Thursday, May 21, 2020

Greetings From the Planet Tralfamadore

1.  The Soldier 

     At approximately noon on Wednesday, February 14, 1945, a group of American POWs climbed out of an underground meat locker in the middle of Dresden, Germany.  It was a break in the middle of a two day, combined British and American aerial attack that would drop nearly 4,000 tons of high explosive bombs and incendiary devices on and around the city, known as "Florence on the Elbe".  The war was nearing its end, and Dresden had thus far escaped the fiery destruction that many other German cities, including Berlin and Hamburg, had already seen.  But time had run out.  The bombing and resulting firestorm destroyed over 1,600 acres and killed approximately 25,000, most of whom were civilians.
     Among the POWs emerging from the meat locker that Valentine's Day was a 22 year old private from Indianapolis, Indiana.  He had enlisted in March, 1943 after leaving Cornell, where he was majoring in bio-chemistry while writing for and editing the university's independent newspaper, The Cornell Daily Sun. Trained as an intelligence scout, he was shipped overseas with the 106th Infantry Division in time for the Battle of the Bulge, part of the final German offensive of the war.  His sector was overrun, and on December 19, 1944 he was captured somewhere in Luxembourg.  He joined a collection of other prisoners, and together they were marched sixty miles before being crammed into small, unheated, unventilated boxcars, part of a train slowly making its way to a large POW camp near Berlin.  On January 10, 1945 he was one of 150 prisoners shipped to Dresden, where by day he labored in a factory that produced vitamin-enriched malt syrup for pregnant women and at night ate and slept locked in an abattoir that had been converted into a barracks.
     When the bombs began to drop on the night of February 13, he, his fellow prisoners and their six German guards took shelter in a meat locker three stories underground.  There, cool amid the dressed cadavers of cattle, sheep, pigs, and horses, they told jokes and listened to the sound of what he would later describe as, "The footsteps of giants marching across the earth."  The prisoners and their guards suffered nothing worse than a light dusting of paint chips falling from the ceiling.  "When we came up the city was gone," he recalled.  "They burnt the whole damn town down."
     Unsure of what to do next, the guards held the prisoners at attention for several hours before leading them on a trek across the rubble to an innkeeper's stable on the outskirts of town.  Two days later the prisoners were marched back into the ruins and put to work.
     
     "We walked into the city and dug into basements and shelters to get the corpses out, as a sanitary measure," he later wrote.  "When we went into them, a typical shelter, an ordinary basement usually, looked like a streetcar full of people who'd simultaneously had heart failure.  Just people sitting there in chairs, all dead.  ...We brought the dead out.  They were loaded on wagons and taken to parks, large open areas in the city which weren't filled with rubble.  The Germans got funeral pyres going...  It was a terribly elaborate Easter egg hunt."
 
     Less than three months after the Dresden bombing, Germany surrendered.
     Twenty-five years later, in March, 1969, the former POW from Indianapolis, Indiana published a book, a book in which he tried to come to terms with the horror of what he had seen, a book that took its title from the abattoir, the one whose meat locker had kept him safe, the one from which he had emerged to witness the aftermath of the destruction of the city called "Florence on the Elbe", the one the Germans called Schlachtof-funf.
     The soldier's name was Kurt Vonnegut.
     The book he wrote was  Slaughterhouse-Five.



2.  The Professor
   
     Less than three miles away, in the city center at Zeughausstrasse Number 1, in a so-called Jews' House, another former journalist, this one a 63 year old professor of Romance language and literature, was having quite a different experience.  Born to a Jewish family in Landsberg an der Warthe, in the eastern part of the Prussian province of Brandenburg, he had converted to Christianity, married a Protestant musicologist and pianist, served at the front in World War One and, in 1920, secured a teaching post at Dresden Technical University.  However his conversion, marriage, position, and war record were of little consequence when the Nazis came to power.  Starting in 1933, and continuing through the 1935 Nuremberg Laws, he was stripped of his citizenship rights, job, pension, house, access to his bank account, freedom of movement, freedom of speech, and even his beloved pet cat.  His status as Jew in a mixed marriage with a Christian woman had thus far enabled him to avoid being sent to a concentration camp, but by the beginning of February, 1945 there were less than 200 registered Jews left in the city, and plans for the final liquidation of the ghetto were in motion.  All Jews capable of physical labor were to report for deportation on the morning of Friday, February 16.  It was a death sentence.  For the professor, time had run out.
     When the bombs started falling on the night of Tuesday, February 13, there was no meat locker sixty feet underground in which to find safe haven.  The makeshift air raid shelters in the "Jews' cellars" of Zeughausstrasse Numbers 1-3 were immediately turned into death traps.  Separated from his wife, out in the open and nursing an eye injury caused by the shattering of the cellar window, he threw himself into a bomb crater, then climbed out and sought safety in a telephone kiosk.  Knapsack on his back, carrying a bag with manuscripts and jewelry, he followed a group of people making their way to a promenade high over the Elbe called Bruhl's Terrace--(forbidden to Jews--but did it matter anymore?)-- where, in shock, he spent the night watching the city burn.
   
