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Unsolved puzzles, open games, and questions still left on the table

Family Trees for Shakespeare’s Histories

Friday, September 19th, 2014

My monthly Shakespeare reading group is gearing up to do the history plays. For the next eight months, starting this Sunday, we’re going to be working our way through the two tetralogies.

Shakespeare, working in the late sixteenth century, was writing about his own country’s history spanning most of the fifteenth century. He could assume his audience was familiar with the stories and the characters to some degree. Our perspective, over four hundred years later and in another country, does not provide the same level of context.

Imagine we were watching a play about the American Civil War and characters made various passing references to “the president,” “Lincoln,” and “Honest Abe.” We would understand these are all the same person, no explanation needed. But someone unfamiliar with our history might get confused. In Shakespeare’s histories, characters refer to each other by last name, nickname, and title interchangeably, and their iconic status in English memory requires very little exposition. When we do actually get a first name, it’s usually one of the same six or seven names recycled endlessly throughout the generations, relying again on context for specificity.

Thus, in order to facilitate the readings, I have created a family tree for the Plantagenets that spans all eight plays. For each play, I have put together a version of the tree that shows the current state of the family as the action begins. It shows who’s living, who’s dead, who’s related to whom, who is actually in the play, and what names might be used to reference them. What’s more, it all fits on one page, so it makes a convenient handout for a reading.

It was quite a project, but now that I’m finished, it’s my pleasure to share the results with the Shakespeare Teacher community:

Whether these charts end up providing more clarity or only more confusion will remain to be seen. I’ll be field testing them with my group and may find a need to do a rewrite in eight months time. If anyone out there sees anything seriously wrong or just has a helpful suggestion, please leave a note in the comments so I can address it in the next round of revisions.

A few notes may be helpful. A shaded box means that the character is dead before the play begins. A bold-faced box means that the character appears in the current play. Each space represents the same character across all eight plays, but there are two characters (Anne Mortimer and Isabella Neville) that are duplicated on the chart because they married across family lines. These are represented by circled numbers.

For the most part, Shakespeare sticks with history as far as the genealogy and chronology are concerned, but where he breaks with history, I generally went with Shakespeare’s version. I did this because the purpose of the chart was to make the readings easier. So if Shakespeare, for example, refers to a character by a title he technically didn’t have yet, I used that title on my chart.

One major exception to this is the case of Edmund Mortimer. Historically, there were two different men named Edmund Mortimer in this story: Sir Edmund Mortimer, and his nephew Edmund, Earl of March. An Edmund Mortimer appears in Henry IV, Part One and an Edmund Mortimer appears in Henry VI, Part One. It appears that Shakespeare has conflated the two men into a single character, as he ascribes to the character biographical details from both men in both plays. I went with the more historically appropriate choice to put Sir Edmund in 1H4 and the Earl of March in 1H6, but you should know that when using these charts with those plays.

A lot of the information in these charts were taken from the plays themselves. But the charts also include a lot of historical information, and for that, I used other sources. I took advantage of the excellent genealogical tables in The Riverside Shakespeare (G. Blakemore Evans, ed.) as well as the Arden editions of Henry V (T.W. Craik, ed.) and Henry VI, Part Three (John D. Cox and Eric Rasmussen, eds.). I found The Cambridge Companion to Shakespeare’s History Plays (Michael Hattaway, ed.) very helpful. I also consulted the official website of the British Monarchy, as well as other online sources as needed.


Conundrum: An Eventful 52

Sunday, January 5th, 2014

The following recap of 2013 has been redacted by overzealous Internet censors! Can you fill in the blanks to restore our memories of the year?

Here’s the catch: all of the missing words are in alphabetical order. Enjoy!

Was it only 52 weeks __(01)__ that we celebrated the arrival of 2013? A lot has happened since then. __(02)__ __(03)__ was __(04)__ from the same network as Mr. __(05)__ later would be. The __(06)__ story of the past 365 days might be that terrible __(07)__ in __(08)__. The __(09)__ of a mayoral __(10)__ ended when he was revealed to be using the name __(11)__ __(12)__. This may have been the most __(13)__ incident of 2013, unless you wish to give that __(14)__ honor to the family of __(15)__ __(16)__, whose __(17)__ member __(18)__ many by __(19)__ his more __(20)__ views, which many felt went too __(21)__. At the movies, the latest __(22)__ & __(23)__ film had a __(24)__ showing at the box office, though it did not __(25)__ as much __(26)__ as the latest __(27)__ __(28)__ film. In music, the artist born __(29)__ __(30)__ released a second LP with that name. Internationally, __(31)__ __(32)__ was removed from power, while domestically, we fought __(33)__ over __(34)__, the __(35)__ signature __(36)__. The __(37)__ __(38)__ it fiercely, and the __(39)__ itself certainly had some __(40)__ spots. In fact, the worst __(41)__ of 2013 may have been the __(42)__ it triggered, though just as __(43)__ was when Mr. __(44)__ __(45)__ out about the government’s __(46)__ on Americans as part of a secret __(47)__ program. In sports, we once again saw that nobody could __(48)__ from the __(49)__ like __(50)__ __(51)__. All in all, it was an eventful __(52)__.

