Tuesday, February 9, 2021

First Lessons

     My first year teaching was both the most difficult and the most exciting of my career.  The workload was staggering and the learning curve was steep, but every day was a new adventure and the thrill of finally having my own class took a long time to wear off.  Looking back, I'm not sure who learned more, me or my students.  Here are three valuable lessons from year one:   

I.  The Gym Teacher

     Mr E, the gym teacher, was on the back nine of his career.  When I first met him he seemed hard-edged, like something bad had happened to him in his past that he couldn't quite get over and was still bitter about.  His size didn't help; he was a barrel-chested 6'4", 250 lbs, so he cut quite an intimidating figure.  I didn't have much interaction with him, just dropping my class off for gym and picking them up, all hot and sweaty, 40 minutes later.
     One day, early in the year, a kid came back to the room from gym class in tears.  Mr E, she said, had yelled at her.   I could believe it-- I had occasionally heard his voice boom out from the all-purpose room as I walked to and from the office.  She said she was scared of him and didn't want to go back to gym class.  I tried to console her, but she was adamant.  She did not want to go back to gym.
     What to do?  
     At that point in my couple-of-months teaching career, the person I felt most comfortable with was my principal.  He had hired me, he was incredibly supportive, and he had told me to feel free to come to him with any problems, that his door was always open.  And, to be honest, I was also a little scared of Mr E.  So I told my principal what had happened, and he told me he would take care of it.  Rookie mistake.  You can guess what happened next.    
     The next day Mr E cornered me.  Have you seen the episode of The Office when Stanley yells at Ryan?  That's kind of what happened.  He got up close, and respectfully but forcefully explained that if there was a problem I should have come to him directly.  I told him I understood, and that it wouldn't happen again.

Lesson: If you have an issue with a colleague, go to the colleague first.  Don't run to the principal every time you have a problem.

     Mr E was still teaching gym some years later when I became our school's union rep.  (I guess he decided to play 27 holes.)  In the interim I had gotten to know him a little better.  (Did he remember what had taken place between us?  After that day we had never spoken about it.)  In the middle of some very contentious contract negotiations, each rep was tasked with organizing their building's staff for a job action.  I knew this would be difficult, as we had several staff members who were skeptical, if not outrightly hostile.  Although I had prepared a rousing call to action, including a call-back to the time, only a few years prior, when district teachers were jailed for going on strike for the better wages and working conditions that the current staff was enjoying, I was afraid that there might be an exodus during the presentation.  Whether or not they ultimately supported the job action was their decision, but they were darn well going to listen to what I had to say.  So I asked Mr E to stand by the closed faculty room door.  He filled up practically the entire frame, and stood there for the entire meeting with his arms folded against his chest.  If anyone was going to leave, they were going to have to get by him.  No one left.  Thanks, Mr E! 

II.  The Messy Desk  

     Nathan was one of those kids who could never seem to pull it all together.  Think Pigpen from the Peanuts comic.  Shoelaces untied, breakfast all over his shirt, nose constantly running.  It wasn't a matter of neglect; he came from a very loving and attentive family.  He was just one of those happy-go-lucky kids who always seemed one or two beats off.  

     His desk was a reflection of his personality.  I mean it was a total disaster area.  No matter how many times I made him clean and organize it, it instantaneously reverted back to its natural state.  Everything was just jammed in there: textbooks, notebooks, stray worksheets from months back, crumpled old tests never taken home to be signed, broken pencils, crushed crayon boxes, dried out markers with no caps, weeks-old half-eaten snacks, little toys... that was Nathan's desk.  

     (This was the opposite of Amanda's desk, meticulously organized with every single thing in its exact place.  She loved to color, and had one of those big boxes of Crayolas, one of those 64 packs.  One day I noticed that, while most of the crayons were worn down, there were a few select colors that hadn't been touched, their points still sharp.  I asked her why she didn't use them, and she told me that they were her favorite colors, and she didn't want to wear them out.  I've never met a kid with so much willpower!)    

     Anyway, back to Nathan.  What infuriated me most was how long it took him to find something.  Waiting for him to excavate his math message book from his desk was like waiting for Godot-- and meanwhile my lesson was being held up.  And then once he found it, forget about finding a pencil to write with.  One day I lost it.  After waiting for what seemed like an eternity for him to get what he needed to start the lesson, I stormed over to his desk and just tipped it over.  No words.  Everything in the desk came crashing down onto the floor.  The class froze.  Nathan looked down at the pile of rubble, looked up at me, and burst into tears.  I immediately understood that I had screwed up.  I publicly apologized, and believe I was able to repair my relationship with Nathan, but I've never forgotten the look on his face.  

Lesson: Never embarrass a student.