     "To the right and left buildings were ablaze, he wrote a week later in his diary, "the Belvedere and--probably--the Art Academy.  Whenever the showers of sparks became too much for me on one side, I dodged to the other.  Within a wider radius nothing but fires.  Standing out like a torch on this side of the Elbe, the tall building at Pirnaischer Platz, glowing white; on the other side, the roof of the Finance Ministry."

     It started to rain.  The city continued to burn.  By seven the next morning the terrace began to empty.  As he began the walk down to the Elbe he found his wife sitting on a suitcase.  She had been pulled into the block's "Aryan cellar", crawled out a broken window, and survived the night in two separate basements, the first in the Albertinum, an art museum, then in the Belvedere Hotel.  Now reunited, they wandered through the hellscape.

     "We walked slowly, because I was now carrying both bags and my limbs hurt, along the riverbank... Above us, building after building was a burned-out ruin.  Down here by the river... masses of empty, rectangular cases of the stick incendiary bombs protruding from the churned up earth... the corpses and smashed vehicles...burned out sheds...fires, at times small, and no more than a bundle of clothes... past the corpses up and down the Elbe.  Every house a burned out ruin... Again and again fires still burning.  Nowhere a sign of attempts to extinguish them."

     After an unsuccessful attempt to find a physician to tend to his injured eye, they made their way to the square in front of Zeughausstrasse.  Their building, the third Jews' House they had lived in since being evicted from their home in the Dresden suburb of Dolzschen in 1940, had been reduced to rubble.
     Although there were no warning sirens, the second wave of bombing that afternoon did somewhat less damage to the city center.  Back at the outer wall of the Bruhl Terrace, the professor and his wife were again separated.  Starving and exhausted, they met back in the basement of the Albertinum, where, amid the wounded and traumatized survivors, they waited out the bombardment, sharing their experiences and trying to sleep.  The next morning they were evacuated to a nearby air base, where they received food and medical attention.  A few days later, carrying the suitcase, bag and knapsack containing all their earthly possessions, they walked five miles to the small town of Piskowitz, where they were welcomed into the home of their former housekeeper, and where the professor wrote down, while it was still fresh in his mind, his nightmarish experience of the firebombing in his diary.
     The professor had been keeping a diary since 1918.  To continue writing during the Third Reich was an act of bravery; discovery meant certain death for him, his wife (who due to her Aryan status was afforded freedom of movement and thus had the ability to smuggle pages out) and their gentile friend on the outskirts of the city who was keeping the ever-growing document hidden.  But he continued.  "I shall go on writing,"  he entered in the diary on May 27, 1942.  "That is my heroism.  I will bear witness, precise witness!"  
     In 1995, 35 years after his death, the professor's diaries were published to universal acclaim.  In its pages he tries to come to terms with how to live his life in a country he loved but no longer recognized, a country that stripped him of everything he had, a country that was murdering members of a tribe to which he no longer belonged, a country that was now coming to murder him.
    The professor's name was Victor Klemperer.
    The book he wrote was I Will Bear Witness: A Diary of the Nazi Years 1933-1945.