Question of the Week

Monday, September 2nd, 2013

So, today was my birthday.

People always seem to want to know how you spent your birthday. Frankly, it’s just another day to me, so it doesn’t bother me that I spent much of it preparing for a workshop tomorrow.

The workshop is going to be on the Danielson Framework for Teaching, a 22-component system for evaluating teacher effectiveness. Last year, New York City was using three of these components, and we all had to learn them inside out. This year, we’ll be using all 22, and everyone is scrambling to catch up.

Over the next two days, my job will be to train all of the teachers in one high school on the extremely comprehensive criteria on which they will be judged.

I did some trainings on the Framework over the summer. Teachers approach it with skepticism, as experience has taught them to be cautious of new initiatives. Added to this is the reasonable perception that the system can often be hostile to teachers. But once we actually delved into the measures, the teachers generally agreed that they are fair, assuming the evaluations are implemented fairly.

I’m guessing that the Danielson Framework will be a very important part of my life between now and my next birthday, so I should say a few words about it. The 22 components are organized in four domains:

Domain 1: Planning and Preparation
Domain 2: The Classroom Environment
Domain 3: Instruction
Domain 4: Professional Responsibilities

New York City is using the ratings based on the Framework as a portion of overall teacher evaluation, and Domains 2 and 3 will be 75% of that portion.

As an interesting side note, I was in Pennsylvania visiting my sister last week, and I happened to be there on the day that the kids were assigned their teachers. Parents were texting and calling each other like mad trying to determine who got what teacher and how the classes would be made up.

Out of curiosity, I asked my sister what parents look for when they decide what teachers they want their children to have. She listed a number of qualities that mainly fall into Domain 2. I asked her if parents in her community care about how much test scores improved for the class the teacher had the previous year. They couldn’t care less.

So that’s not a scientific study, but it is an enlightening data point. As we head back to school, I’d love to turn the question over to the Shakespeare teacher community.

When you send your own children back to school, what do you look for in a teacher?

Top Ten Shakespeare Retrochronisms

Wednesday, October 3rd, 2012

Don’t worry if you don’t know what a retrochronism is. I just made the word up. But feel free to throw it around at the dinner table and the water cooler; it’s a thing now.

Let’s say an author from an earlier time period uses a term in a sense that’s appropriate to that author’s time period. Then, the author dies and the language evolves. New technologies are invented. Culture shifts. Later readers or audiences then interpret the term as used by the author through the lens of their own time period, and incorrectly think it means something entirely different from what the author could have possibly intended. That’s a retrochronism!

This is not to be confused with an anachronism, a term generally used to describe instances where an author uses something from his own time in a work that is set before that thing would have been possible or appropriate. Shakespeare has many such anachronisms, such as the clock striking in Julius Caesar. But a retrochronism is different. It isn’t a mistake by the author; it’s an accident of history.

We’ve had 400 years now to develop a few good examples for Shakespeare. The quintessential example is from Romeo and Juliet:

JULIET: O Romeo, Romeo! wherefore art thou Romeo?

Most readers of this blog probably know that “wherefore” means “why” and not “where.” But this is far from obvious, and many newcomers to Shakespeare, entering his world through this play, assume she’s searching for him from her balcony. Who says “wherefore” anymore?

Another common example can be found in Hamlet:

HAMLET: Madam, how like you this play?

QUEEN: The lady doth protest too much, methinks.

HAMLET: O! but she’ll keep her word.

In Shakespeare’s time, “protest” meant to promise. But today we think of it in the opposite sense of a denial. So when people quote the line, they often mean that a person is denying something so much that it must be true. But Gertrude meant that the lady was promising so much that it must be false!