III. The Candy Thief

     One afternoon, craving a treat, I opened my bottom desk drawer intending to dip into my hidden supply of candy. (Yes, I have a secret sweet tooth.)  Imagine my surprise when I found that an entire bag of Halloween candy had disappeared.  I was crushed.  I took it personally.  One of the kids in my class was a thief and had no compunction about stealing something from me.  What had I done to deserve it?
     I gathered the class together and said all the usual things you might say in that situation: Confess and you won't get in trouble; it's more important to tell the truth; whoever did it can talk to me privately and no one else will know, etc.  Didn't work.  No one came forward, either to admit to the deed or to rat someone out.  The case remained open.  For the rest of the year it bothered me knowing that there was a kid in my class that would steal something out of my desk.  Who was it?    
     Fast forward about 10 years.  I come into school one spring morning and find a note on my desk.  It's from a former student, Damien.  I don't have the note, but I'll paraphrase:

Dear Mr. Schwartz,
     You may not remember me, but I was a student in your second grade class.  I'm a senior in high school now and am going to graduate next month.  I just want you to know that it was me who stole the candy, and I'm very sorry that I did that.
     Damien!?!  Of course I remembered Damien!  So he was the culprit!  And he'd been carrying this guilt around all these years.  What caused him to finally come clean?  I sent a note back to him through inter-district mail, saying of course I remembered him, thanking him for his apology, letting him know that I though it was a courageous act, and wishing him well in his post-HS endeavors.

Lesson: Who your students are now are not who they'll always be.

     The events described above happened 35 years ago, as far away from a first year teacher today as someone who taught in 1951 was from me my first year.  Looking back, I'm not completely sure that I would've thought someone from 1951 would've had anything to teach me about teaching.  I was young and full of myself.  Wasn't I up on all the latest trends?  Hadn't education changed dramatically from 1951 to 1986?  
     Hasn't it changed dramatically from 1986 to 2021?  Yes, notions of pedagogy and best practices have changed, and technology has revolutionized many aspects of what we do in the classroom.  (My 1986 self had high, middle, and low reading groups reading out of basal readers and completing worksheets I ran off on a ditto machine.)  But what hasn't changed, and what will never change, is that our project is a human one.  
     A school is more than a building, more than the sum of its chairs and desks and whiteboards and Smart Boards; more than all its books and tests.  A school, even a virtual one, is an intersection where lives converge, where our lives, and the lives of our colleagues and our students meet in all their messy, intimate complexity.  Yes, I learned a lot in my first year teaching, probably more than my students. How to write lesson plans, how to fill out a report card, how to organize a field trip, how to schedule parent-teacher conferences, how to work the copy machine.  But the most important lessons were the ones that taught me how to be a better human being.  And those lessons are timeless.  





Tuesday, January 26, 2021

Rooting For the Laundry

      Ricky F.  was one of my very first students.  He was a bit undersized for a second grader, but more than made up for it with his boundless enthusiasm and energy.  As an NFL draft expert would say, the kid had a motor.  He also had a love of baseball and an intense dedication to the Chicago Cubs.

     Chicago Cubs fans are not easy to find here in central New Jersey, where we straddle the line between Philadelphia and New York.  We've got Phillies, Yankees, and a smattering of Mets supporters, but Cubs fans are few and far between.  So naturally I was curious.  Why was Ricky a Cubs fan?  Did his family have Chicago roots?  Was Cubs fandom an ancestral heritage?  Was his Little League team the Cubs?  I had to know.

     Turns out he was at home sick one day and by chance tuned into an afternoon Cubs game on superstation WGN.  On the mound for the Cubs was a portly pitcher with the same first name as him: Rick Reuschel.  That's it.  That's all it took for him to become a fan of the Chicago Cubs.  He knew nothing of their storied history, none of the famous players who had worn the uniform, or anything about their iconic ballpark.  (He also didn't know that the Cubs were the poster franchise for disappointment and failure-- they hadn't won a World Series since 1908.  If he had, he might've thought twice.)  It was simply a matter of fate.  He was home one weekday afternoon.  The Cubs, the last major league team to install lights at their home park and play night games, still liked to honor tradition by playing weekday day games.  In the 1980s, as cable proliferated, WGN fed Cubs games into homes all over the country.  The Cubs were in the field and Rick Reuschel was on the mound.  He heard his name and the rest was history.

Rick Reuschel


   My New York Yankee fandom is an ancestral heritage.  One of my earliest memories is sitting with my dad watching a Yankee game, and my dad pointing to the little black and white TV and saying, "That's Mickey Mantle."  The Mick was way beyond his prime, though I was too young to know that at the time.  (A lifetime later my dad joined his brother and three of their cousins at Yankee Fantasy Camp, where a broken down, alcohol-soaked Mantle was barely able to wobble onto the field.)

     Mantle had retired before I saw my first game in person-- Tuesday, May 19, 1970.  I was in fourth grade, and my dad and my paternal grandfather took me to the old Yankee Stadium to see the Yankees play the Orioles.  It was a night game, and the view of the field as we came through the tunnel to our seats in the upper deck--so big, so green, all lit up in the dark Bronx night--took my breath away.  I think fell asleep in the seventh inning.  The Yankees lost, 5-1.            

