Wednesday, September 5, 2018

For Those Going Back

      It's back-to-school week in New Jersey.  But not for me.  Over a million students and over a hundred thousand teachers.  Crossing guards and lunch ladies.  Principals and paras.  Bus drivers and van drivers.  Security officers and social workers.  LDTCs and VPs.  But not me.
     This is my second back-to-school as a retired public educator.  At my wife's urging, I put in one year past my pension eligible 30 years of service and 55 years of age.  One final year spent soaking it all up in the only school in the only district I ever worked in: the last teacher orientation, the last room set-up, the last first day, the last back-to school night, the last picture day, the last Halloween parade, the last holiday party, the last assembly, the last parent-teacher conference, the last field day, the last last day.  One year of closure.  I haven't been back. 
     I'm still in schools, but it's not the same.  More a hired gun.  If I miss anything it's the sense of family you build with your colleagues, with your students, with the wider school community.  That's what 31 years in the same school will do.  So I miss that.  That, and all the noise.  The commotion and the hubbub you get from 400-plus kids and 80-plus full and part-time staff together in a brick building not too far from Exit 9 off the New Jersey Turnpike.
     I want you to know I'm thinking about you all.
     So for everyone going back, in this season of going back, I wish you a school year filled with curiosity, wonder, and human connection.  Stay safe.     
          Across the open mouth of the tent Nick fixed cheesecloth to keep out mosquitoes.  He crawled inside under the mosquito bar with various things from the pack to put at the head of the bed under the slant of the canvas.  Inside the tent the light came through the brown canvas.  It smelled pleasantly of canvas.  Already there was something mysterious and homelike.  Nick was happy as he crawled inside the tent.  He had not been unhappy all day.  This was different though.  Now things were done.  There had been this to do.  Now it was done.  It had been a hard trip.  He was very tired.  That was done.  He had made his camp.  He was settled.  Nothing could touch him.  It was a good place to camp.  He was there, in the good place.  He was in his home where he had made it.  Now he was hungry.

Ernest Hemingway
Big Two-Hearted River: Part I


Monday, August 6, 2018

TMC '18: A Photo Retrospective

I-71 North.  Hello Cleveland!

First-timer Jamie Spinato.  I met Jamie when she student taught at my school.  She got a job in the district, participated in one of my summer workshops, and signed on to twitter.  I convinced her to try TMC, and we co-presented a session on Friday.

Opening Ceremonies.  Lisa reminds us all to be on time.  

Chase Orton led my morning session on Japanese lesson study.  Nobody pulls off a cap like Chase.

Brian Miller led a session on how to use geometry to draw a human eye.

Mine didn't come out so good.  

Brian Miller, Graham Fletcher, and Sheri Walker

Nicole Paris, Wendy Menard, Annie Perkins, and Hedge

Wendy Menard, Jamie, and Edmund Harriss grab lunch.

Jason Henry.  We need Lisa, and Lisa needs Jason.  Ergo we need Jason.
Not exactly sure what Max has in mind here, but it looks like Barbie Bungee without the bungee.

A few blocks from the hotel.  This was a good place for breakfast.  They had fresh squeezed orange juice.

What do you notice?  What are you wondering?
Greta and Jamie outside Phoenix Coffee.  This was a few blocks from the school, and another good place to get breakfast.

John Golden and Elizabeth Statmore share a moment.

Kent Haines did a session on Exploding Dots.  I kinda get it now.  
Bob Lochel did a session on how to make yucky math topics more fun.  I wish Bob had been one of my high school math teachers.

I mathed.  Thanks Bob!

Dinner with Lisa Bejarano, Amie Albrecht, Nicole Paris, and Chrissy Newell.  Amie came all the way from Australia!

Pretty much everybody wound up at Mitchell's at some point.  Their ice-cream was really good, and I'm an ice-cream snob.  
Dylan Kane made a last minute appearance.  He did a session with Lisa Bejarano.  
Megan Schmidt, Steve Weimar, and Annie Perkins were kind enough to run a flex session on Islamic Geometric Design.  Not bad for my first try!