3.  The City



    4.   The Meeting

      I want to believe that somewhere in the bombed out ruins of Dresden, on Valentine's Day, 1945, Kurt Vonnegut and Victor Klemperer crossed paths.  It would be highly unlikely, but not impossible.  We know that Vonnegut and his fellow POWs left the city on the afternoon of February 14.  Klemperer, reunited with his wife after having spent Tuesday night on Bruhl's Terrace, and spent the 14th making his way first to the Jewish cemetery, then to Borsburgstrasse in search of his doctor, then to Zeughausstrasse, before heading back to Bruhl's Terrace and the basement of the Albertinum.   It's true Klemperer makes no mention in his diary of an encounter with a detachment of American POWs; he's a meticulous observer and it's unlikely he'd leave out a detail like that.  And while I'm not sure where the innkeeper's stable was located, I doubt the route taken by the prisoners as they fled the bombing's aftermath would have taken them through the city center.  But like I said, I want to believe. 
     Klemperer passes Vonnegut, and right at that moment their eyes meet.  They sense something, some kind of connection; they're both writers after all.  And maybe that's it.  But I want to believe there's more.
     Vonnegut was a fourth generation German-American, and both his parents spoke German.  Vonnegut wasn't fluent, but he did speak the language--he became de facto leader of the prisoner group due to his ability to communicate with the guards.  Klemperer spoke a little English; he records in his diary that he began taking lessons from an English speaking friend on the off-chance he could find a way to emigrate to America.  They have a conversation.  KV and VK.


5.  "All Moments, Past, Present, and Future..."

     Slaughterhouse-Five (subtitled The Children's Crusade), Vonnegut's sixth book, is the one that made him famous-- an anti-war book published at the height of the social unrest caused by America's involvement in Vietnam.  Impressionistic and episodic; disorienting and disturbing; equal parts science fiction, satire, reportage, and black comedy; a meditation on war and its costs, morality, free will, time, and the nature of humanity; it's a book that leaves an indelible impression--for me a much different one as an adult than it did as a teenager.  The main character, Billy Pilgrim, is an American soldier who has a World War Two experience very similar to Vonnegut's.  (The first chapter, narrated by Vonnegut in the first person, describes the book's origin story.  "All this happened, more or less,"  he explains in the very first line. "The war parts anyway, are pretty much true.")
     Pilgrim becomes "unstuck in time", which means he experiences his life not in a linear fashion, but in free-floating flashbacks and flashforwards, traveling back and forth across moments in an already predetermined life.  One moment he's being captured by Germans, next he's a successful optometrist.  He's a 12 year old boy on a trip out west with his family.  He's in a boxcar in Germany.  He attends a Lions Club Luncheon.  He's abducted by two-foot tall green aliens from the planet Tralfamadore and placed on display under a geodesic dome.  He gets married.  He's one of two survivors of small plane crash in Vermont.  He's in an underground meat locker during the Dresden firebombing.  He's assassinated while giving a speech at an optometrist's convention.  The war ends.  He hears a birdsong. 
     Early on in the book, Billy writes a series of letters to the local newspaper detailing his experience on Tralfamadore, whose inhabitants experience time in four dimensions:

    The most important thing I learned on Tralfamadore was that when a person dies he only appears to die.  He is still very much alive in the past, so it is very silly for people to cry at his funeral.  All moments, past, present, and future, always have existed, always will exist.  The Tralfamadorians can look at all the different moments just the way we can look at a stretch of the Rocky Mountains, for instance.  They can see how permanent all the moments are, and they can look at any moment that interests them.  It is just an illusion we have here on Earth that one moment follows another, like beads on a string, and that once a moment is gone it is gone forever.
   
     

6.  "Everything Is Infinitely Long Ago, Everything Is Infinitely Long in Coming..."