Those two examples are probably the most well known, but below are my ten favorites, culled from years of introducing kids to Shakespeare and from my own journey of working through the language.

TEN. Was Doll Tearsheet a One-Percenter?

DOLL: A captain! God’s light, these villains will make the word captain as odious as the word ‘occupy,’ which was an excellent good word before it was ill sorted: therefore captains had need look to it.

Playgoers who have attended productions of Henry IV, Part Two in the past year must have been taken aback by this statement, possibly even suspecting editorial interference for political purposes.

But in Shakespeare’s time, the word “occupy” was slang for having sex with someone. It’s enough to make you wonder what was really going on at Zuccotti Park after hours.

NINE. Did the Witches prophesy Kitty Hawk?

FIRST WITCH: Here I have a pilot’s thumb,
Wrack’d as homeward he did come.

Most modern audiences are familiar with the word “pilot” as meaning someone who flies an airplane, obviously not what Shakespeare meant in Macbeth.

The word “pilot” meant (and still means) someone who steers a ship.

EIGHT. Was Lord Capulet a pimp?

CAPULET: What noise is this? Give me my long sword, ho!

Here is one that comes up often when working with kids; this example from Romeo and Juliet is as good as any. Shakespeare had a lot of words for “prostitute,” but “ho” was not among them.

If you bring your voice up on the word, it’s an antiquated expression of zeal. If you bring it down, it’s a contemporary form of derisive address. Voices up, please.

SEVEN. Was Bottom a Lea Michele fan?

BOTTOM: Nay, I can gleek upon occasion.

Folks who are “Glee Geeks” might enjoy imagining Nick Bottom from A Midsummer Night’s Dream as one of them. He admitted he can “gleek” after all.

Sure, I’m being a little silly with this one, but why not? “Gleek” means to joke around.

SIX. Did Olivia have some work done?

OLIVIA: We will draw the curtain and show you the picture. [Unveiling.] Look you, sir, such a one I was as this present: is’t not well done?

VIOLA: Excellently done, if God did all.

OLIVIA: ’Tis in grain, sir; ’twill endure wind and weather.

Viola’s quip “if God did all” can set a Twelfth Night audience roaring if delivered just so. Does Viola suspect a little Nip/Tuck help is behind Olivia’s epic beauty?

Don’t start fitting Dr. 90210 for a doublet and hose just yet. Viola is merely making a reference to cosmetics.

FIVE. Was Hamlet a fan of Wayne’s World?

HAMLET: I did love thee once.

OPHELIA: Indeed, my lord, you made me believe so.

HAMLET: You should not have believed me; for virtue cannot so inoculate our old stock but we shall relish of it: I loved you not.

Again, this one came from the kids, though it was more common back in the ’90’s, when Wayne and Garth had more of an effect on the language.

Think of the line from Hamlet (and similar lines throughout the canon) as being delivered like this: “I loved you… NOT!” Yeah, they really used to do that… I kid you not.

FOUR. Was Feste creating a hostile work environment?

MARIA: Nay, either tell me where thou hast been, or I will not open my lips so wide as a bristle may enter in way of thy excuse. My lady will hang thee for thy absence.

CLOWN: Let her hang me: he that is well hanged in this world needs to fear no colours.

MARIA: Make that good.

CLOWN: He shall see none to fear.

Well hanged? Oh, no he didn’t!

Well, no he didn’t. It’s usually a safe bet to assume that any possible sexual innuendo was intended by Shakespeare, but Twelfth Night pre-dates the earliest known uses of the expression “well hung” to refer to a generous anatomical endowment. Plus, in the next line, Feste makes it clear he’s literally referring to a hanging. If the sexual pun were intended, why would Shakespeare have backed off the joke?

THREE. Did Ariel suffer from low self-esteem?

ARIEL: Where the bee sucks, there suck I.

Ouch. It’s not hard to convince high-school students that Shakespeare’s characters do, in fact, suck. But would Shakespeare have said so in The Tempest?

No. Bees, you see… eh, go ask your father.

TWO. Did the Porter invent a new art form?

PORTER: Knock, knock! Who’s there i’ the other devil’s name! Faith, here’s an equivocator, that could swear in both the scales against either scale; who committed treason enough for God’s sake, yet could not equivocate to heaven: O! come in, equivocator.

Rather than answering the knocking at the door, the Porter from Macbeth imagines himself as the Porter at the gates of Hell, and does some schtick about the various characters he might meet in that position. The expression “Knock Knock, Who’s there” is used to introduce new characters in his standup routine.