Ben Sabree was so into it he continued to work on his design on the bus back to the hotel.

Megan did a My Favorite and reminded everyone about the importance of elementary school teachers.  Thanks Megan!

Edmund, Glen Waddell, and John at the Phoenix preparing for their keynote.
Jersey girls Jamie Spinato, Anna Panova, and Sasha Fradkin.  They don't pump gas.

Game night is one of my favorite parts of TMC.  This year, the game of Set was a big hit.  That's Chris Luzniak, Chrissy Newell, and Michelle N.  

Tina Cardone shows off one of her creations.

John O'Malley IV, Glenn Waddell, and a friend exploring tiles.

John Golden finally taught me how to play Magic.  He let me win.

Goodnight TMC '18.  (Photo credit: Tina Cardone)
Where will we be in 2019?  The suspense is killing us!!  

Who's in?

Tuesday, July 31, 2018

Now You Know

     One spring many years ago my principal needed to take some personal time during the week of the grade 5 state standardized test.  As lead teacher (there was no vice-principal), I was nominally in charge, but given the grave importance of the week's events an administrator from central office was sent to help me cover the building.  Not minutes into first day of testing we got a call from the BD room.  One of the students, set off by the stress of the situation, was having a violent, emotional breakdown.  His teacher had removed him from the room and was restraining him in the hallway.  The rest of the students were waiting to continue.  Who would take over the test administration?
     After assessing the situation in the hall, the covering administrator stepped into the breach.  She stayed with the class for the rest of the morning, overseeing the completion of the day's test sections.  At lunch I stopped by the office to see how she had made out.  I found her sitting at the principal's desk, head in hands, visibly shaken.  It looked as if she had been weeping.  She didn't have to say anything.  I knew what the matter was.


     My feelings about high-stakes standardized testing have never been a secret.  Administering them to students was part of my job description, and doing it made me feel morally compromised.  Not having the courage to stand up for my principles, actually becoming a part of a system that was being used discredit myself and my colleagues by weaponizing data in an attempt to delegitimize public education while at the same time causing emotional trauma to children, made me feel powerless, guilty and complicit.  (That's how systems like this are designed.)   Refusing to allow my own children to be used by opting them out helped, but only a little.


        Here's an equation.  See if you can guess what it represents:


     One year I was assigned to administer the NJASK to one of our classified students.  He was a fourth grader at the time.  His IEP stipulated he was to receive the test in a separate room, one-to-one, with all text and questions read aloud and all written responses scribed.  I was chosen to be his test administrator.  The LDTC was asked to vacate her room from 9:00 to 11:30, and it was there we set up shop.  There were actually three of us in the room; myself, the student, and his imaginary friend who stayed under his desk and whom he would occasionally consult.  This went on for an entire week.  Although he answered only a handful of questions correctly (some by lucky guess), he was pretty smart.  He knew he didn't know the answers, but he pretended to try and figure things out.  As much as I encouraged him, and told him that he was putting forth a wonderful effort, I could tell that he knew that I knew that he didn't know much of what was on the test.  I silently prayed he didn't feel he was embarrassing himself in front of me by his performance.  We both did a good job pretending that what was really happening wasn't really happening.  The only way I can describe the experience is to say it was truly surreal.


     Once when I was teaching third grade a kid threw up on his answer booklet.  I had to stop the test administration and call the principal.  The student went to the nurse.  I continued testing and the principal filed an irregularity report.  We had to put the vomited-on test booklet in a plastic baggie and send it back to the state.  I'm not sure what they did with it.  The student had to take a make-up.


