Compass Constructions Made Easy

First up, an easy one: draw a circle!

circle 1circle 2circle 3circle 4circle 5

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A Borrowed Joke (and 15 other math cartoons)

The Fence Post Error

2017.12.1 fencepost problem

I drew this one at the request of Prof. Jim Propp, who writes the excellent Mathematical Enchantments and whose November essay Impaled on a Fencepost explored the kind of off-by-one errors that I make at least 17 times per day. (Or is it 18?)

Greetings from Heisenberg!

2017.12.4 postcard from heisenberg

Tourist bureau of Würzburg, Germany: please feel free to sell these. Continue reading

Things to Know About the Year 2018

Whatever your grievances against 2016 as a year, it was a stellar number. Like a picnic with milkshakes and beer, this integer was fun for the whole family.

Just look at these equations:

1 new year

After this crowd-pleaser came 2017, a prime year, which engendered this brilliant Tweet from Matt Parker:

That brings us to 2018.

It’s not triangular, like 2016.

It’s not prime, like 2017.

Is it, then, worthless?

Well, I myself am neither triangular nor prime. But if the roles were reversed, I like to think 2018 would do its best to uncover my special qualities and catalogue them in a blog post. So I went to do “research” (my codeword for “Google searches”).

What secret mathematical properties and pleasures will our new year contain? Continue reading

The Terrible Truth About Dreidel

From time to time, a journalist may face a soul-shattering dilemma. A scoop so shocking it cannot be withheld, yet so terrible it cannot be told.

And what goes for journalists, goes double for stick-figure cartooning math teachers. Thus, as one who loves truth even at its ugliest, I choose to divulge a fact sure to rattle your faith in humanity itself:

Image (2)

The game of dreidel is built on a lie. Continue reading

The Three Barriers to Deep Thinking in School

Almost a decade into my teaching career, I’ve learned a lot—about recurring decimals, British slang, the life cycle of fidget spinners. But one lesson I seem to relearn in new ways every day: Deep thinking is a very, very delicate flower.

It blooms only under rare and perfect conditions, when you’ve given the seedling absolutely everything it needs.

It's always creepy when your students are as tall as you.

There’s no perfect recipe. What gets my 6th– and 8th-graders’ thoughts blooming might flop with my 7th-graders. This work is wonderfully and maddeningly specific. Each seedling presents its own unique and irreducible case. The best you can do is kneel down in the soil and try to help it along.

Even so, I find a few recurring themes: three crude reasons why deep thinking fails to bloom, and the hardy but colorless perennial of “rote learning” surfaces instead.

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