     I've spent the last two months sheltering-in-place with four people: my wife, my son, my daughter, and Victor Klemperer.  My kids spend a lot of time in their rooms, my wife in a makeshift office in the basement.  But I haven't been alone.  Through two volumes of over 1,000 small print, densely packed pages ranging over 13 years of his life, Klemperer has been my constant companion.  I've been awed by his courage and persistence, infuriated by his indecision, intellectual pretension, and naïveté, and confused by his ambivalent attitude towards Judaism and outright hostility towards Zionism.  I've laughed at his comical attempts at learning how to drive, and rolled my eyes at his constant health complaints.  I saw the city through his eyes, first driving in his car, then riding in a tram when he was forced to give up his car, then on foot when he was no longer permitted to ride public transportation.  I attended funerals with him at the Jewish cemetery, shoveled snow and assembled cardboard boxes with him on forced labor details, stood in food lines with him, spent a week in solitary confinement with him in a Dresden jail cell, and stood by helplessly while his apartment was searched by the Gestapo.  I watched Eva sew a yellow star on his jacket, saw former friends and colleagues cross to the other side of the street when he walked by.  I heard the humiliating taunts and slurs, and the wailing and the crying as, first one at a time, then in large groups, the Jewish residents of the Dresden ghetto disappeared.  Then I heard the air-raid siren.
     Real news was hard to come by in the Dresden ghetto, in all Germany for that matter.  The Nazi propaganda machine saw to that.  And rumors were rampant, many of them false.  (One, for example, was that Churchill's aunt was buried in Dresden and as such the city would be spared destruction.)  Hard to come by, but not impossible.  Klemperer records in his diary (September 14, 1944) an evening in which a friend finds a copy of an old newspaper with a page summarizing events of the previous year.  They are wonderstruck by the tumultuous sweep of the world history they had so recently lived through, and find themselves overcome with a strange sensation:

     ...something else made a greater impression on us--it was the same for both Neumark and myself: the impotence of memory to fix all that we had so painfully experienced in time.  When--insofar as we remembered it at all--had this or that happened, when had it been?  Only a few facts stick in the mind, dates not at all.  One is overwhelmed by the present, time is not divided up, everything is infinitely long ago, everything is infinitely long in coming; there is no yesterday, no tomorrow, only an eternity.  



7.  "One Long Mobius Strip of Time..."

     Among the many casualties of Covid-19 is our perception of time.  Without jobs or classes, weekdays and weekends blur into one long Mobius strip of time, spent in gym clothes we no longer wear to the gym.  Unable to make plans (travel plans, business plans, wedding plans, even lunch plans), we are forced to live in a continuous present.  And yet, some days we feel we've been transported to a world imagined in a futuristic novel-- ...other days, we find ourselves in a time warp defined by old movies, old TV series...and reruns of classic sports games.
  Michiko Kakutani
The New York Times Book Review
May 17, 2020


   All this happened, more or less.  In the summer of 1989 I worked as a head counselor at a day camp out on the east end of Long Island.  I was still single, three years into my teaching career, spending another summer at my parents beach house picking up some extra money.  There were a bunch famous people's kids there.  Chris Jennings (son of the late ABC World News Tonight anchor Peter Jennings) was in my group, as was Kurt Vonnegut's daughter, Lily.  She had been adopted as an infant by Vonnegut (then sixty years old) and his second wife, photographer and author Jill Krementz.  She must have been nine or ten that summer, which would put Vonnegut around 70.
      I was a Vonnegut fan.  Reading him had been a formative adolescent experience, and although in adulthood I'd kind of put him aside, his books had always maintained a special place on my shelf and in my heart.  So when I learned that his daughter would be in my group, I was excited.  He'd show up maybe once or twice a week to pick her up, unmistakable with his thick moustache and bushy head of hair.  Early on in the summer I had gone back to my townhouse in New Jersey to pick up my first edition copy of Breakfast of Champions, with the intention of asking him to sign it.  I kept the book in my car, waiting for the opportunity, but every time I saw him I chickened out.
     It wasn't until mid-August, the last week of camp, that I got up the nerve to approach him.  Time was running out.  One afternoon during pick-up, book in hand, I asked him politely if he might sign it for me.  Without comment he took it and began to walk away, maybe 30 or 40 yards or so, to a bench under the shade of big tree near the camp's main building.  He motioned for me to follow.  We sat together on the bench, just a few feet apart.  He declined my pen, took out one of his own from a jacket pocket, opened the book, and began to write.  He sat there writing for what seemed like a long time, anyway much longer than it would take to just sign his name.  I studied his face, not daring to look at the book.  What was he doing?  I couldn't imagine.
     After what seemed like an eternity he got up, smiled, and handed the book back to me.  I stammered a nervous thank you.  He collected Lily, and the two of them went on their way.  Camp ended, and I never saw him again.
     I'm looking at the book now, a soon-to-be 59 year old man in the Covid-19 spring of 2020, trying to remember exactly what I did yesterday, and trying to figure out what I'm supposed to be doing today, tomorrow, and all the days after that.  And I'm also thinking back to that August afternoon in 1989.  I was 28 years old then, six years older than Kurt Vonnegut was when he climbed out of the meat locker in Dresden, Germany on that Valentine's Day in 1945; only four years younger than Victor Klemperer was on that same day, a day when, wandering around a city in flames, on a continent in ruin, he met a man who would forever capture the moment in a strange kind of amber, a man who, like him, would bear witness.
     A continuous present, a future world imagined, a time warp into the past.
     I bring you greetings from the planet Tralfamadore.





