to similar experiences.  But I was struck by a comment from a fellow specialist.  

     "I never had any trouble with math in school," she explained.  "But I have vivid memories of watching classmates struggle after being called up to the blackboard to work out problems in front of the class.  I felt embarrassed and ashamed for them."

    It was a perfect lead-in to Tracy's Shadowcon slide,  which I used to define our mission:

A call to action.

     After setting the table, we had them jump right into our first 3-Act, Andrew Stadel's classic File Cabinet:

We grouped them randomly, and ran the lesson as if they were students in our class.  We asked them to jot down any questions, reflections, comments, or reactions on a separate piece of paper.

     After a break, and a discussion centered around the notes they had taken, we began deconstructing Act 1 by turning our attention to noticing and wondering.  The notice and wonder prompt is so simple, yet so incredibly powerful.  As the very first step in the 3-Act, it starts the entire process by providing the task with its focus question.  The better a class is at generating mathematical wonderings, the more likely they are to generate the necessary focus question.  That's why I wanted teachers to see it as a discrete activity, one that can be used in a variety of ways.

We practiced with pictures...

 
  And then turned our attention to one of my pet peeves: the traditional "math message".  We explored what it would be like to tweak math messages with a notice and wonder prompt:

   
and...

   We even explored using the prompt to introduce games:

This is a Factor Captor game board, minus any indication that it has anything to do with being a game.  Lots to notice and wonder about here, before any talk about rules or directions.

     At this point, we felt they were ready to meet Annie Fetter.  We took a look at her Ignite talk, Ever Wonder What They'd Notice? (if only someone would ask)




  By then the teachers were ready to head over to the computer lab.  Their assignment: get in grade level teams, look over the new Everyday Math on-line Teacher's Guide, and find a math message, game board, or other resource and change it by adding a notice and wonder prompt.  But before they left I gave them their homework assignment: Take a picture that might inspire some mathematical noticing and wondering, and e-mail it to me.
  Within five minutes after the session ended, I had 3 teachers submit pictures.  By 10 PM that evening, 23 out of 24 had completed their homework.  I felt that the response was a good sign that the teachers were excited about the session.

Day 2:
 
     Theresa and I decided to start Day 2 by introducing the group to Dan Meyer, the originator of the 3-Act task. Four years ago I happened to stumble on  Dan's Ted Talk Math Class Needs a Makeover, and watching it (along with reading Paul Lockhart's A Mathematician's Lament)  was my Road to Damascus moment.  It has over 2 million views, and I joked that at least 1 million of them were mine:


   
 
     We acknowledged the enthusiasm everyone brought to their homework assignment, and I asked the group to look at this submission:

It prompted some great noticing, as well as some wonderings that had 3-Act potential, such as: How heavy was the rack of weights? and How many different ways could the weights be combined for a 100 lb lift?

   We then turned our attention to a math message that one of the fourth grade teachers had found the day before:

Many kids would not even get beyond the first few sentences before disengaging and shutting down.  Text-heavy and full of pseudo-context, it begged for a makeover.  It provoked an interesting discussion, and some suggestions were floated for altering the task to lower the barrier to entry.

We finished up our exploration into noticing and wondering with some text study, and here I chose this user-friendly guide provided by The Math Forum.
       The day's 3-Act was Lisa Anglea's Piggy Bank (Found here in the Georgia Frameworks, Grade 3, unit 1, pgs. 57-62.)  This is a favorite of mine; I used it in all our grade 2 and 3 classrooms last year. The noticings and wonderings were decidedly more "mathy", a tribute to all the work we had done. And rather than random groups, Theresa and I decided to allow the participants to work with whomever they pleased.
      Another benefit to using Piggy Bank was the fact that two of the teachers in the workshop had seen the lesson in action, and were able to explain exactly how it played out in their classrooms.  And I had brought along some student work samples I had collected and saved.  The anecdotal observations from fellow classroom teachers, plus the look at the samples, sparked a lively discussion, and helped the participants visualize what a 3-Act would look like in their classrooms, as well as realize that implementing a 3-Act was not really as complicated or intimidating as some of them may have thought.
     After a break, we turned our attention to estimation180.  As readers know, I've lived and breathed this for several years.  Open number lines, too highs, too lows, and just rights, justifiable reasons, discussions, embedded content...it is, as Graham Fletcher says:

Thanks Graham!

