Monday, September 23, 2019

Houston, 1964

     If I appear to be asking too many questions and not providing any answers, I am merely trying to convey the flavor of MSC ( the Manned Spacecraft Center) in 1964, when we had a mandate to fly to the moon but few hard facts with which to work.  It was primarily a question-asking operation at this stage, defining those things which needed answers...

                                            Michael Collins
Carrying the Fire, p. 67

Michael Collins before his flight on Gemini 10, July, 1966


     For my money, the best part of a 3-Act task is Act 2.  After the focus question has been established, but before any math work has been done, Act 2 is where students need to ask the teacher for the information they'll need in order to solve the problem.  It's crucial to the entire enterprise: if the right questions aren't asked the key information will not be provided and the problem will remain unsolved.  For students used to being given all the information they need embedded within the problem (Johnny has 3 apples.  Billy has 4 apples.  How many apples do they have in all?) understanding what information might be useful, and then asking for it, isn't always easy.  But the skill is all-important.

     Michael Collins is best known as the astronaut who didn't land on the moon (he orbited while Armstrong and Aldrin made the first crewed landing on its surface).  Caught up in the excitement this past summer surrounding the 50th anniversary of the moon landing, I read his book Carrying the Fire, in which he describes his experiences as an Air Force pilot, his astronaut training, and his flights aboard Gemini 10 and Apollo 11.  It's compulsively readable and highly recommended!


    I didn't realize just what an incredible accomplishment it was to put a man on the moon until I read Collins's book.  The lives sacrificed (of the fourteen candidates chosen along with Collins in the third astronaut cohort, four would die in training accidents, as well as Grissom, White, and Chaffee in the Apollo 1 cabin fire), the money, resources, time and expertise dedicated to the mission; in 2019 it's hard to imagine our country uniting behind a project of that magnitude.  

     Like a 3-Act task, the project started with an Act 1 focus question: How do we put a man on the moon before the end of the (1960s) decade?  Then came the complicated part: What do we need to know in order to accomplish the goal?  Well, start asking questions.  And remember, one unasked question could put the entire enterprise in jeopardy, so, no pressure.


   Collins's book has questions on nearly every page.  There are way too many to list them all, but here's a very small sample:
  • Would the possible thickness of the dust layer on the moon exceed the height of the lunar module?  
  • Would the static electricity on the lunar module cause the dust to adhere to the lander, obscuring the astronauts' view?
  • How much fuel would be required for a rendezvous and docking around the moon?
  • What would the temperature be in the spacecraft during the constant sunlight on the way to the moon?
  • What would be the effect of weightlessness on body functions?
  • Could a guidance system find its way to the moon and and back again?
  • If the spacecraft experienced communications failure, would the astronauts be able to take over navigational responsibilities?  How accurately would they be able to measure the angle between a selected star and the moon's or earth's horizon?

     In 1964 in Houston a lot of answers had to be provided before any rational person could assess the chance of success.
   Those questions were answered in test chambers, in flying simulators, in labs and factories and classrooms, on computers and chalkboards and notebooks, and in the data collected from each successive space flight, starting with the first Project Mercury flight on May 5, 1961 through Project Gemini, and culminating with the Apollo 11 flight, July 16-24, 1969.  Before the end of the decade.

Collins (center) flanked by Armstrong (left) and Aldrin (right) in quarantine after Apollo 11 splashdown, July 24, 1969.


    Only a select few had the ability and the talent to be able to answer questions like the ones that needed answering on our way to the moon.  Brilliant mathematicians, engineers, physicists, geologists, and doctors crunched the numbers and solved the equations, collected and interpreted the data.  Once given the necessary information, not every student is going to be able to come up with a solution in Act 3 of a 3-Act task.  Am I interested in that?  Yes.  But I'm more interested in Act 2: What questions did you ask?  What information do you think you need to know?  And remember, one unasked question could put the entire enterprise in jeopardy. 


        If I could use only one word to describe the earth as seen from the moon, I would ignore both its size and its color and search for a more elemental quality, that of fragility.  The earth appears "fragile" above all else.  I don't know why, but it does.  As we walk its surface, it seems solid and substantial enough, almost infinite as it extends flatly in all directions.  But from space there is no hint of ruggedness to it; smooth as a billiard ball, it seems delicately poised in its circular journey around the sun, and above all it seems fragile.  Once this concept of apparent earthly fragility is introduced, one questions whether it is real or imagined, and that leads inexorably to an examination of its surface.  There we find things are very fragile indeed.  Is the sea water clean enough to pour over your head, or is there a glaze of oil on its surface?  Is the sky blue and the cloud white, or are both obscured by yellow-brown air-borne filth?  Is the riverbank a delight or an obscenity?  The difference between a blue-and-white planet and a black-and-brown one is delicate indeed.
     ....The beauty of the planet from 100,000 miles should be a goal for all of us, to help in our struggle to make it as it appears to be.