     They lost a lot when I was a kid.  I came of age during what long-timeYankee fans refer to, not without a little lingering PTSD, as the Horace Clarke Years--a roughly ten year stretch from the mid 1960's to the mid 1970's where the team was mired in mediocrity.  The one bright spot was centerfielder Bobby Murcer, the heir apparent to Mantle.  (The parallels were eerie.  Both from Oklahoma, both converted shortstops, both signed by the same scout.)  So Murcer became my favorite Yankee.  I can remember my dad showing up to my Little League games straight from work, sitting in the stands with one eye on the field and the other on the Wall Street Journal.  On the car ride home he would prank me by saying, "Did you hear the Yanks traded Murcer?"  For a moment I thought he was telling the truth.  With a crushed look and tears welling up I'd turn and say, "Really?"  Then he would make up some ridiculous trade that I knew couldn't be true and we would laugh...until it really was true and Murcer really was traded-- to the San Francisco Giants for Bobby Bonds.  I was heartbroken and outraged, and threatened to leave the Yankees forever and become a Giants fan.  That's when my dad gave me the speech, which in today's terms we'd call the "rooting for the laundry" speech.  I stuck with them, and soon after they began their late1970s ascendency: a pennant in 1976 and World Series wins in 1977 and 1978.  We all sat--my mom and dad, my brother and sister, my grandparents--with our rally caps on rooting for the Yanks through exciting play-off and Series games.  Their success was made ever so much sweeter because I had suffered through such lean years.  


     My daughter inherited her NY Football Giants fandom from me; I inherited it from my maternal grandfather.  He waxed nostalgic about Frank Gifford, Sam Huff, and the glory days of the 1950s; I came of age during the so-called "Wilderness Years", which again made the success the franchise achieved in the mid-to late- 1980s and early 1990s so very sweet and satisfying.  She came of age as a fan post- first decade of the 2000s, after the Coughlin Era Super Bowl successes, during what Giants fans are now experiencing as "The Wilderness Years Part 2."  Like me with Bobby Murcer, she latched on to what's been the only real bright spot during this time, the electric, controversial wideout Odell Beckham, Jr.  She loved his dynamism, his athleticism, his hair and his social media presence.  When he was traded to the Cleveland Browns she cried tears of fury and threatened to never watch another Giants game.  I trotted out the same speech my dad had given to me-- about how while it's natural to get attached to players, the hard truth is that players come and go, that ultimately you need to stick by your team regardless of who wears the uniform, and that one day they will be good again, and we'll watch them win a Super Bowl together, and all the heartbreak and pain we've experienced watching them lose will make the winning that much sweeter.  It took a lot of convincing, and she hates to lose, but she's hanging in there.  



    Based on his age at the time he was in my class, I figure that Ricky F. became a Cubs fan in 1984, during Rick Reuschel's second stint with the Cubs.  In 1985, the Cubs traded Reuschel to the Pirates.  This means that, even after the trade, Ricky remained a Cubs fan.  He continued rooting for the laundry.  In 2016, the Cubs finally won the World Series, their first in 108 years.  (They still hold the streak for longest World Series drought.)  I don't know what happened to Ricky F., but I hope he stayed a Cubs fan.  I estimate he'd have been in his late thirties on that early November night in 2016 when the Cubs, after being down 3-1, defeated the Cleveland Indians 8-7 in 10 innings in what some consider to be the most dramatic Game 7 ever played.  He'd have endured lots of heartbreak in the 30+ years since he first heard his name coming out of the television.  I hope he passed down his fandom to his son or daughter, and that they were sharing the sweet moment of victory and vindication with him, just as I hope to share that feeling with my daughter when the Giants win the Super Bowl again.  

     If you've ever known that feeling, you know there's nothing like it.     

Bears vs Giants
MetLife Stadium
November, 2016



Tuesday, December 15, 2020

Flick Lives!

    Around this time of year, when the temperature really starts to drop and mornings become frosty; when the leaf blowers finally go silent and the smell of chimney smoke begins to pervade the block; when most of the houses in the neighborhood dress themselves in lights and wreaths and the lawns fill up with reindeer, snowmen, sleds and Santas; it's right around now that in one bay window there invariably appears a strange sight:

   This is the notorious leg lamp, made famous in A Christmas Story, the popular holiday movie co-written and narrated by the legendary humorist Jean Shepherd, and based on the semi-autobiographical reminiscences he related in print, in his radio monologues, and in live performances.  Initially overlooked when it was released in 1983, the film now consistently ranks among the top holiday movies ever produced.  Many know it from TNT and TBSs "24 Hours of A Christmas Story", where it is shown 12 consecutive times, from 8 pm on Christmas Eve to 8 pm on Christmas Day.       

