What Graphs Reveal (If You Give Them Time)

A pandemic is wracking the globe. Racial unrest is wracking the U.S. I am wracking my memory trying to remember exactly what “wracking” means.

You know what we need? A brain break. A quick game, from @_b_p. So here we are:

The title, you’ll notice, is missing. Something is growing over time, with an impressive boom around 1980, but we don’t know what.

Is it technological? Cultural? Demographic? Star Wars-related?

Think it over. Note the trends. Make a guess.

And then, when you’re ready, here’s the reveal.

Okay, that’s an unhappy graph. My apologies.

And of course, as you lovable pedants may note, it doesn’t tell the whole story. What else changed in the U.S. during this time? What if we adjust for population? How does trend compare to other countries?

So let’s try another game, from Connie Rivera. This one unfolds a bit more slowly.

What might the bars represent? Number of monkeys petted? Price required to pet various kinds of monkeys? Calories expended in petting various kinds of monkeys?

Well, here’s your next clue:

Okay, so monkeys are maybe not the secret here.

What do the U.S., Rwanda, and Russia have in common? Yes, yes, a shared love of the TV show Friends. But that applies to all countries. Why would India and Sweden be so low? What’s going on here?

Another quick clue. It’s there at the bottom, if you don’t see it on first glance.

Hmm. For the 1.5-billion person nation of India, a total of just 33.

But 33 what?

Something is odd here, if a much smaller country like Spain or Canada can punch so far above its weight class.

Anyway, a good game within this game: can you eyeball the values of the other bars? If India is at 33, what’s Germany at?

Brazil?

The U.S.?

Ready or not, here they are:

Wow! The U.S. is crushing India in this game, whatever it is. We’re beating them by a factor of 20. Take that, India!

And the game is…

Drat. Another game we didn’t want to win.

These images come from Slow Reveal Graphs, a site run by leading elementary math educator Jenna Laib. She’s got dozens of these, organized as slideshows, ready to be employed in classrooms.

(Full disclosure: Jenna is my sister.)

(Even fuller disclosure: Jenna is a champion.)

The logic behind this exercise, as I understand it, is simple and powerful. Graphs tell stories. But stories unfold in time, whereas graphs just splatter you in the face, with all of the information at once.

So, hold back part of the story. Leave the reader in suspense. Let them notice, wonder, ask, speculate.

Then, and only then, deliver the full truth.

To read a graph requires a host of skills, from specific technical matters (where are the axes? how is quantity represented?) to broader, softer virtues (patience, attention, a sense of context). Slow Reveal Graphs help students build those skills.

And they’re fun, too.

I’ve seen Jenna run this instructional routine, and it’s magic. (I’ve run it myself, too – less magic, but still a blast.) Students have sharp eyes. They’ll catch things you missed, interpret features in ways you would never have guessed. They’ll build on each other, quibble with each other, learn from each other.

Perhaps best of all, there’s no shame in changing your mind.

Every kid does it, and it happens naturally. They predict. They watch new information come in. And then they update their predictions.

We humans are usually such stubborn and prideful creatures, clinging to our views long after they’ve melted into mud. But with Slow Reveal Graphs, suddenly we become astute Bayesians, updating our priors on the regular.

I encourage every teacher to check out the Slow Reveal Graphs site. Jenna has curated an admirable resource. (I’ve chosen two that are heavy as a bag of flour, but some are silly and fun!) And if right now isn’t a good time to bring a dose of truth to math lessons, then I sure don’t know when that time will come.

(Also: happy early birthday, Jenna!)