Speaking of palindromes, I’ve been seeing a really good one making the social media rounds:

Wonder if Sununu’s fired now.

This is in response to the following interview he did with Soledad O’Brien, which I wish every voter in America could see:

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.

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?

What number, when written as a word in English, has all of its letters in alphabetical order?

For example, “six” doesn’t work, because the letter S comes before the letter I in the word, but S comes after I in the alphabet.

The word “begin” has all five of its letters in alphabetical order, but, of course, it is not a number.

Can you find the only number that meets this requirement?

UPDATE: Number identified by Jeff. See comments for answer.

I thought it might be fun to try something new with the “Question of the Week” feature here on the blog. Instead of asking my readers a question, I will offer up a question from the statewide examinations that New York City students take each year.

The purpose of this will not be for you to try to provide the correct answer, but rather to join me in examining the question. What does it tell us about student understanding? What do each of the wrong answers mean? What is this question testing? What is it really testing? What would students need to know and be able to do to answer this question correctly?

Sound like fun?

To differentiate this feature from the Question of the Week, I’ll call this the Item of the Week, which is what we call questions in the parlance of standardized testing.

Today’s item comes from the 2010 New York State Grade 4 Mathematics Exam. The strand is Measurement and the performance indicator is “4.M04 Select tools and units appropriate to the mass of the object being measured (grams and kilograms).” You can click the image for a larger view.

I like the layering of this question. First of all, the student needs to know which units measure mass and which don’t. If they answer A or D, they don’t. But to choose between B and C, students need to have some idea of how much a gram really is.

Sometimes these questions will have distractor answers that use numbers from the problem to try to trick students into choosing them. But there are no numbers in this problem. And all of the answers use the same number.

The trick here is in the first sentence. The fact that Mr. Patel moved his chair across the room is not relevant. But if you don’t know what “mass” means, that first sentence might trick you into thinking you are looking for a distance, in which case you might choose D. This assumes, of course, that you have no idea how long a kilometer is.

All in all, it seems like a pretty fair question that tests what it purports to test. In practice, it turned out to be one of the harder items for New York City students taking this exam.

As always, I invite further discussion.

Last year, I wrote that I didn’t need an iPad, because I had an iPhone and a Macbook Air. I still have them both, and they are still working out great. But my nephews got iPads for the holidays, and this is how I bond with them, so I had to get an iPad too. How’s that for a rationalization?

But now that I’ve bought one, I’m glad I did, because it’s adding value in ways I hadn’t anticipated. True, it is basically an iPod Touch with a larger screen, but that larger screen makes a big difference. There are a lot of things I can technically do with my iPhone, but usually don’t because the screen size is too small. And I’m finding it easier to do those things on the iPad.

So here are the top ten things you can do on an iPhone or iPod Touch that you can do better on an iPad:

1. Watch: I’ve been carrying around movies and TV shows on my iPhone for years, but I’ve watched more on the iPad in the last couple of months than I ever watched on the little screen. The Videos app (Included) is the very first app on my iPad. But I’ve also signed up for accounts with Netflix (Free app + $7.99/mo.) and Hulu Plus (Free app + $7.99/mo.) that let me stream video content from their impressive libraries. The combined monthly cost is far, far less than the Cable TV I’m canceling. And apps for YouTube (Included) and ABC Player (Free) help establish the iPad as a truly flexible video viewer you can take anywhere.

2. Connect: The power of social media has risen incredibly in the past year, and the App Store (Included) has kept pace. There are a variety of apps to help keep you connected, but I use Reeder ($4.99) as my Google Reader client, Friendly (Free) as my Facebook client, and Twitter (Free) as my client to access the Twitter account I finally broke down and created so that I could follow the national conversation where it seems to have gone. You can also consolidate the three, and much more, in one app called Flipboard (Free), which formats the content into a friendly magazine layout for casual browsing. There is also a WordPress app (Free), which allows me to blog on the go, and Yahoo! Messenger (Free) – actually an iPhone app – which lets users exchange text messages and participate in voice chat. And the iPad Mail interface (Included), designed for the larger screen, is much easier to use than its iPhone counterpart.

3. Read: The biggest surprise for me on the iPad is how much I love my Kindle app (Free), which lets me download books from Amazon and read them on the iPad. And these are real books that I actually want to read, not the limited eBook selection available through Apple. However, there are a lot of places online to get free books in ePub format, which can then be imported into your iTunes library and read on iBooks (Free), so you should definitely get it. I’m a fan of Offline Pages ($4.99), which allows you to save websites (from the iPad or from your home computer) and read them on the iPad, even after you’re no longer connected to the Internet. I also highly recommend the Shakespeare Pro app ($9.99) if Shakespeare’s your thing, and the Newspapers app ($2.99), which lets you access local newspapers from across the country on a daily basis.