     As an introduction, I chose to work the group through Day 116 (as an example of a standard task with a picture reveal), Day 98 (as an example of a task with a video reveal that would allow a teacher to pause the video periodically for students to reevaluate), and Days 51-53 (as an example of a series).  I also showed them some homemade tasks collected on our district's shared drive.  Since we had grade levels K-5 represented, we had a discussion about appropriate expectations and implementation.
    Before letting the teacher's loose again in the computer lab to explore the site and find tasks they'd like to use with their classes, I introduced them to man behind it all, Andrew Stadel:





     We gathered back together and I had the teachers share what they had found.  The excitement and energy that had been building all day was evident in their enthusiasm for what they had discovered, and I knew that they were looking forward to the final day.  And that was a good thing, because we needed one more day to seal the deal.

Day 3
   Theresa and I decided to start Day 3 by putting the hammer down.  We took a slight detour from the workshop description and introduced the participants to this signature MTBoS activity...

     WODB is emblematic of what I think of as "the MTBoS ethos": low floor/high ceiling, engaging, multiple correct responses, virtually impossible to be wrong, embedded content, tasks submitted by teachers, collected on a site created and curated by a teacher (Mary Bourassa), and completely and totally free of charge.
     The participants loved it.  I mean, it's hardly fair.  I don't care what kind of teacher you are, or how long you've been at it, or what grade you teach: if something like this doesn't make you wish that school was in session so you could try it right away with your class, then I don't know what will.
     We tried several more examples, at which point I thought they'd like to meet another important MTBoS figure, and one who'd been integral in popularizing the WODB task: Christopher Danielson.





    For their final 3-act, Theresa and I chose Graham Fletcher's Shark Bait.  There were kindergarten and first grade teachers present, and we felt that it was important they see a task designed with their students in mind.  Theresa and I had given this one a workout in our kindergarten classrooms last spring, so it was familiar and we knew what to expect.  And again, this time cribbing from my blog post, we had work samples to look at, discuss, and help teachers visualize what it would look like in practice.  (Note to self: Next time make sure you bring a supply of unifix cubes.)  With three 3-Acts now under their belts, we felt they were ready to do some text study, and here we chose the Effective Instructional Practices Guide from the Georgia Frameworks, which includes a wonderful guide to implementing these lessons.
     With roughly 2 hours left, the teachers were eager to get into the lab and work with their grade-level colleagues to find 3-Act tasks. Theresa and I guided them to several of our "go-to" spots: the incomparable Georgia Frameworks, Dan's 101qs, and both Graham Fletcher's and Kyle Pearce's 3-Act collections.   We circulated among the working groups answering questions, and offering advice, opinions, and encouragement.  There were excited cries as teachers found meaningful resources, and I was glad that they were beginning to feel the thrill of MTBoS discovery that by now I knew so well, but that still gives me the feeling of, "I wish I had some kids in front of me right now so I could try this out!"   It wasn't easy getting everybody back.  But I still had some important business to conduct.
     Many teachers volunteered to share what they had found.  Even though they wouldn't be in front of students for another month, I felt optimistic that at least some of the learning would stick.  We took a look back at the slide that I used on Day 1 to frame our work:

Tracy's call to action.  It seemed possible!

I made my pitch:

There was talk at TMC about growing the number of elementary school teachers in the community.  I hoped that after three days, a few more could be added to our ranks.

    I talked about the incredible colleagues...

That's Christopher Danielson's phrase.

 ...and the support, encouragement, and growth they would find there.

More tweeps.

   The final word went to Justin Lanier.  His passionate and humane Ignite talk said everything I wanted to say, only more eloquently:

       
   

     In his talk, Justin paraphrases Archimedes: "If you give me a lever long enough, and a place to stand, I can move the world."  Justin likes, "The optimism and the vastness of that vision," and so do I. And I think he would agree that the more people we can get pushing down on that lever, the more likely it will be that the world will move.

More hands on the lever.  Teachers show off their prizes: estimation180 stickers!

 
     
   
   

On Re-reading Jonathan Kozol

Met Jonathan Kozol tonite. Ended the evening, "Why do we go to school?" answer in @jschwartz10a post. to find joy. https://t.co/wvpx1DfK21

— ekazemi (@ekazemi) June 30, 2015

    The above tweet from Elham Kazemi, linking me with Jonathan Kozol, is the source of profound feelings of honor and humility.  It turns out that Jonathan Kozol, and his book Death at an Early Age,  played an important and formative role in my development as a teacher.
    Death at an Early Age was written when Kozol was 28 years old.  It describes his experience teaching fourth grade during the 1964-1965 school year at Christopher Gibson Elementary, which was located between the struggling Dorchester and Roxbury neighborhoods in the city of Boston. The book was published in 1967, and in 1968 it won the National Book Award.
     Elham's tweet inspired me to dig out my copy:

My edition, from 1985, carried a "20 years later" epilogue from Kozol.  I had picked it up on the recommendation of one of my education professors at the University of Arizona.