  Passing the house on my daily morning walks, I'm reminded of Jean, and the small part he played in my childhood and adolescence.  Jean (he was widely known as Shep, but to us he was always Jean) was friends with my best friend Mike's parents, and he could frequently be found visiting their house on Skyline Drive, where I was also a frequent visitor.  With the same last name as his erstwhile childhood best friend, we had an immediate connection.  I picture him sitting at their big kitchen table, chuckling "There's that Schwartz again," as I passed by on my way up to Mike's room.  He would often attend Mike's birthday parties; I remember one in particular when he accompanied us all to Shea Stadium to see the Mets play the Reds.  At first, I had no idea who he was, other than that he was some kind of special family friend.  But after piling into the back of Mike's family's puke green station wagon for a trip down to Princeton to see him perform at McCarter Theater, I was hooked.    

     Jean had a nightly radio show on WOR, where, after the opening theme (Eduard Strauss's Bahn Frei!), he would spin his incredible monologues, and occasionally read poetry, play the kazoo, and organize listener pranks and hoaxes.  I started tuning in.  Rushing to finish my homework in time, I would sit in my bedroom, listening to the sound of his distinctive voice coming through a little clock radio with the dial at AM 710, entranced by the way he would start out on one path and veer through numerous digressions, twists and turns.  With my eye on the clock, watching the digits click by and knowing that time was running out, I would try to guess how in the world he would tie everything together.  But like Coltrane coming back to earth after flying off into outer space at the end of My Favorite Things, he always did.  And every time one of the stories would refer back to his childhood and his friend Schwartz, as they often did, well, that was an extra special night.  The next day Mike and I would compare notes, because I knew he had listened, too.      

    Jean's books were also a constant presence, especially Wanda Hickey's Night of Golden Memories.  (My original copy became so tattered that the pages started falling out, and I eventually had to get a new one.)  I read and reread the stories, and then read them aloud to my brother, sister, and parents.  Schwartz, Flick, Kissel, Grover Dill, Scut Farkas; they were all alive in our house.  We had next door neighbors who, for reasons that will go unstated here, we referred to as the Bumpeses.  The leg lamp?  We knew about that from Chapter 10 of In God We Trust: All Other Pay Cash  before we saw it in the movie.  Of course there was The Ferrari in the Bedroom, which was dedicated to Mike's parents, with Mike's dad being the inspiration behind the main character in the story Abercrombie's Bitch.      

     After his radio show ended in 1977, it got harder to find him on the air (remember, this was the cable stone age and way pre-internet), although he did write, direct, and edit a show called Shepherd's Pie on New Jersey Network for a time. Mike and I went away to college, his parents divorced, my parents moved to another town.  Jean moved to Florida and I never saw him again.  But I was really happy to see him find mainstream success and recognition with A Christmas Story.  Now, like Proust's madeleine, seeing the lamp in the window brings back a cascade of memories: my childhood bedroom, the WOR radio days (we loved Bob and Ray too), and of course my best friend Mike, who idolized Jean and who I believed Jean loved.  Mike, a journalist by trade, had plans to write his biography.  However it was not to be-- Mike was tragically taken from this world 18 years ago.  (Mike, I miss you every day.  Excelsior, you fathead!)  So if you're a fan of A Christmas Story, and that's all you know of him, do yourself a favor and google Jean and do a little research.  Read about how influential he was.  (Jerry Seinfeld has been quoted as saying, "I learned how to do comedy from Jean Shepherd.")  Listen to some of his recorded monologues.   (Think of them as podcasts.)  Watch him being interviewed by David Letterman in 1982 (where he explains his failures in Algebra class.)  And always remember: Flick Lives!


Jean Shepherd
July 26, 1921-October 16, 1999


Tuesday, September 15, 2020

"Count Be Wrong, They'll Mess You Up."

     One of the most unforgettable characters in David Simon's epic masterpiece The Wire is Wallace.

Wallace is portrayed by a young Michael B. Jordan.  Jordan, who grew up in Newark, NJ, has gone on to star in Fruitvale Station,  Fantastic Four,  Creed, Creed II and Black Panther.

   A low-level drug dealer in the Barksdale crime organization, the sensitive 14 year-old, not much more than a child himself, also acts as a "house dad" to a group of stray youngsters living in an abandoned Baltimore tenement.  He rousts them out of bed in the morning, makes sure they have something to eat, and sees them off to school.  In a scene that takes place late in Season One, he tries to provide some homework help to one of the children, Sarah.  She's having difficulty solving a word problem, which Wallace reads back to her from her textbook:

A bus traveling on Central Avenue begins its route by picking up eight passengers. At the next stop it picks up four more and an additional two at the third stop while discharging one. At the next to last stop, three passengers get off the bus and another two get on. How many passengers are still on the bus when the last stop is reached?