4. Play: Any game you can play on the iPhone, you can play on the iPad, either in the original size, or expanded to fit the screen (sometimes with the expected loss of quality). But the expanded real estate has given developers something to code about, so there is a whole spate of new games and revamped versions of old games at the ready. Plants vs. Zombies is the absolute best game to ever grace the iPhone, and Plants vs. Zombies HD ($6.99) is even better on the iPad. Games like Cover Orange HD ($0.99) and Cut the Rope HD ($1.99), which combine tricky puzzles with engaging animations, demonstrate a new level of what is possible in portable gaming. Even the simple games, like Saving Seeds HD ($0.99) or Aces Traffic Pack HD ($2.99), really make you feel like you’re using a next generation device. I was able to play GT Racing: Motor Academy ($0.99) with my two nephews, each of us on our own iPads, racing each other on the same track. This was cool on a level they could not possibly appreciate.

5. View: I’d be remiss if I didn’t discuss how viewing photos is better on the larger screen, obvious as it may be. The iPad has a built-in Picture Frame feature, which lets the device function as a digital picture frame when it’s not otherwise in use. There are also apps that take advantage of the view, like Beautiful Planet HD ($0.99) that shows high-quality images from across the globe, and The Guardian Eyewitness (Free), which shows a different news photo every day. And The Elements ($13.99), the flagship app of the iPad, is everything it’s hyped to be: an interactive periodic table in which you can rotate high-quality 3D images of each of the elements. But it does take up almost 2GB of storage space, so don’t even bother with it if you’re only working with 16GB.

6. Work: The iPad is expensive to begin with, so it seems worth it to me to invest just a bit more in the iWork suite – Pages ($9.99), Numbers ($9.99), and Keynote ($9.99) – to add value to your device. I’ve also become fond of GoodReader ($2.99), which reads PDF files, and Teleprompt+ ($9.99), which allows you to load up text documents from your desktop and use the iPad as your own portable teleprompter. Try that with an iPhone.

7. Organize: I’ve actually not had a problem with the Calendar app on the iPhone, but the iPad’s Calendar interface (Included) makes it possible to see my whole month at a glance, which is a useful feature. As a MobileMe user, I like to use iDisk (Free app + $99/yr. for MobileMe) to coordinate between my desktop, laptop, iPhone, and iPad, but if you’re not a member, I’ve heard good things about Dropbox (Free app + Dropbox account). And I have to mention the Delivery Status app ($4.99), which lets you follow multiple packages from FedEx, UPS, etc. as they are tracked through the system.

8. Browse: The fact that the iPhone had a fully functioning web browser was a major breakthrough, but the iPad takes it a step further. It’s not only that the screen is larger, but also the fact that it allows you to view the full versions of your favorite websites, as opposed to the version optimized for mobile devices. Safari (Included) also syncs your bookmarks bar from its desktop counterpart (via MobileMe, I think), which I have found very convenient. It’s worth checking to see if the websites you frequent have their own apps as well. I recommend Google (Free), WolframAlpha ($1.99), and Articles ($4.99), which is a sharp-looking Wikipedia client.

9. Explore: Here’s how you know you are living in the future. Download GoSkyWatch Planetarium (Free) to your iPad. Then point it at the sky at night. It will display for you the same stars at which you are gazing, along with their names and even the constellations drawn in. Move the iPad around and the display will adjust. It’s also worth getting Solar Walk ($2.99), which gives you more freedom to move around the solar system and see what’s going on, including watching our own artificial satellites as they orbit around the Earth. The more expansive interface also breathes new life into old favorites such as Maps (Included) and Google Earth (Free).

10. Distract: So you’ve bought your iPad and now the kids want to play with it. What can you download to keep them out of your online banking app? The boys have their favorites, but Elena, who is now almost two, can work the icons along with the best of them, even knowing to hit the menu button when she’s bored with one app and wants to switch to another. Voting with her fingers, she recommends Sound Touch ($2.99), Art in Motion ($2.99), Tesla Toy ($1.99), and Drawing Pad ($0.99). Ian (age six) is really into roller coasters, so he enjoys games like New York 3D Rollercoaster Rush HD ($4.99) and Underground 3D Rollercoaster Rush HD ($4.99). But he really loves an app called Coaster Physics ($0.99), which lets him design his own roller coaster and then ride on it as he learns about kinetic and potential energy. He also likes to practice his Dolch sight words with All Sight Words ($0.99) and play Math Bingo ($0.99), while his older brother Jason (age eight) prefers MathBoard ($3.99) to hone his arithmetic skills. I highly recommend the BrainPOP Featured Movie (Free) and PBS’s SUPER WHY! ($3.99), two excellent educational apps by sources from whom we’d expect no less. And there are a whole host of apps that simulate baking different sugary confections, but Cupcakes! XL ($0.99) makes the best use of the iPad’s capabilities.

