|h/t Pauline Kael|
Tuesday, July 28, 2020
Wednesday, July 15, 2020
Five years ago this month I boarded a plane in Newark, NJ and, after a layover in San Francisco, flew into the small airport in Ontario, CA. I had traveled across the country to attend something called Twitter Math Camp, which in the summer of 2015 was being held on the campus of Harvey Mudd College in Claremont, CA. It was difficult to explain to my family, friends and co-workers exactly what it was, or what I was going to be doing there, because I didn't really know myself. Was it a camp? Was it a conference? What does twitter have to do with it? How is it all organized? What I did know was that I was going to get to see some of the MTBoS people who had inspired me to explore new ways to teach math and who had supported and encouraged my attempts to blog about my experiences. I had never met any of them, and was more than a little apprehensive about what they would be like in person, and how welcoming the community in general would be. I had struck up an online friendship with Graham Fletcher, and he agreed to share a room with me and split what turned out to be a very small rental car. He was standing outside the terminal when I walked out with my bag, and we recognized each other immediately. I reached out my hand, but he shook his head, opened his arms, and gave me a giant bear hug that nearly crushed me to death.
Wednesday, July 1, 2020
ORLANDO, Fla. (AP) -- The world's largest statisticians group added to a chorus of criticism this week against the recent hiring of two political appointees at the U.S. Census Bureau. The American Statistical Association says the appointments earlier this week of Nathan Cogley and Adam Korzeniewski to top posts even though they have little experience at the agency "are in direct conflict with the bureau's mission to ensure proper, accurate, and timely delivery of statistical information to the public." Cogley is a political science professor who wrote a series of opinion pieces against the impeachment of Donald Trump. Korzeniewski is a former campaign consultant to the pro-Trump YouTube personality known as "Joey Salads."
...the suppression of its findings and the murder of those who organized it was nothing less than the obliteration of the capacity for self-analysis. An authoritarian society, however, that is unable to form an idea of itself, whatever social engineering its leadership may have in mind, is doomed to the blind exercise of state violence.
Whether in the cities or on a river steamer, in a yurt in Kazakhstan or in a hotel in Leningrad... from different districts of the capital, from the capitals of the republics, from Kiev, from Ashbagat, from the Taiga and the Pacific ports, from the newly built suburbs. The armada of enumerators ...not only penetrated the furthest corners of the Soviet Union; it systematically explored the social landscape...(and) discovered a Soviet Union in miniature.
They're very well equipped to advance political interests, especially those of the Republican Party. That's their background and their career goals. It's unprecedented for two political appointees to be added to the bureau in the middle of a census count in the recent history of the Census Bureau.
Inspired by recent tweets from @Zakchamp and @K_Larsen_Teach, I am now collecting TURDs (truly unfortunate representations of data) for a “Fix That Graph” unit. Please deposit your submissions in the comments below 👇#MTBoS #iteachmath pic.twitter.com/RsDXsgjrqt— Andrew Gael (@bkdidact) June 25, 2020
Friday, June 12, 2020
None were willing to talk about police unions. Trumka, of the AFL-CIO, was too busy to chat. The president of the United Food and Commercial Workers Union couldn't fit a call into his schedule. Teamsters President James Hoffa declined to comment.Silence from the Service Employees Union, The American Federation of State, County, and Municipal Employees, United Auto Workers, Communication Workers of America, Unite Here and the American Federation of Teachers.
Thursday, May 21, 2020
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.
The soldier's name was Kurt Vonnegut.
The book he wrote was Slaughterhouse-Five.
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.
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
The feeling stronger every day for weeks now, it cannot go on like this much longer. And yet it does go on and on.
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.
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.
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."
September 18 (1941), Thursday evening
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
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.
- 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?|
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:
- 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.