     "Just do it in your head," Wallace tells her.  Distracted by another conversation he's carrying on with a housemate, he impatiently dismisses her when she comes up with two wrong answers, first seven and then eight.  Finally, (and edited for language):

Wallace (focusing): Close your eyes.  You working a ground stash.  Twenty tall pinks.  Two fiends come up and ask for two each, another one cops three.  Then Bodie hands you ten more, but a white guy rolls up in a car, waves you down, and pays for eight.  How many vials you got left?
Sarah (without hesitation): Fifteen.
Wallace (dismayed): How can you keep the count right, but not do the book problem?
Sarah (matter-of-factly): Count be wrong, they'll mess you up.

     Here's Jemele Hill commenting on the scene on her (and Van Lathan's) excellent Wire rewatch podcast Way Down in the Hole:
I thought that was a great way to show how potential is being wasted.  A good reminder about testing 'cause we've all grown up having to take SAT tests, ACT tests, we had the MEAP test when I was in Michigan, the proficiency exams, and those tests and those problems they're so unrelatable to the kids who are actually taking the test.  And this was a very subtle way to make a statement about the cultural inequalities that these tests and the educational system present to children. 

     Hill's analysis of Simon's point, which he will develop in depth in Season Four, is well taken.  (One disagreement: it's not very subtle.)  And it's one that has been discussed and argued about for at least as long as I've been in the field.  Questions and debates related to student engagement with mathematical content, pseudo-context and "real world" problems, true intellectual need vs "you need to know this because it's on the test", how we measure mathematical proficiency and intelligence, the implicit and explicit biases embedded in our curricula and our practice-- these are all encapsulated in this one small scene.
     The bus scenario from Sarah's math book is downright tame compared to others we've seen.  Consider Dan Meyer's classic dog bandana.  Or Cathy Yenca's diner sign:   

How about Geoff Krall's trail mix:

     They leave us shaking our heads in dismay.  And they'd be hilarious if the stakes weren't so high.
     But here I'd like to explore Hill's analysis further, because what's happening here goes beyond simply transcribing Wallace's problem and substituting it for the bus problem in Sarah's textbook to make it more relatable.  For one thing, the bus problem is not contrived, like the dog bandana, diner sign, and trail mix problems.  I mean, it's contrived for math class, but it's not that much of a stretch.  After all, buses do pick up and discharge passengers at bus stops.  Growing up in an urban environment, we can assume Sarah has a frame of reference for a city bus picking up and discharging passengers.  And for the sake of the discussion here, let's also assume that she can read, and that the issue is not one of comprehension.  So why would Sarah have so much trouble with the bus problem?  It's not the arithmetic.  Is the bus problem one she can't relate to?  Just because buses exist in the real world does it necessarily follow that the problem is real for Sarah?
     The reason Sarah gives Wallace for her ability to solve his alternate problem is "Count be wrong, they'll mess you up."  Sarah, whose after-school activity is running back and forth between a Barksdale drug stash and the customers, understands that an error on the count has very real, very dangerous consequences.  This is intellectual need in the extreme.  For her, the stakes of mentally adding and subtracting couldn't be higher, and the stakes of correctly solving the book problem pale in comparison.  She's got more things on her mind than buses.  Wallace, who throughout his time on the series shows real intelligence and curiosity, connects the bus problem to the ground stash problem in order to make it more meaningful.  He would excel in a school setting.  Sarah cannot make that connection.                       
     The math Sarah does outside of school, the math any of us do outside of school, arises organically from the situations we find ourselves in.  We may or may not recognize them as overtly mathematical, and their consequences may range from critical to trivial, but they're there: in the work we do in and around our homes, in our jobs, in what we choose to do with our leisure time.  For our students, especially our young ones, it most likely arises from simple play.  Let's call it "math in the wild."  But there's a wide gap between that math and the math that we encounter in school.  Good teachers try to bridge that gap as best they can, and some students (i.e. Wallace) can bridge that gap for themselves.  But the gap remains, especially on assessments, especially, as Hill notes, on high-stakes standardized assessments. Unfortunately, it's the performance on those measures that generate our grades and our scores, our opportunities for further educational advancement and, perhaps most important, our feelings of self-worth as learners and human beings.  Sarah will likely fail her next math test.  But it won't be because she can't add and subtract.  So what does her performance on the test really mean?  Wallace, who in an alternate universe would be in honors classes, no longer even attends school.   
     Sarah's situation, like so many others in the show, is a human tragedy.  Growing up amidst the violence, poverty, insecurity, systemic racism and trauma that is the Baltimore depicted in The Wire, she faces much bigger obstacles than a word problem in a math book.  It's just one small piece of Simon's complex tapestry.  But the "wasted potential" Hill is talking about in this particular scene is one that transcends Simon's Baltimore.  It happens everywhere students who are smart and capable are meant to feel "less than" in math class.       
     Fans of The Wire know what happened to Wallace.  Here's David Simon in Jonathan Abrams's oral history of the show All the Pieces Matter: 
People are going to remember Wallace.  Wallace is going to bother them for a long time after the whole show is forgotten.
     He's right.  Around for only one season, his impact is felt throughout the rest of the show's run.  But here's what I'd like to know: What happened to Sarah?