But if you’re expecting him to answer “Ophelia,” you’re going to have a long wait. The Knock-Knock joke as we know it is a twentieth-century creation.

ONE. Is Dromio of Syracuse a pothead?

DROMIO S: I am transformed, master, am not I?

ANTIPHOLOUS S: I think thou art, in mind, and so am I.

DROMIO S: Nay, master, both in mind and in my shape.

ANTIPHOLOUS S: Thou hast thine own form.

DROMIO S: No, I am an ape.

LUCIANA: If thou art chang’d to aught, ’tis to an ass.

DROMIO S: ’Tis true; she rides me and I long for grass.

Zing! Dromio’s jonesing for some weed! The Comedy of Errors is a drug play!

But not really. Dromio just longs for the freedom of greener pastures. Grass means grass, baby. However, the “she rides me” part probably does mean what you think it means.

So those are my ten favorite retrochronisms from Shakespeare. Did I miss any? Feel free to add to the list!

Conundrum: Russian Roulette

Tuesday, January 25th, 2011

In Russian Roulette, a six-chambered revolver is loaded with one round, the cylinder is spun to place the round in a random position, and participants take turns pointing the gun to their heads and pulling the trigger until one player loses.

Imagine you are playing this game (for whatever reason) with one other person, but do not wish to die.

1. Assume there is one round and the cylinder is spun only once, at the beginning of the game. Is it better to go first or second?

2. Assume there is one round and the cylinder is spun after each player’s turn. Is it better to go first or second?

3. Assume there are two rounds in random position and the cylinder is spun only once, at the beginning of the game. Is it better to go first or second?

4. Assume there are two rounds in random position. The first player shoots an empty chamber. You have the option of shooting the gun as is, or spinning the cylinder first. Which do you choose?

5. Assume there are two rounds in a random position – but you are told that the two rounds are in consecutive chambers. The first player shoots an empty chamber. You have the option of shooting the gun as is, or spinning the cylinder first. Which do you choose?

6. Assume there are two rounds in a random position – but you are told that the two rounds are in consecutive chambers. The cylinder is spun only once, at the beginning of the game. Is it better to go first or second?

These are pure probability questions, for entertainment purposes only. Shakespeare Teacher in no way condones the use of firearms in this manner.

Item of the Week

Monday, January 24th, 2011

This week’s testing item is a favorite of mine to use as an example, because it illustrates just how careful we need to be when looking at standardized testing data.

We will be looking at Item 16 on the 2009 New York State Grade 6 Exam. The performance indicator is “5.G14 Calculate perimeter of basic geometric shapes drawn on a coordinate plane (rectangles and shapes composed of rectangles having sides with integer lengths and parallel to the axes).” You can click the figure below to enlarge.

What is this question testing? Does it fit the performance indicator? Which of the wrong answers would you predict students would choose the most often? Why? What would students need to know and be able to do to answer this question correctly?

Question of the Week

Monday, January 3rd, 2011

Last month, I was giving a workshop for principals on Instructional Rounds, a method of structuring conversations about best practices based on classroom observations conducted in teams, when an interesting question arose. I asked them if teaching was an art or a science.

In this context, it was more than just a philosophical question. If teaching is an art, like music or painting, then each teacher should be allowed as much freedom and creativity as possible in developing a personal teaching style. If, on the other hand, teaching is a science, like medicine or physics, then we must determine best practices through research and establish standards and methodologies for the profession that all are expected to follow.

Carol Ann Tomlinson calls teaching a science-informed art, an answer the group liked, but I’d like to take a closer look at the question. The way we view the profession affects everything from how we train teachers to how we evaluate their performance. So is it an art, or is it a science?

Perhaps the distinction between the two isn’t as clear-cut as we think. Teaching may be a “science-informed art,” but what art hasn’t been influenced by the sciences? Each artistic discipline codifies what works and what doesn’t, and even the most promising young talents must study for many years to perfect their craft. There are certainly examples of highly successful art forms and artists that are defined largely by breaking the rules, like jazz or Picasso, but even they are influenced by science. Would Picasso’s “Blue Period” have been possible if Heinrich Diesbach hadn’t developed an affordable blue paint? And you can’t just play anything you like in improvisational jazz; you really have to know what you’re doing. In other words, it doesn’t mean a thing if it hasn’t got that swing.