     When New Jersey implemented its regimen of testing every single child every single year from grades 3 through 12, the test developed for use was called the NJASK (New Jersey Assessment of Skills and Knowledge).  The summer before the test went "live" I sat for a week in a conference room at a hotel in Monroe with a bunch of other elementary school teachers from the state.  Our job was to read through stacks of booklets containing student responses from the pilot version and, using that as a guide, set cut scores for proficiency.  I was proud to have been selected for the task.  It was an important job, and we took it very seriously.  Towards the end of the week we provided our cut score numbers to the Department of Education and ETS overlords who had been monitoring our work.  They told us to go back to the drawing board.  Why?  Because given our numbers, "Too many students would pass."  It was then I realized that the entire exercise had been a farce.  They could have just set the cut scores themselves.  They were using us as cover.  I protested, and refused to participate in re-setting the cut scores.  After the work was finished, they asked for three volunteers to go before the state Board of Education and present the findings.  I volunteered along with two others.  Guess who didn't get picked to go.


     Remember that equation?  Here's what it means:

      The project of using standardized test scores to evaluate teachers has been discredited.   We've known this for a long time.  The sordid underside of testing industry's scoring practices has been exposed.   We've known that for a long time too.  For a teacher, the results come back too late to be actionable.  And even if they didn't, they still wouldn't help, because if something was wrong I'd have little idea why.  If there is value in using them to evaluate larger populations, then sampling would do the job just fine.  It just isn't necessary to test every single child.  To paraphrase Stephen Krashen, when you go to a doctor for a blood test, he doesn't take all your blood.  To understand why it continues, follow the money.  Billions of dollars have gone to line the pockets of test developers, curriculum and test-prep writers, publishers, and providers, computer software developers and tech companies tasked with bringing school wireless capacities and other technologies up to standardized testing requirements (and of course providing continuing tech support).  This is all in addition to those school operators who profit from the corporatization of education when public schools are shut down.  Thought experiment:  If you had billions of dollars to spend on education, how would you spend it?


     When I found the central office administrator behind the principal's desk that long ago spring,  I wanted to ask, "What did you think went on?  How exactly did you think all that data got harvested?"  But I didn't.  She had witnessed something sad, disturbing, and frightening, and I felt bad for her.  I guess it was her first time.   All I offered was, "Well, now you know."          


Tuesday, July 17, 2018

Commencement Address

     My daughter graduated from high school last month.  (I told you not to worry so much.) Several days before the end of the final term, she brought home her cumulative folder.  It contained absence records, consent and registration forms, proof of residency, various permission slips, and, of course, report cards and standardized test scores.
     I could brag about many of her school accomplishments.  And I don't mean to show off, but here's one I'm especially proud of:

Grade 7 PARCC report.

     Determined not to have our children used by the testing-industrial complex, and inspired by a visit to Washington, DC, where as a family we attended an Occupy the DOE protest and a march to the White House, we made the decision in 2013 to opt-out of our state standardized testing.  We faced pressure from the school, the district, and the state, but our minds were made up.   The superintendent refused our request to have our daughter moved to another room to read, study, or do schoolwork.  She sat at a desk in a classroom hour after hour, day after day, as the rest of her classmates filled in bubbles and wrote constructed responses in their test booklets.  (That first year we learned an invaluable lesson; even if you have no intention of taking the test, you need to actually crack the seal on the booklet.  Day one she had left the book unopened, and we were informed that when the week of testing was over the district would insist she sit for that day's make-up, missing actual instructional class time.  As if we needed any more proof that the system was completely out of control.  Of course now things are different and I'm not sure what the computerized equivalent of cracking the seal might be.) 
    She was bored and self-conscious, but children have suffered much, much worse in displays of civil disobedience.  The following year she did it again, and my son, two years ahead of her in school, did the same.  My hope was that the opt-out movement would grow, ultimately reaching some type of critical mass.  I pictured the entire corrosive system as a giant monster with an insatiable appetite for data.  Data was its fuel.  Data was its sustenance.  It needed data to live.  Withhold the data and the monster would die.  As the years went by the movement did grow, as more students elected to opt out.  And the district softened its policies.  They provided rooms for the refuseniks to read and study while their classmates were testing.  But the critical mass I had hoped for never materialized, and the insanity continues.
     In recent weeks New Jersey has moved to eliminate some of its testing requirements, and I can't help but think we played a small role in making that happen.  Yet federal law still requires that all children starting in grade 3 be tested each and every year.  States can work around the edges, lessen the number of testing days and change the name of the assessment, but the monster still lives, feeding off the data generated by the sweat, tears, and humiliation of hundreds of thousands of children.  They won't be mine.