Tuesday, July 28, 2020

Kiss Kiss Bang Bang

    To mark the 10th anniversary of the Common Core's publication, here are my capsule-length reviews of selected K-8 standards:
(All reviews stolen from movie listings posted daily in The New York Times.)

By the end of Grade 3, know from memory all products of two one-digit numbers.
 Curiously retrograde

Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.  For example, which of the following equations are true and which are false?  
6 = 6,  7 = 8 - 1,  5 + 2 = 2 + 5,  4 + 1 = 5 + 2 
 Top notch existential confusion

Understand that attributes belonging to a category of two-dimensional figures also belongs to all subcategories of that category.  For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.
 Laborious brainteaser

Develop a probability model (which may not be uniform) by observing frequencies in the data generated from a chance process.  For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down.  Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?
 Predictable but hard to hate 

Find all factor pairs for a whole number in the range 1-100.  Recognize that a whole number is a multiple of each of its factors.  Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number.  Determine whether a given whole number in the range 1-100 is prime or composite. 
 Disaster by the numbers

Analyze and solve pairs of simultaneous equations.
Zoom, crash, repeat

 Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number.  If p and q are integers, then -(p/q) = (-p)/q = p/(-q).  Interpret quotients of rational numbers by describing real-world contexts. 
 Almost willful lack of fun

Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. 
 Answers questions no one needed to ask

Use place value understanding to round multi-digit whole numbers to any place.
 Blunt and sadistic

Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.  For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3.  (In general (a/b) ÷ (c/d) = ad/bc.)  How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally?  How many 3/4-cup servings are in 2/3 of a cup of yogurt?  How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?
 Overstuffed spectacle

Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies using $ and ¢ symbols appropriately.  For example, if you have 2 dimes and 3 pennies, how many cents do you have?
 Melancholy melodrama
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch.  Show the data by making a line plot where the horizontal scale is marked off in appropriate units--whole numbers, halves, or quarters.
 Best when no one's talking 

Solve multi-step real life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically.  Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.  For example, if a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50.  If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches for each edge; this estimate can be used as a check on the exact computation.
 Turgid schedule filler

Fluently multiply multi-digit whole numbers using the standard algorithm.
 Incredibly tedious

Fluently add and subtract multi-digit whole numbers using the standard algorithm.
 Strictly formulaic

Solve unit rate problems including those involving unit pricing and constant speed.  For example, if it took 7 hours to mow 4 lawns, then at that rate how many lawns could be mowed in 35 hours?  At what rate were lawns being mowed?
 Hack work
Model shapes in the world by building shapes from components (i.e. sticks and clay balls) and drawing shapes.
 Broad, freewheeling fun


Wednesday, July 15, 2020

A Requiem For Twitter Math Camp

    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.  
     TMC '15 was everything I could have hoped for, and much, much more.  Beyond the amazing sessions, it was an opportunity to meet people from all over the country, all over the world, actually.  People who were involved in math education in all kinds of different ways: elementary school teachers and district administrators, university professors and math coaches; private school, public school and home school; urban, suburban, rural; big, small, and in between.  We were all there, on our own time and on our own dime, because we were passionate about what we did and eager to learn from each other.  During the day we went to sessions, interspersed with keynotes and quick hit "My Favorites".   After, we hung out in the courtyard of the hotel till all hours of the night.  I couldn't sleep, my head was spinning at 100 miles per hour.  I kept Graham up all night, blabbering away non-stop about who I had met, what we had talked about and what I was going to do when I got back to the world.  He told me I was drinking from a firehose.  He also told me to stop talking and go back to sleep.  By Sunday morning's final assembly I was emotionally exhausted.  When a group of participants stood up and sang a goodbye song, I started to tear up.  And when Lisa Henry announced the date and location of next year's TMC, I immediately phoned my wife and told her to block it out on the calendar.
     When I got back home everyone asked: "What was it like?"  
     All I could think of was something that Christopher Danielson had said: "It's like being in the faculty lounge of your dreams."  Like baseball fantasy camp, except with math teachers.  