Carrying the Fire, pgs. 471-472

Michael Collins, July, 2019




Thursday, August 8, 2019

The Earth Appears Fragile Above All Else

     Inspired by the 50th anniversary of the moon landing, I read Carrying the Fire, Michael Collins's compelling, funny, honest account of his astronaut training and experiences aboard both the Gemini 10 and historic Apollo 11 space flights.  He had no ghostwriter; every word is his own.  Here are some excerpts.  I put them in verse (and added titles) because they just seemed like poetry to me.  
    Hope he doesn't mind.

Only One Word

I would ignore both its size and its color
and search for a more elemental quality, that of
The earth appears
above all else.
I don't know why but it does.
almost infinite 
as it extends flatly in all directions.
But from space
there is no hint of raggedness to it;
smooth as a billiard ball,
it seems delicately poised 
in its circular journey around the sun,
and above all
it seems

Carrying the Fire

I have been places and done things you simply would not believe, 
I feel like saying;
I have dangled from a cord a hundred miles up;
I have seen the earth eclipsed by the moon, and enjoyed it.
I have seen the sun's true light, unfiltered by any planet's atmosphere.
I have seen the ultimate black of infinity in a stillness undisturbed 
   by any human being.
I have been pierced by cosmic rays on their endless journey from God's place
   to the limits of the universe,
   perhaps there to circle back on themselves
   and on my descendants.  
I have no intention of spending the rest of my life looking backward
   I do have this secret, 
   this precious thing,
   that I will always carry with me.

What Any Pilot Knows Is the Most Useless Measurement

any pilot knows
from ready-room fable 
or bitter experience that
the length of the runway behind him is the most useless measurement he can take;
it's what's up ahead that matters.
We know we cannot dwell 
on those good things that have already happened,
but must keep our minds one step ahead, 
especially now,

In Memoriam: 
June 16, 1961-November 16, 2002
His humor, courage and character are indelible, 
like footprints on the moon.


Thursday, November 1, 2018

"All in All, a Pleasant and Educationally Sound Experience for the Children."

OK, not the first math lesson I taught, but pretty darn close:

December 17, 1986

     At the time this lesson took place, I had been teaching for about 3 1/2 months.  The administrator conducting the observation was Dr. Frank Gardella, the district's math supervisor.  (Frank, who would soon leave East Brunswick, is now a professor at Hunter College in New York City.  Years later we would reconnect during some summer PD at Middlesex County College.)
     Even after reading the write-up, I'm not exactly sure what happened during this lesson.  Did it come out of a teacher's manual?  If not, where did it come from?  Did I make it up?  Clearly it was aimed at developing the relationship between addition and subtraction.   Unifix cubes were handed out.  I tried to connect my students' ideas of what related meant in their lives (family relations) to what it might mean for addition and subtraction equations.  Best I can tell I led the students through some direct modeling with addition facts with sums of 14, matching them to subtraction facts with a minuend of 14, and then did the same with addition facts with sums of 13.  The unifix cubes were used.  I modeled what I wanted on a piece of chart paper and the kids followed my lead at their seats on paper of their own.  It appears that this took 22 minutes.  Then we played a game of "practice races" for 10 minutes.  Finally I collected the unifix cubes and gave a homework sheet.
Here are Frank's comments:

A kind, humane administrator is a blessing for any teacher, first year or otherwise.