     The truly educated become conscious.  They become self-aware.  They do not lie to themselves.  They do not pretend that fraud is moral or that corporate greed is good.  They do not claim that the demands of the marketplace can morally justify the hunger of children or denial of medical care to the sick.  They do not throw 6 million families from their homes as the cost of doing business.  Thought is a dialogue with one's inner self.  Those who think ask questions, questions those in authority do not want asked.  They remember who we are, where we came from and where we should go.  They remain eternally skeptical and distrustful of power.  And they know that this moral independence is the only protection from the radical evil that results from collective unconscious.  The capacity to think is the only bulwark against any centralized authority that seeks to impose mindless obedience. 
     ....We must fear, (Hannah) Arendt warned, those whose moral system is built around the structure of blind obedience.  We must fear those who cannot think.  Unconscious civilizations become totalitarian wastelands.

     The path to graduation wasn't always smooth.  Classified the summer between grades 4 and 5, by the time her middle school career was over she would, by sheer force of will, work her way from a self-contained class to a resource room to full declassification.  And despite the continued protestations from the state and the district, she would never take the PARCC.  The earth continued to spin on its axis and circle the sun.  She went to class, did her homework, and took an untold number of school quizzes and tests.   She became a bat-mitzvah, danced, got her driver's license, and worked 20 hours a week as a server in a retirement community dining room (no cash register.) She has attributes that no standardized test can measure, like courage, persistence, and empathy.  What could a PARCC score have possibly told me about her that I didn't already know?  That her teachers didn't already know?  What could taking it possibly do for her except reinforce the notion she was a less than adequate student?  Whose interests would be served?  Ultimately, who would care?  Not any of the six universities that were happy to have her enter with their freshman class.





Wednesday, June 13, 2018

With More Love And Appreciation Than There Are Even Words For

1.  An Epiphany

     This happened one morning, many years ago.  I was driving past one of my town's elementary schools, on the way to work in a neighboring district.  The local teachers were embroiled in contentious contract negotiations, so I wasn't surprised to see them gathered en masse outside the building on a job action, waving signs and chanting.  I honked my horn to show support, and, right at that moment, had an epiphany: "It's all women!  It's like suffragettes protesting for the right to vote!  This isn't a teacher thing, it's a woman thing!"  Then I got to work and forgot about it.

2.  A Creepy Resemblance To An Abusive Husband

     For the last ten years, I've been a covert operative in Women's World, a.k.a. Public School.  I am not a typical elementary teacher.  I am male. 

     So writes Seth Nichols in a recent post titled: Why Teachers Are Walking Out.   Here's Nichols on the recent uprisings in states like Oklahoma, Arizona, North Carolina, and West Virginia:

Women are done being taken advantage of.  That's what this is about.  Don't think that it's a coincidence that mass walk-outs are happening within a year of the #metoo movements, the sex abuse revelations, or the women's marches.  

    About 77% of the nation's teachers are female.  In elementary school it's nearly 90%.  I know exactly what Nichols is talking about; I was an operative in Women's World for 31 years.   Nichols again:

The system, in many places, bears a creepy resemblance to an abusive husband.  If she loses "him" (her job), she feels like she would lose everything.  He constantly tells her she's not good enough, and has spreadsheets with scores to prove it.  He blames her for the kids problems, and offers no real help in fixing them.  But she stays and puts up with him--because she loves the kids.