      I went back to Twitter Math Camp in 2016, 2017, and 2018.  Each time I was afraid that the magic would be gone, that I would be disappointed, that it wouldn't live up to my expectations.  Each time I was wrong.  Part of it was the different locations--it was fun to explore a new city each summer.  Part of it was reconnecting with old friends.  Part was the fact that each time I went back I connected with new people, widening my network of friends and colleagues, which made our virtual interactions during the rest of the year richer.  Part of it was my own increasing confidence presenting sessions.  Although I knew that attendance was capped and I wasn't guaranteed a spot, I began to count on it to recharge my batteries for the coming school year. 
     More than the venues, more than the cities, more than the sessions, more than the keynotes, more than the math, for me TMC was a place where, for four brief days, 200 lives intersected in a very intimate way.  Shared breakfasts, lunches, and dinners.  Early morning coffees and late nights in hotel courtyards and lobbies and, on one special occasion, in a college dorm.  Clusters in the corners of classrooms.  On stairwells and in hallways, on Ubers and in airports.  I couldn't even begin to count all the different conversations I had with all the different people I met along the way.  They challenged me, informed me, encouraged me.  They agreed and pushed back.  They listened, and no matter how crazy I sounded they made me feel like I had something worthwhile to say.  For me, it was different than the big, industrial NCTM conferences.  Nobody was selling anything, nobody was angling for a deal or working the room, or trying to impress anybody.  It wasn't institutional.  It was t-shirts and shorts.  It was, as we would say in Yiddish, haimish.
     In 2018 I convinced a former work colleague to join me.  Now I was the old hand and she was the nervous newbie.  I was curious to see her reaction and to look at something I had begun to take for granted through her eyes.  How would she would find the experience?  I told her that I'd always be around for her, that I wouldn't leave her without someone to have breakfast, lunch, or dinner with, or to hang out with after the day's sessions were through.  There had been talk that things had gotten cliquey, that newcomers weren't being made to feel especially welcome.  I knew that people experienced TMC in different ways, and that the leadership had made attempts to make people feel more included.  I knew that not everyone felt the same way about it that I did.  Turns out I had nothing to worry about: after the first day she had met a bunch of people and made her own friends, some of whom became my new friends.  She talked about going back.  I started making plans with Brian Miller to submit a proposal to co-present a session at TMC '19 in Berkeley.

      I didn't see it coming.  One day the acceptances came out, and then, suddenly, it imploded.   I've worked through the stages of grief, and I think I've finally arrived at acceptance.  Looking back these last few weeks at my pictures, revisiting the archives and the old tweets, my heart is filled with gratitude for all those who worked so hard to make it happen.  I'm sorry if I didn't let you know just how thankful I am.  I know I was blessed to be able to experience those 16 special days in the summers of 2015, 2016, 2017, and 2018.  It's not my intention to reopen any wounds or reignite any debates.   It's just I never got the chance to say goodbye.



Wednesday, July 1, 2020

And Then They Came For the Statisticians

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."

Mike Schneider
Associated Press
June 26, 2020 


...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.

Karl Schlögel 

     For one 24 hour period, from midnight January 6, 1937 to the following midnight, life in the entire breadth of the Soviet Union, one-sixth of the world, came to a stop.  On that day, after weeks of extensive training, one million enumerators (census takers) with a list of fourteen questions spread out over the entire country.  Their mission was to collect the information that, when analyzed and pieced together, would form a detailed picture of what Soviet society looked like twenty years after the Bolshevik Revolution.  The enumerators knocked on the doors of apartment blocks in Moscow, skied across the Arctic tundra to remote villages, and rode with passengers on the Trans-Siberian Express.  As Karl Schlögel describes in his book Moscow 1937:   

     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.
     The populace was ready.  The census protocol had been highly publicized in workplaces and shops and over state media outlets.  The questions submitted to the Party leadership by the Census Board were edited by Party leader and supreme ruler of the USSR Joseph Stalin personally (he had removed eight and added one) and had been released in advance so citizens knew exactly what to expect when an enumerator showed up on their doorstep.  It was a remarkable achievement, one that required careful planning, tremendous resources and a nationwide mobilization.  What makes it even more astonishing is that, according to Schlögel, historians and demographers with access to the formerly suppressed results--made available in the 1990s after the Soviet Union's collapse--have calculated the margin of error at a low 0.5 to 0.6 percent.  
Information poster

It was Stalin who had ordered the census, and he had a lot riding on its outcome.  It had been eleven years since the last one, a time of rapid industrialization and societal upheaval.  A program of forced agricultural collectivization and two Five-Year Plans had run their course.  Stalin believed that the demographic figures would prove that the Soviet Union had built a vibrant, happy and healthy society.  High growth rates were predicted, outstripping those of rival capitalist countries.  Officially, a population figure of 170-172 million was expected (a number extrapolated from the 1926 census); Stalin was hoping for something closer to 180 million. 