     
   
       
    
   
     





   
 

Friday, April 10, 2020

How One Experiences History

August 11, Sunday (1935)
     The feeling stronger every day for weeks now, it cannot go on like this much longer.  And yet it does go on and on.

*

     When the Nazis took power in Germany in 1933, Victor Klemperer was a professor of Romance Languages at the Technical University of Dresden.  Born in 1881 to a Jewish family, he converted to Christianity, married an Aryan woman, and served in the German Army in World War I.  He considered himself fully and completely German in every way.  Didn't matter.  According to the Nuremberg Laws he was Jewish, and now a state subject with no citizenship rights.

*

March 30, Thursday (1933)
   In fact I feel shame more than fear, shame for Germany.  I have truly always felt German.  I have always imagined: The twentieth century and Mitteleuropa was different from the fourteenth century and Romania.  Mistake.


*
  
     Klemperer (first cousin of the conductor Otto Klemperer) was a writer and a diarist, and his journals were published in 1995.  The ones covering the Nazi years are now standard primary sources for historians researching daily life in the Third Reich.  In the first volume, which covers the years 1935-1941, Klemperer recounts in excruciating detail the incremental erosion of his way of life: the loss of his job and the drastic reduction of his pension, the confiscation of his house and the move to the Dresden ghetto, the loss of his car and his phone, the loss of Jewish friends to emigration, deportation, jail, and suicide and gentile friends to fear of association, the loss of his freedom of movement, even the loss of his typewriter.  The curfews.  The stores where he can no longer shop.  The doctors he can no longer see.  The ration coupons.  The taunts on the streets.  The ever increasing restrictions, indignities, and humiliations.  The tightening of the noose around his neck. 

*

June 13, Wednesday (1934)
    And on every side consistent reports about the tremendous lack of money.  ...In addition, the constant rumors of war.  Everywhere uncertainty, ferment, secrets.  We live from day to day.  

*

    The two volume set of Klemperer's diaries has sat unread on my shelf for at least ten years, probably more like fifteen.  I bought them used ($6.00 each) at book sale.  Two reasons compelled me to pick Volume One up a few weeks ago: 1) I'm working on a project involving a diary from the year 1926 that my grandmother kept when she was 17 and I wanted to read a diary, and 2) the coronavirus.  What's it like to live through a time of uncertainty, fear, and societal disruption?  I thought, maybe a little perspective will help.  I mean, what we're living through now can't possibly be worse than living through the rise of the Third Reich.

*

December 2 (1935)
   Today it occurred to me: Never has the tension between human power and powerlessness, human knowledge and human stupidity been so overwhelmingly great as now.  


*
     
    Reading Klemperer's diary is like watching the replay of a train wreck, but in slow motion.  It's painful to read because he's recording in real time what we already know has happened, and speculating on what we already know will happen.  (Although he has reasons for staying in Germany,  I frequently found myself yelling at him, "Get out!  Now!")  He debates emigrating, but by the time he decides to leave it's too late.  The conversations he has with his friends and acquaintances, especially in those first years of the Third Reich, are heartbreaking.  They alternately look for any reason to feel optimistic (he tries tracking popular sentiment by keeping count of how many people greet each other with "Heil Hitler" and/or the Sieg Heil salute vs. how many with just "good morning" or "good day") and then descend into depression and fatalism.  They remind me of the conversations we've had, and are still having today, about the uncertainty of our future.  And I find myself thinking: What will someone in the future reading a diary that details what's going on now think?  That we were naive?  Brave?  Smart?  Doomed?  Delusional?  Will they be yelling at us?  Will they be proud of what we did or ashamed and embarrassed?  Are we headed for a train wreck and we just don't know it?  Or have we averted disaster in time?            