     The post triggered a memory.  The memory of driving to work one morning, past a school similar to my own, and having an epiphany:  "It's a woman thing!"  But what was that thing?  At the time I didn't know.  I had honked my horn in solidarity.  But it was in solidarity as a fellow teacher, not as a man in solidarity with women.

3.  Standing In The School Parking Lot

     I was a proud, dues paying member of the union my entire teaching career, and served many years as a building rep, with all the responsibilities that position entails.  Although we never went out on strike, I participated in plenty of job actions: writing letters, wearing buttons and shirts, working "to the contract" by entering and/or leaving the building not a minute before/after the negotiated start/end time, showing up and speaking out at Board of Ed meetings, rallying outside central office during negotiation sessions.  During all that time, even standing in the school parking lot, waiting for the clock to strike 8:35, when we all would march into the building together, a male amidst a sea of women, it never occurred to me to connect our labor unrest to gender.

4.  A School Just Like Our School

     On December 14, 2012,  Adam Lanza shot and killed his mother, then drove to Sandy Hook Elementary School in Newtown, Connecticut and shot and killed 20 first graders and six adults.  Then he shot himself in the head.  Teachers and support staff died protecting their students from the gunman.  This hit us especially hard, even harder than all the other ones.  Previous school shootings seemed to take place in high schools or on college campuses; this one took place in an elementary school.  Connecticut was close to New Jersey, geographically, culturally.  Newtown seemed to be like our town.  Sandy Hook seemed like a school just like our school.
     As it happened, the 2012-2013 school year saw another round of heated contract negotiations between my union local and the Board of Education.  One Board of Ed member had two children enrolled at our school.  His work schedule allowed him to be home in the afternoons.  During the days when I had dismissal duty,  I would often see him standing outside, waiting to pick up his kids and walk them home.  As the negotiations dragged on, reports of the Board's intransigence filtered back to us.  I remember standing outside one afternoon, watching him hug his kids as they ran happily out the front door of the school, and, with Sandy Hook still so raw, thinking angrily: Every single adult in that school would act as a human shield, putting their bodies in front of your children.  And you're trying to nickel and dime us on a contract.  You should be ashamed of yourself.
     In subsequent years I had occasion to work with both of his kids, and struck up a cordial relationship with him.  He seemed like a very nice guy.  But I never forgot the feeling I had that afternoon.

5.  Before Or After Columbine?

     When did we start having lockdown drills?  Before or after Columbine?  I think it was after, but I really don't remember.  What's the difference between lockdown doors and lockdown windows again?  When we shelter-in-place, we can go about our normal business inside but just can't go outside, right?  And what's the all-clear code? I know we've been over it again and again at faculty meetings but could we review it one more time?   When did we hire B. and F., the two women who took turns sitting at a desk in the front lobby to check people in?  When did we replace them with shifts of retired cops, who we euphemistically called school resource officers?  When did they build the outer vestibule onto the front of the school?  When did we start carrying walkie-talkies?  When did the back entrance get locked?  When did we get photo IDs to wear?  When did the IDs become swipe cards?  When did they install the security cameras in the hallways?  When did it start to hit us that our job, besides being really hard, could also actually be dangerous?
      On February 14, 2018, Nikolas Cruz killed 14 students and 3 staff members, and wounded 17 others at Marjory Stoneman Douglas High School in Parkland, Florida.  Two days later my former district announced it was hiring armed police officers to supplement the 71 retired law enforcement officers already present in the schools.  According to someone I know still working in the district, there's now an armed officer in each building during school hours, although during Field Day last week the one assigned to his school was patrolling outside.  In a bullet-proof vest.
     Since the announcement there have been 10 shootings at high schools and 1 at a middle school, leaving 14 dead and 24 injured.  This includes the shooting at Santa Fe High School in Santa Fe, Texas.  The shooter used a shotgun and a revolver, and authorities found multiple IEDs, Molotov cocktails, propane tanks, pipe bombs, and other explosives around the school and the parking lot.