I certainly mean no disrespect to the iPhone. It’s still, hands down, the coolest thing I’ve ever owned, including the iPad. It has a phone and a camera and it fits in my pocket, so the new kid is really no threat. The iPhone is also better for listening to audio, recording voice memos, MusicID, and playing Doodle Jump or Catan. Most of the things I do with the iPad are things I wasn’t really doing with the iPhone anyway. So the iPad did add value after all.

And now all of my portable digital requirements really are met, and I therefore have no need for any new thing that should happen to be introduced by Apple or anyone else.

Do I?

Here’s a cool math video by a “mathemusician” named Vi Hart, with a hat tip to Jeff Branzburg for the link.

It’s time once again to check in on what searches people have done to find themselves at Shakespeare Teacher, and to respond in the name of fun and public service. All of the following searches brought people to this site in the past week.

That’s a great question. I think it’s fair to say the idea that human beings develop in distinct stages was pioneered by Sigmund Freud in the 20th century, when he outlined his psycho-sexual stages of development in childhood. Erik Erikson, a developmental psychologist strongly influenced by Freud, described his own set of psycho-social stages, which carried through to adulthood.

Groundbreaking as these ideas were, they were to some degree anticipated by Shakespeare in his Seven Ages of Man speech from As You Like It. In the speech, Shakespeare describes seven developmental stages that carry through from childhood to adulthood, and the common characteristics that men display at each stage. Freud and Erikson would later codify this scientifically, but the Bard was able to figure it out just by observing the human condition. Point: Humanities!

It’s worth noting that both Freud and Erikson wrote about Shakespeare, and Hamlet in particular, to describe their theories. In a 1962 article entitled “Youth: Fidelity and Diversity,” Erikson actually references Shakespeare’s “ages of man” before spending about four pages examining fidelity and identity in Hamlet. So it would seem that the answer to the question is, yes, Erikson was influenced by Shakespeare to some degree, as was Freud. But influence often tends to be reflective, and the developmental psychologists certainly left their mark on Shakespeare as well.

I touched on this a bit about a month ago. I used to use “Mosh” to teach poetic devices, and I’m having trouble finding a more contemporary replacement. I’ll just give a sampling of each of the poetic devices I mentioned in that post. I tend to use only the middle stanza and the chorus, which I make into a handout. I also distribute the Prologue for Romeo and Juliet as a handout, so we can compare the two.

Repetition: “We gonna fight, we gonna charge, we gonna stomp, we gonna march”; “All you can see is a sea of people”; “If it rains let it rain”; “Rebel with a rebel yell”

Rhyme: Not only is there end rhyme, but there is internal rhyme as well. “They tell us no we say yea, they tell us stop we say go/ Rebel with a rebel yell, raise hell we gonna let em know”; “yea the wetter the better”; “that we need to proceed”

Rhythm: “Mosh” is written in anapestic tetrameter, which I always point out is the same meter as “‘Twas the Night Before Christmas”… and other popular poems as well. The Prologue for Romeo and Juliet, of course, is in iambic pentameter.

Alliteration: Note that in “we gonna mosh through the marsh” the words “mosh” and “marsh” start and end with the same sounds. Compare with “doth with their death” in the Prologue for Romeo and Juliet.

Antithesis: “They tell us no we say yea, they tell us stop we say go”; “from the front to the back”; “some white and some black”

Allusion: There’s a reference to George W. Bush in the passage.

Emendation: This is where I edited the reference to George W. Bush. I usually change it to “Stomp, push, shove, mush, [mock] Bush” even using the brackets like a Shakespeare editor.

In a 2006 interview with Brian Williams, President Bush claimed to have recently read “three Shakespeares” in addition to curling up with some Camus:

WILLIAMS: We always talk about what you’re reading. As you know, there was a report that you just read the works of a French philosopher. (Bush laughs)

BUSH: The Stranger.

WILLIAMS: Tell us the back story of Camus.

BUSH: The back story of the the book?

WILLIAMS: What led you to…

BUSH: I was in Crawford and I said I was looking for a book to read and Laura said you oughtta try Camus, I also read three Shakespeare’s.

WILLIAMS: This is a change…

BUSH: Not really. Wait a minute.

WILLIAMS: A few months ago you were reading the life story of Joe DiMaggio by Richard Ben Cramer.