*
   

September 11, Sunday (1938)
    If I talk to the butcher or the butter man here in Dresden, then there will certainly be peace, but if (as the day before yesterday) I listen to Wolf, the car man, then, "Things are coming to a head now!"  If I read the newspaper, see and hear the film reports, then we're doing sooo well, we love the Fuhrer soo much and sooo unanimously---what is real, what is happening?  That's how one experiences history.  We know even less about today than about yesterday and no more than about tomorrow.


*


      Although I've yet to start Volume Two, I know what happens to Klemperer.  Two of only a handful left in the Dresden ghetto, he and his wife Eva flee the city during the Allied firebombing in February, 1945.  They join a refugee column and escape to American controlled territory.  He remains in what becomes East Germany, and continues his career as a respected and honored academic until his death in 1960.  He was one of the very few who made it through the inferno.  Europe, and the world, changed forever.  
   What about us?  Most immediately, how many of us won't make it?  How many will be permanently scarred?  What will the economic consequences be?  And: How does it end?  How do we know when it's over?  What will our world be like after?  What will we have learned about ourselves? What about next time?
   A few weeks ago my daughter asked if this was going to be in the history books.
   "It's going to be its own chapter!"  I told her.  "You're going to be telling your grandchildren about this."
*

July 9, toward evening (1941)
   Perhaps, probably, it is the greatest good fortune to experience so much world history.  But shall we survive it?

*

  I thought I knew a lot about this history.  Most Jews grow up learning about what happened in Germany when the Nazis took over.  Turns out there was a lot of stuff I didn't know.  Little details.  Like you weren't allowed to own pets.  (Klemperer goes to a vet to have their tomcat Muschel euthanized.)   Like when you were relocated to the ghetto and your house was turned over to someone else, you still had to pay the property taxes as well as for repairs and improvements.  (The greengrocer is given Klemperer's house and he has to cover the cost of a new roof.)  Like when the Nazis ordered you to wear the yellow star, when you went to pick it up you had to pay for it yourself.

*     

  September 18 (1941), Thursday evening
     The "Jewish star," black on yellow cloth, at the center in Hebrew-like lettering "Jew," to be worn on the left breast, large as the palm of a hand, issued to us yesterday for 10 pfennigs, to be worn from tomorrow.   ...For the time being at least Eva will take over all the shopping, I shall breathe in a little fresh air only under the shelter of darkness.
   Today we were outside together in daylight for the last time.


*
  
May we all see daylight again soon.  


Eva and Victor Klemperer, 1940.
















Thursday, March 26, 2020

A New Favorite

    Something I've been carrying around in a folder for years finally got a trial run this past winter in one of the grade 2 classrooms I visit, and it was a big hit.  Lifted from the Georgia Frameworks (you can find a detailed lesson plan, directions, and game sheets in Grade 2, Unit 1, pgs. 80-89), it's called Capture the Caterpillar, and if I can make any sort of contribution during this current crisis, it's an activity I'd highly recommend.  It will work just as well at home as it does in the classroom.
    Capture the Caterpillar combines place value, comparing numbers, addition and subtraction, number sense, and strategy as you attempt to get as close to a target number as possible.  All you need are:
  • A deck of cards (10s and face cards removed, though Queens can be 0s)
  • A pair of dice
  • A game sheet and a score sheet 
  • Counters or anything that can stand in as counters, such as beans, paper clips, etc.
Here's how it works:



  • Pick two cards and generate a target number.  In the example above either 28 or 82; I chose 28.
  • Roll two dice.  Find the sum.  Take that many counters.  I rolled a 3 and a 2 and that makes 5, so I took 5 counters.  
  • Place the counters in the caterpillar and try to get as close to 28 as possible.  You can place them anywhere you want, but you need to use them all. 

Here I made 14.  1 ten and 4 ones.  That's 14 away from 28.


23.  2 tens and 3 ones.  That's 5 away.  Closer... but can we do better?


32.  3 tens and 2 ones.  How far away from 28?  Is this the closest we can get?  How do you know?