6.  ...And Be Prepared To Take Bullets For Them, Too

Seth Nichols:
     It's not about the pay.  It's about all of the ways an entire sector of the country's most selfless givers have been complicit to a system that has evolved to bilk them every way it can: of their time, their money, their energy, and their emotions.  
Pay for it yourself.  
Create it yourself.  
Stay late and put on that function yourself.  
Meet during your time. 
Work during your week-end.
Be kind to people yelling, ignoring, cussing, and hitting you.  Then, make sure they pass the new standards.
...And be prepared to take bullets for them, too.

7.  It's Also About The Pay

     Kayla Melton (an Oklahoma kindergarten teacher) said she had brought in her tax returns returns to show her state senator that in the past three years she had spent twenty-six hundred dollars on school supplies.  The senator, a Republican named Rob Standridge, "wouldn't even look at the returns," Melton said.  
      The Teachers' Strike and the Democratic Revival in Oklahoma, Rivka Galchen
      The New Yorker, June 4-11, 2018
     Is it a coincidence that the season of teacher unrest has coincided with rise the #metoo movement and the Parkland/Santa Fe massacres?  Teachers are tired of being bullied and abused.  (New Jersey teachers know all about that, too.)  They're tired of being told it's all their fault.  And they're tired of hearing about students getting shot.  And they're tired of hearing about teachers getting shot.  They want to be heard.  And they want to get paid.  They should get paid.  It's also about the pay.

8.  Even Though I Am Scared Of The World We Live In I Am Comforted

     On December 17, 2012, three days after Sandy Hook, a grade 3 teacher at my school received an e-mail from the parents of one of her students.  It was addressed to her, the school's student assistance counselor, the principal, and the staff:

...In light of recent events I felt it is necessary to just say thank you for all you do in a day.  I would be a nervous wreck if I did not know that M. was in a school that had such great educators, support staff, and mental health workers.  I am there enough to see how you help people, how you know the children who seem to have behavior challenges and social issues.  I see how the women in the office seem to know exactly which kids need a little TLC and which kids need to be firmly reminded to go back to their classrooms quietly.  I drive into the back parking lot at pick up to see about a dozen support staff, aides, and teachers helping children that need more attention onto busses with care and asking questions that show they know more about the student than their name and serial number.  I truly feel blessed to be part of this school.
     .....You are all doing the very best you can with a lot of students, people who seemingly constantly have an issue, parents that complain there is too much security and then turn around and say it is the school's fault when people are let in and let's face it there is never enough money to educate our children.
     .....I want to take this horrible time in our country and let you know that our most precious gift is in your school every day and that even though I am scared of the world we live in I am comforted knowing the the people of C____ School would be heroes in a time of crisis and are the everyday heroes in an average day.  
     In closing, we as communities ask so much from our schools.  We rely on them to be parent, caregiver, educator, behavior modifier, lunch room monitor, and the list goes on and on.  From the art teacher...who remarkably ALWAYS knows exactly what is going on when, to the Phys Ed teachers...who seem to know exactly what to say to a kid when they are being too wild, to the music teachers who are listening to the horrible noise of those recorders all day and still are smiling at the end of the day, to M, in custodial care who always wishes me a good afternoon, and makes sure that the building looks like a place the kids can be proud of...THANK YOU!!!!!!!
     If anything positive came out of the tragedy in CT.  In our house it was reminding our daughter that you are all part of her team.  THANK YOU, THANK YOU, THANK YOU!
     With more love and appreciation than there are even words for,
      SDN and BN
(And M. too even though she won't know how much you are doing for her till she gets older.)

I saved the e-mail.
Now I know why.