BUSH: Which was a good book.

WILLIAMS: You’ve been on a Teddy Roosevelt reading kick.

BUSH: Well, I’m reading about the battle of New Orleans right now. I’ve got an eclectic reading list.

Williams didn’t ask him what “Shakespeares” he read, but I have my guess at one of them, as well as a selection I wish he’d read.

The constant pi is nature’s random digit generator, stretching out infinitely long and with no predictable pattern. This means that any finite string of numbers can be found somewhere out in the vast expanse of digits.

So if we were to express the Complete Works of Shakespeare in, say, ASCII code, it would indeed be represented as a very long, but certainly finite, string of digits. This string of digits is represented somewhere in pi, not once, but an infinite number of times. What’s more, the very first time it appears would be a finite distance in. Which means, there is some number X where you could say that if you start X digits into pi, you can read the Complete Works of Shakespeare.

Before you get too excited by that, you should realize that X is so unfathomably large that it would most likely be beyond human comprehension to even find a way to express it, let alone come anywhere near identifying it. You may think of the monkeys-at-typewriters thought experiment (and for our purposes, we can consider both the digits of pi and monkeys typing to be generating random characters). Even using theoretical monkeys, the number of simian typists needed would be beyond astronomical.

But, yes, the Complete Works of Shakespeare are somewhere in pi with a probability of 1. If the thought of that makes you smile, I’ve done my job.

Henry IV was often referred to as Henry Bolingbroke, but actually, his last name was Plantagenet.

In fact, all of the English kings from Henry II to Richard III carried the surname Plantagenet. This means that throughout the entire Wars of the Roses, the Yorks and Lancasters all had the same last name, which is found throughout the history plays. This is because both sides were led by male-line descendants of Edward III. There is a reference to this in Richard III, as Richard hits on the widow of the cousin he killed:

Glo. He that bereft thee, lady, of thy husband,
Did it to help thee to a better husband.
Anne. His better doth not breathe upon the earth.
Glo. He lives that loves thee better than he could.
Anne. Name him.
Glo. Plantagenet.
Anne. Why, that was he.
Glo. The self-same name, but one of better nature.
Anne. Where is he?
Glo. Here.

The long Plantagenet line comes to an end in 1485, when Richard III is defeated by a young man named Henry Tudor.

Rick Astley, before he became well known as a singer, did a bit of acting and even performed in some Shakespeare. Most of his Shakespeare work was done on stage and not screen, but there is a video clip of him performing the “never give her o’er” speech from The Two Gentlemen of Verona. The video can be found on YouTube here.

I leave the task of responding to the remaining search terms to my readers:

I was both amused and frustrated by VerizonMath, a website dedicated to an odd billing discrepancy, and the agonizing exchange that followed. You should really listen to the whole phone call, but here is the basic issue:

George Vaccaro was quoted a price of .002 cents per kilobyte for data usage while traveling in Canada. He later learned that he was being billed at a rate of .002 dollars per kilobyte. So instead of being charged an extra 71 cents, as he had expected, he found a 71 dollar charge on his bill. When he called to complain, he was unable to get anyone to understand what he was talking about, no matter how clearly he tried to explain it.

My .002 cents is that the exchange reminds me of the Upton Sinclair quote (made popular recently by Al Gore):

It is difficult to get a man to understand something when his job depends on not understanding it.

If they understood what he was saying, they’d have to take the charge off of his bill, which they clearly were not prepared to do.

I had the pleasure of observing a science teacher teach a fantastic lesson on genetics last week, and it got me thinking about the mathematics behind eye color. This Conundrum will be purely a probability question (two, actually), so I apologize in advance for over-simplifying the science.

Assume that everyone has two genes that determine eye color. For the sake of the math, we will stipulate that each gene must be either brown or blue. An individual inherits one gene from each parent. A parent will pass on one of his or her own two genes with equal probability.

Brown is dominant, which means that if an individual has one brown gene and one blue gene, then the individual will have brown eyes. An individual will also have brown eyes if both genes are brown. Only an individual with two blue genes will have blue eyes.

Now imagine this hypothetical scenario: Susan and David are a married couple, and both have brown eyes. David’s father had blue eyes, and his mother had brown eyes. Susan’s parents both had brown eyes, but her brother Bill has blue eyes. Susan and David are expecting their first child, baby Jason.

Question 1: What are the chances that Jason will have blue eyes?

Question 2: Suppose Jason had brown eyes. Susan and David are now expecting a second child, baby Ian. What are the chances that Ian will have blue eyes?

UPDATE: Both questions answered correctly by Micah. See comments for answers and discussion.