   Although I knew its exact spot on my bookshelf, I hadn't opened it in 30 years.  And while I couldn't remember details, I did recall that it had a tremendous effect on me.  I was a pre-service teacher at the time, pursuing a path somewhat at odds with family expectations, and if I needed any validation that I had chosen the right career, reading this book convinced me that I had made the correct choice.  What would it be like to read it again, 30 years later, with 30 years of teaching  behind me?  I had to find out.
   Kozol's description of his experience at this inner-city elementary school is powerful and heartbreaking.  Institutional racism, crumbling infrastructure (a bank of windows collapses into his classroom, narrowly missing a student's head), corporal punishment, outdated textbooks, overcrowding (some classes reach 40 students, others are held in a urine-smelling basement or squeezed into hallways, and Kozol teaches his class with three others running simultaneously in the auditorium), and a revolving door of substitutes (one class has 7 in 10 days) are all described in harrowing detail.
     In an attempt to reach his students with something meaningful, Kozol reads them a Langston Hughes poem called "Ballad of the Landlord".  They are spellbound.  Some ask for copies of the poem to take home and memorize.  But with just 8 days left before the school year is scheduled to finish, Kozol is called into the principal's office and informed that he is being fired for "curriculum deviation".  He is asked to leave the school grounds without saying goodbye to his students.  The poem is not in the approved grade four "Course of Study".
    Jonathan Kozol's experience inspired him to explore the nexus of poverty and education, and he continued to report on, write about, and advocate for children in the most distressed corners of our country.  In 1991, after reading his book Savage Inequalities, I was inspired to write him a letter, in which I quoted some lines from John Dewey's The School and Society:

     What the best and wisest parent wants for his own child, that must the community want for all its children.  Any other ideal for our schools is narrow and unlovely; acted upon it destroys our democracy.

     Several weeks later I received a reply:

It was my intention to bring this note, along with my copy of the book, to the 2012 NJEA convention in  Atlantic City, where Kozol was to deliver the keynote address.  Hurricane Sandy had other plans.

     Jonathan Kozol has spent his life championing the economically disadvantaged and the educationally under-served, bearing witness and forcing us to confront unpleasant truths about our country and our society.  I've spent my career in a relatively privileged, suburban school district, and would never, even for a minute, pretend I have the courage to work in a school like Kozol describes in Death at an Early Age, or in the communities that he describes in Savage Inequalities.  They existed in 1965, and in 1991, and they exist today.
     Looking back over a 30 year career of grading papers, planning and delivering lessons, administering assessments, parent-teacher conferences, field trips, class management schemes, faculty and committee meetings, workshops, after school activities, curriculum writing, report cards, and the thousand other things, both big and small, that make up a teaching life, I think I know what I learned from Jonathan Kozol in those first, formative years: To remember that my students are, first and foremost, human beings.  To remember that they are much more than the sum total of their test scores.  To remember that they have abilities and talents that do not always manifest themselves in a school setting.  To remember that they have wonderfully complicated inner lives.  To remember that they deserve to be treated with humanity.
     I know there have been times over the course of 30 years when I've fallen short.  But maybe it's the Jonathan Kozol in me that has provided the inspiration for my current work as a math specialist: to take a subject that often has children asking, "Why do we go to school?" and try to answer, as Elham put it in her tweet, "To find joy."

Thank you.

   
   
 
   
     
 

Learning to Fish

     The 2014-2015 school year is now over.

      And while the year held its share of challenges, there were also many highlights:

• We made a start at putting an end to the traditional Math Message:

Much better than the status quo.

• I got to participate in an amazing PD experience:

Andrew Stadel made me figure out how many times a swing's chain would wrap around a pole.

• We got hooked on 3-Acts, from kindergarten to fifth grade, and we even made our own:

The faculty lounge coffee drinkers had to go without sugar and sweeteners for a few weeks.

• I met Bill McCallum and Phil Daro, and got their autographs :

How much do you think I could get for this on ebay?