Monday, May 7, 2018

What I Learned In Kindergarten, Part 1: On Pattern Blocks

     8 schools.  24 classrooms.  30 teachers.  Over 500 kids.  I spent a lot of time this year in kindergarten.  Armed with Amy Noelle Parks's Exploring Mathematics Through Play in the Early Childhood Classroom and Julie Sarama and Douglas Clements's Early Childhood Mathematics Education Research, I watched, listened, and learned from some incredibly talented and thoughtful kindergarten teachers and their incredibly talented and thoughtful students.  What should a kindergarten math classroom look like?  What kinds of activities should students be engaged in?  What's the appropriate balance between free exploration and direct teacher instruction?  How are students held accountable for their work and learning?  This first in series of posts will attempt to illustrate how we tried to answer those questions.

   Here are two students working with large, foam pattern blocks.  What are they learning?

pattern blocks free play from Joe Schwartz on Vimeo.

     So much about what these kindergarteners were doing fascinated me.  The quiet way they worked together.  The symmetry.  The way they thought about the negative space.  The trial and error.  The teacher, who you can hear in the background running a guided math group, put no constraints on the activity, and she trusted the the students would work cooperatively and use the pattern blocks in an appropriate way.  That doesn't happen by chance; the teacher made sure that her students knew just how to act in this independent center using these specific materials.

A different classroom.  Again, no teacher direction.  This took four students close to 20 minutes to create.

     Play settings like this, Parks writes,
     Often provide children with far more genuine opportunities to engage in mathematical practices than in formal lessons.  Because in lessons, teachers have clear goals about what they want students to do and understand, and they are able to nudge students in subtle and obvious ways to complete the task.  ("Ivan why don't you see if you can make the smaller rectangle fit?")  In providing these hints, teachers often take over a good deal of the mathematical reasoning, while also cutting down on children's opportunities to persevere on their own.  pgs. 9-10

     As I read, watched, listened, and learned, I began to encourage teachers to explore the many different ways their students could interact with pattern blocks in independent, non-teacher directed centers:

Colored and outlined, I thought of these as "entry level" pattern block puzzles.
No color, just outlines.  The prompt in the top left corner provides a nice way to combine this geometry activity with counting.  I stood by and watched as a student worked for over 10 minutes trying to complete a similar puzzle.  His perseverance was astonishing.

These puzzles are more challenging because all the pattern block outlines are missing.  It was interesting to watch the students work on these.  They struggled at times, like the student in the video below.  Watch how she fills the missing triangular space with a triangle...that doesn't fit in the outline.

pattern block puzzle from Joe Schwartz on Vimeo.

      Some teachers asked their students to create their own pattern block puzzles...

Trace and color.

Matching shapes.

     One teacher I've relied on heavily to help me navigate my way though the world of kindergarten math is Cristina Arena.  She deserves a follow, people!!  She took this idea to another level:

     Her students took pictures of their creations (one way to hold students accountable for their work) and posted them in their Seesaw journals.  Later, she printed them.

     Other teachers combined pattern blocks with playdough.  Another way to help those fine motor skills develop:

Copy a shape.

Do your own thing.

    Navigating their way through Sarama and Clements's progressions for the composition of 2-D shapes, from piece assembler to picture maker, to shape composer and decomposer to everything between and beyond, these students were engaged in valuable learning experiences.  Parks calls them play based contexts (47), and some teachers expressed concern that, should an administrator walk in and see their students playing around with pattern blocks, they might be called to task.  Not to worry, however.  According to Sarama and Clements,
     For early childhood, the area of geometry is the second most important area of mathematics learning.  One could argue that this area--including spatial thinking--is as important as number.  (160)

The kids agree.


Sunday, April 22, 2018

Annie and Joe's NCSM Presentation

     Here's the PDF of the slides.

  • Noticing and Wondering posts can be found here and here.
  • Posts detailing my experiences with the Tell Me Everything You Can... prompt can be found here, here, and here.
  • Read about efforts to connect reading and math here.
  • I blogged about my PLC experience here.
  • Andrew Stadel's File Cabinet Three-Act is here.
  • Numberless Word Problems are here.
  • Tina Cardone's post is here.
  • Max Ray-Riek's Ignite: What We Talk About When We Talk About Teaching is here.