         What might I tell my "rookie self"?  What might I do differently?
  • The lesson was very teacher directed.  Now, as an intro, I might throw up some related facts on the board and ask: What do you notice?  What are you wondering?  Allow the kids to do more of the mathematizing.
  • I liked that I used unifix cubes.  But now I would let them explore on their own, in pairs or groups of three.  Maybe something like: Take 13 unifix cubes.  How many different addition and subtraction equations can you make? Then I might walk around and monitor their work, and find some related equations that I could use as examples.  (How did we do that in 1986?)  After consolidating some of the learning, I would give them a choice of using any number up to 20.  
  • I'm not sure what "practice races" are, but I feel confident I wouldn't be doing those.
  • I need a better closure.  Collecting cubes and giving a homework sheet doesn't cut it.  Maybe: Tell me everything you can about: 6 + 5 = 11  and 11 - 5 = 6
     Some other thoughts:
  • As a first year teacher, I was fortunate to have, in addition to Frank Gardella, some very supportive administrators.  For example my principal, Mike LaRaus.  I'll never forget what he told me back on my first first day of school, that September of 1986.  I showed up at like 6:00 AM, after a sleepless night, nervous as anything.  He found me, near paralyzed in my classroom.  He told me it was normal to feel that way, that I would always get that feeling on the first day of school.  Then he said, "Just relax and do your thing.  No one's going to bother you.  I'm not even going to set foot in your classroom for the first two weeks of school, and neither will any other administrator.  Get your footing and then we'll talk."  I can't tell you how relieved that made me feel.  Thanks, Mike!
  • Are you surprised I have a copy of the evaluation? I have them all.  Every single one I received during my 31 years of teaching.  What strikes me is how bare bones it is.  Three pages.  The two narrative paragraphs above, the first on page 1 and the second on page 3, with a checklist of performance practices, from Exceeds Expectations through Not Observed, on page 2.  The last formal observation I received was on January 31, 2017, and it came to me via e-mail.  I printed it out.  It's 14 pages long.  No wonder Frank left.
  • It's interesting to think back to the 25 year-old, first year teacher that I was.  Yes I was nervous at first, but I was also a little cocky.  I thought I knew a lot more than I really did.  (Now I know I don't know all that much.)  Also, I was a bit stand-offish.  (If you don't believe me, ask my wife.)  In time I learned how to be a good colleague; a supportive and sharing grade-level teammate and a helpful and contributing member of the staff and the wider school community.  That is to say, I grew up.
  •  I'm spending a lot of time this year coaching first year teachers.  They're brand new, right out of college.  Many of them have wanted to be teachers since they were kids, when they'd spend hours in their rooms "playing school".  Now their dreams have become realities.  They're nervous and excited, overwhelmed and overworked, and stressed out.  I love them.  I want so much to help them, to make their lives a little less stressful.  To let them know that they're doing a good job.  They're not much older than my own kids, and when I sit with them and talk to them I think about how I'd want someone in a position of authority to treat my son and daughter when they are just starting out in their first jobs.  Frank could've torn the lesson apart, but he didn't.  (Maybe he did think it was a "good lesson!"  Maybe he saved his real criticism for our post-observation meeting.  I don't recall.)  But I didn't yell at anyone, didn't make anyone feel stupid; I wasn't sarcastic or intolerant.  He recognized that.  My issues were with pedagogy and instruction, and those things can be improved with time, patience, and a desire to work at getting better at the craft.  I'm still trying to get better.

My first class.


Thursday, October 18, 2018

In Memory of the Overhead Projector

 In schools all over America there are overhead projector graveyards.

Quick, save one to put in the Museum of Outdated EdTech!

When I first started teaching, these projectors were invaluable.

Having one in your room was a status symbol.

     If you wanted to show something to the class, you had to have a transparency.  Some programs came with transparencies already made.  Awesome!  If they didn't, or if you wanted to show a sample of a student's work to the class, you had to make one yourself.  Not awesome!   You had to put a blank transparency in the paper tray of the copy machine and pray the copier didn't get jammed.  It always got jammed.  And it was always in the morning, five minutes before the opening bell, with a line of teachers waiting to make copies for their classes, moaning and groaning and giving you the hairy eyeball.  Then spreading the news all over the school that it was you who jammed the copy machine, so you'd have to skulk around the hallways all day and maybe even avoid eating lunch in the faculty lounge.  Also the bulbs always burned out, often right before you were getting observed doing a lesson that required the overhead projector.  Then you had to beg a colleague to borrow theirs, because there was always a shortage of overhead projector bulbs because they cost like hundreds of dollars and didn't get put in the budget.  And also because teachers hoarded them.  I know this to be true because once a teacher in my building retired and when the new hire came in and looked in the desk there were three brand new unused overhead projector bulbs in the bottom drawer.
     Happily, those days are behind us.  Behold one of the greatest advances in education in the last half century:

The document camera.

      We can show anything we want to the class without the hassles of the old overhead projector.  A picture in a book, the directions to a game, and, most importantly, student work:

     No longer do we have to wait.  We can share the work immediately, in the moment.  Imagine implementing the 5 Practices for Orchestrating Productive Math Discussions.  Now imagine having to make transparencies of any student work you wanted to share.   Document camera for the win.
     Of course many classrooms don't have document cameras.   Not to worry; take a picture with your phone's camera:

Everybody's got a phone.  Email it to yourself, or AirDrop it.