     But overall I am most proud of my PLC.  This past school year, it consisted of myself, my co-specialist Theresa, our two fifth grade math teachers, our fourth grade math teacher,  one each of our third and second grade teachers, and one of the district's elementary TAG (Talented and Gifted) teachers.  My supervisor also sat in on several of our meetings.  We met once a month, for about an hour, alternating before and after school.  Our stated objective was to gain a deeper understanding of the Danielson Framework's domain 3b: Using Questioning and Discussion Techniques, but informally, I thought of our sessions as MTBoS 101.

     In September, inspired by Justin Lanier's course Math is Personal, we examined our own personal relationships with mathematics, and reflected on how those relationships impact our teaching practice. 
     In October, we watched Annie Fetter's Ignite talk, Ever Wonder What They'd Notice (If Only Someone Would Ask), discussed the benefits and advantages of using the noticing and wondering prompt as a way to open up student thinking in math class, and left with a homework assignment to use the prompt in class and report back the following month.
    During the November meeting, participants shared their experiences using the notice and wonder prompt, in subjects ranging from math to science to social studies.  We used this crib sheet from The Math Forum during our debriefing.
    The December meeting was a highlight.  I engaged the PLC participants in Andrew Stadel's File Cabinet 3-Act, asking them to work out the aspects of the task while at the same time keeping notes on their reflections, comments, and questions.  I was a little nervous during this one.  My supervisor was there, and was using the session as one of my two observations.

The group enjoyed sharing their solution strategies.  And my supervisor loved it.  It was his first experience with a 3-Act, and he later told me he used it during a department meeting at the middle school.

       At the January meeting we debriefed the File Cabinet 3-Act.   Several of the participants expressed feelings of nervousness and anxiety during the experience, and we discussed the importance of putting ourselves in the place of our students and maintaining empathy for their emotions.  The feedback was overwhelmingly positive, especially for the thinking required during Act 2, where the students need to develop questions.  As one participant said, "It forces kids to use different muscles."  Yes!  The PLC also liked the fact that 3-Act tasks embed many different skills in a single problem, and expressed excitement about the prospect of integrating more 3-Act tasks into their practice.
     We kept the 3-Act momentum  going in February.  We used this comprehensive guide from the Georgia Frameworks as our discussion text, and focused on different ways to put students in collaborative groups during Act 2.  Participants were given time to explore the trove of 3-Act tasks created and collected here, here, here, and here.
     We spent the following month taking and submitting pictures that might inspire notice and wonder prompts, estimation activities, or even 3-Act tasks.  I collected them in a file on the district's shared drive, and during the March meeting we took a look at our efforts.  Some samples:

Jane submitted this picture, taken at her son's birthday party.  The group felt this had the potential to spark a lot of mathematical thinking, including: How many slices?  Unit cost per slice?  How tall is the stack?  How about categorize by topping and find fractional part of whole?

Jeff submitted this picture...

...followed by this close-up.  This also generated a lot of mathematical thinking, from: How much trash can the bin hold?  to: How much milk would you have to drink to make a trash can?

I encouraged the participants to continue taking mathematically inspiring pictures.  Our cell phone cameras are powerful tools!  My supervisor framed this activity in a conversation we had soon after this session by quoting for me the old saying: "Give a man a fish and he eats for a day. Teach a man to fish and he eats for a lifetime."  He made me realize just how empowering it is to be a creator of content, not just a delivery mechanism.  I wanted the PLC participants to feel that power.
     After the long, cold winter, the PLC was relieved to see signs of spring.  In April we explored the rich discussion opportunities afforded by Which One Doesn't Belong? tasks. We started with one that I made:

and discussed an example from Christopher Danielson's book:

    
The enthusiasm was contagious.  Several days later Larissa was proud to show me one that she had created...

...and I encouraged her to submit it to the site.  She learned how to fish!

     In May we dipped our feet in Jessica Shumway's book, Number Sense Routines:

I like this book so much that I had my principal order copies for all our primary grade teachers to use in our PLC next year.

I was interested in exploring the use of counting circles.  We started by doing a counting circle of our own, starting at 1 and stopping at 18 (there were 18 days of school left.)  Theresa recorded the count on the board, and the group noticed some interesting patterns.  We looked at several examples I had collected during the school year:

Grade 1

Grade 5

Grade 3

      During the June meeting, the PLC took a reflective look back and shared their important "takeaways".   Listening to the discussion, I could only hope that the teachers would carry their enthusiasm for noticing and wondering, 3-Act tasks, and an all-around more student-centered, engaging approach to teaching mathematics into the following year, that they would make these activities an integral part of their practice, and that they would take them and make them their own.     

And everyone got a present!