Tuesday, February 20, 2018

"I Never Really Worried About Why."

 Just another day in grade 5, toiling away in the fields of 5.NF.A.1:

Students learned how generate equivalent fractions in grade 4, and are doing just what their teacher has told them to do:

"Whatever you do to the top, you have to do to the bottom."  Whenever I hear this, I think of The Golden Rule.  Do unto the numerator what you would do unto the denominator.  Something like that.
     There's a page to complete.  It encourages the students to apply The Multiplication Rule for Equivalent Fractions, which, in case they forget, is written in the middle of the worksheet:

When the numerator and the denominator of a fraction are multiplied by the same number,  the result is a fraction which is equivalent to the original fraction.

     There are lots of opportunities to practice, and there are fraction circles available so students can model what they've created.

     I approach a student and start talking to him:

Me: Hi!  What are you doing?
Student: Making equivalent fractions.
Me: Great!  How do you do that?
Student: Whatever you do to the top, you have to do to the bottom.
Me: Say more about that.  What do you mean exactly?
Student: So if I have 1/2, and I want to make an equivalent fraction, I have to multiply the numerator by 3 and the denominator by 3 and that will make 3/6.
Me: Sounds like fun!  What would happen if I multiplied the numerator and the denominator by different numbers?
Student: You'd get the wrong answer.
Me: (As I write out  1/2 X 3/5 = 3/10 on a piece of paper) So if I multiply 1 x 3 and 2 x 5 and get 3/10, that would be wrong?
Student: (politely, blithely, but somewhat exasperated) All I know is that the teacher said, "Whatever you do to the top, you have to do to the bottom."  I never really worried about why.

    Later, the math coach and I talked about the interaction.  We filled up a whiteboard with our own equations and visual models, explaining to each other what we understood, or thought we understood, about what was going on in that grade 5 class.  There's lots happening underneath the deceptively simple, oft-repeated phrase Whatever you do to the top, you have to do to the bottom, just as there is underneath the student's reflection that, "I never really worried about why."
    More than the math, it's the I never really worried about why that's had me thinking.  Here's what I've been asking myself:
  • Is there a compelling reason that the student should have to worry about why?  A reason not that we think is important, but that the student thinks is important?
  • Is there a difference between being worried about why and wondering about why?  What exactly did the student mean?  
  • We already know what might make a student worry about why: It's going to be on the test!  You'll have trouble next year if you don't know!  But what has to happen in a classroom to make a student wonder why?  
  • Is it always bad just to follow a rote procedure without understanding, wondering, or worrying about why?  Maybe that needs time to develop.  Maybe it will come later.  
  • What routines or rote procedures do I follow without worrying about why?  Should I be worried about them?  Should I be more curious about them?   
     Many students I encounter are more than happy to share their thinking, their work, their questions, and even, on occasion, their life stories with me.  I'm constantly amazed by this, because I'm often a total stranger to them; some random guy who just happened to stop by their room that day during math class.  This particular 10 year old didn't have much use for me.  He probably had other, more pressing things on his mind, like getting through the assignment as quickly and painlessly as possible.  He was following the teacher's instructions and the directions on the worksheet, and was going to get all the answers on the page correct.  Who was I to add this element of stress into his life?  1/2 x 3/5?  What was that all about?  He had the how, and, in that moment, it was all he needed.  And he seemed pretty happy, maybe because he wasn't going to worry about things that, in his mind, weren't worth worrying about.  But that's OK. Sometimes you just have to damn the torpedoes and do to the bottom whatever you did to the top, and trust that later someone who knows why will help you figure it out.  Who knows?  Maybe you'll figure it out for yourself. 
     On your timetable, not 5.NF.A.1's.