I love probability. I love stories. And I love marshmallows. So I wrote these probability lessons disguised as stories. Or perhaps they’re stories disguised as probability lessons. (I couldn’t figure out a way to work in the marshmallows. Sorry, folks.)
The Bear in the Moonlight consists of seven tales about a curious student and a wise, Zen-like teacher. Each little fable aims to impart a truth about probability, and is followed by an explanation of the underlying ideas. (In the pdf versions you’ll also find discussion questions, in case you’re hoping these can garnish your lesson plans).
They’re for students. They’re for teachers. They’re for anyone curious about the mathematics of the unknown and the unknowable.
Introduction: Why Probability? Why Stories? | pdf
Moral: Probability is beautiful, useful, and… oh yeah, totally befuddling.
Topic: Definition of probability; obstacles to understanding.
Ch. 1: The Bear in the Moonlight | pdf
Moral: A probability is an expression of uncertainty.
Topic: The subjective nature of probability.
Ch. 2: The Blindfold and the Chestnuts | pdf
Moral: It’s all right to be blind. But don’t pretend you can see.
Topic: Probability as a ratio; hidden assumptions.
Ch. 3: The Riddle of the Odorless Incense | pdf
Moral: See the world as it is, not as you imagine it to be.
Topic: Sample spaces; discrete probability; more hidden assumptions.
Ch. 4: The Swindler’s Coin | pdf
Moral: Everyone makes mistakes. Only fools stand by them.
Topic: Conditional probability; the Bayesian approach.
Ch. 5: The Wise Monkey | pdf
Moral: Read cautiously of rare events.
Topic: Randomness, coincidences, and unlikely events.
Ch. 6: The Mountain Where Rain Never Falls | pdf
Moral: Use everything you know.
Topic: Conditional probability.
Ch. 7: The Patterns in the Stonework | pdf
Moral: The eye sees chaos, and the mind imagines order.
Topic: Randomness, coincidences, and explaining patterns.
All Stories, Ch. 1-7 (pdf)
Answer Keys, Ch. 1-7 (pdf)
I’m posting a new chapter every Monday, starting 9/30 and ending 11/11. If you have quibbles/suggestions/critiques/thoughts, please let me know!
I’d like to thank my father, James Orlin, for providing some foundational ideas for these stories, as well as helpful feedback and conversations. Also for being one cool cat.
Copyright 2013 by Ben Orlin. Feel free to give this stuff to students as you see fit. For other uses (reposting online, sharing publicly, printing and folding into tricorner hats) check with me first.