"Nobody Puts Kindergarten in the Corner!"

    If the MTBoS has a signature teaching move, it's got to be the 3-Act.  It incorporates so much of the MTBoS ethos: noticing and wondering, estimating, premium student engagement and student-directed learning, collaboration, low floors and high ceilings...a good 3-Act wraps it all up in one beautiful  package.
    Created and spread by middle and high school teachers like Dan Meyer, Andrew Stadel, and Kyle Pearce, until somewhat recently the pickings have been slim for us primary grade folk.
    Enter Graham Fletcher.  Graham has worked on developing 3-Acts for the elementary school set, and he hasn't neglected kindergarten.  One look at Shark Bait and I knew I had to give it a spin.  So last month, armed with some baskets of unifix cubes...

...I set off for kindergarten.

ACT 1: The Question





Seated on the carpet in the front of the room, the kindergartners engaged immediately.  I mean, aren't worms right in that 5 year old wheelhouse?    They clamored for another viewing, and another one after that.  I had them do some noticing and wondering:

• The worm is long!
• That worm is disgusting!
• Why is it raining?  
• Is that worm real?
• I saw a really big worm once!  Bigger than that one!

and, finally, the focus question:

• How many cubes will it take to make that worm?

I had the kids make some estimates, which got recorded on the board:

ACT 2: The Work
      
     I explained to the kids that I was going to give them some clues to help them figure out the answer.  In a true 3-Act, the students would need to request the information; here I decided simply  to provide it.  It was their first experience, and I did not want the task to become too overwhelming.   Here's what Graham provided for Act 2:

I showed this to their teacher several days before the lesson.  She was concerned that the kids might not be able to read all the words.  She made a suggestion...

...and Theresa  modified it by adding some color hints.  She ran off a bunch of copies and laminated them.

Their teacher and I had discussed whether or not to read it out loud.  The teacher felt the students still might have some difficulty, but I wanted to see what would happen if we just handed it out.  So I asked the kids to go back to their tables, distributed the clues, and let them have at it.

They got right to work.

There was very little problem.  The struggling readers got help from their classmates.

They compared their worms.  Some kids were a little short.

ACT 3: The Big Reveal

     The kids brought their unifix cube worms back to the carpet for the reveal:






We counted the cubes, both by ones and by fives (plus 2) and established the correct answer as 22 cubes.  The kids who had forgotten the extra oranges went back to their baskets and retrieved the missing cubes, and kids that had too many put the extras back.  Again, they insisted on viewing the video several times, and paid careful attention at the end as the worm began to extend.

ACT 4: The Sequel
     What's a 3-Act without a sequel?  For this task, I wanted the kids to draw and then measure their their own worms, using whatever combination of cubes they wished, then record the results, using whatever way made sense to them.  They dug right in!

A standard response.  This student made a worm 22 cubes long like the worm in the video.

This student made groups of 5 and included an addition number model!

This student used a different method.

Worms have segments, right?

Clever.

Because he did not group like colors together, this student had a counting challenge.  Can you figure out his method?

.  My favorite worm.  It's partly underground!

 It was time for me to go, so I had the kids come back to the carpet for a final activity: a counting circle, from 1 to 22 and then backwards from 22 to 1.  To follow up, I encouraged the teacher to try having the kids order their worms from smallest to largest.

Act 5: The Reflection
   I had several thoughts looking back on the lesson:

• The task was perfectly suited to kindergarten.  
• I was glad that I hadn't helped them read the clues in Act 2, but that I had provided them with the color hints.
• Maybe I should have pushed them more in Act 2 to come up with what they needed to answer the question, instead of going straight to the clues. I've admitted that my feel for kindergarten isn't all that great, although it's gotten better this year because I've spent more time there.  I think it's time to level up my expectations.  As one of our great kindergarten teachers likes to say, "Nobody puts kindergarten in the corner!"
• I was struck by their resourcefulness.  I told their teacher that I was impressed by how well the kids spelled the color words; that I thought they would need more help.  Turns out they were copying from the clue cards, as well as from the color words that were posted on a wall in the back of the room. And I loved that there was so much diversity in the ways they used the cubes to measure, and in the way they recorded their results.

     One final reflection: The 3-Act lesson, which reflects so much of what's good about MTBoS project, has another huge selling point: its adaptability.  So while the mathematics of the task changes to reflect the competencies and standards attached to the particular grade level, the core template remains the same.  From kindergarten through high school and beyond, it's something every math teacher should have in his or her tool kit.