     The overhead has gone the way of the ditto machine, and the opaque and filmstrip projectors.  Most teachers today have probably never used one, and if they do remember them, it's from their days as students.  And while I will admit to some nostalgia for the calming whirr of the cooling fan and the intimate mood lighting, as well as a touch of sadness at the thought of those once proud machines piled forlornly and haphazardly in the back of a forgotten storage closet, their time has come and gone.

A document camera graveyard??


Sunday, October 14, 2018


     The days had become cooler and shorter.  The leaves on the trees began to yellow and I saw birds flying in flocks--probably on their way to warmer climates.  The nights were colder and longer.  I could not sleep and I went outside for a breath of fresh air.  There were no more lights coming from the bungalows and the sky was full of stars.  God, or whoever He is, was still there, observing his creation.  A new theater?  A new man?  The old idolatry was here again.  The stone and clay idols had been exchanged for a Gertrude Stein, a Picasso, a Bernard Shaw, an Ezra Pound.  Everybody worshipped culture and progress.  I myself had tried to become a priest of this idolatry, although I was aware of its falsehood.  At its best, art could be nothing more than a means of forgetting the human disaster for a while.  I walked over to the colony.  Most of those whose names the bungalows bore had departed this world, with its illusions, forever.  Those who worshipped them would soon follow.  I lifted up my eyes to the starry sky again and again as if in hope that some revelation might descend upon me from above.  I inhaled the cold air and shivered.

Isaac Bashevis Singer
Lost in America


Monday, September 24, 2018

The D Word

     In the course of my work with teachers, I'm often asked about a little something called differentiation.  Maybe you've heard of it.
     They might say something like:
     Admin is requiring us to have differentiation options in our lesson plans.  What's a good way to account for all the levels of learners in my class?

    More often than not they won't use the d word.  They'll say something along the lines of:

    I've got a lot of low kids in my class.  It takes them forever to solve a problem.  Some of them can't even read.  The high kids finish right away and then just sit around and wait while I try to help the others.  What can I do?

    When I hear comments like this, I set aside (for the moment) my concerns about labeling learners as high and low.  I compliment the teacher on her observation that something is wrong, that not all needs are being met, that precious class time is being wasted, and that she wants to do something about it.  But what? 
     Sometimes teachers will assign certain groups of students certain problems, or adapt assignments, like this:

    One common method I've seen employed is dividing students into ability-based groups.  Teachers might call this guided math, or math workshop.  After a whole-class lesson, the teacher will meet with the so-called struggling students and lead them through the problem set while the "high fliers" work through the problems on their own, and then move on to some game or other activity.  If there's time, the students in the teacher-led group may get to play a game.  There's rarely enough time.
   While I do believe there is a time and place for teachers to meet with small, skill-based groups, too often this model becomes the daily, default structure.  The groups calcify, and all the inherent social, emotional, and academic implications manifest themselves.  So what's the answer?
    Here's a differentiation template that I've used.  I take no credit for inventing it, only experimenting with it in some of my elementary classrooms to good effect.  I've written about this before, but as we begin the 2018-2019 school year I feel it's a good time for a revisit.  It goes like this:

Step One:
   Grab a scissors.  Take whatever problem you want the kids to solve and remove the question.  Keep just the text.  If the questions are generated based on a chart or some other graphic, keep just the graphic.
   Some examples:




Step Two:
     After a quick notice and wonder, ask the students to write their own questions, questions that can be solved using the information in the prompt.  First in their notebooks and then, after vetting, on chart paper.  Ask students to vary the question type between "thin" and "thick" questions.
   Some examples:

Gr 5

Gr 2

Step 3
    Select a variety of questions and post them around the room.  Allow students freedom of choice to solve whichever problems they want, using whatever strategies they want.
     Some examples:

     I like this model because it avoids the stigmatization of students being put in high, middle, and low groups and it allows for students to self-differentiate, both in terms of the questions they write and the questions they elect to solve.  Engagement is increased because, rather than being told which questions to answer, students have been given the opportunity to pose their own questions and decide which they'd like to tackle.  It's the definition of a low floor/high ceiling task, and it provides opportunities for small group interactions within a whole group community setting.  The teacher can elect to work with whatever students she feels need guidance without the students feeling that they've been singled out in an ability-based group.  Most important, it's fun.
     If you'd like to know more about how this has played out in classroom settings, see posts here, here, and here.  Comments are open for your ideas, observations, and reflections.


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