Census data being processed
     They knew they were in trouble almost immediately.  Preliminary results indicated that average growth, while surpassing Germany, England, and France, was exceeded by both the United States and Japan.  Stalin's added question was about religious affiliation; he expected the state's anti-religion policies to reflect a high number of non-believers.  Yet close to 60% of the adult population identified themselves as believers.  Most alarming, the final count would be somewhere around 162 million, 8 million people shy of the official pronouncement.  I.A. Kraval, the Census Bureau Chief, ordered a recount, but only several thousand unenumerated persons were found.  In late January, the provisional results were presented to the Party leadership, and a further report in March confirmed the original figures.  Kraval and his team of demographers and statisticians, fighting for what they knew were their lives,  did their best to excuse the results, but the difference between the final count and the publicly stated number of 170 million was too great to explain away.
     Where were the missing 8 million?  And who was to blame?  The biggest discrepancies between the expected numbers and the actual count were in the regions hardest hit by the devastating 1932-1933 famine caused by Stalin's policy of forced collectivization.   Historians are still debating the actual death toll--estimates range up to 7 million--and also to what extent anyone at the time had an accurate fatality count.  (Ironically Kraval was sending false reports to Stalin, downplaying the numbers.)  In any case, the famine had been officially denied, and anyone who talked about it risked imprisonment and death.  The census data, which reflected the tragic consequences of Stalin's policy, had to be suppressed.  So did those involved with the data collection.  
     The arrests began in March.  No one was safe; from the members of the central Census Bureau to the chiefs of the regional census centers, right down to administrators at the local level.  Statisticians assigned to replace the imprisoned were soon imprisoned themselves. The statisticians and demographers were accused of sabotage and "wrecking", and labeled "Trotskyite-Bukharinite spies" and "enemies of the people".  Many of those imprisoned were eventually executed.  Kraval himself was condemned to death in August and shot.  A new census was planned for 1939.  Schlögel links this to the Great Terror:  

...having destroyed the analytical matrix which disclosed the contours of the nation and its people, and having sacrificed the very instrument that would enable them to interpret these things, the leadership... (was) overcome by a blind flight into terror, an intensification of violence whose excesses would surpass the very disasters that the census had just diagnosed.  As a result, for the catastrophe that followed there were no longer any instruments that might have diagnosed what was to come.     

      Not surprisingly, the new census resulted in a population count of 170.6 million people.  Just what Stalin had ordered.  The question about religious affiliation was eliminated.  There would not be another census until 1959.      

     Suppression of truth and truth-tellers isn't exclusive to the former Soviet Union.  It's not hard to come up with examples of our own.  The data linking smoking to cancer and the cover-up of abuses by clergy in the Catholic Church are two that come to mind.  We know stories of individual whistleblowers coming to bad ends (see Karen Silkwood) and we also know of consumer advocates forcing changes to promote public safety (see Ralph Nader).  Thankfully, we have avenues to access information, mechanisms to uncover truths, protections for those who would speak truth to power and independent media outlets to publicize those truths that would be unthinkable in the Soviet Union under Stalin.  Our system of government is based on checks and balances, and while it may not always work the way we want it to, it does provide a measure of protection against the worst autocratic tendencies of an executive, protections that, again, would have been unthinkable to Stalin.
     Consider the case of our census, currently in progress.  When the Trump administration tried to add a question related to citizenship, it was met with resistance and criticism, not only from progressives, but from statisticians and demographers, who argued it would threaten its integrity, estimating that inclusion of the question could lead to an undercount of 9 million people.  The pretext for adding the question was seen as strictly political; it was a way to depress the count in heavily Democratic areas, which would have consequences for proportional representation in Congress, how many electoral votes a state receives, and how and where some $1.5 trillion in federal money is allocated. A lawsuit challenging the question made its way to the Supreme Court.  In a fractured and complicated 5-4 decision, the court ruled that the justification for adding the question was invalid.  Unable to delay the implementation of the constitutionally mandated decennial census, the administration threw in the towel.  
     However the recent appointments of Cogley, a frequent radio commentator and former head of the department of government, legal studies and philosophy at Tarleton State University and Korzeniewski, who once worked as a consultant for the failed Staten Island congressional run of Joey "Joey Salads" Saladino, a YouTuber famous for racist pranks, and whose primary qualification seems to have been that he once worked in a census bureau field office, to top positions at the U.S. Census Bureau should be cause for alarm.  It certainly is to Kenneth Prewitt, a former Bureau director.  "These are two people ill equipped to actually manage the census," he said in a Politico report:
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.

     What influence will they exert on the counting and reporting of the census figures?  Will they be guided by best statistical and demographic practices?  Do they even know (or care) what those practices are?  Were they put there to do the bidding of the administration that appointed them?  Will the final census be an accurate reflection of America in the year 2020?  And if it isn't, will we even know?

    All this is to say that our community has a very important role to play.  Math helps build the models, math looks at the data, math runs the statistical analysis.  It's our job to call bullshit when we see it...

...and it's our job to give our students not only the tools they need to be discriminating and critical consumers of information, but the confidence to use their voices to speak out when they see data being used to deliberately manipulate and confuse; whether it's related to: 
something as innocuous, like how many people attend an inauguration, 
something important, like a census count, 
something serious, like the death toll from the coronavirus, or 
something that threatens the very existence of life on the planet, like climate change.  
So whether you're in kindergarten teaching kids how to count with one-to one correspondence or in high school teaching AP Stats, or anywhere else above, below, in between or sideways, please keep your shoulder to the wheel.