Science, on the other hand, has a lot more intuition and creativity than it generally gets credit for. It comforts us to think of medicine as a hard science, but a lot of times doctors just have to go with their best instincts. I may have seen too many episodes of House, but let me ask you this: If you had to go in for surgery, would you prefer a young surgeon who recently graduated from a top medical school with a high GPA, or would you prefer a doctor with 25 years of experience doing this kind of surgery with a high success rate? And the most creative, mind-blowing stuff we’ve seen lately is coming out of the field of theoretical physics. Einstein famously said that imagination was more important than knowledge, and we have more knowledge because of his imagination.

So in deciding if teaching is an art or a science, we have to look at art and science for what they really are: two ends of a continuum, rather than binary opposites. But where on the continuum does teaching belong? The term “Instructional Rounds” borrows its name from the medical profession. But others refer to a similar activity as a “Gallery Walk” which takes its title from the arts.

There is, of course, a third option that falls outside of this continuum. In this option, teaching is neither an art nor a science, as each word implies a skilled and knowledgeable practitioner. It is simply a trade, one that can be standardized and learned. In this view, teaching is not a profession at all. I reject this idea, but it becomes part of the conversation nevertheless. And so, I bring back the Question of the Week by asking you this:

Is teaching an art or a science?

Conundrum: The Big Picture II

Tuesday, January 26th, 2010

In a normal “Pic Tac Toe” puzzle, there are nine pictures in a 3×3 grid, like Tic-Tac-Toe. In each of the three rows, three columns, and two diagonals, there is a common theme that unites the three pictures. The challenge is to find the eight themes.

In a “3D Pic Tac Toe” puzzle, there are 27 pictures in a 3×3×3 grid, like a Rubik’s Cube. In each of the nine rows, nine columns, nine pillars, eighteen lateral diagonals, and four cross-cube diagonals, there is a common theme that unites the three pictures. The challenge is to find the 49 themes.

A “Big Picture” puzzle is just like a “3D Pic Tac Toe” puzzle, except that each of the 49 themes will be a movie. Each of the three images in that theme will picture at least one actor who was in that movie.

Imagine stacking the three levels below on top of one another. For reference, and notation guidelines, check out my last Big Picture puzzle, including the comments. The rules here are identical to that puzzle.

Looking at that puzzle will also help identify the actors in Image B5; tragically underused in that puzzle, it now plays a more central role. Although many of the same actors appear in both puzzles, none of the 49 movies in the solution to this puzzle is the same as any of the 49 movies in the previous puzzle’s solution.

In Image B3, you will use the actors who voiced the animated characters shown, but none of the movies in the solution is animated, a documentary, or Robert Altman’s The Player.

You can click on each image to see a larger version:

Top Level – Level A

Middle Level – Level B

Bottom Level – Level C

Please post whatever you come up with in the comments section.


UPDATE: See comments for correct themes provided by Lee (12) and Neel Mehta (20). The following 17 themes remain unsolved:







Lateral Diagonals


Your Move: Conundrum

Tuesday, February 24th, 2009

The Shakespeare Teacher is out. It’s your move.

Today’s challenge is based on the most recent Conundrum, which was a logic problem called Poker Game 2.

The answer is the Queen of Spades and the Six of Spades.

Your challenge is to select the five cards on the board to make that answer correct. Everything else about the problem will stay the same.

First person to post a correct entry (by March 10) is the winner.

UPDATE: I’ll leave this challenge active a little longer if anyone wants to try it.

Conundrum: Nim, Part II

Tuesday, June 17th, 2008

You have defeated Iachimo at his own game, and he’s not happy.

“I usually go first,” he says icily. “Surely you will allow me a rematch, and allow me to go first this time.”

You know that, with his standard set up using piles of 1, 2, 3, 4, and 5, he can force a win by going first, so you decline. But he comes up with a surprising offer: you can increase the number of piles.

As before, the piles will start at 1 coin and will increase by 1 coin until the desired number of piles is reached. So if you decide to increase to six piles, the coin amounts must be 1, 2, 3, 4, 5, and 6. You’ve only got a limited number of coins available, so you may not exceed ten piles.

Iachimo will go first and you will take turns drawing coins from the piles. On your turn, you may remove as many coins as you like from any one pile. The winner is the one who takes the last coin and leaves his opponent without a move.

“Double or nothing,” he dares you, with a bit of desperation in his voice. You’re not sure what would happen if you decline. It doesn’t matter, though, since you see a clear path to victory, even allowing Iachimo to go first.

How many piles do you set up? What’s your strategy for winning?