     In the above example, 32 is the closest number to 28 we can make given the 5 counters.  We would score 4 points because the difference between 32 and 28 is 4.  Play as many rounds as you like (in the game it's 5) and try to get the lowest score possible.
   Here are two second graders playing this game.  Their target number is 22 and they have 9 counters.  Pay attention to how they collaborate; how they count, how they determine the differences between their numbers, how they talk through the rules, how they plot strategy:




Here's a completed scoresheet:



Two more versions:







Some notes:
  • The Georgia Frameworks include only the 100s and 1000s caterpillars.  Honestly, it's been so long I'm not sure where the 10s caterpillar came from.  I can't find it on either the new (2019) or older (2014) edition of the Frameworks.  Did I do a cut and paste job and make it myself?   Here's the image in a google doc.  Or you can make your own.  Better yet, have your kids make it!  (Actually you don't even need the caterpillars.  Just circles will do.)  
  • The scoresheet in the Frameworks has a column for expanded form.  We eliminated that column and replaced it with a column to indicate the difference between the two numbers. Here it is.   We were about to experiment with having the kids plot their target numbers along with their attempts on a number line, but never got the chance. 
  • An alternative to competing against another individual or team is competing against your (or the class's) best score.  I like that better anyway.  
  • For a change, try to make the number that's farthest away from the target number and try for the highest score possible.
  • Try it with 3 dice. 
  • Forget drawing cards and trying to get close to a target.  Instead roll the dice, grab counters, and see how many different numbers you can make.  Is there a systematic way to go about the task?  Is there a relationship between the number of counters and the number of different numbers you can make?  
  •  One possible assignment: take a picture of a set up and ask students to come up with the   closest/farthest number possible.  This is a good number sense routine.
    My hope is that this activity can be used by parents working with their children at home and teachers working virtually with their students.  I can only imagine what it must be like for all those trying their best to continue to provide meaningful educational experiences for their kids right now.  Know that, when all is said and done, you will be counted among the many heroes who held our society together during this most difficult and challenging time. 

     


Sunday, March 1, 2020

Math Class Needs A Makeover Turns Ten

     Ten years ago this month, on March 6, 2010, a tall man in a maroon sweater vest gave a Ted Talk.  It clocked in at 11 minutes and 24 seconds.   Here's how he described what he did for a living:
     "I sell a product to a market that doesn't want it but is forced by law to buy it.  I mean, it's just a losing proposition."
     He called the talk "Math Class Needs a Makeover."  His name was Dan Meyer.  He was a high school math teacher, and he was tired of losing.




*

     How long does it take to change your life?  I remember exactly where I was the first time I saw it.  Sitting at my computer in Room 10A, in that elementary school somewhere off the New Jersey Turnpike, I was an unlikely math specialist with a very conflicted relationship to the subject, searching for something, anything, that might make a difference in the lives of the basic skills kids I was supposed to be helping.  What I saw took my breath away.  Here was an actual math teacher giving voice to and validating everything I felt was wrong about math instruction while showing a way forward.  It was a manifesto.  It was a challenge.  And, for me, it was nothing short of revelatory.  From there it was a few mouse clicks to his blog, which I devoured, anxiously awaiting each new post, and his "Blogulty Lounge", where I discovered the work of Andrew Stadel, Fawn Nguyen, and Michael Pershan, among others.  (I'll admit here for the first time that it was years before I got the pun: of course an online Faculty Lounge was a Blogulty Lounge.)  I began to experiment with ideas I found in this new online universe in the K-5 classrooms in my school and, in emulation, started my own blog as a way to record and reflect on that work.  How long does it take to change your life?  11 minutes and 24 seconds.

*

     Ten years, 33 languages, and over 2,800,000 views later, "Math Class Needs A Makeover" is as powerful and important today as it was then.  Will we ever truly be able to measure its influence?  One of the very first comments on the talk came from a 17 year old named Timo Bronseth.  He wrote:
     "By the time Meyer's idea has overthrown our school system, maybe I'll be teaching it!"  
     Timo's now 27.  I'd like to imagine he's out there somewhere, doing a 3-act task with his class, trying to overthrow the system.

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?
*

Collins:  
     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

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 raggedness to it;
smooth as a billiard ball,
it seems delicately poised 
in its circular journey around the sun,
and above all
it seems
fragile.




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.  
   ...Although
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: 
MDW
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.