Tip of the hat to Tanya Khovanova for sharing this problem: Is it possible to place seven points on a plane so that among any three of them, two will be at distance 1 from each other? This comes from… Read More ›
Teaching & Learning
What is a city?
Massachusetts has 50 cities and 301 towns—collectively known as “municipalities.” Does it matter which ones are cities and which ones are towns? And should you care about the definition of “city”? Perhaps; perhaps not. If you’re studying civics anywhere in… Read More ›
What lies on the other side of the River Styx?
Who knows? You’ll have to read the engaging novel Across the River Styx to find out. You might have a rough voyage, but the reading won’t be rough. Looking at the cover image below, you’ll see what this novel is:… Read More ›
How does gerrymandering harm you?
Elbridge Gerry has a lot to answer for. As you probably once knew—but have now forgotten—Gerry was vice president of the United States under James Madison, a role for which nobody remembers him (as is the case for most vice… Read More ›
Who knew?? Iterating Dorchester takes you to philosophy!
TIL what TIL means. No, wait! I learned that last year. Let’s start again: TIL that an extremely simple iterative process always takes you philosophy. Here’s how you do it: Go to any article in Wikipedia. Click on the first… Read More ›
Taking creative risks in the classroom
John Spencer’s essay, “What Happens When Teachers Take Creative Risks,” is well worth reading if you’re a teacher. Actually, it’s also worth reading if you’re teacher-adjacent, such as a parent or a student. I was particularly struck by his initial… Read More ›
How worried are you about “learning loss”?
Parents and teachers alike are understandably worried about learning loss during the pandemic. How real is the worry? Is there something else that should worry us more? And what exactly does “learning loss” mean anyway? John Spencer helps you and… Read More ›
Surely schools are not supposed to teach critical thinking. Right?
As you know, there has been a recent uptick in banning books, in attacking teachers for teaching inconvenient truths, and in promoting undemocratic ideas and ideals. As Diane Ravitch has pointed out, schools and libraries are being pressured to remove… Read More ›
Ayliean (who?)—and her Hitomezashi patterns (what?)
No, I don’t know how to pronounce Ayliean. My Scots Gaelic isn’t what it used to be. (It never was.) And I’m not so sure about Hitomezashi either, as my Japanese isn’t what it used to be. (But I did… Read More ›
Trains, Rock Paper Scissors, & Hannah Fry: What do these three have in common?
How can Rock Paper Scissors (RPS) have a winning strategy? It’s all just luck, isn’ it? Well, no, actually. It’s true that if your opponent plays strictly randomly, then you have no winning strategy. It’s really all just luck. But… Read More ›
The Queen’s Gambit: what’s it all about?
Is it about chess? You may be tempted to say yes. It seems to be about chess. In high school English—a hundred years ago or so—I learned to distinguish plot from theme. If we’re talking plot, then The Queen’s Gambit… Read More ›
The hidden meaning of crypto
What does the word “crypto” mean to you? For many decades it has been a term of art in applied mathematics—shorthand for both “cryptography” and “cryptology,” being thereby particularly useful for those of us who don’t want to argue about… Read More ›
Never—no, always—take the shortcut!
“Abjure the hypotenuse!” That’s what our busy high school dean (also assistant headmaster and sole college counselor) George Grenville Benedict—called G2 by the students (behind his back)—was famous for saying. As my classmate Alba Briggs publicly observed on screen in… Read More ›
Whining about Daylight Saving Time
If I were a pedant (which of course I’m not), I would feel compelled to articulate four pet peeves related to Daylight Saving Time: Some people—I’m thinking of you, Ethel—call it Daylight Savings Time! (Apparently it has something to do… Read More ›
Look it up! But first understand the purpose of dictionaries.
A dictionary in every room. That was an essential feature of our home when I was growing up. That way, when a question came up in conversation, no matter which room we were in, we could always look up a… Read More ›
On the planet of the apps: Between Glossika and DuoLingo, who wins?
I have been trying these two language-learning apps every day for a month now. You may recall that I wrote about them three weeks ago, when I continued to review my rusty German, since I used to be pretty good… Read More ›
Democracy? How could geometry tell us anything about democracy? To find out, read Shape, by Jordan Ellenberg!
Even if you don’t usually read applied math books, you need to read Shape, by Jordan Ellenberg. The subtitle tells you more than the title: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else. Yes, I know, it… Read More ›
A Lincoln-Sudbury alumnus stars in Gifted.
Chris Evans—an actor you may recognize, but I don’t—is a Lincoln-Sudbury alum (’99?) and the star of the movie Gifted, which you should definitely see. See it even if you have no connection whatsoever with either Lincoln or Sudbury! Evans… Read More ›
“Scientific discoveries are never given the names of their actual discoverers.”
When I teach cryptography, my students learn that the Caesar Cipher wasn’t actually invented by Julius Caesar, that the Playfair Cipher wasn’t created by Lyon Playfair, that the Vigenère Cipher is wrongly attributed to Blaise de Vigenère, and so forth…. Read More ›
They say that America’s math curriculum doesn’t add up. But is that true?
What’s wrong with America’s math curriculum? I’ve written endlessly on this subject, but for now I want to focus on the claims of Steven Levitt and others in a new version of an earlier Freakonomics episode. Levitt et al. are… Read More ›
Learning Strategies 